William M. Briggs

Statistician to the Stars!

Summary Against Modern Thought: God Is Unable To Make Square Circles

This may be proved in three ways. The first...

This may be proved in three ways. The first…

See the first post in this series for an explanation and guide of our tour of Summa Contra Gentiles. All posts are under the category SAMT.

Previous post.

This is long, but, oh my, is it worth it. I beg you will stick with it; just get over the first couple of paragraphs and you will be well rewarded. God can’t change the past, God can’t make square circles, God can’t make something simultaneously exist and not exist. Just look at all the things God can’t do!

Chapter 25 How the Almighty is said to be unable to do certain things (alternate translation)

[1] FROM the foregoing we may gather that though God is almighty, He is nevertheless said to be unable to do certain things.

[2] For it was shown above that in God there is active potentiality: while it had already been proved in the First Book that there is no passive potentiality in Him: whereas we are said to be able in respect of either potentiality. Wherefore God is unable to do those things the possibility of which belongs to passive potentiality. What suchlike things are must be the subject of our inquiry.

Notes Review, active potentiality vs. passive potentiality. Roughly, God can do something vs. nothing can be done to God. Recalling God is Being Itself, the distinction is amplified in the next arguments.

[3] In the first place, then, active potentiality is directed to action, while passive potentiality is directed to being. Consequently potentiality to being is in those things only which have matter subject to contrariety. Since therefore passive potentiality is not in God, He is unable as regards anything that appertains to His being. Therefore God cannot be a body, and so forth.

[4] Again. The act of this passive potentiality is movement. Wherefore God, to Whom passive potentiality is unbecoming, cannot be changed. It may be further concluded that He cannot be changed in respect of each kind of movement: for instance that He cannot be increased, nor diminished, nor altered, nor generated, nor corrupted…

[6] Further. Every failing is in respect of some privation. But the subject of privation is the potentiality of matter. Therefore He can nowise fail…

[10] Again. Since the object and effect of an active potentiality is something made, and since no potentiality is operative, if the ratio of object be lacking,–thus the sight sees not if the actually visible be lacking:–it follows that God is unable to do whatever is contrary to the ratio of being as being, or of made being as made. What these things are, we must inquire.

Notes Ratio of object and being? The alternate translation helps: “The object and effect of an active power is a being made, and no power is operative if the nature of its object is lacking; sight is inoperative in the absence of the actually visible [you can’t see in the dark]. It must therefore be said that God is unable to do whatever is contrary to the nature of being as being, or of made being as made.” Mentally swap nature for ratio to assist in reading.

[11] In the first place that which destroys the ratio of being is contrary to the ratio of being. Now the ratio of being is destroyed by the opposite of being: as the ratio of man is destroyed by the opposite of man or of his parts. Now the opposite of being is not-being. Consequently God is unable to do this, so as to make the one and same thing to be and not to be at the same time; which is for contradictories to be simultaneous.

Notes The principle of metaphysical non-contradiction, anybody?

[12] Again. Contradiction is included in contraries and privative opposites: for to be white and black is to be white and not white, and to be seeing and blind is to be seeing and not seeing. Hence it amounts to the same that God is unable to make opposites to be simultaneously in the same subject and in the same respect.

[13] Moreover. The removal of an essential principle of a thing implies the removal of the thing itself. If, then, God cannot make a thing at the same time to be and not to be, neither can He make a thing to lack any of its essential principles while the thing itself remains: for instance that a man have no soul.

Notes Soul? This.

[14] Further. Since the principles of certain sciences, for instance of logic, geometry, and arithmetic, are taken only from the formal principles of things, on which the essence of those things depends, it follows that God cannot make the contraries of these principles: for instance, that genus be not predicable of species, or that lines drawn from centre to circumference be not equal, or that the three angles of a rectilinear triangle be not equal to two right angles.

Notes Trumpet this to all who say theology isn’t concerned with math and science.

[15] Hence it is also evident that God cannot make the past not to have been. Because this also includes a contradiction, since it is equally necessary for a thing to be while it is, and to have been while it was.

