William M. Briggs

Statistician to the Stars!

Reasoning To Belief: Feser’s The Last Superstition: A Refutation of the New Atheism — Part IV


Read Part I, Part II, Part III, Part Interlude, Part IV, Part V, Part VI. Part Last.

It’s God All The Way Down

Talk about causality without foreshadowing a tie to God is coming and, if they can maintain an interest in the subject, people are receptive and willing to debate the argument on its merits. But hint that God is at the bottom of it all, as He will be here, and scholarly repose morphs into a sharp and anxious wariness. People tear into the argument with the zeal of Bill Clinton lecturing us about is. This is fine if the criticisms which arise from the increased scrutiny are valid, but usually they are not. In their suspicion that no good can come from tying causality to God, people are apt to convince themselves of objections which have long been refuted.

So I repeat the warning which I gave as we commenced this review: unless you are a specialist, it is unlikely the counter-arguments which occur to you are valid; further, it is highly probable that they are common and have well known rebuttals. This warning is not proof that the argument to come is valid, of course. It is instead a reminder that space is limited; I can only present a sketch while Feser offers chapters (in TLS and Aquinas). Dip into these volumes if you are convinced of a fallacy.

History, as it has been said, is one damn thing after another. Events which are one damn thing after another often form part of a causal series. Moe slaps Larry which causes him to slap Curly which induces him to slap Moe, etc. (start at 30 seconds). My great grandfather William produced a son William, my grandfather, who in turn produced my father William, who had a hand in me (William), and then I had a go with my number one son, William. This is where this time series stands at the moment.

Both of these are examples of causal series per accidens, first one thing, then another, etc. The object to notice is that my great grandfather, after he had done the work which resulted in my grandfather, no longer had to be present when my grandfather helped produce my father, and so on. And my grandfather need not have been alive when my father made me, etc. And this is so for all series per accidens: whatever set the chain in motion need not be present for the continuance of the chain.

This is not the only kind of causal series. There is another called per se, or essentially ordered causal series. This is the juicy kind, which when understood proves that God exists, and so forms Aquinas’s First Way.

Suppose you are incensed that the owners of Chick-fil-A have political opinions which dare to differ from your own. And so you buy up a bagful of chicken sandwiches and head over to the Family Research Council offices with gun in hand with the intent of teaching Chick-fil-A a lesson. You take out the gun and pull the trigger. Out flies the bullet, wending its way toward and eventually lodging itself into the arm of a security guard. So far we have a series ordered per accidens: you fire, the guard is eventually hit.

But consider the moment you squeeze the trigger. The movements of the hammer and of your finger happen simultaneously. The pressure of your finger is in turn simultaneous with the nerve impulses sending the squeeze signal to your muscles. The contraction of the muscles is simultaneous with the individual molecules in the muscles changing from one state to another, which in turn in simultaneous with the changing of the atoms in the molecules, which in turn is simultaneous with the changing of the forces operating to change the various sub-atomic particles, which in turn in simultaneous with whatever it is that operates on those forces which cause the change, and so on. But not “and so on” forever. This simultaneous, here-and-now series must come to an end: it cannot extend infinitely, otherwise nothing would ever get moving.

Now recall our earlier lesson: nothing that is a potential can be a cause, only something actual can be a cause. As Feser says in the article quoted below, “No mere potency can actualize a potency: only something actual can do so.” All those changes in the trigger-per se series are changes into potentials caused by something actual below them, and this series has to end in a first mover.

Now, a first mover in such a series must itself be unmoved or unchanging; for if it was moving or changing—that is, going from potential to actual—then there would have to be something outside it actualizing its potential, in which case it wouldn’t be the first mover. Not only must be be unmoved, though, it must be unmovable. For notice that, especially toward the “lower” levels of the series we were considering—the nervous system’s being actualized by its molecular structure, which is in turn actualized by its atomic structure, etc.—what we have is the potential existence of one level actualized by the existence of another, which is in turn actualized by another, and so forth…[T]he only way to stop this regress and arrive at a first member of the series is with a being whose existence does not need to be actualized by anything else. The series can only stop…with a being that is pure actuality. [Feser uses the example of a hand holding a stick moving a stone.]

And that being is, as Aquinas said, what we call God. Now I know that this example is too telegraphic to be convincing, or lastingly convincing. But let’s be clear what this argument is not saying. There isn’t one word here about the origins of the universe. For Aquinas, the universe could have begun at a single point in time, or existed forever, or even existed as a multiverse. Consequently, any physical discovery about branes or M-theory or cycles in big bangs, or whatever, have no bearing. This is not an argument about what caused things to be, or what set things moving as in a series per accidens, but about what causes any change whatsoever here and now.

To emphasize: the Unmoved Mover is an argument about what happens now, right now, this second, this very instant, about what is the first cause of every change. Anything that becomes actual is subject to a per se causal series, which must always terminate in a first cause, which is Pure Actuality. Feser continues:

[There cannot be] more than one being who is Pure Actuality [because] in order for there to be two (or more) purely actual beings, there would have to be some way of distinguishing them, some feature that one of them had that the other lacked…For to lack a feature is just to have an unrealized potentiality, and a purely actual being, by definition, as no unrealized potentialities…

A being of Pure Actuality, lacking any potentiality whatsoever, would also have to be immaterial, since to be a material thing entails being changeable…The Unmoved Mover is in any event that to which every motion or change in the material universe…traces back.

Besides monotheism, other traits of God can thusly also be deduced: like Omnipotence, Omniscience, Goodness, and so forth. Feser lays these out well, but in his discussion “privation,” which explains how God who has every perfection, relates to causing the absence of perfection, he stops short. It would surely be a privation to you if you were have your arm bitten off by a shark, but it would be a privation to the shark to miss his lunch. So there appears to be an order or hierarchy of privations (or perhaps this is only apparent due to my poor reading).

He also says little on the implications of the Unmoved Mover to us as rational creatures. Intrigued readers will be left with questions. Since God causes everything, at base, that seems to imply that God is with you as you err, even helping you pull the trigger, as it were. Is this God doing evil? Well, it was your will to do evil, not His. But since you’re dragging Him along in the per se trigger series, no wonder He’s not so happy about sin. Good grief! Can any of that be right?

True, Feser was not attempting to give us a complete theological treatise, but since his purpose was to show the errors of New Atheism, he might have expected to cause a few conversions, that some of his audience would want to know What’s Next?, where to go to resolve the tougher questions. Perhaps then in his second edition, he can provide a reading guide. It’s unlikely many will jump right to the Summa Theologica or Summa Contra Gentiles. A list of intermediate works would thus be of extreme utility.

Feser gives us two more of Aquinas’s Five Ways (in Aquinas, which he highly recommends, we get the whole package), each as compelling, but we’ll skip these and move on to his discussion of the soul.

Technical addendum

Here is a quotation from Feser’s article “Existential Inertia and the Five Ways” published in American Catholic Philosophical Quarterly. This version of the proof won’t be to everybody’s taste; but as somebody trained in mathematics and physics, I find its shape familiar and the chain of reasoning particularly compelling. Perhaps you will as well.

  1. That the actualization of potency is a real feature of the world follows from the occurrence of the events we know via sensory experience.
  2. The occurrence of any event E presupposes the operation of a substance.
  3. The existence of any natural substance S at any given moment presupposes the concurrent actualization of a potency.
  4. No mere potency can actualize a potency: only something actual can do so.
  5. So any actualizer A of S‘s current existence must itself be actual.
  6. A‘s own existence at the moment it actualizes S itself presupposes either (a) the concurrent acutalization of a further potency or (b) A‘s being purely actual.
  7. If A‘s existence at the moment it actualizes S presupposes the concurrent actualization of a further potency, then there exists a regress of concurrent actualizers that is either infinite or terminates in a purely actual actualizer.
  8. But such a regress of concurrent actualizers would constitute a causal series ordered per se, and such a series cannot regress infinitely.
  9. So either A itself is purely actual or there is a purely actual actualizer which terminates the regress of concurrent actualizers.
  10. So the occurrence of E and thus the existence of S at any given moment presupposes the existence of a purely actual actualizer.

Read Part I, Part II, Part III, Part Interlude, Part IV, Part V, Part VI. Part Last.

129 Comments

  1. One problem I see is the assumption that a cause must be singular and joint cause doesn’t exist. I think it just as likely that some causes are mutual. A singular cause isn’t required.

    The logic presented by Feser may be impeccable given the assumptions but you just can’t waive your hand and say those assumptions are Truth because we believe them to be. That I think is the problem with relying solely on logic.

    A subtle thing with Feser: he seems to imply petitioning God to make something happen is pointless since “a first mover in such a series must itself be unmoved or unchanging”?

  2. The decisive characteristic of per se causal series is *not* simultaneity but the instrumentality of each link in the chain, that is, whatever causal power each link has is derived from something else; simultaneity just makes it easy to illustrate the point. Prof. Feser has a blog post about this — see Edwards on infinite causal series.

  3. Briggs

    17 August 2012 at 2:53 pm

    G. Rodrigues,

    Thanks!

  4. [U]nless you are a specialist, it is unlikely the counter-arguments which occur to you are valid; further, it is highly probable that they are common and have well known rebuttals. This warning is not proof that the argument to come is valid, of course.

    Isn’t the above true for arguments on both sides?

  5. Of course, with all your wit and eloquence, to which I praise you for this post (you outdid yourself up there, perhaps except when you tried too hard for an argument from authority – “if you are a layman, don’t even try”), you cannot even begin by showing why should we take these funny categories “per accidens” and “per se” (and quite others) seriously enough to prove the existence of a “prime mover”.

    Dear Briggs, you are playing a word game here, not unlike when kids make up rules for their imaginary fights between their imaginary super-heroes. You confuse the act of categorization with an actual finding of an actual “object” that has some kind of “properties”.

    For all your words, you never showed why I should ever take seriously the notion that things are “potentials” or “actuals” or “movers”. The only thing you did was to declare that you divide stuff that way. Well good for you, if that rocks your boat. To conclude from this ancient categorizations that you somehow have proven the existence of a super-natural “thing” because it would “fancy” the big picture is…. even painful to witness.

    I was expecting more of you.

    Really, you just talk like Deepak Chopra.

    (In this case, however, it’s more akin to a muslim metaphysics, but whatever, I have long quit to try to understand christianity as a “single” coherent belief).

    To emphasize: the Unmoved Mover is an argument about what happens now, right now, this second, this very instant, about what is the first cause of every change. Anything that becomes actual is subject to a per se causal series, which must always terminate in a first cause, which is Pure Actuality.

    You know, if you really were serious about this “Pure actuality”, if you really believed in this “thing”, then you would honestly try to prove its existence empirically. The idea is simple enough. If things only happen because this “first mover” is always doing its own thing and not because of other things, then it would be detectable. We would see it beneath the quantum cloud. It would show its bias.

    However, it does not. It performs exactly as you would expect if there was no prime mover nor any sort of extra-natural phenomena.

    Or perhaps the prime mover only exists within the safe parameters where science couldn’t ever aspire to detect its presence. Color me unsurprised.

  6. PS: All in all, nice post. I appreciate the effort you now place in the moment of “Now”. As I said earlier, pretty Deepak Chopraist. Again, the God of the gaps. Because science hasn’t still figured out the details of our strange way of experiencing the world, you name this experience (the now) as “GOD”.

    The funny part is, of course, when you then confuse these statements with “proof” that the new atheists “are wrong”. You got lost in the categories so much you ended up becoming a straw man yourself. Watch the crows for me, will ya? I’m going to sleep. Nighty night.

  7. Luis,

    Since you’re so smart, perhaps you could explain how change is possible without making any reference to actuality or potentiality. Thanks.

  8. When do we get to the zombies? I like zombies.

  9. Also, please explain how one could empirically test for something that could not even be comprehended if it was seen. And, while you’re at it, explain how empirical evidence tells you that empirical evidence is the only method for locating truth.

  10. When my teenage kids mention how a God makes no sense, I always bring up this argument of First Cause, and leave at that. However, a First Cause and a God that “sees” what we do is two different things. If I remember my Ancient Greek philosophy classes of way back, the ultimate conclusion of this deduced God (if you continue the reasoning) was a sphere closed on itself that had no interaction with its surroundings. That is a far cry from our understanding of a God. Theism usually implies an active God that influences things (more that just the First Cause, which is really the Unknowable). Anything Aquinas brings up has no relation to a God “active in the governance and organization of the world and the universe” (definition of theism). This implies he does not bring any support to theism. Therefore, atheism is not refuted. You can go even a step further: if God is only the First Cause, he’s rather useless, and can be put aside as an object of worship (why bother, the first cause has happen, the dominoes are already falling, no prayer can change things).

  11. David,

    Four of Aquinas’s Five Ways give us a God that is totally involved in the constant “governance and organization of the world and the universe”.

    First Way: As discussed by Briggs, it tells us that God is the source of all motion at every moment, and not merely the beginning of motion in the distant past.

    Second Way: Aquinas tells us that nothing could exist even for a second if God did not cause it to exist at every moment.

    Fourth Way: Aquinas tells us that all goodness, truth, beauty and so forth derive from God directly, who imparts them at every moment.

    Fifth Way: Aquinas tells us that God directs final causes to their ends–at every moment.

  12. Ye Olde Statistician

    17 August 2012 at 9:31 pm

    Luis: If things only happen because this “first mover” is always doing its own thing and not because of other things, then it would be detectable.

    But, Luis, the only thing you did was to declare that you divide stuff that way. Well good for you, if that rocks your boat. To conclude from this ancient categorizations that you somehow have disproven the existence of a super-natural “thing” because it would “fancy” the big picture is…. even painful to witness.
    + + +
    Alas, the endpoint of such anti-reasons always seems to be to deny something obvious and, well, “empirical.” Whether that the self even exists or that things have causes or that motion/kinesis exists in the world, etc.

    Condider that among those things that cannot be demonstrated empirically are the irrationality of SQRT(2), the existence of an objective universe, nor the proposition that only things demonstrated empirically can be known. Show us “dog” rather than simply a particular dog.

    Luis: the God of the gaps. Because science hasn’t still figured out the details of our strange way of experiencing the world, you name this experience (the now) as “GOD”.

    Aristotle’s argument was not an attempt to “explain” any particular problem of physics. It was a series of deductions from empirical experience of change in the world; the consequences of experience, as it were. Physics is concerned with explaining the secondary causes regarding how such change occurs. The study of secondary causes does not clarify primary causes.

    David: a First Cause and a God that “sees” what we do is two different things.

