If you haven’t yet been convinced of St Thomas’s argument for God’s existence, re-read all of the posts on Chapter 13, starting with this one. The terminology and concepts we have developed are absolutely necessary to know before continuing on. We have learned that the Unmoved Mover, the Unchanged Changer, must exist, or nothing else could move or change. But that’s all we learned. Today, we start with the consequences of this knowledge. But we’re not doing much in today’s lesson. Is everybody away on vacation?
Chapter 14: That in order to acquire knowledge of God it is necessary to proceed by the way of remotioni
1 ACCORDINGLY having proved that there is a first being which we call God, it behooves us to inquire into His nature.
2 Now in treating of the divine essence the principal method to be followed is that of remotion. For the divine essence by its immensity surpasses every form to which our intellect reaches; and thus we cannot apprehend it by knowing what it is.ii But we have some knowledge thereof by knowing what it is not: and we shall approach all the nearer to the knowledge thereof according as we shall be enabled to remove by our intellect a greater number of things therefrom.iii
For the more completely we see how a thing differs from others, the more perfectly we know it: since each thing has in itself its own being distinct from all other things. Wherefore when we know the definition of a thing, first we place it in a genus, whereby we know in general what it is, and afterwards we add differences, so as to mark its distinction from other things: and thus we arrive at the complete knowledge of a thing’s essence.
3 Since, however, we are unable in treating of the divine essence to take what as a genus, nor can we express its distinction from other things by affirmative differences, we must needs express it by negative differences. Now just as in affirmative differences one restricts another, and brings us the nearer to a complete description of the thing, according as it makes it to differ from more things, so one negative difference is restricted by another that marks a distinction from more things.
Thus, if we say that God is not an accidentiv, we thereby distinguish Him from all accidents; then if we add that He is not a body, we shall distinguish Him also from certain substances, and thus in gradation He will be differentiated by suchlike negations from all beside Himself: and then when He is known as distinct from all things, we shall arrive at a proper consideration of Him. It will not, however, be perfect, because we shall not know what He is in Himself.v
4 Wherefore in order to proceed about the knowledge of God by the way of remotion, let us take as principle that which is already made manifest by what we have said above,[1] namely that God is altogether unchangeable.vi This is also confirmed by the authority of Holy Writ. For it is said (Malach. iii. 6): I am God (Vulg., the Lord) and I change not; (James i. 17): With Whom there is no change; and (Num. xxiii. 19): God is not as a man…that He should be changed.vii
—————————————————————————————
iOED: “The method or process of examining the concept of God by removing everything which is known not to be God; (also) a thing known not to be included in a concept.”
iiThe analogy given earlier is that we can know, say, that infinite numbers exist, and even describe some of their characteristics, but we cannot know everything about the infinite; we certainly cannot experience it. For example, Don Knuth invented the following notation: 
Knuth, a computer scientist, invented the terminology because, as he says in his classic paper, “Finite numbers can be really enormous, and the known universe is very small. Therefore the distinction between finite and infinite is not as relevant as the distinction between realistic and unrealistic.” That’s true for mechanical computer operations, but if you rely, as some are tempted, on “really very big” to replace “infinite”, you’ll go astray. The two just aren’t the same. Even K is still infinitely far from infinity. It is a small number in that sense, but incomprehensibly large to us. But we are not God.
iiiIt’s too tempting not to quote Sherlock Holmes here, expressing a related sentiment: “How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?”
[1] Ch. xiii.
ivaccident: “In Aristotelian thought: a property or quality not essential to a substance or object; something that does not constitute an essential component, an attribute.” OED again!
vFinite minds cannot grasp the whole of the infinite. Most of us cannot even remember what we had for lunch two weeks ago Tuesday.
viThis was proved in Chapter 13. It’s the Unmoved Move, the Uncaused Cause, the Unchanging Changer. It followed from the premise that whatever is moved is moved by another. The Unmoved Mover is not moved by another, and is therefore unchanging. Now we called this necessary force, the Prime Mover, God, but that to modern ears sounded like a cheat. Why call what after all is a physical force “God”? Well, that’s what we’re about to find out. Not uncoincidentally, Ed Feser was talking about the First Cause argument the other day.
viiThere are any number of poor critiques of Biblical passages in which God is shown to have changed, because, for instance, He “changes his mind.” Atheists are awfully prone to read the Bible everywhere literally and, worse, are then satisfied that they have plumbed all possible depths.
Next week we learn God is eternal. Eternal? Change? What’s that? Stick around.
Ironically, yet another “fine” professor at U of Penn, Anthea Butler, [unequivocally] described what God was like in 2013 when she said God was a “…white racist god with a problem. More importantly, he is carrying a gun and stalking young black men.” (http://religiondispatches.org/the-zimmerman-acquittal-americas-racist-god/)
I am sad and embarrassed for the depths that my alma mater has sunk to. I am also never giving a penny more to Penn until (and if) things change. I would urge any other Penn Alums to do the same.
Regarding the atheist reading the Bible literally, all pieces that are supposedly ment to be read non-literally can be replaced by the literal meaning. When you can read the Bible literally, there would be no argument about what it ment.
We supposedly have talked about this, but I want to bring this up again: actual and potential. A being that is all actual and has no potential means like you are in Cleveland and everwhere else too.
A being can be in potential in Cleveland on January 2. 2015. But being in Cleveland on Jan 1 2015 BC.is impossible. Mainly beacuse Cleveland did not exist then. Being in Rome on 1 Jan 200 AD was possible, but is impossible now.
So, what does actual and potential really means?
Please clarify: How does ‘remotion’ differ from ‘elimination’ ?
Ad 1: It cannot be proven that God exists, because then it would not be called ‘faith’ anymore, but ‘science’.
QED
Hans, you’re in error. Not everything that can be proven belongs to the domain of “science”. I have said before, and repeat: science requires an experimental confirmation (or refutation) of predictions made by theory(ies) that can be embedded in or are an extension of the general theoretical framework of science. You don’t “prove” Newton’s Laws, since the confirmation of Newton’s Laws (and other scientific theories) is an inductive rather than a deductive process. Is this now clear?
As an example of a provable proposition that does not belong to science:
Major premise: all cows are purple
Minor premise: Elsie is a cow
Conclusion (proven): Elsie is purple.
and you can add all sorts of logic, math to this example, none of which would be science.
