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.

Comments

Reasoning To Belief: Feser’s The Last Superstition: A Refutation of the New Atheism — Part IV — 129 Comments

  1. 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.

  2. 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).

  3. 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.

  4. 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.

  5. 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.

  6. @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.

  7. 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!

  8. 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.

  9. @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.

  10. 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.

  11. @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.

  12. 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.

  13. @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?

  14. 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.

  15. 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

  16. 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.

  17. @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?

  18. @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.

  19. @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.

  20. 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?

  21. 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.

  22. 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.

  23. @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.

  24. 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.

  25. @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.