    The existence theorem is is only one of the earlier Questions. Thomas wrote several hundreds of pages following up with the consequences. The first book TOC is here: http://dhspriory.org/thomas/ContraGentiles1.htm and the remainder can be found from that. In particular, in Book 1 of the Contra gentiles, is the Question: That the divine will extends to singular goods (http://dhspriory.org/thomas/ContraGentiles1.htm#78)

    This is like a man reading Euclid’s first theorem and complaining that he cannot how this would lead to an angle formed by two tangents to a circle is equal to one-half the difference of the intercepted arcs.

    Luis: the first cause has happen[ed], the dominoes are already falling,

    For some weird reason, even though it has already been pointed out by Our Host in this very post (and by Aristotle, Thomas Aquinas, and many others, earlier) “first cause” does not meant “prior in time,” and “falling dominoes” are paradigmatically an example of accidental order and not of essential order, it seems to go in one ear and out the other of far too many readers, so accustomed are they to thinking only in terms of accidents. Primary causation in essentially ordered series is concurrent with the secondary (or instrumental) causes because, simply speaking, a clarinet makes no music in the absence of a clarinetist.

    In particular, in Book 2 of the Contra gentiles, is the Question: That in creation no succession exists (http://dhspriory.org/thomas/ContraGentiles2.htm#19)

    Hope this helps.

  13. Ye Olde Statistician

    17 August 2012 at 9:34 pm

    Oops. That was David in the final cite. Apologies.

  14. Since you’re so smart, perhaps you could explain how change is possible without making any reference to actuality or potentiality. Thanks.

    Of course it is possible. The only thing you need is “Changities”, that is, the characteristic of things to “change”. See, we can all become amazing philosophers. All you have to do is itify some verbs, make some narrative sense, and bang, you can prove anything you want.

    Also, please explain how one could empirically test for something that could not even be comprehended if it was seen

    But it is comprehended. At least, it is comprehended by its abilities, by the fact that such “prime movers” are able to “change things”. Well, that’s a start at least.

    YOS,

    But, Luis, the only thing you did was to declare that you divide stuff that way. Well good for you, if that rocks your boat. To conclude from this ancient categorizations that you somehow have disproven the existence of a super-natural “thing” because it would “fancy” the big picture is…. even painful to witness.

    Exactamondo, big shot. I agree with this paragraph above a frakkin 100%, and if you hadn’t predicted that outcome, then you failed to understand my point big time. FFS.

  15. @Luis Dias:

    “Of course it is possible. The only thing you need is “Changities”, that is, the characteristic of things to “change”. See, we can all become amazing philosophers. All you have to do is itify some verbs, make some narrative sense, and bang, you can prove anything you want.”

    You have not answered rank sophist’s answer. There is a reason why he asked the specific question he asked. You complained in the post rank sophist was replying to that “For all your words, you never showed why I should ever take seriously the notion that things are “potentials” or “actuals” or “movers”.” The positing of the primary division in being by Aristotle, that between potency and act, is precisely to answer the paradoxical argument of Parmenides that change does not exist. Now one can rehearse several possible answers to evade, dodge or deny Aristotle. Yours, which I will not deign to qualify, is definitely not one of them.

    “But it is comprehended. At least, it is comprehended by its abilities, by the fact that such “prime movers” are able to “change things”.”

    First, what one can know about God and how one knows, knowing in the sense of rationally understanding, is different of what one can know or how we can know about things such as horses, planets, rocks or dumb combox posters. And before you respond, this is not a presupposition, but rather the *conclusion* of arguments about God’s nature.

    Second you betray profound misunderstandings in practically every sentence you write. The First Way is not about how the Prime Mover (singular, because if there is one, there can only be one) “changes things” or a God of the gaps arguments where we plug a hole in our scientific knowledge and fill it with God. Saying that “Because science hasn’t still figured out the details of our strange way of experiencing the world, you name this experience (the now) as “GOD”.” just shows that you do not have the faintest inkling of how the argument runs or what it purports to prove, or even understand that these are metaphysical arguments that take as premises things that Science itself must *presuppose* to do its job, so complaining about how “the prime mover only exists within the safe parameters where science couldn’t ever aspire to detect its presence” or to ask for an empirical proof of God’s existence is just muddleheaded. It is like, upon seeing Euclid’s proof of the infinitude of the set primes, to complain that the conclusion is unfalsifiable and then ask for an empirical proof. It is category mistake, and a particularly stupid one. Now, the arguments may be ultimately invalid, but it is not your misunderstandings that will show it.

    “Exactamondo, big shot. I agree with this paragraph above a frakkin 100%, and if you hadn’t predicted that outcome, then you failed to understand my point big time.”

    And you failed to understand Ye Olde Statistician’s reductio. Big time.

  16. I’m curious about how specialists in this field deal with quantum physic’s non-causal behavior. According to quantum mechanics, events can just happen. In fact, there is very strong evidence that this is correct.

    Of course, one has to wonder where the laws of QM come from and who keeps them working…

  17. Hey, Rodrigues. Funny meeting you here.

    Of course it is possible. The only thing you need is “Changities”, that is, the characteristic of things to “change”. See, we can all become amazing philosophers. All you have to do is itify some verbs, make some narrative sense, and bang, you can prove anything you want.

    As Rodrigues said, you’re going to have to do better than that. Explain the process of change to me–right now–without referencing actuality and potentiality. Go on. For instance: describe eating a sandwich, in detail. Put your money where your mouth is, Luis. No one is impressed by your bluster unless you can back it up.

  18. The problem with all these arguments is that God( monotheism) is only a recent belief( perhaps 4000 years old ) Paganism is thousands of year older if not tens of thousands of years older. Monothiesim seems to be an invention of the human spirit not a fact,

  19. So I am sitting here in my chair and ponder all the dependencies that in actuality contribute to this state of affairs. The sensory world appears to me to be an unfinished reality, since I have to accept that at some arbitrary level there is a necessary something causing it all that is not a part of it.

    The property of the sensory world seems to be that anything actual is only potentially so. But now I have to assume that an actual something of a different order acts on the whole chain, however acting on the chain means to be a part of it. Doe that not constitute a contradiction?

  20. I’ll take Mr. Briggs’s words for it that some experts probably have refuted Aristotle’s unmoved first mover. Unmoved first Mover!

    The first mover concept reminds me of what Lao-Zi said in Verse 40, Tao Te Jing:

    All things are born of something. Something is born of nothing.

    (My own translation. Here is another one.

    Lao-Zi concluded that something is born of nothing, which also allowed him to avoid the question of who-created-God. Instead of the Big Bang theory or circular motion theory or unknown, many people subscribe to the concept of a first mover, whom they call God. I am fine with that. I’ll go with Lat Zi’s nothing-ness that encompasses many meanings, including unknown and doing nothing about it because it seems fruitless.

    I like the answer given to me by my children and spouse, all Catholic-educated, the best: It’s a belief; no proof and reasons are necessary.

  21. Darn, did I not enclose my tag with a right arrow?

  22. Mr. Briggs, thanks for the lightening-fast correction.

  23. Briggs

    18 August 2012 at 9:38 am

    JH,

    You misread again (I would do worse with Chinese, so do not fret). I do not say that “experts” have “probably” refuted Aristotle/Aquinas. I say that my powers of explanation are weak and that it is better to seek out superior sources. I say that if you believe you have thought of a contradiction to the argument I present, it is you who are wrong (or I that have explained badly). I say that Aristotle/Aquinas have not been refuted and that their arguments are true, deduced to be true, valid, and which are therefore proof, reasons for belief. For the same reasons, e.g., you doubtless believe the central limit theorem true.

    Go Red Wings!!,

    Aristotle has roughly two-and-a-half millenia going. That good enough? Anyway, we did not know until a couple of weeks ago the Higgs boson was real. Does its infancy make it false, or does the ancientness of Ptolemy’s physics make it superior?

    Luis,

    My dear old friend. At the risk of missing the plank in my own eye, allow me to observe that you are not pausing to consider you might be wrong (and you are). I was, brother, in your camp at one time: an angry (or, better said, exasperated) atheist. I tell you it was just the sort of arguments we read today that convinced me of my error. These are profound arguments which merit better attention than you are paying them. Listen to Ye Olde Statistician.

    First, as Aristotle told us, and using Feser’s example, this blue rubber ball is potentially a pile of goo. But it is not the goo which turns the potential into an actuality. Only something actual, like fire, can turn this potential into an actuality. And this is so for all potentialities: only an act can turn potential into something actual. Pause here and consider this deeply. If we don’t get this, we can’t go on. This deduction applies to all of physics, of all change of any kind. That means of the kind we have already discovered and of the kinds yet undiscovered.

    Second, essentially ordered series are just different than accidentally ordered series. In your haste, you have failed to appreciate this. Again, we do not need to know exactly what (if anything) lies below quarks, strings, and the like. There just is no gap in this deduction that need be filled in later with some empirical observation. Instead, we deduce that now, at this instant, in any change there must be at base a First Mover, or First Changer. And after that, we can deduce the properties of this First Mover. First, He is Unmovable: if not, something would be below him, able to move him. Second, there can be only one. Third, He must be everywhere. Etc., etc.

    All,

    I think the problem is, or at least it was so with me once time, you see the argument as a whole, glance at the conclusion, are repulsed by it, and then you take a scattershot approach of dismissing it. “I don’t need to consider it, or answer it directly. The conclusion’s a belief; no proof and reasons are necessary.” I would never have been satisfied with such blatant lack of rigor in dealing with, say, mathematical arguments. But for this (or should I say the) argument I was content with a gloss. When I think of how I treated arguments like this before, how I now blush!

    What we have is an argument which many are saying is valid. It has certain premises and then a conclusion which follows. In order for you to prove invalidity, you need to do one of two things: show which premises is false or show that the conclusion does not follow. Glib dismissal does neither.

    It was actually the (non-theist) David Stove who showed me how foolish I was. Once again, I’ll recommend his Rationality of Induction, especially the second half of that book and his lovely arguments proving deductive logic is not formal. Incidentally, let’s not discuss these there: we can do a separate post.

  24. Mr. Briggs,

    And you misread me. I do no think the concept of unmoved first mover is false. I don’t think anything of it. Nothing-ness! To be exact,it’s unknown to me, perhaps, until you can test its existence… just like the test of the existence of the Higgs boson. I’ll admit I know nothing about the Higgs boson except what’s reported.

    You think that Aristotle/Aquinas have not been refuted, many others think the opposite. I am applying the same logic you’ve used to imply that you can choose whatever theory/argument you want to believe.

    Aristotle thought that women had “fewer” teeth than men. An I supposed to believe him because he has roughly two-and-a-half millenia going?!

  25. I do not think the concept of unmoved first mover is false.

  26. Oh, yes, I do believe that under certain premises and assumptions the central limit theorem (CLT) shown true mathematically. I also believe that CLT is created by mathematicians.

    Back to my Saturdays chores!

  27. Briggs

    18 August 2012 at 11:44 am

    JH,

    Rather, something discovered by mathematicians.

  28. Briggs,

    Here’s the problem as I see it.

    You more or less stated at the beginning one can find God through logic. Well, I agree you can provided you can prove your starting point but none of what I’ve seen to this point goes to establishing the truth of the premises.

    We can believe them to be true but belief does not necessarily equal truth. Likewise, a “not invalid” conclusion doesn’t mean the conclusion is necessarily valuable.

    Since it all hinges on the truth of the premises, what is being accomplished here? As I see it, the premises are based belief so the conclusion also amounts to belief. It’s a fun exercise with no point.

    You may consider this a “gloss” but it really is the heart of the argument.

  29. Leonard Weinstein

    18 August 2012 at 12:55 pm

    Again the basic disproof is: If God is the actuator to potentials, where did it come from? All you have done is remove the lack of knowledge by making an assumption. The argument about potentials and actuators are pure assumptions of semantics, with no foundation other than assumption. An equally valid assumption is that the never ending unfeeling multi-universe is the actuator.

  30. Rather, something discovered by mathematicians.

    Ah, discovered! I have always thought the word “discover” is associated with some sort of observed evidence. You’ll have to pardon my shallow understanding of English, so I won’t argue with your choice of the word.
    However, based on my understanding of mathematics proofs, I agree with Terry Tao’s view that mathematics is created.

  31. Briggs,

    There just is no gap in this deduction that need be filled in later with some empirical observation. Instead, we deduce that now, at this instant, in any change there must be at base a First Mover

    This is an example of belief. We deduce this how? Based on observation that everything seems to have a cause? But what if we have been restricted in our observations and some things just happen for no particular reason whatsoever? Effectively, an accident? Do we have observations of those? Are they being discounted in the deduction of a First Mover?

  32. Mr. Briggs,

    If you want to convince me of something, please use some logical and reasonable explanations. Simply telling it to me won’t work, and expecting me to accept the reason of “Aristotle has roughly two-and-a-half millenia going. That good enough?” is an insult to my intelligence.

  33. JH,

    However, based on my understanding of mathematics proofs, I agree with Terry Tao’s view that mathematics is created.

    You can be only discover something if it’s already there. There is no evidence that mathematics exists anywhere but within our minds. Math may be a built-in attribute of humans allowing the conclusions to be discovered but I doubt it. It’s far more likely that mathematics was created by us.

    Even then, mathematical conclusions are stumbled upon instead of being constructed. That’s probably what Matt meant.

  34. What I find amazing is that such gibberish can come from such a clever man.

  35. @JH:

    “However, based on my understanding of mathematics proofs, I agree with Terry Tao’s view that mathematics is created.”

    Could you explain what sort of understanding is this that leads you to conclude that mathematics is created?

    @DAV:

    “This is an example of belief. We deduce this how?”

    Ex nihilo nihil fit; every argument proceeds from a premise or premises, presumably self-evident or at least reasonable, to a conclusion. You want to dispute the premises of the First Way and for example, *seriously* argue that there are events with no cause? By all means, do it. But stringing together a series of what-ifs does not an argument make; reality is not dictated by our imaginations.

    “There is no evidence that mathematics exists anywhere but within our minds.”

    Actually, you are wrong.

    But let me turn this around: what sort of evidence do you have that mathematics exists solely in the human mind?

  36. every argument proceeds from a premise or premises, presumably self-evident or at least reasonable, to a conclusion

    “Reasonable” doesn’t mean “True”. It only means “believed true”.

    I’m not proposing anything other than consideration that some (or more) of the premises haven’t been established. I didn’t claim the original premise(s) and offered an alternative which is just as reasonable and also based on observations.

    As you say: Ex nihilo nihil fit. Guesses in premises result in conclusions amounting to guesses and premises based on faith only result in conclusions amounting to faith.

    “But let me turn this around: what sort of evidence do you have that mathematics exists solely in the human mind?”

    The same sort as you might have for the opposite: none that I can point toward. Can you show me an example of mathematics existing anywhere outside of world model analogies? I hope you’re not one of those who confuses the world with the model.