Bob, perhaps a better example would be:
Major premise: all bachelors are unmarried
Minor premise: I am a bachelor
Conclusion (proven): I am unmarried
As soon as the premises contain a posteriori knowledge, they want to be justified by observation, and are therefore falsifiable. We may say, “we’ve never seen a cow that isn’t purple, therefore we assume all cows are purple,” which is an induction based on empirical evidence.
Brandon, point taken. However, the syllogism is self-contained. The truth of the premises is outside the context of logic… That is to say, the truth of the premises is assumed in a syllogism. If you want to make use of syllogism then you do empirical testing…and of course you can easily prove that not all cows are purple.
Note also that in your example, bachelor also denotes a degree holder (who could be married and/or female), e.g.a bachelor of arts…and, finally, in zoology, a male animal or bird prevented from breeding by other males. I wonder if the academic and zoological definitions could be combined?
Thank you Bob, you have proven that God belongs to the realm of literature and has no interference with physical realities, for if He were, he would be experimentally provable,
You can’t have it both ways.
Math and logic are inductive processes, physics is a deductive process. How do you think Maxwell came to his equations?
Don’t be too sure. No text is self-explanatory. There is always con-text, or as statisticians are wont to say, “auxiliary data.” Even Constitutions need Supreme Courts. Augustine wrote an entire book showing the many different ways Genesis could be read literally.
So, you claim that a being of pure actuality must then necessarily be omnipresent. I think you’re on to something.
For one thing, it means that motion is possible.
An objection (adversus) is something set up to be disproven. The full text of what you apparently refer to is:
However, the original text reads “philosophical disciplines”:
But this leads to a response:
Hey Bob, I’m reading some Baltic history and your last name came up! Fascinating lineage you got there!
Guys, this “proof of God” thing is not working. It doesn’t matter whether God moves or changes. There is no God. You do not need God to prove anything about the universe. We don’t even know if a “prime mover” is necessary in the first place. This is all conjecture on conjecture on conjecture. Who knows how much you have to eliminate? How can you assume what you have left? What does it matter what the Bible says? Either you have faith it is the inspired or direct word of God, inerrant or whatever, or you don’t. Beyond the Bible, you have no argument at all.
JMJ
That circular reasoning. You are assuming the conclusion.
What universe?
And you don’t need Darwin to prove anything about auto repair. So what? Even the Bible says that God looked on all he had created and saw that it was good. At the very least, this has to mean that given a universe in the first place, that universe works.
Actually [pun intended] this is the one thing we do know. We don’t yet know that it is “God” in the traditional sense. Further theorems are coming.
That some things in the world are moving seems a fairly safe “conjecture.” So it the logical necessity that a thing cannot be in potency and in act with regard to the same motion at the same time. Which conjectures do you think are ill-founded?
This does not appear to make any sense.
In this regard: nothing. It has not been cited at all, except in the aside covered in this very post: viz., that God is unknowable as such.
I hate to point out the obvious, but Aristotle did not have a Bible.
@Hans
“Math and logic are inductive processes”
Can you please provide me with an inductive proof of the Brouwer fixpoint theorem? Thanks.
YOS,
“What universe?”
The one we’re in, you and I, together.
“Even the Bible says that God looked on all he had created and saw that it was good. At the very least, this has to mean that given a universe in the first place, that universe works.”
Works how?
“We don’t even know if a “prime mover†is necessary in the first place.
Actually [pun intended] this is the one thing we do know. We don’t yet know that it is “God†in the traditional sense. Further theorems are coming.”
My pun was intended too.
And no. You don’t know that. I don’t know that. We don’t know that.
“That some things in the world are moving seems a fairly safe “conjecture.†So it the logical necessity that a thing cannot be in potency and in act with regard to the same motion at the same time. Which conjectures do you think are ill-founded?”
That you even have to have a first mover, that there is a first anything, that you would need God to be a first mover, that you would need a God at all, and on and on and on.
“”Who knows how much you have to eliminate? How can you assume what you have left?
This does not appear to make any sense.”
From Briggs post: “It’s too tempting not to quote Sherlock Holmes here, expressing a related sentiment: “How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?—
“God is unknowable as such.”
OMG
“Beyond the Bible, you have no argument at all.
I hate to point out the obvious, but Aristotle did not have a Bible.”
Aristotle didn’t have a lot of things. I wonder what he’d think given what he’d have today.
JMJ
A bit of tongue-in-cheekery. You had said “You do not need God to prove anything about the universe.” Well, you don’t need Frank Whittle to prove anything about the workings of a jet engine, either. What you need Frank Whittle for is to understand why there is a jet engine in the first place. All methods of natural science presuppose the universe a priori and cannot therefore say anything about the universe as such.
Oh, you know: gravity, electromagnetism, strong force, all that kind of stuff.
Of course, we do. It was proven as a logical necessity, given that we can see potential being actualized. The proof was but recently concluded. But Late Moderns have grave difficulty distinguishing per se from per accidens or even understanding what motion is. Natural science is great for measuring motion or for studying how motion may change; but it must take motion as such as a given.
That there is a primary mover is a conclusion, not a conjecture. It is simply not possible for an instrument to act on its own. Period. Something has to use it. But you may still be stuck in a paradigm in which you read “first” as “first in time.” But a first mover is first in distinction to a secondary mover. (There is no “third” mover. “First” and “second” in movers are orders of logical priority; not sequences.)
That there is a “first anything” is neither a conjecture nor a conclusion. It has nothing to do with the proof.
That you need God to be a first mover has not yet been proven. Be patient, my friend. Besides, your objection is badly stated. It’s not that we are casting a part called First Mover and God is auditioning for it. We are exploring what the characteristics of First Mover are and will consider what they add up to.
Irrelevant. You claimed that the Argument from Motion has nothing to it beyond the Bible, and I simply reminded you that the argument comes originally from Aristotle, and he did not in any way reference or depend upon the Bible. Therefore, there must be something not only “beyond” the Bible but even “instead of” the Bible to the substance of the argument.
Bob,
No argument here; I absolutely agree.
One non-purple cow would be sufficient to falsify it. The observed phenomenon of other colors than purple is sufficient reason to ask whether green cows are possible: IOW, why is it that all cows MUST be purple?
It wouldn’t be a question we’d ask at all if there weren’t some experiential knowledge already baked into the premises of the syllogism. We (normally) take existence to be axiomatic, but that does not make it an a priori form of knowlege.