[16] There are also some things which are incompatible with the ratio of thing made, as made. These also God cannot do, since whatever God makes, must be something made. Hence it is evident that God cannot make God. For it belongs to the ratio of thing made that its being depends on another cause. And this is contrary to the ratio of that which we call God, as is evident from the foregoing

Notes We long ago proved that nothing created God; God’s existence is necessary. Here’s what follows.

[17] For the same reason God cannot make a thing equal to Himself. Because a thing whose being depends not on another, is greater in being and other excellencies than that which depends on another, which belongs to the ratio of a thing made.

Notes Hence Satan is not God’s “opposite,” as some have it. God is not yin and yang.

[18] Likewise God cannot make a thing to be preserved in being without Himself. For the preservation of a thing in being depends on its cause. Wherefore if the cause be removed, the effect must needs be removed. Consequently, if there could be a thing that is not preserved in being by God, it would not be His effect.

Notes As the man said, God doesn’t have to do anything to keep the universe in existence; He must stop doing something for that to happen.

[19] Again. Since He is an agent by will, He cannot do those things which He cannot will. Now we may realize what He cannot will if we consider how it is possible for necessity to be in the divine will: since what is of necessity is impossible not to be, and what is impossible to be, necessarily is not.

[20] It is therefore evident that God cannot make Himself not to be, or not to be good or happy: because He necessarily wills Himself to be, and to be good and happy, as we proved in the First Book.

[21] Again, it was shown above that God cannot will anything evil. Therefore it is evident that God cannot sin.

[22] Likewise it was proved above that God’s will cannot be changeable: and consequently it cannot make that which is willed by Him, not to be fulfilled. It must however be observed that He is said to be unable to do this in a different sense from that in which He is said to be unable to do the things mentioned before. Because God is simply unable either to will or to make the foregoing.

Whereas God can do or will these, if we consider His power or will absolutely, but not if we presuppose Him to will the opposite: for the divine will, in respect of creatures, has no necessity, except on a supposition, as we proved in the First Book. Hence all these statements, God cannot do the contrary of what He has decreed to do, and any like sayings are to be understood in the composite sense: for thus they imply a supposition of the divine will with regard to the opposite. But if they be understood in the divided sense, they are false, because they refer to God’s power and will absolutely.

[23] And as God acts by will, so also does He act by intellect and knowledge, as we have proved. Hence He cannot do what He has foreseen that He will not do, or omit to do what He has foreseen that He will do, for the same reason that He cannot do what He wills not to do, or omit to do what He wills. Also, each assertion is conceded and denied in the same sense, namely that He be said to be unable to do these things, not indeed absolutely, but on a certain condition or supposition.

Notes This means the end will come someday. Get ready. And see Wednesday’s podcast.

33 Comments

  1. Sander van der Wal

    April 17, 2016 at 4:58 am

    in short, God plays by the Rules he has Created. But then you can still argue that God could have Created better Rules.

    Regarding changing the past, as God is outside time there is no such thing as changing the past as far as God is concerned. He can change things all over spacetime, past, present, future, here, there, everywhere, or he can change nothing at all. If God cannot change anything at all, how can he be the First Cause?

    So, what is consisten is that God turns a potentiality in to this actuality, and not one of all the other actualities. At the next change, He is consistent, the next actuality is reachable from the current potentiality.

    If God chooses the next actuality, you get Determinism. Which we do not have, so God plays dice, He picks one at random.

    There is of course a degenerate case, for each potentiality there’s always just one possible actuality. Which is Determinism again.

  2. “… that the three angles of a rectilinear triangle be not equal to two right angles.” I suppose we can’t blame Aquinas for not being familiar with non-Euclidean geometry.

    “Trumpet this to all who say theology isn’t concerned with math and science.” Is that what they say? I am under the impression that they say that theology is too concerned with math and science.

    “He make a thing to lack any of its essential principles while the thing itself remains: for instance that a man have no soul.” The complexity of human evolution had yet to be encountered.

    The question of the Trinity has yet to be discussed.