  37. @DAV:

    “As you say: Ex nihilo nihil fit.”

    Yes, there can be no infinite regress and the buck must stop somewhere. Any argument must start from some agrred-upon premises, axioms, first principles or whatever you want to call it. Do you have anything of actual substance to add?

    “The same sort as you might have for the opposite: none that I can point toward.”

    Thanks for the honesty.

    “Can you show me an example of mathematics existing anywhere outside of world model analogies?”

    First you have to tell me what exactly are “world model analogies”.

  38. G. Rodrigues,

    Let’s think of Lp space (http://en.wikipedia.org/wiki/Lp_space). What is a Lp space, or a measure space or a measurable function? The development of those terms came from mathematicians’ creativity, and was nowhere to be discovered.

    Please visit http://mathforum.org/library/drmath/view/51551.html and check out the proof of 1+1=2. Does it exist in human mind? I just want to know what it means to you to say that it exist in human mind.

    DAV, understood, and thank you. I don’t agree with you on everything though. Well, I am getting off topic, plus the answers won’t affect how I come up with an idea or a problem and how I go about solving a problem.

  39. First you have to tell me what exactly are “world model analogies”.

    You read here and don’t know? OK. A world model is an approximation of reality. Many world models are mathematical. The model isn’t reality. It is only an analogy.

    Do you have anything of actual substance to add?

    Yes, and I supplied it. You seriously reject the idea that there can be a confluence of circumstance without any plan, purpose of reason? There are NO accidents and all correlation is real?
    Hmmmm.

  40. G. Rodrigues, when I come up with an idea, I’d like to think I create the idea. If somehow God has clued me in, God should let me know in a more obvious way.

  41. “But consider the moment you squeeze the trigger. The movements of the hammer and of your finger happen simultaneously….”

    No, they do not. They happen faster but they do not happen simultaneously. Someone familiar with real time processing should be able to assure you what we see as simultaneous acts are easily captured as separate events by a CPU running at a few hundred megahertz. I’m not claiming that matter doesn’t act simultaneously on other matter — for it does appear that gravity does this. But all examples that I’ve seen of a “per se” chain fall short. And they all fail on the level of analogy. Those chains are concerned with force and motion, not with being. So they aren’t applicable to being itself.

  42. @JH:

    “What is a Lp space, or a measure space or a measurable function? The development of those terms came from mathematicians’ creativity, and was nowhere to be discovered.”

    I am really baffled at what you purport to prove by this example. Let us assume for the sake of argument that the L_p spaces exist as extra-mental beings as say, a Platonist like Goedel would contend. Since they are not material objects, no amount of observation can stumble upon them, only the proper operations of the intellect can be expected to discover them. So what you call creativity, a Platonist would call the proper operation of intellect contemplating the eternally existing Platonic realm — in more prosaic terms, discovering or charting the mathematical universe.

    For the record, although I am a realist, I reject Platonism. My only point in bringing it up is to make clear that your example proves absolutely nothing.

    “G. Rodrigues, when I come up with an idea, I’d like to think I create the idea. If somehow God has clued me in, God should let me know in a more obvious way.”

    Once again, I am really baffled on what you purport to prove by this non-observation. And why exactly are you bringing God into this question anyway, as I never even mentioned Him?

    @DAV:

    “A world model is an approximation of reality. Many world models are mathematical.”

    Many world models are mathematical, sure. And then again, vast portions of mathematics have absolutely nothing to do with “reality” (one of those words that seem to need to be guarded by quotes wherever it is used) or any scientific theory about reality. But this has absolutely nothing to do with whether mathematical objects have any extra-mental reality or are just pure beings of reason. In fact, suppose for the sake of argument that all mathematics were of the “world model” sort; this would in fact be an argument in favor of the objective, extra-mental existence of mathematical objects. I will not expand the argument though, and content myself with saying that methinks you are confused about what the real question is.

    “You seriously reject the idea that there can be a confluence of circumstance without any plan, purpose of reason?”

    Aristotle already furnished an account of chance events; in the Scholastic jargon, and to summarize, it is the intersection of independent causal chains. But if I am reading you right (which to be quite frank, I am not so sure), you are once again confused, as the issue of chance has nothing to do with whether there can be events without causes in the sense of the principle of causality used in the First Way — that every potency can only be reduced to act by something already in act.

    By the way, when I pointed out the specific issue of uncaused events, I was not so much asking for an argument, but rather pointing out that an argument was absent. And still absent, actually — but to repeat myself, I am not asking for one, I am just pointing out that one is needed. Rhetorical questions do not count as an argument.

  43. I see that Luis skipped out on my challenge. Not surprising.

    DAV,

    Think about this for a second.

    (1) Logic is false.
    (2) If logic is false, then the deduction leading me to (1) is false.
    (3) Therefore, logic is true.

    Now that we know that logic is incapable of being false (only its premises), we can move on to the truth of Aristotle’s system. First, another argument.

    (1) The only two states of existence are “being” and “not-being”.
    (2) Not-being does not exist, by definition.
    (3) Therefore, only being exists.
    (4) Change is the appearance of being from not-being.
    (5) But not-being does not exist.
    (6) Therefore, change does not exist.

    This is my approximation of the argument made by Parmenides. Remember: only his premises can be false, unless he commits the non sequitur fallacy. (He doesn’t.) Now, do you accept the insanity that change is impossible, and therefore that everything we see is an illusion? I would hope not. Aristotle’s act/potency distinction gets us out of the paradox and allows change to exist. Your other options are pretty limited.

  44. Any god in particular?
    There’s an awful lot of them amongst the world’s religions.

  45. G. Rodrigues,

    Yes, only proper operations of the intellect can be expected to produce mathematics including definitions, axioms, proofs, and theorem. Those definitions (in the link about Lp space) demonstrate this point beautifully! Note also that they came to existence because of mathematicians, and hence were created by mathematician. I have explained what I thought the use of ““discover” meant.

    There is no particular reason; it indicates that I don’t get “GOD” who has been credited to have created everything by some people. I don’t think those people meant to say that God has discovered everything.

  46. @JH:

    “Note also that they came to existence because of mathematicians, and hence were created by mathematician.”

    Whether they “came into existence” is what is in dispute in the first place. Now, do you have any non-question begging argument?

  47. Luis,

    you cannot even begin by showing why should we take these funny categories “per accidens” and “per se” (and quite others) seriously enough to prove the existence of a “prime mover”.

    Exactly. These are rhetorical games meant to filter out conflicting points of view. I’d like someone to show any point in the universe that is *not* changing, or any event that moves one direction from cause to effect — just one.

  48. I’d like someone to show any point in the universe that is *not* changing, or any event that moves one direction from cause to effect — just one.

    Any description of change presupposes that which is changing. This is why the Heraclitean flux fell out of fashion 2,400 years ago. (Some post-modernists started endorsing it after Nietzsche, but their logic is absolutely backwards.) If something changes, then the “something” must be other than change itself. Why? Because, if what change changes is change, then you begin a vicious regress: change changes change, which changes change changing change, onward forever. Therefore, we are necessarily left with two aspects: that which is change and that which is other than change.

  49. rank sophist,

    Can you really use logic to prove logic?


    G. Rodrigues,

    Not the same as quoting Aristotle (if that’s worth anything at all) but

    David Berlinski:
    Accept my premises and I will lead you infallibly to my conclusions. Your conclusions can be completely wrong even though your logic is completely right.

    As such I really don’t care what the point is about the First Way or any other way if based upon questionable premise.

    If you want to do something constructive then prove the premises ending in the deduction of a First Mover. Waving your hands in the air (or simply declaring the premises “obviously true”) won’t cut it.

    Don’t need the whole argument. Make a list of the premises and defend them.

    But this has absolutely nothing to do with whether mathematical objects have any extra-mental reality or are just pure beings of reason. … I will not expand the argument though, and content myself with saying that methinks you are confused about what the real question is.

    There was no real question. It was part of a comment I made to JH about mathematics that you had a problem with. Specifically, you said: you are wrong.

    Now that I have asked you to back that up you want to weasel away. That’s fine, it’s OT anyway. Another day but in the meantime stop the jabber.

  50. Perhaps I can sharpen some of the above criticisms. The central issue seems to be identified in the first item in the technical addendum. And it hinges on the definition of the word “follows”:

    1. That the actualization of potency is a real feature of the world follows from the occurrence of the events we know via sensory experience.

    If this is an assumption, then why is the entire argument not “begging the question”.

    Or, if this is a hypothesis, as it appears to me to be, how is it observationally falsifiable? (The point being: If not falsifiable, apply Occam’s razor.)

    It does not good to say that any rational explanation for sensory experiences must include the above hypothesis because Mother Nature can be anything She wants to be. Only our explanations of our observations about Her to each other have to be rational. Aristotle’s Law of Non-Contradiction is an assumption of the scientific method. Not a deduction.

  51. Ye Olde Statistician

    18 August 2012 at 8:01 pm

    All this commentary and still no one has shown the premises to be false or the conclusions not to follow! Instead, countless repetitions of “IT JUST IS!” in various forms, and suggestions of hints of possibilities curiously overlooked by fools like Voltaire.

    John Moore said:
    I’m curious about how specialists in this field deal with quantum physic’s non-causal behavior. According to quantum mechanics, events can just happen. In fact, there is very strong evidence that this is correct.

    YOS:
    No, quantum physics, like Newtonian mechanics, simply has no term “t” in its equations, and Moderns assume that causality is a time sequence, that, following al-Ghazali and Hume, it’s just one damn thing after another. That virtual particles appear spontaneously does not entail that they are uncaused by (say) the vacuum energy. Being unpredictable is not the same thing as being uncaused. Otherwise, why wait for quantum theory (and which quantum theory)? Why not point to the man who is unpredictably struck by an automobile while crossing the street. (“The car just came out of nowhere!”) This objection, so familiar by now, sounds like an Ungod of the Gaps: “We don’t know how this was caused, therefore it must not have been caused! IT JUST IS!!”)
    + + +

    JH said:
    unmoved first mover is unknown to me, perhaps, until you can test its existence… just like the test of the existence of the Higgs boson.

    YOS:
    Seems the Higgs boson was known long before something was found that sorta kinda acted a bit like Higgsy was supposed to act. But unlike mathematics, physical science is underdetermined. There are always multiple explanations for the same set of observables. However, what physical test demonstrates the existence of the objective universe? “Physical test” presupposes an objective universe to begin with, and would constitute Begging the Question. Better yet, what is the physical test that “something is unknown until you can [physically] test its existence”?
    + + +

    DAV said:
    none of what I’ve seen to this point goes to establishing the truth of the premises.

    YOS:
    Again, which premise do you think is unestablished? That there is κινεσις in the world? That something that doesn’t actually exist cannot cause anything? That an instrumental cause like a clarinet, golf club, etc. can play music or strike a golf ball without a concurrent clarinetist or golfer to play or swing it? In what way are the truths of these premises unestablished? Because the World is Illusion? Because clarinets are alive and self-willed? That species “poof” into existence without previous potential in matter?
    The Briggsian cri de coeur is to present the argument for this, not simply chuckle and walk away. It makes your position seem weak.
    + + +

    Leonard Weinstein said:
    If God is the actuator to potentials, where did it come from? All you have done is remove the lack of knowledge by making an assumption. The argument about potentials and actuators are pure assumptions of semantics, with no foundation other than assumption.

    YOS
    The existence of a BPA (Being of Pure Act) was a conclusion, not an assumption. Should play with revolvers until you know which end the bullet comes out. The assumption of the First Argument is that there is κινεσις in the world, sometimes translated as “motion” or “change.”

    Potency and act are not “semantic” assumptions, except insofar as semantics deals with meaning and content. They are, rather, the answer to Parmenides’ paradoxes of motion. If you have a different answer to why motion in the world is real — all motion, not just motion of location — trot it out. Or if that is beyond your job description, at least cite a counter-example and explain how you would rewrite physics to eliminate physics as the minimalizing of potential functions, as in gravitational potentials being actualized from potential energy to kinetic energy.

    Leonard Weinstein said:
    An equally valid assumption is that the never ending unfeeling multi-universe is the actuator.

    YOS
    Actually [pun intended] it’s not valid at all, let alone “equally valid.” The Primary Mover is necessarily a being of pure actuality (BPA). As such, it is itself unchanging. (This is logically prior to whether anyone calls it “God.”) But the universe* consists of things that are in motion — test: kick a football — and therefore cannot be the Primary Mover.

    (*) Universe means the collection of everything that has material existence and does not exist apart from the existence of material bodies. “Multiverse,” aside from the violence it does to plain English, posits either a) a reality that is undetectable from our own continuum (in which case, it is not an object of empirical scientific study) or b) one that is detectable (in which case, it is simply another part of the universe). If folks mean “separate space-time continua,” they should say that. Otherwise it amounts to the bold assumption that in addition the the World, there is a Heaven, a Hell, etc.

    The eternity of the World is irrelevant and was assumed by both Aristotle (who simply believed it was so) and by Aquinas (who believed the contrary, but knew of no proof for a “big bang” thingie). But notice that the eternity of the BPA is a conclusion deduced from its nature as Pure Act, while the Multiverse is simply declared to be eternal “just because” the declarers didn’t like the implications of a beginning to time.

    Whether the World is unfeeling — one of those “Duh?” moments — is also a contradiction, since certain attributes can be deduced about the BPA which would preclude that.
    + + +

    DAV said:
    But what if we have been restricted in our observations and some things just happen for no particular reason whatsoever?

    YOS:
    Simple. You would then have pulled the foundation from under the entire edifice of natural science. Amazing the babies one can throw out with the nihilist bathwater.
    + + +

  52. Ye Olde Statistician

    18 August 2012 at 8:30 pm

    DAV said:
    (contra Rodrigues: “But let me turn this around: what sort of evidence do you have that mathematics exists solely in the human mind?”)
    The same sort as you might have for the opposite: none that I can point toward.

    YOS:
    But you can point to the theorem that the interior angles of all plane Euclidean triangles sum to 180°. This is true regardless who conceives of it. If it were entirely in the human mind, then different minds could apprehend different sums. (We are not talking about different notations or dividing the circle into other increments — that the circle contains 360° really is a human construct — or even that imprecision of measurement or construction leads to physical triangles that are less than ideal with sides less than perfectly straight, corners not entirely closed, cut from felt or drawn with chalk, etc..) But if the conclusion is mind-independent, then it must have a real extra-mental existence and would remain true even if no human mind ever had existed to contemplate it. Conceptualism is incoherent and undermines natural science: why should not scientific laws have at least as much subjectivity — the result of genetically-wired pattern-seeking — as what you, in your anxiety, attribute to mathematics?