What I am saying is that empiricism is lurking in the givens.
Thank you for that bit of word play, it gave me a good chuckle.
Zoologists cannot agree on taxonomy to save their lives. I’m sure that if a married researcher observed a green cow the findings would be immediately dismissed as nonsense. After all, everyone knows all cows are purple; therefore either the color data are wrong, or it wasn’t really a cow. Not to mention that all married people are insane, by definition. QED. 🙂
YOS,
The parsimonious explanation is that Aristotle’s existence itself is the “instead of”.
“Thus, if we say that God is not an accident, we thereby distinguish Him from all accidents; then if we add that He is not a body, we shall distinguish Him also from certain substances, and thus in gradation He will be differentiated by suchlike negations from all beside Himself: and then when He is known as distinct from all things, we shall arrive at a proper consideration of Him. It will not, however, be perfect, because we shall not know what He is in Himself.”
I think this is how the IPCC deduced that CO2 is going to destroy the planet….
@YOS
“That circular reasoning. You are assuming the conclusion.”
Lol. This is Thomas in a nut shell.
@YOS
“”A being that is all actual and has no potential means like you are in Cleveland and everwhere else too.”
So, you claim that a being of pure actuality must then necessarily be omnipresent. I think you’re on to something.”
No, I am not claiming. I am asking what this means.
“”So, what does actual and potential really means?”
For one thing, it means that motion is possible.”
Ok, then. An object can be in many states, and it is always in one state. It can move from one state to another. It cannot be in more than one state, and it cannot be in no state at all.
In actual/potential parlance, the object is real because it cannot be in no state at all, it can move because there are other states than the one it is in, and the only way for it to be actual and have no potential is for the state space to have just 1 state.
I can see that it is possible to logically define a being as having no potentiality, but in state space terms that logical definition makes no sense, i.e it is not a description on how state spaces work, unless they are the most trivial ones.
@Sander van der Wal
“I can see that it is possible to logically define a being as having no potentiality, but in state space terms that logical definition makes no sense, i.e it is not a description on how state spaces work, unless they are the most trivial ones.”
Which only means that God is not to be described in “state space terms”. To borrow from Dr. Johnson: clear your mind of cant; you will never get anywhere by thinking in terms of state spaces.
“A being that is all actual and has no potential means like you are in Cleveland and everwhere else too.”
“So, what [do] actual and potential really [mean]?”
There is a dictum in quantum mechanics, (borrowed by Gell-Mann from the ants of ‘The Once and Future King’,) that ‘Everything not forbidden is compulsory’. Everything that can happen, does happen, all at once and in parallel. This is the Everett-Wheeler interpretation of quantum mechanics, recapitulated in the Feynman sum-over-histories picture, in which all possible histories consistent with the basic conservation laws (which themselves are no more than symmetries reflecting the fact that the rules are the same everywhere) happen in superposition, added together.
To take a specific example, a radioactive atom decaying does not happen at a random time in a random direction, it happens at all times and in all directions, simultaneously and in superposition. An observer of the atom is actually a superposition of observers (or rather, a superposition of the different possible states of a single observer), each seeing one possible outcome, summed. The symmetry is never broken, a choice of outcome is never made, and nothing actually changes. But each observer state only sees the decay occur at one specific time in one specific direction, and so thinks it has.
All the potentials are actually actual, but are on different branches that can’t sense or interact with one another. The emitted electron is in Cleveland and it is here too, both at the same time. That’s what it means for an electron to be a wavefunction. There can be no “why” to explain it being in one place and not the other, because it’s in both. There is no “why” to explain the change, because it doesn’t change, either. In the past it was a superposition of an undecayed atom and a spreading electron cloud. In the future it will (locally) be the same superposition of undecayed atom and spreading radiation. Just as a second before there were other versions of the observer that had already seen it decay earlier, so a second after there will still be versions of the observer that have not seen it happen yet.
And in ‘block time’, all history is laid out, and exists all at once. ‘Now’ is not a well-defined concept: the plane of ‘now’ tilts and moves as you do. Walk one way across the room and it is currently Tuesday in the Andromeda galaxy, turn around and walk back, and it is Monday there again. (Do all the things that happened there unhappen?) So again there is no actual change, just events strung out along a time line, and observers simultaneously at every point on the line each of them remembering a past and seeing a now, and assuming that they are singular and that what they see is all there is.
Combined with the sum-over-histories, we can add that not only is all history laid out and exists all at once, but every alternative history is so laid out also; every different possibility. Conversely, we can not that there being such things as ‘different times’ is just a special case of there being different histories. For if you shift the start of the universe forwards or backwards in time, and everything that comes after, those are *also* possible histories, and must therefore exist in superposition with the start time we see. So just as it is an illusion that the radioactive atom decays at a single specific point in time, so it is an illusion that the universe itself started at such a single point. In some possibilities, it started only a few minutes ago and the big bang is in progress. In others it started 10^100 years ago. (If it could happen at all, it could happen any time.) And both possibilities must exist together *now*, in superposition with our present time.
Thus the universe is eternal, unchanging, necessary, omnipotent. And we are a part of it. The reason we (considered as individual observer states) think it is finite, changing, contingent and limited is only because we cannot perceive the whole. We ourselves (considered as a superposition) see all our own alternatives and possibilities, everywhere in the universe that we could be (even Cleveland!), but no single part of ourselves sees it all at once. Potentiality is an illusion. Everything is actual.
Pantheism was where humanity started, long before the guy with the beard showed up. 🙂
@G. Rodrigues
The Thomists are the people claiming they have a logical proof. Therefore, the Thomists need to show where the state space model logically fails.
If I were a believer looking for proof your argument might help, but I’m not a believer, and your argument makes no sense.
@Nullius in Verba
The Everett-Wheeler interpretation is not the way I interpret QM.
Sander,
Your choice. But all that’s actually required is that you understand it. It illustrates one way to interpret what the terms ‘actual’ and potential’ could mean.
@Nullius in Verba
If I understand the Wheeler-Everett interpretation correctly, each possible state transition in a state space will create a real copy of the real universe. If you were throwing coins with two sides (states), each throw will result in twice as many universes, in one set you would have thrown head and in the other tails.
I would not consider this a correct interpretation of actual and potential. Nobody was saying that reality got twice as big each time a binary choice was made before Wheeler and Everett. Religions with a morality that could get you in Heaven or Hell would be completely pointless, for instance.