  3. Ye Olde Statistician

    April 17, 2016 at 3:35 pm

    I’m not sure that in non-Euclidean geometry one has a “rectilinear” triangle. Or that a figure in such a geometry can rightly be called a “triangle” save in an allegorical sense. In any case, we must take the terms Aquinas uses [‘triangulus rectilineus’] in the sense in which he used them rather than suppose he meant to write a treatise on plane geometry.

    Human evolution cannot deprive a human being of soul [‘anima’] since ‘soul’ means simply that the being is alive and in this instance possesses rational powers. [cf. ‘ratio’ once again]. One may as well talk of a triangle with only two sides, as to speak of any thing lacking that which it needs to be that thing. Nominalists may have trouble, since a name may be extended or contracted in application for various human purposes. E.g., mute swans and black swans are both called ‘swans’ even though they do not normally interbreed and form separate populations even when introduced in the same area. Evidently, the swans themselves do not regard themselves as being the same kind of thing even though humans with a scientific attitude have given them related names.

  4. “Again. Contradiction is included in contraries and privative opposites: for to be white and black is to be white and not white, and to be seeing and blind is to be seeing and not seeing. Hence it amounts to the same that God is unable to make opposites to be simultaneously in the same subject and in the same respect.”
    OK, let’s say that a spin pointing up is one attribute and a spin pointing down is another (there would be other analogs of such–light polarization, for example). Does the quote say that quantum mechanics is not true when it says that a state can contain, by superposition, the spin pointing both up and down? (Or, for a more homely example, the Schrodinger Cat Paradox).

  5. YOS, please read what I actually wrote, unless you think that my succinct observations need elaboration for other readers. I’ve recently been watching the A&E version of Tom Jones. Much superior to the book version which I was once forced to read. In any case I tend to share the Author’s opinion of critics.

    P. S. It is refreshing to see that you are unsure about something.

  6. Ye Olde Statistician

    April 17, 2016 at 5:00 pm

    @Bob
    Either that or we are talking about potencies, or we are using terms in an analogous sense. My cosmology friend tells me that paradoxes and singularities are signs of a defective model, not signs of a defective cosmos; and recall that Schroedinger proposed his cat paradox to show that the Copenhagen interpretation was incoherent. In fact, his paradox may be a good illustration of potencies being actualized. After all, Heisenberg, who set up the strangeness, was well versed in Aristotelian thought:

    “[T]he atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts.” — Werner Heisenberg

    After all, a pile of lumber is both potentially a house and potentially a grandstand at one and the same time. And when Socrates changes from white to black, he is during kinesis both white and black, though not of course in the same parts. To say that something is ‘in motion’ [kinesis] is just to say that it is both what-it-is and that-toward-which at the same time. Since the English tongue is gifted with the present participle, we can illustrate this with the lumber when we say that “a building is a-building.”

  7. YOS, that’s an interesting interpretation which I haven’t seen before. I’ll have to chew on it a while to see if it makes sense in the general framework of quantum mechanics.

  8. Semantics. I suppose this arguments was devised to make the notion of God seem more reasonable and realistic, but in the end, these things God can’t do are just silly oxymorons.

    JMJ

  9. @Bob Kurland:

    ” Does the quote say that quantum mechanics is not true when it says that a state can contain, by superposition, the spin pointing both up and down?”

    This is ambiguous; could you elaborate in what sense does a quantum state “contain” “the spin pointing both up and down”?

  10. swordfishtrombone

    April 18, 2016 at 5:33 pm

    @Bob Kurland, @YOS: “Schroedinger’s Cat”

    Schroedinger’s Cat is a misinterpretation of QM. The cat is either alive or dead at any moment, not some wierd superposition of both states. We don’t know which state it’s in until we open the box, but that doesn’t mean it’s in both states. The cat knows! The spin up/down thing is the same.

  11. Ye Olde Statistician

    April 18, 2016 at 5:44 pm

    @swordfishetc.
    Precisely.