    It’s all just a construct of the mind… (And then, in another context, let’s deny that “minds” exist, which pulls the rug out from under the fellow pulling the rug out from under — or perhaps an effort to sweep the rug under the rug. The ultimate bottom is intellectual nihilism, not a friendly environment for natural science and rational thought.)

    That the discoveries of mathematicians are real can be seen in identical discoveries in widely separated times and places: e.g., Archimedes method of exhaustion also discovered in Japan. The Pythagorean Theorem reflected in the Shang Gao theorem. And from Babylonian tablets listing what we call “Pythagorean triplets” we find actual examples of the intellectual pitfall of confusing mathematical proof with empirical trials: viz., a hodge-podge of particulars without any unifying universal.
    + + +

    JH said:
    when I come up with an idea, I’d like to think I create the idea. If somehow God has clued me in, God should let me know in a more obvious way.

    YOS:
    You have a very peculiar notion of what it means to be a source of existence. Johann Christoph Denner was the (efficient) cause of the clarinet, the source for its existence; but that does not mean he wrote Mozart’s Clarinet Concerto or used Sharon Kam as a sock puppet to play it. Simile modo, a Primary Mover can endow intellect without thinking your thoughts for you. For that matter, Sharon Kam has no need to consider the Denner Hypothesis to teach others to play the clarinet.

    contra Briggs: “But consider the moment you squeeze the trigger. The movements of the hammer and of your finger happen simultaneously….”

    donjindra said: No, they do not. They happen faster but they do not happen simultaneously. … But all examples that I’ve seen of a “per se” chain fall short.

    YOS
    But this was explained to you on Feser’s blog long ago. The term “simultaneous” is imprecise. It does not have physical referents since, as Whitehead pointed out (in The Principle of Relativity), there is no such thing as a durationless instant, affirmed in philosophy by Oderberg. There are only events. The more correct term would be “concurrent.” The marker of a sequence per se is not “simultaneity” but rather the dependence of the intermediate movers, which lack the power to move another unless concurrently being moved by something prior to them. Thus the music we hear is caused by compression waves in the ear moving our eardrums (etc.). But the air would not wave in that manner if the clarinet were not playing. But the clarinet has not power to produce music unless Sharon Kam (or someone like her) were not playing it. Now, regardless whether Ms. Kam’s embouchure and fingering is “simultaneous” with the emission of the sound, it is quite clear that her playing must be concurrent with her playing of the instrument.

    (Note, keep in mind that the Latin imperfect present, often translated as English simple present, carries the connotation of the English present progressive. Hence: that which is changing is being changed by another. Questions of inertias are part of this. The medievals called the the problem of “first and last moments.” It was their assertion that there was no first moment to a motion, which put them within spitting distance of “open sets” and Dedekind cuts.)
    + + +
    george crews
    contra: That the actualization of potency is a real feature of the world follows from the occurrence of the events we know via sensory experience.

    If this is an assumption, then why is the entire argument not “begging the question”.

    Because it is not an argument attempting to prove that some things in the world are changing, It is perfectly fine to assume that change is real in order to prove something else.

  53. YOS,

    But you can point to the theorem that the interior angles of all plane Euclidean triangles sum to 180°. This is true regardless who conceives of it. If it were entirely in the human mind, then different minds could apprehend different sums.

    So we tend to view things the same way. Just because two people can start with the same premises and end at the same point in a mental exercise proves nothing about non-mental existence. It in no way means that Euclidean triangles are fundamental properties of the real world. If anything they are an idealization that lets us simplify. Try constructing an exact Euclidean triangle on paper (or elsewhere) and you’ll see what I mean.

  54. Can you really use logic to prove logic?

    The truth of logic is undeniable. Any attempt to undermine it is self-refuting, automatically.

    Or, if this is a hypothesis, as it appears to me to be, how is it observationally falsifiable? (The point being: If not falsifiable, apply Occam’s razor.)

    How do we establish the truth of falsificationism, or the truth of Ockham’s razor?

    It does not good to say that any rational explanation for sensory experiences must include the above hypothesis because Mother Nature can be anything She wants to be.

    Says who? Looks like you’re the one begging the question.

    Only our explanations of our observations about Her to each other have to be rational. Aristotle’s Law of Non-Contradiction is an assumption of the scientific method. Not a deduction.

    Oh boy. Another follower of scientism who thinks that the LNC is just a shot in the dark.

    If the LNC is false, then the LNC would be both true and false at the same time. Likewise, we would all exist and not exist, and all science would be both right and wrong–simultaneously.

  55. To the question: What sort of evidence is there that mathematics exists solely in the human mind?

    An entertaining place to start would be Lakoff/Nunez’s Where Mathematics Comes From. The book: emphatically rejects the Platonistic philosophy of mathematics. They emphasize that all we know and can ever know is human mathematics, the mathematics arising from the human intellect. The question of whether there is a “transcendent” mathematics independent of human thought is a meaningless question. That is like asking if colors are transcendent of human thought- colors are only varying wavelengths of light, it is our interpretation of physical stimuli that make them colors.

  56. rank sophist,

    “If something changes, then the ‘something’ must be other than change itself.”

    I don’t claim change is existence itself. I claim it’s the nature of everything that exists to be in a constant “state” of change. If this is the case there is no physical necessity to invoke a Prime Mover. Additionally, the reasoning used to reach that Prime Mover falls apart. For it assumes change propagates from a changing thing to an unchanging thing.

  57. Can you really use logic to prove logic?
    The truth of logic is undeniable. Any attempt to undermine it is self-refuting, automatically.

    I seem to recall something from the last century: In 1931 German logician Kurt Gödel announced his discovery that complete certainty was never to be encountered in mathematics by any route founded on traditional logic.

    There are problems inherent in self-reference. I believe that also includes using logic to prove logic.

  58. rank sophist said: “The truth of logic is undeniable. Any attempt to undermine it is self-refuting, automatically.”

    But note that smooth infinitesimal analysis (SIA) (a type of non-standard analysis) allows neither proof by contradiction nor the law of the excluded middle. Yet SIA does, for example, engineering calculus just fine. So the important question is, how much of logic and math is absolutely required for understanding the nature of reality. IMHO, for logic: Aristotle’s Law of Non-Contradiction. For math: SIA.

  59. , it is our interpretation of physical stimuli that make them colors.

    Which, when push comes to shove, is a word game. How is that any different than saying it’s our interpretation of physical stimuli that leads us to call a piece of furniture a chair?

    Color seems to be more than a mind construct — which is what “transcending human thought” means. There is evidence that other creatures also react to them.

    The situation is quite different for mathematics and answering the question for mathematics is far from meaningless.

  60. I don’t claim change is existence itself. I claim it’s the nature of everything that exists to be in a constant “state” of change. If this is the case there is no physical necessity to invoke a Prime Mover. Additionally, the reasoning used to reach that Prime Mover falls apart. For it assumes change propagates from a changing thing to an unchanging thing.

    You totally missed my point. It’s logically impossible for only change to exist, as I demonstrated above. The statement that something changes presupposes the existence of something that does not change. You have only two remaining options: deny the existence of change (Parmenides), or posit a system that includes both change and not-change. Basically the only candidate for the latter is act/potency.

    I seem to recall something from the last century: In 1931 German logician Kurt Gödel announced his discovery that complete certainty was never to be encountered in mathematics by any route founded on traditional logic.

    There are problems inherent in self-reference. I believe that also includes using logic to prove logic.

    As Rodrigues has argued in the past, Godel’s theorem is not relevant to logic. You’ll have to ask him, though, since I don’t know 1/100th as much about math as he does.

  61. @DAV

    I will grant you that it is a meaningful answer that the question is meaningless. :-)

  62. As Rodrigues has argued in the past, Godel’s theorem is not relevant to logic.

    Convenient, is it not?

  63. @DAV:

    “Don’t need the whole argument. Make a list of the premises and defend them.”

    So soon, and it seems we have already reached the point of talking past each other. You are completely in your right to ask for a defense of the premises of the argument — for that, the only advice I have is the same of Mr. Briggs: go read a book. What I tried to do (and seemingly failed) was:

    1. When you asked “This is an example of belief. We deduce this how?” to point out that first principles do not admit of demonstration, but only of dialectical justification. We either present reasons for their reasonableness, or show that their denial leads to absurdities.

    2. If you wanted to dispute any of the premises of the First Way like the principle of causality (in its Scholastic formulation, which is different from more modern formulation, like the Leibnitzian PSR) then an argument is needed; stringing together what-ifs or posing rhetorical questions do not count as rebuttals. I was also fairly explicit that I was not asking you for the argument, meaning I was not engaging in this specific debate, just pointing out that one was needed.

    3. Then on 18 August 2012 at 2:49 pm you asked “You seriously reject the idea that there can be a confluence of circumstance without any plan, purpose of reason?” I assumed, and still do, that this refers to the causality principle. Then I answered that you are confused, since the issue of chance does not impinge on the validity of the principle of causality, all the while inserting a parenthetical remark that I could be misreading you — in other words, the confused one could very well be me.

    “There was no real question. It was part of a comment I made to JH about mathematics that you had a problem with. Specifically, you said: you are wrong.”

    You said in 18 August 2012 at 1:30 pm to JH: “There is no evidence that mathematics exists anywhere but within our minds.” I said you are wrong. Instead of substantiating my claim, I asked you for evidence that mathematics was only a product of human minds. The reason I framed the question in this way is because I was curious to know what sort of evidence convinced you of that. In 18 August 2012 at 2:20 pm, you admitted you had none, so as far as my original purpose the issued died there.

    “Now that I have asked you to back that up you want to weasel away.”

    What you asked in 18 August 2012 at 2:20 pm was and I quote: “Can you show me an example of mathematics existing anywhere outside of world model analogies?” This is not the same thing as asking if mathematical objects have an objective, extra-mental existence, precisely the point I made in 18 August 2012 at 4:00 pm. And I think I did answer your question; if anything is not clear in it, by all means do tell. If all along what you wanted was evidence that mathematical objects do have real, extra-mental existence, then well, you should have formulated your question more precisely as I am not a mind reader. Ye Olde Statistician already gave one argument in favor of the reality of universals — and no, your objection does not fly. The best advice here is the same as for the First Way: go read a book. There is a long and vast tradition of arguments in favor of (some form of) realism, from Plato to Frege and his followers in modern analytical philosophy. Maybe you will find the arguments weak or at the very least, non-compelling, but then you will be able to criticize them from a position of knowledge.

    “In 1931 German logician Kurt Gödel announced his discovery that complete certainty was never to be encountered in mathematics by any route founded on traditional logic.”

    No, that is not what Gödel’s incompleteness theorems tell.

    “There are problems inherent in self-reference.”

    There are several instances of benign self-reference as well as proofs of Gödel’s incompleteness theorems that do not go through the construction of weird self-referential statement, so no, there is no necessary, intrinsic connection between self-referentiality Gödel’s incompleteness theorems.

    “I believe that also includes using logic to prove logic.”

    rank sophist was not using logic to prove logic. He said the perfectly correct, perfectly logical point that you cannot use logic to refute logic. There is a difference and it is a difference that makes a difference.

  64. @George Crews:

    “But note that smooth infinitesimal analysis (SIA) (a type of non-standard analysis) allows neither proof by contradiction nor the law of the excluded middle.”

    While you are correct on the law of excluded middle, you are incorrect on proofs by contradiction. The deductive rule ~p, p -> F: ~p is constructively valid; on the other hand the rule p, ~p -> F: p is not, because ~~p is not constructively equivalent to p.

  65. YOS,

    So, do you think that Denner invented or discovered the clarinet (initially)? That’s all I was trying to clarify… nothing more.

    I didn’t mean to imply anything about whether Denner wrote any music or how one can learn to play clarinet, but I agree with what you said though.

    I really should have said a realized idea… an idea that’s been solved and proved. I don’t want to give you an example, e.g., my paper, because I treasure my anonymity here.

  66. The reason I framed the question in this way is because I was curious to know what sort of evidence convinced you of that. In 18 August 2012 at 2:20 pm, you admitted you had none, so as far as my original purpose the issued died there.

    So you are saying, in effect, you can merely state: you are wrong and, if I don’t prove otherwise, claim you were quite justified. Sorry, but I think that makes you — well insert your own pejorative here — but it amounts to sniping.

  67. G. Rodrigues,

    Whether they came into existence is what is in dispute in the first place?

    I thought the question under discussion was whether mathematics was/is created or discovered. But, fine, my answers sometimes invite more questions in my class. I like it because it means we all are thinking!

    The mathematical truth has been mentioned several times in previous posts. I sure wish you had asked this question then. So you want to know whether (not how) they came to existence, where they = definitions, axioms, and theorem. How about reading the following first in addition to Mr. Crew’s comment?

    (Mr. Briggs, I apologize for posting it twice.)

    http://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/
    Terry Tao, a great researcher and expositor of mathematics, is often compared to Einstein by mathematicians. His view on mathematics:

    My view is that mathematics is primarily a language for modeling the physical world, or various abstractions of the physical world(*). So in one sense it is purely formal, in much the same way that English is a formal combination of letters of the alphabet. On the other hand, as our understanding of mathematics improves, our models fit the physical world better (both in terms of predictive power, and in terms of agreement with physical intuition) and so the mathematical objects we study begin to more closely resemble physical objects, though of course they are never actually physical in nature. It is certainly helpful though, when trying to create new mathematics, to think of mathematical objects as being analogous to physical objects; for instance, a mathematical object may “obstruct” another mathematical operation from taking place, and thinking about obstructions is a very useful way to make progress in mathematics.

    (*) The physical world generally refers to tangible objects, but one can also consider abstractions of these
    objects, abstractions of abstractions, and so forth. For instance, a children’s ball is a physical object; it might be red. The property of “redness” is then an intangible abstraction, but still physical. The phenomenon of “colour” is then an abstraction of an abstraction, but again still physical; the concept of a “sense” is a yet further abstraction; and so forth. Somewhat analogously, mathematics tends to start with “primitive” objects such as numbers or points, then moves up to sets, spaces, operations and relations, then functions, then operators, (and then functors and natural transformations, in category theory), etc. [It's true that in set theory, all of these mathematical objects can be described as sets - much as all parts of speech in English can be described as strings of letters - but this is only one of many equally valid interpretations of these objects, and not one which corresponds perfectly to physical intuition.]

  68. YOS,

    “There are only events. The more correct term would be ‘concurrent.’”

    Every example I’ve seen (rock shatters window, stick pushes stone, etc.) happens in reality as a temporal sequence. “Concurrent” (or “per se”) looks so only because we humans cannot process the sequence fast enough, so it merely appears to us as a single event. Nobody at Feser’s blog was able to demonstrate otherwise. The only thing that I know of which may act concurrently or simultaneously is gravity. And that appears to be bodies acting on each other *always,* at any distance, not one acting on another as a discreet event.