NV
All the potentials are actually actual,
No the wavefunction is a probability density, it is not a physical object.
So here we are again. Philosophers, in this case Christan, bring in the ironclad proof of God, in this case from 800 years ago. They use logic, negation, contradiction and most other handy arguments from their toolbox.
There is an astounding lack of any empirical data since the existence was proven.
But anyway, God is a given, he/she actually created the universe, proven centuries ago.
This fact, this piece of knowledge, which given its extaordinary fundemantel importance, has led to…….. crickets.
Sorry for spelling errors, at office.
Sorry for spelling errors, at office, must be quick.
Mario,
“No the wavefunction is a probability density, it is not a physical object.”
No, it *isn’t* a probability density. Even in those interpretations where a probabilistic collapse actually happens, its squared amplitude is a probability density, but it itself is not. And as I just explained, in Everett-Wheeler there is no collapse, with all possible outcomes realised, so nothing for it to be a probability of. And the wavefunction is a physical object.
“So here we are again. Philosophers, in this case Christan, bring in the ironclad proof of God, in this case from 800 years ago.”
Unfortunately, the arguments aren’t ironclad. For example, I showed a few episodes ago how Aquinas’s argument resulted in a Zeno-style paradox. But whatever…
@Sander van der Wal:
“Therefore, the Thomists need to show where the state space model logically fails.”
There is no such thing as “state space model logic”, that is just a silly invention of yours. In standard physics fare, “state space” is simply the geometric locus for the possible states of a given physical system: a symplectic manifold in classical physics (more generally, a Poisson manifold), the (projective space of) a complex Hilbert space in QM, etc. A state is then a point in this space, time evolution is a curve, etc. But all this has exactly zero metaphysical relevance for the issues in discussion. Or are you arguing that for each quantum system, there *really* is a complex Hilbert space out there?
Either way, it is a *logical consequence* of the arguments laid out before that pure act is not changeable being. So ẃhat you are saying boils down to the fact that you cannot imagine how unchangeable being (technical term of art) is not changeable or does not have potentialities — but the problem is yours, not Aquinas. Or at least you have not moved an inch towards showing such.
As far as you not being convinced? Shrug shoulders. We are discussing metaphysics and philosophy of nature, not rhetorics (to which Aristotle also contributed to as well as the latter tradition, from the Roman rhetoricians to the medievals).
Show us the circle.
@Nullius in Verba:
“It illustrates one way to interpret what the terms ‘actual’ and potential’ could mean.”
Who would’a thunk it that to understand Aristotle and Aquinas’ use of the terms “actual” and “potential” we had to consult an interpretation of QM? What could possibly go wrong with this move?
I was deceived by the lack of question marks.
No. Not sure ‘state’ language is appropriate.
That may be why the ‘state’ language doesn’t sit right. You don’t ‘define’ a being as having no potency; it just works out that way. And as it happens, a being of pure act (BPA) turns out to be immaterial, so physics-thinking does not apply. This dog may be one state, and that dog in another; but in what state is “dog,” per se?
“Who would’a thunk it…”
Oh, I’ve no doubt that Aristotle’s and Aquinas’s understandings of potentiality/actuality were radically different from QM’s. But a large part of the problem with this argument is that the terms Aquinas uses are unfamiliar to the modern reader, and the argument tangled and full of assertions claimed to be ‘obvious’, so it is very difficult to understand and check. A modern version of the same sort of distinction that resolves the issue a different way may be of use in figuring out what went wrong with A&A’s reasoning.
It’s not at all unreasonable that they should have failed to anticipate QM weirdness. I find it fascinating that nevertheless they did seem to manage to do so with at least some aspects of it. As did many other Greek philosophers, like Zeno and Parmenides, of course.
@Nullius in Verba:
“But a large part of the problem with this argument is that the terms Aquinas uses are unfamiliar to the modern reader”
Maybe you and I have different conceptions on what “problem” is, but quite obviously, this is not a “problem” with the argument, but with the modern reader.
“Maybe you and I have different conceptions on what “problem†is”
I was referring to the argument we’re having about what Aquinas meant and whether he was right, rather than the argument Aquinas offered. Apologies for the ambiguity.
NV
And the wavefunction is a physical object.
http://physics.stackexchange.com/questions/10068/on-the-nature-of-the-collapse-of-the-wave-function?rq=1
I think I understand what Wheeler is trying to construct but the only objectivity in a wave function is that it is an equation, there is no corresponding physical entity.
Mario,
There is another school of thought that rejects all claims to realism in QM. It’s often satirized as the “Shut up and calculate” school, as it treats QM as simply a recipe for making predictions, rather than an ontological statement of how the world actually is. The philosophical difficulties with wavefunction collapse are part of the reason they do so.
But under the Everett-Wheeler interpretation, which is what I was talking about, the wavefunction is real. The theory is realist, local, deterministic, unitary, and mechanistic. There is no ‘spooky’ action at a distance; the EPR-type observations are easily explainable with local interactions. And there are no discontinuous non-linear irreversible jumps, triggered by mysterious and unknown processed related to vitalist ideas like ‘consciousness’ or ‘awareness’. There is no distinction made between the ‘quantum’ and ‘classical’ realms. All it requires is that you take the rules of QM seriously and apply them to everything, without prejudging the issue.
The primary problem people perceive with it is that it implies there is a lot of the universe that we cannot observe. Whether that violates Ockham depends on whether you prefer to apply his razor to the laws of physics or the stuff the laws apply to.
The Everett-Wheeler interpretation is not the way I interpret QM.
Careful. You may have just demonstrated free will.
+ + +
Aquinas … tangled and full of assertions claimed to be ‘obvious’,
Aside from “some things in the world are changing” and “a thing cannot be in actuality and in potency to the same thing in the same way at the same time”, what else are these “claimed to be ‘obvious’ ” assertions?
+ + +
violates Ockham
Ockham’s formulation of the then long-known Principle of Parsimony is best translated into modern language as “Don’t have too many terms in your model, or you won’t be able to understand your own model.” It’s an epistemic principle, not an ontological one. Ockham went on to add that the physical world may be as complex as God desires, but our models have to be simple enough for our understanding. (Hence, later, perfectly elastic collisions, ideal gasses, frictionless planes, infinite atmospheres, and so on.)