  12. Swordfish, YOS,

    This is correct for the cat because of QM decoherence at the macroscopic level. Schrodinger posed it as a though experiment in an analysis of the transition from the QM to the classical realm. The spin up/down system is not the same however. Here he have superposition of states and the wave function does not collapse until a measurement is made, i.e. an interaction with the outside world. QM weirdness can’t be disposed of with a wave of the hand (pun intended).

  13. G. Rodrigues: By “contain” I mean the state functions is the superposition of both up and down: |state > = (2^(-1/2))( |UP> + |DOWN>)
    Swordfish trombone: as Scotian pointed out you’re not correct except for macroscopic objects: phase relations between the components of a superposed state are removed by decoherence–interactions with the environment. If you consider not spin up, spin down but a particle going through the double slit experiment, if it was either one or the other you’d see a particle hit opposite one or the other of the slits. But what you do see is not that but particles hitting at spots that indicate a phase relation–coherence–between the components |slit up> and |slit down>, i.e. a diffraction pattern that shows wave-like behavior.
    So after thinking about it, I’m not satisfied with YOS’s explanation of potentiality. That doesn’t explain the double slit experiment.

  14. Ye Olde Statistician

    April 18, 2016 at 10:59 pm

    That doesn’t explain the double slit experiment.
    But “explanations” of facts are precisely what is usually at issue in science. The facts generally are not in dispute. (Unless they travel faster than light.) De Broglie had a different explanation, which Bohm has followed up on. Recently, the double slit experiment was replicated at the macroscipic level, so it may be that mystical woo-woo is not needed to account for the facts:
    http://www.wired.com/2014/06/the-new-quantum-reality/

  15. YOS, I’m not sure what you mean by “mystical woo-woo”…please be more explicit. As far as the bouncing ball and diffraction type behavior–I don’t agree that this is a replication of the double-slit experiment. You can create phase relations in liquids by any matter of artificial disturbances. Moreover, (and I realize there is not space in a brief comment to justify the following remark): while much of quantum mechanics behavior can be explained* by Bohm’s pilot-wave model, there are many phenomena in physics that are not readily explained by Bohm’s pilot-wave theory, particularly in quantum field theory. Finally, there is nothing to show that the pilot-wave interpretations is “true” and “others'” are not. As a non-physicist, you’re quite free to follow any interpretation that agrees with your sensibilities.
    *By the way, I follow Humpty-Dumpty’s dictum about using words: when I use a word (e.g. “explained”) it means exactly what I choose it to mean–neither more nor less.

  16. Ye Olde Statistician

    April 18, 2016 at 11:29 pm

    there is nothing to show that the pilot-wave interpretations is “true” and “others’” are not.

    Certainly. And vice-versa. The same goes for Cramer’s transactional theory and Wheeler’s many-worlds theory. Cramer was confident that the Afshar experiment supported transactionalism, but the Copenhageners ingeniously interpreted the results to support their model. I’m sure Bohm or others can explain how the things you suppose are not explained by the standing wave model really are explained by the standing wave model. After all, the other physicists are probably not entirely stoopid. My cosmologist friend told me the last time we spoke of it that that Milne’s theory of relativity still stood as a viable alternative to Einstein’s. But no explanation is ever held more dearly than the one we were taught in school by revered teachers from respected texts.

  17. Regarding the Schrodinger’s Cat, I feel that the physicists are taking too many liberties with biology to even write the living/dead Cat as a part of a wave function.
    Where have the physicists established that a living body can be even approximately described by a wave function? Have they performed experiments?

    There is too much hand-waving among physcists (and I say this as a PhD holder in physics myself). and too much supersitition.
    By the neglect of the realism, that the object before one’s eyes must be affirmed to be real, without any qualifications whatsoever, the physicists have managed to confuse themselves and lots of others, into bargain.

  18. @swordfishtrombone
    “The cat knows”
    Does it? Is it established that a cat is an observer in the sense intended by the Copenhagen interpretation?