    “Thus the music we hear is caused by compression waves in the ear moving our eardrums (etc.). But the air would not wave in that manner if the clarinet were not playing.”

    Once the clarinet stops the waves continue traveling at the speed of sound. It appears to me to be no different than one billiard ball striking another then another …

  69. rank sophist

    “The statement that something changes presupposes the existence of something that does not change.”

    You might as well say the existence of red presupposes the existence of not-red. In the most trivial sense this is correct. We humans distinguish red from non-red because that’s how our biology works and we create language that reflects that. Likewise with change. Our limited abilities cannot sense atoms are in constant motion. Our language reflects that human limitation too (appearance of non-change). But we’re wrong.

  70. You might as well say the existence of red presupposes the existence of not-red. In the most trivial sense this is correct. We humans distinguish red from non-red because that’s how our biology works and we create language that reflects that. Likewise with change. Our limited abilities cannot sense atoms are in constant motion. Our language reflects that human limitation too (appearance of non-change). But we’re wrong.

    And with that, all of science was consigned to the flames. Well done.

    Also, for there to be atoms in the first place, something has to be “not changing”. That is, the atom has to be there, as an atom. Otherwise, there is no atom to change. Again, what changes has to be something, in this case an atom, rather than change itself–this would be a vicious regress. You seem to agree that some things change while others stay the same, which is good. Unfortunately, you don’t seem to realize that you agree.

  71. @George Crews:

    There is a typo in the deductive rules — delete the comma and what is at its left. There was some preceding text that was cut off but I forgot to delete the “~p,” and the “p,”. It was late and I was tired. Apologies for any confusion.

    @DAV:

    “So you are saying, in effect, you can merely state: you are wrong and, if I don’t prove otherwise, claim you were quite justified.”

    1. There may be some understanding about what exactly was my claim: you were wrong in saying that *there is no evidence* that mathematics has objective, extra-mental reality as opposed to being a pure product of the mind.

    2. Now, of course, it should be clear that I do find the evidence for mathematical realism compelling, and thus believe mathematical realism to be true. The problem is that there are several versions of realism and the most widely held, Platonism, is precisely one of the versions I reject. To substantiate all these claims, a combox is not appropriate, that is why I “turned around” and formulated the question in the way I did; that is also why I never even tried to defend mathematical realism and instead urged you to go read a book if you really want to know the evidence, that is, the arguments.

    3. I said I was curious about what sort of evidence lead you to believe that mathematical objects exist solely in the mind; you said you had none. Curiosity satisfied. As a corollary of this and the preceding 2., saying that “you can merely state: you are wrong and, if I don’t prove otherwise, claim you were quite justified” is putting words in my mouth. Doubly so, because while one may not have evidence for p, maybe only a couple of barely articulable intuitions about its truth, this by itself does not imply that p is false. Whether the belief in p is warranted or not, that is a whole different question, and quite the thorny one.

    @JH:

    “I thought the question under discussion was whether mathematics was/is created or discovered.”

    It is. If you say that mathematics is discovered, say, if you are a Platonist, then mathematical objects while discovered, exist eternally and never come into being. On the other hand, if mathematics is created and mathematical objects are mere beings of reason, there is a perfectly legitimate sense in saying that they come into being — as beings of reason.

    As far as the Terry Tao quote, I disagree with his view on the nature of mathematics, but then again this is besides the point. For as it concerns the matter under discussion I cannot find in there a single *argument* for why mathematics is created as opposed to discovered. It could be that I am just being obtuse, in which case can you point out what the argument is?

  72. @DAV:

    In 1. replace “understanding” by “misunderstanding”.

  73. I will have to rephrase this to understand the nucleus of the argument. I am looking at my fence and I am considering what is required for it to be actually a fence. It is an actualization of something that is only potentially a fence, namely the wood it is made of. In itself wood is an actualization of a potential of certain compounds to form wood through organic activity. Following this through I must finally acknowledge that there must be something to start with. This something must be understood as being “actually there” solely by itself.

    But does this line of argument really signify anything with regard to the foundation of the world around us?

    Now I have come this far it seems to me that this argument also reflects the way we operate in thought. One thought depends on another, but ultimately everything in thought depends on thinking. Thinking itself however only depends on itself. Any argument that could possibly be brought against this assertion will demonstrate this in the act. May it be true that certain conditions need to be fulfilled in order for me to think, these condition are never to be regarded as a collection of potentials with regard to thinking. A fence may be a potential of wood, but thinking is not a potential of neurons in the same way. That’s a whole new discussion in its own right though…

    I guess what I am really trying to say: I am not convinced the argument, which might be valid, really exposes God. For all I understand it might equally well expose our intellectual organization. Thinking occupies precisely the position of the first mover and what is more: it is detectable be it through accurate inner observation…

  74. G. Rodrigues.

    I am not a Platonist then. I don’t see how the existence or establishment or proof of the Poincaré conjecture is independent of mathematicians. I would imagine that there are objections to Platonism in the literature of philosophy of mathematics.

    It is certainly helpful though, when trying to create new mathematics, to think of mathematical objects as being analogous to physical objects;…

    You don’t have to agree Terry Tao. He describes what mathematics is and how it’s done in layman’s language! You are basically questioning whether he created or discovered the numerous mathematics theorems he has produced because Platonism insists that he discovered them.

    Can you somehow apply Platonism to our existence? That is, is our existence independent of God?

  75. @JH:

    “I am not a Platonist then.”

    Me neither, although I am a realist of Aristotelian-Thomist variety.

    I am sorry, but there is no argument in the quote, just an assertion. An assertion is not an argument.

    To preempt a possible misunderstanding that seems to have occurred with my exchange with DAV, my posing the question was just to satisfy my curiosity about what sort of evidence you had that convinced you that Platonism was false. Since you have presented no arguments I suspect that your rejection is driven by other philosophical commitments, maybe naturalism? But as I said, I posed the question just to satisfy a curiosity. I am not going to argue for mathematical realism, so while I think you are wrong, feel free to dismiss my indictment.

    “Can you somehow apply Platonism to our existence? That is, is our existence independent of God?”

    Sorry, but I cannot make heads or tails of your question.

  76. It seems reasonable to assume some mathematics is discovered, because it is demonstrably inherent in natural phenomena and some is made up, that is not originally part of “creation” but created by human minds and implemented (so to speak) through technology. I mean: what evidence do we have to assume that a single answer, created or discovered, exists for the whole of mathematics?

    Or alternatively some parts of mathematics would seem to justify a realist position, where other parts (I would venture to say in set theory) are best understood as nominalist. I don care that much how I am categorized, yet the symmetrical distribution of my body parts is very dear to me.

    Anyway there seems to be a difference.

  77. G. Rodrigues,

    I said I was curious about what sort of evidence lead you to believe that mathematical objects exist solely in the mind; you said you had none. Curiosity satisfied. As a corollary of this and the preceding 2., saying that “you can merely state: you are wrong and, if I don’t prove otherwise, claim you were quite justified” is putting words in my mouth.

    Putting words in your mouth?

    My original statement: There is no evidence that mathematics exists anywhere but within our minds. You led with Actually, you are wrong (http://wmbriggs.com/blog/?p=6002&cpage=1#comment-73059) then asked me to supply evidence to support a negative, which I declined.

    So, if I was wrong about “no evidence” how about an example?

    You don’t have any evidence to support your lead sentence, do you? I’ve asked you for it and instead get many paragraphs of why you don’t have to supply it.

    You were sniping — a sign of intellectual bankruptcy. By all means: run away.

  78. Sander van der Wal

    19 August 2012 at 10:47 am

    A metaphysial theory cannot be disproven, but it can have competition of other metaphysical theories that explain the same facts and that are also internally consistent.

    So tnere is no need to disprove the Unmoving Mover theory, the only thing needed is a competing theory that is as good as the Unmoving Mover theory in explaining the world.

    Fortunately there are several such theories. The simplest one is me being The Solipsist, and everything else is a figment of my imagination. This explains everything there is. Period.

    Something more sophisticated is the scientific method. Basically, one stops with explanations at the level needed to explain all observed phenomena. The reason this works is because there is not one Unmoving Mover theory, there are an infinite many of them. The bottom might be the Unmoving Mover, but what is between him and the observable world? Angels? Gnomes? Nothing? A new kind of exotic particles? Lots of new words describing effects we have not yet witnessed? Could be anything. Given that many possibilities the change one picks the right one are zero.

  79. rank sophist,

    And with that, all of science was consigned to the flames. Well done.

    You’re going to have to explain that because it appears to be totally unrelated to what I’ve been arguing — unless you happen to think science is non-empirical.

    “Also, for there to be atoms in the first place, something has to be ‘not changing’. That is, the atom has to be there, as an atom. Otherwise, there is no atom to change.”

    That makes no sense. Why is “thereness” dependent on changelessness?

    Again, what changes has to be something, in this case an atom, rather than change itself -– this would be a vicious regress.

    You seem to be identifying change with existence. I’m not doing that. I’m simply arguing change is a permanent property of anything that exists.

    You seem to agree that some things change while others stay the same, which is good. Unfortunately, you don’t seem to realize that you agree.

    I’ve been arguing the exact opposite which should have been clear. Everything is changing and always has been changing. Nothing stays the same. I asked originally, show me any point in the universe that is *not* changing. Until you do that you have no evidence of a “state” of non-change.

  80. Ye Olde Statistician

    19 August 2012 at 4:21 pm

    DAV
    It in no way means that Euclidean triangles are fundamental properties of the real world. If anything they are an idealization that lets us simplify. Try constructing an exact Euclidean triangle on paper (or elsewhere) and you’ll see what I mean.

    YOS
    Excellent. This was part of Dr. Feser’s discussion in the book being discussed! As Aristotle said, physics deals with the abstracted properties of material bodies while mathematics deals with the abstracted properties of ideal bodies. It is sometimes true that problems with the former inspire re-search into the latter. It is wonderful – EInstein called it ‘miraculous’ – that the discoveries of the latter so oft have applications to the former. However, discoveries in the ideal world of Euclidean geometry (and/or in other mathematics) are determined in a manner in which physical theories regarding the metrical properties of material bodies are not.
    + + +

    DAV
    In 1931 German logician Kurt Gödel announced his discovery that complete certainty was never to be encountered in mathematics by any route founded on traditional logic.

    YOS
    Actually, not. What he proved amounts to this. On the landscape whose points consist of true statements and whose roads are mathematico-logical proofs, there are places where the roads don’t go. That is, there are true statements that are not provable. That’s not the same thing as “no certainty,” which sounds much more general the way you have stated it. That a closed and bounded set is compact in Hausdorf spaces is known with “complete certainty” and would be true to general topology regardless whether any human mind had formulated it. An interesting consequence of Gödel’s Theorem is that while a “Theory of Everything” may be possible in physics, we can never be certain we have found it. (There may be places where the roads don’t go.) Another consequence is that human minds are not computers, and hence, not brains. [Off to the side is Gödel's version of the Ontological Proof of God.]
    + + +

    JH
    I really should have said a realized idea… an idea that’s been solved and proved. I don’t want to give you an example, e.g., my paper, because I treasure my anonymity here.

    YOS
    But if it is a realized idea, there must have been an idea to realize. This is not an objection, and in fact was cited by Aquinas and others. But it still remains that the existence of a Primary Mover who, let us suppose, has endowed human nature with the power of intellect, does not obligate it to do your thinking for you. That is entirely within the purview of the power of human nature, hence, entirely natural.
    + + +

    JH (quoting Tao)
    My view is that mathematics is primarily a language for modeling the physical world, or various abstractions of the physical world. So in one sense it is purely formal… On the other hand, as our understanding of mathematics improves, our models fit the physical world better (both in terms of predictive power, and in terms of agreement with physical intuition) and so the mathematical objects we study begin to more closely resemble physical objects, though of course they are never actually physical in nature.

    YOS
    Not too bad from an Aristotelian point of view. All universals are abstracted from sense experience. That doesn’t make them physical but it does make them real. That is, there is no such physical substance as “dog.” The only physical substances are Fido, Rover, Spot, etc.; but that does not mean that “dog” is not real. If there were not really any species, how could there be an “origin of species”? Conceptualism is subversive of the scientific program.
    + + +

    djindra
    Every example I’ve seen (rock shatters window, stick pushes stone, etc.) happens in reality as a temporal sequence. “Concurrent” (or “per se”) looks so only because we humans cannot process the sequence fast enough, so it merely appears to us as a single event. Nobody at Feser’s blog was able to demonstrate otherwise. The only thing that I know of which may act concurrently or simultaneously is gravity. And that appears to be bodies acting on each other *always,* at any distance, not one acting on another as a discreet event.

    “Thus the music we hear is caused by compression waves in the ear moving our eardrums (etc.). But the air would not wave in that manner if the clarinet were not playing.”

    Once the clarinet stops the waves continue traveling at the speed of sound. It appears to me to be no different than one billiard ball striking another then another …

    YOS
    You would think that Aristotle never saw a stone continue to roll after being pushed or that the waves in a pond continue to ripple after the stone splashes in them. How much more brilliant you are to see this!

    The fact that an induced motion does not cease instantaneously is not an objection to the dependency of instrumental causes, since “instantaneous” is a figment, a limit state of real things rather than a real state itself. There is always duration. It remains true that the clarinet has no power to make music unless a primary mover is playing upon it. And those sound waves do come to an end once the playing stops, even if it takes a moment. No one claims that a sequence ordered per se cannot trigger a subsequent sequence ordered per accidens. Imagine the sound waves produced by the clarinet cause the first domino to topple in a chain of dominoes. The domino chain is ordered per accidens, but this does not mean that the musical instrument can spontaneously produce music without a player. That per se sequences are typically concurrent is not the main thing; it’s that the intermediate elements in the sequence are instrumental, lacking the power to move unless concurrently being acted upon. You really must learn to appreciate the present progressive tense.
    + + +

    JH
    I don’t see how the existence or establishment or proof of the Poincaré conjecture is independent of mathematicians.

    YOS
    The proof, surely; but the conjecture is either true or false in itself, regardless whether the path through the wilderness has been hacked or not. Otherwise, two mathematicians could reach different conclusions and not different chains of reasoning. Mathworld is full of folks who have independently proven the same theorem. It is not so full of people who have independently proven the theorem true while another has proven it false. (Errors in reasoning do not count. “Proven” ≠ “Thought I had proven”)
    + + +

    rembie
    It seems reasonable to assume some mathematics is discovered, because it is demonstrably inherent in natural phenomena and some is made up

    YOS
    It is no more required of mathematics that it be applied to material natures than it is required of the physics of boiling water that it be applied to the making of tea.
    + + +

    Sander
    So tnere is no need to disprove the Unmoving Mover theory, the only thing needed is a competing theory that is as good as the Unmoving Mover theory in explaining the world.