@Nullius in Verba:
“And there are no discontinuous non-linear irreversible jumps, triggered by mysterious and unknown processed related to vitalist ideas like ‘consciousness’ or ‘awareness’. There is no distinction made between the ‘quantum’ and ‘classical’ realms. All it requires is that you take the rules of QM seriously and apply them to everything, without prejudging the issue.”
I have let your comments on the Everett-Wheeler go by; I will break my rule this one and say this much: this is more like the seedy advertisement of a used car salesman than a sober appraisal of the real status of Everett-Wheeler. Whether or not the projection postulate is necessary, the Born rule certainly is. The most formidable attack by Everettians (to alight on a catchy nick) to derive the Born rule is to date, by David Wallace, who avails himself to… wait for it… optimal betting strategies of rational agents as conceived in Decision theory, which, as David Albert pointed out, is just changing the subject.
NV
I suppose I would fall into the calculate bin, head first.
I understand that in EWI the wave function is physical and all the associated pros and cons of its reality including Ockhams test of this reality.
The philosophical difficulties with wavefunction collapse are part of the reason they do so.
I believe it was Heisenburg who for want of a better term coined the term wavefunction collapse. He put into words what happens when a probabilty
becomes a reality, a measurement. Now we and all before us interpret, sometime through a philosophical lens, what is going on. The hard truth , as even Mr. Briggs tried to explain in earleir posts is that probabilty does not cause anything, it is not a physical object. To say that a wave function is real like an EM wave is flawed at the start.
“I have let your comments on the Everett-Wheeler go by; I will break my rule this one and say this much: this is more like the seedy advertisement of a used car salesman than a sober appraisal of the real status of Everett-Wheeler.”
Tut! I could say as much for the arguments here in support of the Cosmological argument! 🙂 But I would hope we can manage to discuss matters without getting all personal and insulting…?
“Whether or not the projection postulate is necessary, the Born rule certainly is.”
Agreed. Everett derived the Born rule in his thesis (p71) by considering the state that resulted from a long sequence of successive measurements and showed the squared amplitude was the only measure that had the required additivity property for the combination of subsets of the state. There are arguments about whether this is really an independent derivation from first principles, or whether there is some circularity in it in that a measure was implicitly selected/assumed partly because it gave the observed result.
Whether or not he succeeded, he did at least see the need and make the attempt, as opposed to the standard approach that asserts it as an axiom without any attempt at justification. If you don’t like Everett because he doesn’t properly explain the mechanism behind the Born rule, then shouldn’t you reject Copenhagen even more resoundingly on the same grounds? 🙂
Mario,
“I suppose I would fall into the calculate bin, head first.”
🙂
“To say that a wave function is real like an EM wave is flawed at the start.”
That’s ironic, because according to the standard model, that’s exactly what the EM field is! The wave function has a complex phase factor which is unobservable – you can multiply the wavefunction by exp(iz) for any constant z and get exactly the same physics. If you turn this global symmetry into a local symmetry, by allowing the arbitrary phase shift to vary from point to point, and then adding in terms to cancel the effect on the physics of doing so, the extra terms describe the electromagnetic field (satisfy Maxwell’s equations, quantise charge, etc.).
Electromagnetism is the gauge field corresponding to the quantum wavefunction’s complex phase factor. Whether either of them is “real” is of course a much more difficult question, but I think one is as real as the other.
Hello anona,
Thank you for bringing up Luitzen Brouwer, indeed I shouldn’t have written induction, but construction.
Mathematics is constructive, physics is deductive.
Brouwer is also the founder of Intuitionistic logic which rejects proof by contradiction, and as such made way for Kurt Gödel.
Aquinas and Aristotle use a binary approach to logic, things are true or false, however, Gödel introduced the “unknown” to the binary spectrum.
Don’t make the mistake to fill the “unknown” gap with “God”.
NV
Electromagnetism is the gauge field corresponding to the quantum wavefunction’s complex phase factor. Whether either of them is “real†is of course a much more difficult question, but I think one is as real as the other.
Sigh,I suppose I will wait till someone invents a device which measures the wavefunction or images it or counts its frequency or perhaps , returning to the original article, What’s God like?, one day someone sees its image on a piece of toast.
Gödel introduced the “unknown†to the binary spectrum.
You are unfamiliar with Gödel’s ontological proof for God?
@G. Rodrigues
A state is a point in the state space, time evolution is a curve, and a being that is all actuality is a …
a being that is all actuality is a …
That’s what we hope to learn in subsequent theorems.
@Hans Erren:
“Mathematics is constructive, physics is deductive.
Brouwer is also the founder of Intuitionistic logic which rejects proof by contradiction, and as such made way for Kurt Gödel.
Aquinas and Aristotle use a binary approach to logic, things are true or false, however, Gödel introduced the “unknown†to the binary spectrum.
Don’t make the mistake to fill the “unknown†gap with “Godâ€.”
Oh brother…
Mathematics is a deductive science, physics is not, or not totally.
Brower “did not made way” for Kurt Gödel, and most surely, not because he rejected proofs by contradiction. And if by proof by contradiction you mean a proof that starts with “Suppose that…” and ends with “contradiction”, then no, Brower did not rejected proofs by contradiction. Gödel did not anywhere introduced “the “unknown†to the binary spectrum.” And what the heck this has to do with any alleged gap argument is anybody’s guess.
@YOS
What is it about actual versus potential that makes it possible to describe beings with lots of potential in a state space, and not beings that are all actual? Actual and potential is saying that a being can move, a state space is saying which moves a being can make. So a being can move if the list of possible moves is not empty, right?
a being can move if the list of possible moves is not empty, right?
A potency is always a potency toward something. This toward-ness is what is called natural teleology. An acorn is an oak tree in the sense that it is in motion toward that end. (Not all acorns succeed.) A pile of lumber has a potency toward a house or toward a gazebo or etc. But it does not have a potency toward an armadillo. These potencies do not actually exist, which is why nothing can “move” itself. Something that does not actually exist can’t do diddly-squat and requires something actual to move it.
The first actualization is, in a sense, the actualization of the potency as such: when construction begins on the house (in Aristotle’s example), the various potencies “collapse” onto the house potency. At this point we say the lumber is in kinesis or motion toward the house. The second actualization is when the house is completed. Notice that this is the act of the lumber, not the act of the house.
When we say that the puppy is growing or that the apple is ripening we mean that the puppy or apple is not merely “the complex of characteristics it possesses right now,” but also that “something-the-thing-is-not-yet already belongs to it as that toward which it is, right now, ordered.” To say that something is in motion [kinesis] is just to say that “it is both what it is already and something else that it isn’t yet.”
http://www.iep.utm.edu/aris-mot/#H4
I think there may be instructive parallels here with “state” talk, because, after all, modern science grew out of this potential-kinetic metaphysic, even when it was being denied. The idea of a potential function and of the attractor basin (as telos) seems much like a return to the Aristotelian metaphysic on the part of post-modern science. (Just as the vacuum energy has many of the properties of the Aristotelian aether.)
@Sander van der Wal:
“A state is a point in the state space, time evolution is a curve, and a being that is all actuality is a …”
I am sorry, but this is like asking roses are red, violets are blue and the Stone-Cech compactification of the natural numbers is…
“What is it about actual versus potential that makes it possible to describe beings with lots of potential in a state space, and not beings that are all actual?”
Nothing.
Look, physics deals with the metric, *quantifiable* properties of changeable being. That is it. It does not tell us what changeable being is or what a quantifiable property is — for that you need metaphysics and philosophy of nature. And once you have quantities (in a broad sense) that evolve through time (in a broad sense), the inner Geometer that lives inside every physicist will pop out and say “Hey, let us organize the aggregate of all possible values of all possible observable quantities into a space and view time evolution as a curve in this space. Pretty cool huh?”
Although the geometrization of physics took a long time to get off the ground, in large part because the mathematical tools were not available, it is now a pretty much settled fact. So much so, that in many contexts of mathematical physics, the boundaries have been pushed and some of the spaces used have no points, or have not enough of them, of if they have points, points are not what we usually take them to be but rather strange thingumajigs carrying fat internal groups of isometries, etc. and etc. There is nothing particularly mysterious here.
To repeat myself, physics is one thing, metaphysics (and philosophy of nature) is another, a more fundamental and general discipline, for which the categories of mathematicals, are inappropriate. *Because* it is also one of the tasks of metaphysics to clarify what a mathematical is, what is mathematical being. It certainly is not nothing, for there is nothing to be known about nothing, and we do know a lot about mathematics, so it must be something. And if it is something, it must exist in some sense. And if it has being in some sense or other, how is it, if indeed it is, different from the beings of our common experience like trees, dogs, planets, blog commentators, etc.?
If you persist on treating everything in the same uniform manner, all you will end up with is a confused and addled mind.
“To say that something is in motion [kinesis] is just to say that “it is both what it is already and something else that it isn’t yet.—
That’s easily translated into phase space talk. Phase space does not just contain points representing states, it contains trajectories representing the entire history of a system over time. In block time, a trajectory represents the idea of the entire history existing all at once. If the dynamics are deterministic, then there is one trajectory passing through each point, and for a system in the state represented by that point the trajectory represents its future and its past.
Where the dynamics are not deterministic, or the current state is uncertain, you instead get a bundle of trajectories, that spread out and scatter across the phase space. So for any given starting point (or patch of points) there is a range of potential futures.
So ‘potential’ apparently just means considering a state as not just a point but a point on a trajectory (or bundle of trajectories). The trajectory specifies what it is in potential towards. The future trajectory bundle of this ‘pile of lumber’ passes through that part of phase space labelled ‘a house’. The future trajectory bundle of this ‘acorn’ passes through the phase space labelled ‘oak’ as well as the phase space labelled ‘squirrel’s dinner’.
Hence, ‘collapsing potentiality into actuality’ means moving the point along the trajectory. What moves it? The dynamics; the rules. The tiny little arrows attached to each phase space point telling it where to go next. The tangent lines to the curves of the trajectories. The differential equation.
Or maybe it’s the passage of time. Or the change in perspective – looking at one part of the curve rather than another. Or maybe it’s the mechanism behind the differential equation; the Lagrangian clockwork of the universe. Or as you say, maybe it’s the attractors, or the limit cycles and recurring patterns – the grand tropes endlessly repeated in kaleidoscopic reflections in different contexts: the catastrophe singularities, swallowtails and butterflies, the universality of fractals and conics?
What do you think? Is that along the right lines, or did you mean something entirely different?
@Nullius in Verba:
“Phase space does not just contain points representing states, it contains trajectories representing the entire history of a system over time. In block time, a trajectory represents the idea of the entire history existing all at once.”
Phase space *just* is a space whose points are states. It “contains” trajectories only in the analogous, quite trivial, quite uninteresting sense that a space “contains” trajectories (*). Furthermore, a trajectory represents the entire history of the system whether one accepts four-dimensionalism or not; the issues are orthogonal.
(*) as a curiosity, there are spaces *without* isolated points and such that between any two different points there is *no* curve between them. Obviously, such spaces cannot be manifolds, which by definition are locally connected.
And a technical point: only in an attenuated sense, or in certain specific, limited scenarios, can one meaningfully talk of trajectories of the whole system (e.g. universe) in GR or QGR, or any proposal thereof. While field theories pose no problem, as field configurations are themselves points in a space (although the complications in the ensuing infinite-dimensional geometry are nightmarish), it does pose a problem for a theory like GR, and moreso for any would-be QGR.
“Where the dynamics are not deterministic, or the current state is uncertain, you instead get a bundle of trajectories, that spread out and scatter across the phase space. So for any given starting point (or patch of points) there is a range of potential futures.”
This is again a gross misunderstanding.
Neither in Statistical mechanics nor in QM… nah… too tired for this.
“So ‘potential’ apparently just means considering a state as not just a point but a point on a trajectory (or bundle of trajectories).”
No, potential does not mean anything like that. At all. I understand that you have this fetish with Science ™, but you are not going to advance one yota if you insist on translating everything to your private little crank language.
“What moves it? The dynamics; the rules. The tiny little arrows attached to each phase space point telling it where to go next. The tangent lines to the curves of the trajectories. The differential equation.”
Right. The tiny little arrows move the points in the phase space. The rules move things. Literally. And the phase space is out there as well, just like the North Pole, The Center of The Earth, Andromeda and Nirvana. And unbeknownst to us, “rules” really are like invisible genii living in an ethereal plane pushing things around this and that. Plato’s got nuthin’ on ya.
“When men choose not to believe in God, they do not thereafter believe in nothing, they then become capable of believing in anything.
― G.K. Chesterton”
“What do you think? Is that along the right lines, or did you mean something entirely different?”