    YOS
    But it is not a hypothesis put forward to “explain” the World. It is a deduction from empirical properties of the World. In that, a metaphysical determination is much more like a mathematical demonstration than either one is like a physical theory. The Physics abstracts from concrete particulars by induction toward a hypothesis. Metaphysics – at least the Aristotelian family – deduces from concrete particulars toward a conclusion. (And Mathematics deduces from ideal bodies toward conclusions in mathematics which may or may not also have something to say about physical bodies.) The Argument from Motion is an argument from motion; it is not an attempt to “explain” motion by proposing a hypothesis. Neither “motion” nor “cause” have the same meaning as in physics.
    + + +

    djindra
    I’m simply arguing change is a permanent property of anything that exists.

    YOS
    Excellent. Except that you must add “…anything that exists physically” You are on track with Aristotle and Aquinas! It’s hard to justify your statement other than as a Bold Assertion unless you also buy into Potency and Act, hence Matter and Form. Matter is the principle of potency and hence the proper object of change [= motion]. This is the starting point of the First Way! “We observe that in the world there are things changing.” Now you need to follow the consequences all the way. Although you won’t.

    “Change” is not actually a “property,” but we’ll give you a pass as speaking loosely and colloquially.

  81. @DAV:

    “You were sniping — a sign of intellectual bankruptcy. By all means: run away.”

    1. If you are asking for evidence for mathematical realism, I never said I did not have to supply it, what I said was I did not want to supply it, explained why and urged you to go read a book. Read it as “let us agree to disagree”. Or as “weasel away”, “sniping”, “intellectual bankruptcy” or “run[ing] away”, I really couldn’t care less. Want book references?

    2. About the different question you posed, “Can you show me an example of mathematics existing anywhere outside of world model analogies?”, I said “And then again, vast portions of mathematics have absolutely nothing to do with “reality” (one of those words that seem to need to be guarded by quotes wherever it is used) or any scientific theory about reality.” This is an easier one, do you want examples?

  82. “If you are asking for evidence for mathematical realism, I never said I did not have to supply it, what I said was I did not want to supply it,”

    See? Just the thing I was talking about! Toodle-oo.

  83. YOS,

    Excellent. This was part of Dr. Feser’s discussion in the book being discussed!

    Huh! Never read the book. Fancy that.
    When do I get my gold star?

    Re Gödel:On the landscape whose points consist of true statements and whose roads are mathematico-logical proofs, there are places where the roads don’t go. That is, there are true statements that are not provable. That’s not the same thing as “no certainty,”

    Can I claim poetic license? As in proof equating to certainty and lack of proof with uncertainty?

  84. @YOS I agree with your comment, but what does it have to do with mine?

    A triangle is a universal, but a set might be any collection of unrelated things. a set can coincide with a universal (as is the case with dogs), but not necessarily so.

    Is it not true that there is a big difference between Cantor and Pythagoras, yet they are both mathematicians and have contributed to mathematics? Where is the universal in “mathematics”?

  85. You’re going to have to explain that because it appears to be totally unrelated to what I’ve been arguing — unless you happen to think science is non-empirical.

    Our conceptions and perceptions of the natural world are the basis of science. You say that these things are wrong. Therefore, science is wrong. Have fun hanging out with Hume over there.

    That makes no sense. Why is “thereness” dependent on changelessness?

    Are you seriously not getting this? If change was the only thing, then there would be no atoms. Atoms would changes into Taom, Mato, Omat and so on, infinitely, without our even being able to perceive it. There would be no atoms to study–no concrete things at all–if atoms themselves were subject to the Heraclitean flux. Of course, since it’s obvious that atoms exist, it can’t be the case that only change exists. Even if an atom is in constant motion, it isn’t undergoing constant, universal change: otherwise, there would be no atom in the first place.

    This fits with the logical idea that change presupposes that which is changing–that is, it presupposes something concrete. It’s also perfectly consistent with act/potency.

    You seem to be identifying change with existence. I’m not doing that. I’m simply arguing change is a permanent property of anything that exists.

    If something exists, then it’s actual. It has the potential to move around, and it actualizes this potential all the time. Even if it’s a permanent property, the “thing that exists” is still already actual, and it’s still actualizing its potentials to move in certain ways. Sorry.

    I’ve been arguing the exact opposite which should have been clear. Everything is changing and always has been changing. Nothing stays the same. I asked originally, show me any point in the universe that is *not* changing. Until you do that you have no evidence of a “state” of non-change.

    A single atom, even while moving, is not changing its nature as an atom. If it was changing its nature, then it wouldn’t be an atom. Again, change changes something–something concrete that remains the same.

  86. YOS

    “How much more brilliant you are to see this!”

    Aristotle didn’t have the benefit of modern technology. High school kids know things he couldn’t have. We can’t ignore modern physics simply because Aristotle didn’t have our advantages.

    “The fact that an induced motion does not cease instantaneously is not an objection “

    If it doesn’t happen instantaneously then the *only* difference between “per se” and “per accidens” is human perspective.

    “It remains true that the clarinet has no power to make music unless a primary mover is playing upon it. And those sound waves do come to an end once the playing stops, even if it takes a moment.”

    It remains true that when a cue stick hits a cue ball the ball continues in motion even without constant contact with the stick. There is no logical difference between the two examples. We just replace cue stick with violin string and billiard balls with air molecules. Yet you claim one is “per se” while the other is obviously not.

    “Imagine the sound waves produced by the clarinet cause the first domino to topple in a chain of dominoes. The domino chain is ordered per accidens, but this does not mean that the musical instrument can spontaneously produce music without a player.”

    That complication just adds together “per accidens” events.

    “this does not mean that the musical instrument can spontaneously produce music without a player.”

    This would be relevant if either of us believed a “per accidens” event spontaneously happens. I sure don’t.

    “That per se sequences are typically concurrent is not the main thing; it’s that the intermediate elements in the sequence are instrumental, lacking the power to move unless concurrently being acted upon.”

    I know and that’s why your wave examples fail. Once the violin string sets a compression wave in motion the string can stop yet the compression wave continues at the speed of sound. Until you show an example of a causal chain happening in the present progressive tense I’ll assume language convention has a different scope than basic physics.

  87. YOS

    “You are on track with Aristotle and Aquinas!”

    Not quite. They both thought matter had to be put into motion in the first place. I doubt that. Matter is always in motion and always has been. So there’s no reason for the Prime Mover or the Act/Potency thing (which I see as a different issue).

    Yes, I believe “change” is probably an actual, inherent property of matter.

  88. rank sophist

    “Even if an atom is in constant motion, it isn’t undergoing constant, universal change: otherwise, there would be no atom in the first place.”

    Okay, I think I finally get what you’re talking about. But you’re locked into a certain perspective. Atoms are continuously changing. Electrons are in constant motion around the nucleus, etc…

    “A single atom, even while moving, is not changing its nature as an atom. If it was changing its nature, then it wouldn’t be an atom”

    It doesn’t need to change its nature to be in a constant “state” of motion. Motion is change. As I understand Aristotle he was not locked into a notion of change strictly as change in a thing’s nature. Billiard balls knocking into each other don’t change their nature.

  89. It doesn’t need to change its nature to be in a constant “state” of motion. Motion is change. As I understand Aristotle he was not locked into a notion of change strictly as change in a thing’s nature. Billiard balls knocking into each other don’t change their nature.

    This is true. However, because we agree that there are such things as unchanging natures, it follows that certain things are actual while others are only potential. For instance, the atoms inside a billiard ball are constantly moving, but the billiard ball itself remains a billiard ball. A billiard ball can potentially be crushed into powder, or it can potentially be thrown across a room. These actualize potentials that are different from its constant motion, even though its constant motion is also a kind of actualization. (For instance, everything is constantly being pulled by imperceptible levels of gravity, but this remains the actualization of a potential.)

  90. Don,

    Do you know what ontological dependence is? The stuff per se chains exhibit that per accidens don’t? It’s very clearly and obviously basis for a logical and real distinction.

  91. @DAV:

    “See? Just the thing I was talking about! Toodle-oo.”

    I take this to mean that you were never interested in learning if there is and what is the evidence for mathematical realism, but rather in establishing that I personally do not have such evidence. A refrain like “I have no evidence in mathematical non-realism, but neither do you for mathematical realism, toodle-oo” seems to be played by you over and over again. If I had known that you would be so contented with such cheap and mean rhetorical victories I would have obliged sooner: I have no evidence for mathematical realism. There you go. Now that we have left this childish foolishness behind, if you actually want to learn something instead of weaseling your way out by claiming poetic license, just holler for the book references.

  92. Josh,

    “Do you know what ontological dependence is? The stuff per se chains exhibit that per accidens don’t? It’s very clearly and obviously basis for a logical and real distinction.”

    Of course. But creating a category is one thing. Proving it exists is another. I can create a category called green unicorns. They’re logically different than white ones.

  93. rank sophist,

    “because we agree that there are such things as unchanging natures, it follows that certain things are actual while others are only potential.”

    To me this is a separate issue. In a sense it’s true but it’s not the whole story. We know from Einstein that a billiard ball is potential energy. And that energy is potential mass. We can theoretically take that billiard ball and change it into anything. So it’s potential is theoretically infinite.

  94. To me this is a separate issue. In a sense it’s true but it’s not the whole story.

    It isn’t a separate issue. It’s proof of act/potency. Now, if you’ll excuse me, I’ll take my leave of this combox.

  95. Sander van der Wal

    20 August 2012 at 4:31 am

    Now for an example of a system that has a bottom level in the sense that its next state is completely determined by its previous state: Conway’s Game of Life. A cell has two colors, black and white. A cel has nine neighbours. The next color of a square is determined by the number of black squares around it.

    This system doesn’t have an Unmoving Mover. It has a kind of execution engine, but that engine doesn’t determine the next color based on its own internal state, the next color is determined by the state of the system. And it is possible to run the system on different kinds of execution engines. For example, the system can be run on a digital computer, but also by a human with a pencil, lots of paper and even more patience.

    That is two of the assumptions behind the Unmoving Mover theory being shown to be unneccesary.

  96. Sander van der Wal,

    But couldn’t it be argued that the Unmoving Mover in Conway’s Life is the entire system? IOW: the Unmoving Mover is the Universe itself? Not that I am arguing it. Just pointing out the Unmoving Mover concept can be applied to Conway’s Life.

  97. rank sophist,

    “It isn’t a separate issue. It’s proof of act/potency.”

    Not hardly.

    “Now, if you’ll excuse me, I’ll take my leave of this combox.”

    Good choice.

  98. A lot of words there…and the usual fatal flaw is incorporated, not addressed:

    The “first mover” in the example is attributed to being a diety (“And that being is, as Aquinas said, what we call God. Now I know that this example is too telegraphic to be convincing, or lastingly convincing”).

    That conclusion was based on a series of volitional actions, the first of which (the impetus of the subsequent actions) is attributed to a diety.

    And the rationale for that is unstated explicitly, but, clearly derived from the “we don’t know what THAT is … therefore… it MUST be God.”

    That’s the fatal flaw, analysis by anology and where ignorance rears its head & becomes apparent “God” is inserted as the placeholder.

    Thing is, for the example presented numerous cases of head injury, stroke, etc. are shown to disrupt the process from its outset. That indicates a biological/physical initiate…not diety…unless…one believes the biological organ, the brain, is somehow a sort of “radio receiver” to God (and all that implies).

    This doesn’t indicate the conclusion is wrong, but the rationale & model used for reaching conclusion is fatally flawed as it presumes, then assumes as fact–it postulates as fact–facts not in evidence to compensate for areas of ignorance.

    God/gods throughout history have been postulated to account for all manner of not-understood phenomena (Thor’s hammer for lightning, etc.). Concocting some seemingly complex logical model to reach a conclusion for a diety, such as this blog essay’s, can be neatly rejected when recognized as being just another example of “I/we don’t know & cannot explain, today, how this phenomena occurred therefor it just must be God’s doing….therefore God exists.”

    It doesn’t take much effort to spot the other fallicy in the arguement presented–the one that presumes the conclusion at the outset and then conspiciously works to find the answer desired.

  99. Ye Olde Statistician

    20 August 2012 at 11:43 am

    dj
    Aristotle didn’t have the benefit of modern technology.

    YOS
    So what? The argument is not based on our ability to make nerve gas or nuclear bombs. It’s a metaphysical argument: a series of deductions from empirical experience based on the preconditions for physics.
    + + +

    dj
    If it doesn’t happen instantaneously then the *only* difference between “per se” and “per accidens” is human perspective.

    YOS
    No. Bruce has the power to father Charlie even if his own father Adam has disappeared from the universe. Domino #2 can topple Domino#3 even if Domino #1 has disappeared from the universe after tipping it. But the clarinet will cease playing Mozart’s Clarinet Concerto in A if Sharon Kam is removed from the universe after she has started. You seem to think it highly significant that the tone may waver in the air for an instant. It isn’t. You come across like the creationist who thinks he has refuted Darwinian evolution because dogs don’t turn into cats.
    + + +

    dj
    Once the violin string sets a compression wave in motion the string can stop yet the compression wave continues at the speed of sound.

    YOS
    And there are also echoes and the like. But they do stop.
    + + +

    dj
    Until you show an example of a causal chain happening in the present progressive tense

    YOS
    Present simple: “The sun shines.”
    Present progressive: “The sun is shining.”

    dj
    I’ll assume language convention has a different scope than basic physics.

    YOS
    Ganz natürlich. But you can’t expect physics to cover everything. In particular, you can’t use the physics to demonstrate a proposition in mathematics or in metaphysics.
    + + +

    dj
    They both thought matter had to be put into motion in the first place. I doubt that. Matter is always in motion and always has been.

    YOS
    Here I thought that a change in motion requires an outside force. Who knew. Why just the other day I saw a bunch of “atoms” happen to stick together to form a big blue bouncy ball, just from their motion.

    But how can something be in motion – even trivial local motion – if it is not “in the process of” moving from this location to that location; i.e., to be first potentially at that location, then to be actually at that location? IOW, that Aristotle and Aquinas (and ibn Sinna and Maimonides and…) defined matter as the principle of change/motion only means that prime matter is pure potency. To be actually something requires that matter take on some form. Form is the principle of act. So if everything sensible is some form of matter, and form and matter are Act and Potency on what basis do you deny that there are such things; and given that you do deny, how do you account for motion other than with a kerygma of faith that matter has “always” been in motion.

    Aristotle: Why do you keep your hammer in the freezer?
    djindra: We have always kept our hammer in the freezer!