I cannot, and will not, speak for YOS, but if instead of spilling of cybernetic ink on inconsequential drivel, people would just try to grasp the arguments on their *own terms*, maybe, just maybe, they would actually understand them — understand, not automatically agree with.
“Phase space *just* is a space whose points are states.”
It’s a set, and it “contains” all subsets.
“(*) as a curiosity, there are spaces *without* isolated points and such that between any two different points there is *no* curve between them.”
I suspect this is not relevant to physics or potential/actual, but I’m curious what you’re talking about or why you bring it up. These are used as phase spaces? Because it’s easy enough to construct sets without the topology needed for differential equations, but rather harder to apply them in physics. There are state transition diagrams used in discrete systems, Markov processes and so on, but they do in effect have curves between the points. You know of a case of a phase space with no points to represent states or curves to represent dynamics? That sounds quite interesting…
“Neither in Statistical mechanics nor in QM… nah… too tired for this.”
Yeah, right…
“No, potential does not mean anything like that. At all. I understand that you have this fetish with Science â„¢, but you are not going to advance one yota if you insist on translating everything to your private little crank language.”
So what *does* it mean, and what’s the difference?
And if there’s no translation between your crank language and my crank language – something I highly doubt – then can we agree that Aquinas and Aristotle cannot be demonstrably related to how the universe works? Which after all, is what scientific/mathematical language is for.
“if instead of spilling of cybernetic ink on inconsequential drivel, people would just try to grasp the arguments on their *own terms*, maybe, just maybe, they would actually understand them — understand, not automatically agree with.”
I’ve tried to grasp the arguments on their own terms and they do indeed sound a lot like “inconsequential drivel”. They sound like people chasing definitions and arguments in circles trying to prove a desperately desired conclusion, that doesn’t really follow from them, in the hopes of justifying entire lifetimes of intelligent men thrown away on following a literary delusion, instead of doing something *useful* like inventing farm machinery. Their ingenuity in doing so is amazing, but it doesn’t convince.
I’m *trying* to find something in them beyond that. In the process of chasing God, they were also putting down some interesting thoughts on physics and causality and so on, that might mean their lives weren’t a *complete* waste. And maybe what they were labeling ‘God’ corresponds to something interesting in the modern view, which it might be useful to think about. I do think it’s worth extracting that, and seeing if there are any valuable insights I’m not aware of. In this case, YOS’s explanation of potential/actual maps onto phase space talk quite neatly. Not perfectly, as you point out, but we can fill in the gaps easily enough. And if we can agree that, then we have a modern framework in which a modern can start to understand the rest of their argument, and see if it works. If we can give ideas like “put into motion” a geometrical interpretation in phase space, or similar physics language, we can figure out what it means and what it implies, and then – if required – we can step back and try to understand how Aquinas or Aristotle understood it.
I agree that agreement will not be automatic, even if I do manage to understand them. Maybe they were wrong. If so, it would be nice to know how and why, and it’s only right to make sure of it before saying so. But at the moment, every time anyone tries to draw any conclusion from what they apparently say, somebody like YOS or yourself pops up and tells them they’ve misunderstood; that the terms have changed their meaning in modern times and moderns are therefore mistaking the arguments. The original arguments in their original language are clearly not working, so if we’re going to make any progress we need a translation.
What moves it? The dynamics; the rules. The tiny little arrows attached to each phase space point telling it where to go next.
Really? There are tiny little arrows attached to mathematical abstractions that physically move matter? Who knew.
But at the moment, every time anyone tries to draw any conclusion from what they apparently say…
The problem seems to be trying to interpret a metaphysical argument about being not even into a physical theory about the causes of motion, but into a discussion over the mathematical model used to approximate the physical theory. Aquinas’ “first way”/Aristotle’s “argument from motion” is not an attempt to formulate a physics theory about how motion works. It is a deduction from not an induction to motion.
“Really? There are tiny little arrows attached to mathematical abstractions that physically move matter? Who knew.”
[Rolls eyes.] Anyone who’s ever seen one of those phase space diagrams with lots of little arrows drawn on them.
You know what I mean. What’s your point?
“The problem seems to be trying to interpret a metaphysical argument about being not even into a physical theory about the causes of motion, but into a discussion over the mathematical model used to approximate the physical theory.”
At the moment, we’re just trying to get a handle on what is meant by “motion”. (And ‘potential’/’actual’.) We’ll get to the “causes” once that’s been sorted out.
“Aquinas’ “first wayâ€/Aristotle’s “argument from motion†is not an attempt to formulate a physics theory about how motion works.”
I didn’t say it was. But we need to know what is meant by the word before we can understand the argument. We’ve discussed in the past the problem with saying “motion” to someone with a modern understanding of physics. Take for example Newton’s first law: “Further, no one could say why a thing once set in motion should stop anywhere; for why should it stop here rather than here? So that a thing will either be at rest or must be moved ad infinitum, unless something more powerful get in its way.” If something moves at constant speed through the void ad infinitum, what moves it? If you change your frame of reference to move with it, it is now stationary. What just happened to the cause? Motion (of at least some sorts) is therefore to some degree not a property of the world, but of the way we look at it. (Although not entirely, because if two things are in relative motion we can usually stop one or the other but not both.) If this sort of motion is included, then why does it need to have something else cause it? The whole point of the first law is that this is what happens in the absence of external causes. If this sort of motion is not included, then where does it say so? How are we supposed to know? And how on Earth are we supposed to judge the validity of an argument (or be convinced by it) when we don’t even know what the basic terms in it actually mean?
My default interpretation is that Aquinas had a faulty understanding of physics inherited from Aristotle, and that his argument is based on it, and fails when we use the modern notion of motion or change. The argument is invalid, as stated. But if you can identify what aspect of ‘motion’ is really being used here, there may be some subset of or alternate perspective on the modern understanding for which it is valid. What is that perspective?
Considering a system’s state as not just a point but as a representative of a trajectory in phase space is a way to associate that state with its eventual destination, or its potential destinations if there are many. Doing so shows that the particle moving in a straight line at constant speed isn’t a problem for the theory, because one can immediately see it can still have an ‘actual’ and a ‘potential’ in any frame of reference. It can also more clearly be generalized to ripening apples and acorns growing into oak trees. It ought to be helpful. If we can agree that this is what is meant, then we can maybe move on to what ’causes’ are and why things in motion need them.