    Parmenides: the paradoxes imply that motion/change is an illusion. Explain how there can be real change in the world.
    Aristotle: there is a real state called potency, which can be acted upon by an outside force that reduced the potential to actuality.
    djindra et al.: There is no such thing as potency/actuality.
    rank sophist and others: Then you claim there is no accounting for motion.
    djindra et al.: IT JUST IS!!!
    + + +

    sander
    Conway’s Game of Life… doesn’t have an Unmoving Mover.

    YOS
    So the app (rule set) which moves the squares from one color to another is itself in constant flux? Who knew.

  100. @Don

    Don:
    “There is no logical difference between the two examples.”

    Me:
    “[Ontological dependence is] very clearly and obviously basis for a logical and real distinction.”

    Don:
    “Of course. But creating a category is one thing. Proving it exists is another.”

    YOS:
    Owns Don with simple explanation showing that very thing; Don will subsequently pretend it’s anything but simple, and easily denied.

    Me:
    Not dumb enough to get roped into arguing with Don Jindra again. Wishes YOS best of luck.

  101. YOS,

    Yes, people can work independently and show the conjecture is true, possibly in different ways. How about the independence of the conjecture and mathematicians. How was the conjecture postulated to begin with? How could the conjecture be explained and proved to be true without mathematicians? Both are impossible without mathematicians. Anyway, I attended a lecture on the conjecture by Tao, I’d have to dedicate several years to study it understand the abstract proof! ^_^

    G. Rodrigues,

    Let me give another go: Lp space: http://en.wikipedia.org/wiki/Lp_space. I’ll be more specific. Next click on http://en.wikipedia.org/wiki/Riesz-Fischer_theorem and let’s look at the completeness of Lp. Keep in mind that differentiation and integration both involve limits at infinity.

    Another theorem that I have studied during this summer: The 0-connection is the Riemannian connection with respect to Fisher metric. Some of the necessary mathematical background can be found here: http://en.wikipedia.org/wiki/Information_geometry)

    Are you, a realist, saying that the definitions and proof of the above theorems can be somehow explained or realized in a physical way? I see them as constructed by human mind. So don’t hide behind those –isms under which there could be different versions, explain how the above can be viewed or explained by “realism.” I am open to any explanations and can be convinced otherwise.

    No, not driven by any philosophical commitments. I don’t subscribe to any specific of those –isms as if any one of them can definitely and completely explain what mathematics is. I agree with Tao based on what I do at work. I see what mathematics is through practicing.

    You seem to know about the philosophy of mathematics, how about assessing what philosophical commitment I might have made unknowingly? I did skim through the site http://en.wikipedia.org/wiki/Philosophy_of_mathematics. Loooooks like that I could be an embodied mind theorist! A wild guess since the descriptions of all the schools of thought are awfully brief.

  102. I just submitted a comment. Where did it go?

  103. This is a test. I submitted some comments that seem to have disappeared.

  104. I particularly like the following paragraph from here, which, I think, is what’s happening in Bayesian statistic. ^_^)

    When philosophy discovers something wrong with science, sometimes science has to be changed — Russell’s paradox comes to mind, as does Berkeley’s attack on the actual infinitesimal — but more often it is philosophy that has to be changed. I do not think that the difficulties that philosophy finds with classical mathematics today are genuine difficulties; and I think that the philosophical interpretations of mathematics that we are being offered on every hand are wrong, and that “philosophical interpretation” is just what mathematics doesn’t need. (Putnam, 169-170).

  105. Josh,

    You ignored the issue. That’s no answer.

  106. YOS,

    It’s a metaphysical argument: a series of deductions from empirical experience based on the preconditions for physics.

    I’m glad you threw in the empirical part. Would you agree Aristotle was at an extreme disadvantage in collecting empirical data? I think our technology would have helped him more than a little. And that makes all the difference. What appeared to him — because of that technological limitation — as per se was no such thing.

    The sun is not a per se chain, btw. And neither is a flashlight. Light continues to travel even after the source is extinguished. We collect light from stars that are no longer there.

  107. “You ignored the issue. That’s no answer.”

    Ah, vindication. Love it.

  108. YOS,

    “Here I thought that a change in motion requires an outside force.”

    Physicists keep finding smaller and smaller building blocks of matter. As I understand it, those building blocks are vibrating. If that’s true then they are in motion, possibly by themselves — that’s just their nature. Motion is change.

  109. YOS,

    I don’t deny a window has a potential to break, or that throwing a rock at it is not an act. I do deny act/potency has any explanatory power.

  110. @JH:

    “Let me give another go: Lp space: http://en.wikipedia.org/wiki/Lp_space. I’ll be more specific. Next click on http://en.wikipedia.org/wiki/Riesz-Fischer_theorem and let’s look at the completeness of Lp.”

    And?

    “Keep in mind that differentiation and integration both involve limits at infinity.”

    Thanks for the warning.

    note: no need to paste wikipedia links to L_p spaces as I am not ignorant of them. And why exactly L_p spaces and say, not some elementary arithmetic proof, like Euclid’s proof of the infinitude of the set of primes? If you wanted to parade your knowledge of functional analysis, linking say, to the Argyros-Haydon construction of a hereditarily indecomposable Banach space where every operator is the sum of a scalar and a compact would be much more effective.

    “Are you, a realist, saying that the definitions and proof of the above theorems can be somehow explained or realized in a physical way? I see them as constructed by human mind.”

    No. Methinks you severely misunderstand the nature of the problem so my suggestion is to do some actual reading.

    “So don’t hide behind those –isms under which there could be different versions, explain how the above can be viewed or explained by “realism.””

    This one is funny. Not only you misunderstand the problem, you charge me with “hiding” behind isms, in other words I am “hiding” behind… knowledge of what has been written about the problem. Which leads me to conclude that, by your own hiding criteria, you are hiding behind your ignorance.

    “I see what mathematics is through practicing.”

    So you know that mathematics is created as opposed to discovered based on the subjective impressions borne by your own specific mathematical work? Is this what you call an argument? Why should I value your subjective impressions, rather than those of say, Erdős or Gödel, just to give two examples of mathematical realists (alas, of a Platonist persuasion)?

    This is going nowhere, so unless you have something of actual substance to add, I suggest we just put it to rest.

  111. G. Rodrigues,

    You don’t have to value my subjective experience. The completeness of Lp is nothing worth parading. I was hoping you would use it to explain to me how or why a realist sees it as discovered. (I have explained to you what “discover” and “create” means to me.)

    When I say “keep in mind…” it’s reflective of me with an inclination of not thinking thoughtfully within a short period of time. That’s what I say a lot in my class. Perhaps, I shouldn’t use it anymore.

    I was not hiding my ignorance of the philosophy of mathematics, isn’t that obvious? I’ve made a fool of myself plenty of times at work. It’s no big deal, as a Chinese proverb says, “There is a Mount Everest between areas of study.” I already knew there is vast amount of literature out there to be read but the lazy me has other priories. To save me days of digging through literature, I thought I could get something out of you who seem to know about the philosophy of mathematics. Instead I get a series of unnecessary insults. I shall avoid talking to you from now on. Darn!

  112. I think it is cowardly not to finish the argument of the hand holding a stick moving a stone, so I will do it here…

    The stone is moved by the stick, which does not have any causative power, other than conveying the force exerted by the hand to the stone. The hand does not have any causative power were it not that the vital principle is acting on it, without it it would be dead and not able to cause anything. However the living hand would not be instrumental were it not sentient and able to feel. It needs to sense the stick in order to hold it. So we have moved up to the sentient principle that operates causative on the vital principle in the hand. Then we have to move up again since the movement of the hand is a willful one, it is intended by me to illustrate a point of view. So we have yet to move up from the sentient principle to that which brings about our recognition of self, which I will call the I in want of a better term. So the causative chain leads all the way up to the I and further, as we will see, for the human spirit is a first mover in his own right, yet surely not something that can support itself without the spiritual food coming from the Good, the True and the Beautiful, which ultimately can only come from God.

    I am sorry to cut it short here, but you see what I mean. Quit all the fuzzy talk of molecules and elementary particles since following that trail I feel I enter Tartarus.

  113. Sander van der Wal

    21 August 2012 at 12:52 pm

    @YOV

    “It is a deduction from empirical properties of the World.”

    Which makes it a theory (Popper). In particular, it theorizes there is an Unmoving Mover, the mechanism used to explain why the world is like it is.

    @DAV

    If the entiere system is the Unmoving Mover, then we have a problem. It is possible to create a computer in the Game of Life. Now, it would be possible to run an instance B of the Game of Life on the computer created in a different Game of Life, A. Hence, an Unmoving Mover running on top of a different Unmoving Mover.

    But in the top level B Game of Life you can run a new computer running Game of Life C. And so on.

    By definition a Game of Life and the execution engine is not an Unmoving Mover, as an Unmoving Mover must be unique.

  114. I can understand Dons disappointment with the level of causal reasoning with regard to physical matters in the examples above. It just seems so inadequate to identify the drop of domino A as the cause and the subsequent drop of domino B as the effect (a series par accidens). In physics we would just care less about this sequence of cause and effect, we would instead concentrate on the impulse that is transferred, we can even predict if a slightly larger domino will drop or not when it is placed in the row. The explanatory power of our concepts with regard to these things is so much better nowadays. However the argument does have validity, but only if you can construct an ontological hierarchy (like I tried to show above), not if you stay within the same plain.

    Imagine a pile of domino stones. I will now construct a series per se. I will assume that we can point to the elevated position of the top domino as the effect, the domino supporting it is causing it to stay there and is right underneath it. However, this domino in turn derives its causative power from the one beneath it as well, and so all the way down until God comes in. Now you would expect for the lower stones to be somewhat closer to God then the upper ones, but that does not seem intelligible does it? Furthermore: suppose your domino’s are made of marble. Next to the pile of domino’s you put a pillar of marble. Now look and try to construct a sequence of cause and effect per se. Now you can’t point to the individual stones, but perhaps you could try to locate the individual crystals? You see, modern physics abstracts from all that and talks of forces acting instead, that is already much better in a way. So, my idea is, reading most of the posts here and understanding some of them, that we must look up, not down, if we are looking for God. We have to climb the ontological ladder.

    But there is another problem which refers to the comments made by DAV. We are modern man and not easily convinced by reason alone. I admire the rigor of the reasoning and the dedication to thought we encounter by the scholastic thinkers. At the same time I realize that we are living in times that require more than an appeal to reason to find it’s way to God. Or find its way to a hold on reality even. It is just that DAV was pushing it by demanding for God to be detectable. God will not be detected like a particle by a Geiger counter. We must rely on a correct interpretation of the phenomena around us and accept that we will in all probability progress slowly. At some point in time we might experience our eyes being opened, when we have become worthy of the sight. That is truly my opinion.

  115. @JH:

    “Instead I get a series of unnecessary insults.”

    Although it seems you have missed the irony directed at myself in the note, it is still the case that the “parading” bit was unfair and unjustified. For that, my apologies.

    But a “series of insults”? Seriously?

    “I was hoping you would use it to explain to me how or why a realist sees it as discovered.”

    If you had payed attention to what I wrote, you would know the answer: he does not. More precisely, let us take the stock example of a syllogism:

    Socrates is human
    All humans are mortal
    Socrates is mortal

    By knowing what Socrates *is*, human, we have derived a piece of knowledge about him, that he is mortal. In other words, it is by virtue of knowing Socrates’ nature — his humanity — that we know that he is mortal. In the same way, it is by knowing what L_p is, that we know that L_p is complete, albeit by a more complicated argument than a mere syllogism, but an argument all the same. This is all independent of whether L_p has any an extra-mental reality or not. In other words, your question is just misguided and irrelevant.

    Now there is no doubt that there is something in reality, in the objective, extra-mental nature of things, that makes the proposition “Socrates is mortal” a true proposition (note: actually, some philosophers would doubt even this. I will take it as uncontroversial here). What exactly that is, is a bone of contention between realists and non-realists. This is the famous problem of universals of which the problem of mathematical realism vs. non-realism is a subspecies of. Returning to your example of L_p spaces, a naive Platonist would say that the L_p spaces are abstract particulars, real, extra-mental objects “living” in a Platonic third-realm, and it is in virtue of their nature that they are complete, the proof of their completeness being the mathematical analogue of the syllogism that lead us to the true proposition “Socrates is mortal”, and we no more create L_p spaces or Lebesgue’s dominated convergence theorem or Cauchy sequences or Banach spaces or the closed graph theorem than we create humanity or mortality, rather, we discover these things as objective, extra-mental features of reality (note: different realists would articulate this in different ways. I stick to naive Platonism because it is the easiest to explain). That it is precisely their objective, extra-mental reality that accounts for the truth of the proposition “The L_p spaces are complete” and that under non-realism, since L_p spaces are just an idea or thought in the human minds, and therefore of necessity private and particular to each mind, it is mysterious what accounts not only for the *objective*, *mind-independent* truth of the proposition “The L_p spaces are complete” but also of such modalities as necessarily true instead of contingently true, that mathematical truths seem to enjoy.

    This is just a sketch of one argument for realism; there are several other, and in my judgment powerful and compelling. Non-realists will respond to them in a number of ways; this over-extended and pedantically minute explanation is just to convey why your question is misguided. I thought I owed you this much after the unjustified “parading” dig.

  116. Sander van der Wal

    21 August 2012 at 5:21 pm

    The Game of Life can also be seen as consisting of a collection of cells with a binary state, a way of sensing the state of its immediate neighbours and a switch which toggles the state if a given number of neighbours are in a certain state. This means that you do not need a level below these things, the cells can do everything that is needed to run a Game of Life.

    The Unmoving Mover theory has no such mechanism, it states that at each and every level, there is always something missing. But there is no need for a theory to state there is always something missing at each and every level in reality. A theory can also state that at a certain level, the world is complete.

    In the Game of Life you can see that it is complete, all the actions that can happen, the state toggle of a cell, are completely determined by the state of the 8 (not 9, my counting mistake) neighbouring cells, and the single rule that says how many neighbours need to have a certain state.

    So, theories that competes with the Unmoving Mover theory are certainly possible. Such theories will postulate a bottom level at which enough things happen that all layers above them are working, which is exactly what the Unmoving Mover theory is doing too. They are scientific, because they are falsifiable.

  117. @G. Rodrigues

    I was writing clumsily earlier in an exchange with YOS, but what I meant to say is: how mathematics touches on reality cannot be answered generally, you need to consider the particular mathematics at hand. What do you think?

    Or, alternatively: some parts of mathematics might have more to do with realism than others. Id like to hear from an expert since I am not a mathematician.

    Now I do subscribe to the view that mathematics is objective. If we are both thinking of the theorem of Pythagoras, we both think the same thought. There is only one. Yet we receive the thought individually or subjectively.

    Yet something interesting happens when we think of a (for instance) right angled triangle. We definitely know what it means for a triangle to be a right angled triangle, yet we must fix our attention on a specific one in order to demonstrate its particularities. So in the way the triangle makes its appearance in our minds, its actual being seems only partly expressed.

    Now I understand a realist to say: may there be an infinite many instances of a right angled triangle, there is only one right angled triangle expressing itself in many forms. Yet a non realist might say: what a pedantry, these are just triangles that comply by the same set of rules. But then you might say: how then can you be certain that you will never find one that does not comply? Well, the non realist retorts, I will just avoid calling it a right angled triangle then.

    Is this a fair portrait of the situation?

  118. rembie said: So, my idea is, reading most of the posts here and understanding some of them, that we must look up, not down, if we are looking for God. We have to climb the ontological ladder.

    An interesting idea. Have you run with it? Or know anybody who has?

    Do you mean something that would be somewhat analogous to the concept of energy? Energy is quite abstract. We don’t ever detect energy, per se, it’s just that there is an invariant between different equations (e.g., kinetic, potential, etc.) about certain quantities we *can* measure. Yet, I believe in energy. Even though it has no pure form.

    Or does the idea require a paradigm shift? Like when we go from the kinetic theory of gases to the thermodynamics of gases. So the issue would become: Is there a high-level paradigm in which a theory of God demonstrably makes some general behaviors of the world more simply understandable? Occam’s Razor would then work for believing in God.

  119. It’s known that the Big Three dominated the foundations and philosophy of mathematics for much of the twentieth century: logicism, intuitionism, and formalism. They seem more agreeable to modern mathematicians. Realism is outdated.

    http://plato.stanford.edu/entries/philosophy-mathematics/#Int

    >>2.1 Logicism
    >>The logicist project consists in attempting to reduce mathematics to logic. Since logic is supposed to be neutral about matters ontological, this project seemed to harmonize with the anti-platonistic atmosphere of the time.

    >>2.2 Intuitionism
    >> According to intuitionism, mathematics is essentially an activity of construction. The natural numbers are mental constructions, the real numbers are mental constructions, proofs and theorems are mental constructions, mathematical meaning is a mental construction…

    >>2.3 Formalism

  120. rembie,

    “Imagine a pile of domino stones. I will now construct a series per se. I will assume that we can point to the elevated position of the top domino as the effect, the domino supporting it is causing it to stay there and is right underneath it. However, this domino in turn derives its causative power from the one beneath it as well, and so all the way down until God comes in.”

    There’s a problem with this chain. Gravity works both ways. Earth and domino attract each other and they do it whether they are touching or not. At the very minimum you’ll have to have a god at both ends.

  121. @Don

    There’s a problem with this chain

    Indeed. As you can see in my text I did not try to construct the argument from the position of physics other than mentioning the fact that forces would come in if we were to try it. It seems you are right though and God is actually acting on himself in keeping the domino in position.

    I would regard a causal reference to forces superior over a causal reference to the next object in line. I suppose you do too. Now you have to find a way to take the next step: what comes into view if we try to understand where (gravitational) forces derive their causative power from?

  122. @rembie:

    “how mathematics touches on reality cannot be answered generally, you need to consider the particular mathematics at hand. What do you think?”

    The answer depends on the particular brand of realism you espouse. If you are a Platonist, since mathematical objects are objective and extra-mental, they *are* reality. Other brands may carve out a particular subset of mathematics as instantiated in reality according to different criteria. What to make of what is left out of reality also depends on the particular brand of realism.

    “Now I do subscribe to the view that mathematics is objective. If we are both thinking of the theorem of Pythagoras, we both think the same thought. There is only one.”

    I agree with you. But if Pythagoras’ theorem is an objective truth, it is also a truth about specific objects, namely right-angled triangles. And if it is an objective, mind-independent truth, it is hard to fathom how right-angled triangles are not themselves objective, mind-independent realities. What this means exactly, depends once again on the specific brand of realism.

    “Yet something interesting happens when we think of a (for instance) right angled triangle. We definitely know what it means for a triangle to be a right angled triangle, yet we must fix our attention on a specific one in order to demonstrate its particularities.”

    Consider the following:

    1. Have you ever seen or done geometric proofs with compass, straightedge and a ruler, the way the ancient Greeks did? This is a proof by pictures, but its clear that the picture (of circles, triangles, etc.) *cannot* be identified with the concept of mathematical triangle, circle, etc. For one, because a circle drawn with a compass is not a perfect circle. Such drawn circles, triangles, etc. also have accidental attributes that derive from their material realization, e.g. they have color. And yet, these proofs are perfectly valid.

    2. Suppose you can do such type of proofs in your head, similarly to the way some chess players can play blindchess. You will recall to your imagination figures of circles, triangles, etc. But these figures, being recalled from memory and thus indirectly from sense data, also *cannot* be identified with the mathematical triangles, circles, etc. because for one, being recalled from memory, they cannot but have accidental attributes like color that mathematical triangles lack. But once again, this would also count as a perfectly valid proof.

    3. So what is going on here? Since I do not want to tackle the epistemological side, let me add a mathematical bit that may shed some light. Many mathematical theorems are of the form “all X are Y”. The proof starts by “Let x be an X”, so it seems that we are picking a *specific* particular exemplar x of X to prove a universally quantified statement about all X’s. Why does this work? Because in the course of the proof we do not use any specific features of x other than those dictated by the fact that x is an X. There is even a deductive rule that formalizes this type of reasoning — just consult a good book on logic.

    “But then you might say: how then can you be certain that you will never find one that does not comply? Well, the non realist retorts, I will just avoid calling it a right angled triangle then.”

    If I am reading you right, what I said above provides an answer, and one that is *independent* of whether you are a realist or not, but I quoted this last sentence to point out that the last move, and the very question prompting it, are based on misunderstandings. It is part and parcel of mathematical definitions, that when you define some object or class of objects, at the same time you supply (perhaps only implicitly) the identity conditions that allow us to identify when a given object is or is not an exemplar of the definition. In the case of right-angled triangles, the very definition stipulates the identity conditions for a triangle to qualify as right-angled. So asking how can one be certain that one will “find one that does not comply” is misguided. In other words, and taking Pythagoras theorem as an example, the fact that you are dealing with right-angled triangles is the *premise* of the theorem. So if by chance you come across a triangle that you do not know if it is right-angled or not, then you simply are not justified in applying Pythagoras’ theorem. Nothing mysterious here. Once again, this has nothing to do with realism vs. non realism divide.

    note: one must also be careful with “there is only one right angled triangle expressing itself in many forms”. There *are* many right-angled triangles, all abstract particulars but with different accidents such as orientation, or length of hypothenuse, etc. They all fall under the genus of right-angled triangles and *that* is indeed unique, that is, there is only one universal right-angled triangle of which there are many instantiations, *both* in the mathematical world (using this expression loosely and with no implied Platonistic connotations) and in the material world, albeit imperfectly instantiated as I said above.

  123. @George Crews

    I think you catch my drift, but I need a little more time to come up with an answer

    @G. Rodrigues

    Thanks for your comprehensive reply. I have to digest it. I was at the beach the other day and saw a jellyfish. It had a beautiful star drawn on its “back”. My son pointed it out to me. I was struck with amazement since it was so accurate and geometrically correct. I just felt that mathematics is at the hart of things, no doubt. The jellyfish can produce a star and I can construct one in my mind, we must have something in common. In comparison to this elementary geometry set-theory seemed such a bleak and abstract thing, which is what inspired my question. I also felt that my thought had not matured yet so I wasn’t arguing.

  124. dj
    Once the violin string sets a compression wave in motion the string can stop yet the compression wave continues at the speed of sound.

    YOS
    And there are also echoes and the like. But they do stop.

    Me
    Where does this leave the conservation of energy?

  125. I am quite surprised to find in this website the use of causality as an argument for God. When viewing any mechanical system, like firing a gun or following a Rube Goldberg contraption, it is often easy to identify a cause & effect relationship for each step in the series. Unfortunately nature is not a billiard ball system but is instead a simultaneous, spontaneous wonder. The formation of a cloud or a subsequent tornado are the ‘result’ of a complex system and the attempted search for causality generally requires the division by time of the natural system. Tracking the migration of individual raindrops might help with an understanding of the process but that narrow focus will inevitably obscure the events of a larger scope. Infinitely dividing any natural process will not necessarily result in the complete understanding of it. Chopping up an earthworm reveals all the internal organs but that exercise does not reveal how they interact when alive.

    Chopping up the universe by time does not actually change the universe from a simultaneous, spontaneous system to a narrowly restricted linear mechanical system (like a gun). That chopping is an exercise to help reach an understanding by identifying variables that might be more significant than others. This exercise does not mean the universe really operates that way. A mathematical model is just a model; it is not reality.

    The argument of first cause is really just an extension of a claim that every event must have had another earlier event before it. I see no problem with saying time passes in the universe but there is a logical leap (as it is based on the assumption everything works according to its process being split by time for analysis, and since it is based only on the reader’s religion also an unscientific leap) that says there must be something ‘else’ (and hence this ‘else’ must be supernatural) before the first moment in time. Science does not require there to be a first moment in time since time is simply a measure of the relationship between two events; either A happened before B or B before A or they happened at the same instant.

    This proof is not agreeable to my taste.

  126. The argument of first cause is really just an extension of a claim that every event must have had another earlier event before it.

    No, it is not. Read the article again:

    Both of these are examples of causal series per accidens, first one thing, then another, etc. The object to notice is that my great grandfather, after he had done the work which resulted in my grandfather, no longer had to be present when my grandfather helped produce my father, and so on. And my grandfather need not have been alive when my father made me, etc. And this is so for all series per accidens: whatever set the chain in motion need not be present for the continuance of the chain.

    This is not the only kind of causal series. There is another called per se, or essentially ordered causal series. This is the juicy kind, which when understood proves that God exists, and so forms Aquinas’s First Way.

    This proof is not agreeable to my taste.

    No wonder, since you used the wrong proof. To quote the internet: plz l2r, kthxbai.

  127. @Nate
    I am sorry to say this is in no way any kind of proof. To try to understand your view, I did a search for series per accidens and so I read this article on the web (which right or wrong I assume is probably representative) at cor ad cor loquitor: Whether existence at this moment is explained by an infinite series of per se causes? By Neil E. Bakker

    Everything about this approach is the billiard ball view of the world. The fundamental 4 four forces in nature in this perspective is strange, like billiard balls where the cue strikes one ball and then that ball in turn strikes one ball after another. Gravity is not like that. Gravity is a mutually arising force – as two particles of matter get closer the gravitational force between them increases. The same with electromagnetic forces, except that force can be attractive or repellent based on relative polarity. The universe is never a matter of one particle of matter being isolated and then some other billiard ball now subjects it to some unreciprocated force. The real world is spontaneous and simultaneous, and I see no relevance in reading an ancestral sequence.

    I am unimpressed and unconvinced by such descriptions of chains as some kind of proof. Time slicing is an analysis tool, not a proof.

    Everyone has their own perspective on religion and some require there to be the wizard behind the curtain keeping everything in order and sequence, to (impossibly) prevent the natural chaos.

  128. I just read Edwards on infinite causal series, to see if I am missing something about this argument about causes. An instrumental cause of course assumes there is something external pushing on something else. Any interpretations based on such an assumption for a system continuing forward in time will be based on something continue to push or the consequences of that first push. The principle cause is still based on some mechanical action, leading to even considering an infinite loop of a series of causes.

    Alan Watts in his book ‘The Book’ tells the simple story of someone who has never seen anything like a cat but happens to see one through a narrow slit in a fence. As the cat walks back and forth, the head is always seen before the tail. He never sees a deviation from the consistent sequence, no matter the speed or direction. Therefore he reaches the obvious conclusion that the event of this head is the cause of this tail. In reality one part of the cat does not cause the other part; they are both part of the same natural process. Cause and effect is only an attempt to divide nature by time. Pushing a stone with a stick is obviously an outside force on the rock but if that same scenario is the basis for subsequently watching nature what else is to be expected but to ‘see’ an outside force acting on everything?

    I hope my original post was not dismissive. It was meant to suggest consideration of an alternate view. The recent book by Jonathan Haidt The Righteous Mind points out there seem to be two distinct world views, and I suggest the same dichotomy seems to exist with religions where many need a god or gods working behind the scenes managing nature while many others can accept natural processes without an external guide.

    When observing people living in a city, one will see roads in a rectangular grid with traffic signals at perpendicular intersections to maintain order.

    When observing life in the wilderness, one will see annual and seasonal cycles, from bud-blossom-fruit-decay-dormant cycles in plants to migration patterns in animals. As observed long ago with the Law of the Minimum, the natural processes adapt to variations in temperature, moisture, soil content, and so on. Animals do not migrate on a specific day of each year; plants do not bud on a specific day of each year. These actions depend on the environmental conditions; they are part of the natural process, not an effect for a single cause.

    Radioactive decay is a random process and yet the rate is constant. This rate is based on the numbers and ratio of protons and neutrons in a nucleus. There is no identifiable cause for the instant of decay in one particular atom.

    Some will feel wonder at this spontaneous and simultaneous activity in nature while others feel there must be something external keeping it all in order. Feser’s book can never be successful convincing those who do not require an external force in nature that there is a god, just as a book by Harris or Dawkins can never be successful convincing those who require an external force in nature that there is not a god.

  129. @Dave:

    To try to understand your view, I did a search for series per accidens

    So epic fail, since my point (and the majority point with Briggs’ article) is not “series per accidens” but “series per se” which I highlighted in the previous reply. Again: LEARN TO READ.

    I am unimpressed and unconvinced by such descriptions of chains as some kind of proof. Time slicing is an analysis tool, not a proof.

    Of course you are unimpressed, no one here is using that proof. Not even the original post. Epic fail.

    Cause and effect is only an attempt to divide nature by time.

    The real world is spontaneous and simultaneous, and I see no relevance in reading an ancestral sequence.

    Yes, let us quote from the original blog post (and since you seem incapable of reading, i’ve highlighted all the incidents of “simultaneous” in order to help you catch up to where everyone started):

    The movements of the hammer and of your finger happen simultaneously. The pressure of your finger is in turn simultaneous with the nerve impulses sending the squeeze signal to your muscles. The contraction of the muscles is simultaneous with the individual molecules in the muscles changing from one state to another, which in turn in simultaneous with the changing of the atoms in the molecules, which in turn is simultaneous with the changing of the forces operating to change the various sub-atomic particles, which in turn in simultaneous with whatever it is that operates on those forces which cause the change, and so on. But not “and so on” forever. This simultaneous, here-and-now series must come to an end: it cannot extend infinitely, otherwise nothing would ever get moving.

    Again, stop assuming you know the point and actually read what the point is.

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