Or if, as you seem to indicate, the argument has nothing to do with physical motion/change at all, then perhaps you could pick a different word for it, that expresses the idea more precisely, and reword the argument in terms of it? Because at the moment all we have is confusion and crossed purposes.
But we need to know what is meant by the word before we can understand the argument.
Sachs, Joe. “Aristotle: Motion and its Place in Nature” (Internet Encyclopedia of Philosophy)
http://www.iep.utm.edu/aris-mot/
++++
If something moves at constant speed through the void ad infinitum, what moves it?
The original source of its motion, or “impetus” (a/k/a “momentum”). As the Aristotelian natural philosopher Jean Buridan de Bethune put it:
In another sense, it may not be moving at all, since it is in an inertial frame, we can center the frame on the body itself; and if there is no “privileged place” or “absolute frame,” it can be considered as stationary. In fact, Aristotle considered bodies in regular, repetitive motions (like orbits) to be “at rest” in the sense he intended — entelechia. If you like, we could say “in equilibrium.” That is, it is not changing. Considered in this manner, Aristotle’s kinesis or change is a kind of acceleration, a change in motion; at which point, Aquinas’ dictum that “whatever is changing is being changed by another” becomes equivalent to Newton’s first law.
@Nullius in Verba:
“I suspect this is not relevant to physics or potential/actual, but I’m curious what you’re talking about or why you bring it up.”
The sentence you quoted started with “As a curiosity”, so that tells you the why. As for the what, well let’s just say, very roughly, that they make their appearance as classical “snapshots” of quantum systems.
“You know of a case of a phase space with no points to represent states or curves to represent dynamics? That sounds quite interesting…”
Are you asking if it is possible to do geometry without points and curves? (well not quite asking, but I cannot really interpret what the … is doing there). Yes, in different senses, ranging from the trivial and unintesting to the highly non-trivial and interesting. Are these relevant to physics? Yes.
“I’ve tried to grasp the arguments on their own terms and they do indeed sound a lot like “inconsequential drivelâ€. They sound like people chasing definitions and arguments in circles trying to prove a desperately desired conclusion, that doesn’t really follow from them, in the hopes of justifying entire lifetimes of intelligent men thrown away on following a literary delusion, instead of doing something *useful* like inventing farm machinery. Their ingenuity in doing so is amazing, but it doesn’t convince.”
(1) Twice the word “sound” is used; one in “sound a lot like” followed by “inconsequential drivel” (quotes in the original) and another in “sound like” followed by “people chasing definitions and arguments in circles”.
(2) The “arguments” are desperate attempts of “people” to justify desired conclusions.
(3) Conclusions that do not follow from the arguments.
(4) In advancing them, the real hope is to justify an entire life wantonly wasted “following a literary delusion”.
(5) And their guilt, or sense of guilt, is even grander because all that wasted time could have gone into doing “something *useful* like inventing farm machinery”.
(6) These “people” were “amazingly ingenious”.
(7) But not convincing.
For someone who demonstrably has no understanding of the arguments in question (just in a previous paragraph, you were asking what is the difference between actual and potential…) you surely have some strong opinions on them.
Classy, real classy.
YOS,
“Sachs, Joe. “Aristotle: Motion and its Place in Nature†(Internet Encyclopedia of Philosophy)”
Thanks. Interesting article.
“To say that something is in motion is just to say that it is both what it is already and something else that it isn’t yet. […] Motion is the mode in which the future belongs to the present, is the present absence of just those particular absent things which are about to be.”
So a trajectory is both what it is at the moment, and what it isn’t yet, but which it is about to be. That fits.
“By Thomas’ account, motion is not ultimate but is a consequence of the way in which present states of things are ordered toward other actualities which do not belong to them. One could build on such an account a physics of forces, that is, of those directed potentialities which cause a thing to move, to pass over from the actuality it possesses to another which it lacks but to which it is ordered. Motion will thus not have to be understood as the mysterious departure of things from rest, which alone can be described, but as the outcome of the action upon one another of divergent and conflicting innate tendencies of things. ”
“A physics of forces” describes the dynamics, that direct the point along the trajectory from the state it posesses to to another state which it currently lacks but which the dynamics is pushing it towards. That still fits. The last bit doesn’t, though. Rest only occurs as the result of the equilibrium between such forces? That’s often the case, but not always.
“The original source of its motion, or “impetus†(a/k/a “momentumâ€). […] In another sense, it may not be moving at all, since it is in an inertial frame, we can center the frame on the body itself; and if there is no “privileged place†or “absolute frame,†it can be considered as stationary.”
So how do we reconcile these? If the cause of the motion is a change in reference frame, is that the original source of the motion?
I was actually thinking of the case of an eternal universe and an eternal linear motion. There would, in that case, be no initial source. But that raises some other difficulties which would distract from the point.
“Considered in this manner, Aristotle’s kinesis or change is a kind of acceleration, a change in motion; at which point, Aquinas’ dictum that “whatever is changing is being changed by another†becomes equivalent to Newton’s first law.”
That’s good. That’s a considerable improvement.
But there’s still a problem. If we consider two bodies in orbit around one another, each is accelerated, and does indeed have to be accelerated by an object external to it. But each is accelerating the other, which Aquinas (citing Aristotle) elsewhere says is impossible.
G.
“The sentence you quoted started with “As a curiosityâ€, so that tells you the why.”
So basically irrelevant, yes?
“Are you asking if it is possible to do geometry without points and curves?”
I was really asking for more technical details, or a link, or even sufficient information to identify what you were talking about and perhaps find more information. Of course, what you provided doesn’t tell me anything.
“(1) Twice the word “sound†is used;”
You can count to two…?! Well done!
“For someone who demonstrably has no understanding of the arguments in question (just in a previous paragraph, you were asking what is the difference between actual and potential…) you surely have some strong opinions on them.”
I’m explaining how the existing presentation of the argument appears to a modern reader, and why it would be useful therefore to translate the argument into a form comprehensible to a modern physicist. Of course, if you don’t mind people thinking the argument is idiotic…
“Classy, real classy.”
You started it. On the whole, I generally prefer to keep the discussion friendly and civilised, but if somebody comes along who is incapable of that, I don’t mind playing along for a bit. 🙂
@Nullius in Verba:
“On the whole, I generally prefer to keep the discussion friendly and civilised, but if somebody comes along who is incapable of that, I don’t mind playing along for a bit.”
Well, here is something we can agree.