  19. Ye Olde Statistician

    April 19, 2016 at 7:23 am

    To be fair, it is not the cat in the quantum state, but the particle which may or may not have been emitted to trigger the poison gas. That is, the uncertainty lies in the particle, but the particle entails a chain of deterministic causes and effects.

  20. swordfishtrombone

    April 19, 2016 at 12:18 pm

    @Mactoul: “Is it established that a cat is an observer in the sense intended by the Copenhagen interpretation?”

    Yes, but only in the cases of the Iberian lynx, the tiger, the jaguar, the mountain lion and certain domestic cats 🙂

    Seriously, my “the cat knows” was just a throwaway line as, apart from anything else, it wouldn’t know if it was dead! The Copenhagen interpretation is just that – an interpretation – it has no bearing on the facts of the matter. Disclaimer – I’m not a physicist.

  21. swordfishtrombone

    April 19, 2016 at 12:27 pm

    @Scotian: “The spin up/down system is not the same however. Here he have superposition of states and the wave function does not collapse until a measurement is made, i.e. an interaction with the outside world.”

    Then sounds exactly the same as that darned cat to me. Quantum states are indeterminate until interaction with something.

  22. YOS, I’m going to ignore your comments on the interpretations of quantum mechanics since they do not have the physics approach that I need to understand or appreciate, but I do want to thank you for kindling an interest in a Thomistic approach to the interpretation of QM. There’s a book, “The Quantum Enigma”, by Wolfgang Smith that I’ll try to pick up that does have that approach and the author does have a background in physics.

  23. Swordfish,
    Well unless you are willing to read through Bertlmann’s socks there is not much more to be said.

    https://cds.cern.ch/record/142461/files/198009299.pdf

  24. swordfishtrombone

    April 19, 2016 at 6:08 pm

    @Scotian:

    You say: “The spin up/down system is not the same however. Here he have superposition of states and the wave function does not collapse until a measurement is made, i.e. an interaction with the outside world.”

    I say: “Quantum states are indeterminate until interaction with something.”

    They’re both the same. Thank you for the link. I’ve read that article before but it was nice to read it again.

  25. swordfishtrombone

    April 19, 2016 at 6:26 pm

    @Bob Kurland: “you’re not correct except for macroscopic objects: phase relations between the components of a superposed state are removed by decoherence–interactions with the environment. If you consider not spin up, spin down but a particle going through the double slit experiment, if it was either one or the other you’d see a particle hit opposite one or the other of the slits. But what you do see is not that but particles hitting at spots that indicate a phase relation–coherence–between the components |slit up> and |slit down>, i.e. a diffraction pattern that shows wave-like behavior.”

    Well, I agree with the point you’re making, but I was talking about Schroedinger’s poor old cat. With regard to the double-slit experiment, as I understand it, if you check each slit individually, you ‘see’ particle-like behaviour, but if you look at the experiment as a whole, you see an interference pattern. I’m not entirely sure this is the same as a ‘superposition’ of states (like spin-up/spin-down) as the two states (particle-like and wave-like) are not mutually exclusive, but depend on the way the experiment is conducted. But you’re the physicist!

  26. Thanks Swordfish for keeping an open mind.
    The situation is a little more than what you said in the reply. Go to http://rationalcatholic.blogspot.com/2016/03/the-resurrection-of-dead-and-quantum.html
    scroll down and look at the particles going through the slit–the one on the left is for no superposition, i.e. a mixture; the one one on the right is for superpositon (phase relation between components of the superposition).
    No measurement is taking place for the left hand situation but it isn’t what happens. I hope this clarifies.

  27. I tried to paste the images here, but it didn’t work…

  28. @Bob Kurland:

    Appologies for answering only now. Just in case it still matters:

    By “contain” I mean the state functions is the superposition of both up and down: |state > = (2^(-1/2))( |UP> + |DOWN>)

    “Superposition” is a technical term of art: it means (complex) linear combination (*) of states (**). It simply means that there is a mathematical relationship between certain states — so why use the word “containment”? What exactly do you have in mind? After all, *any* state is so related to infinitely many other states in infinite ways: just pick orthogonal decompositions of the quantum Hilbert space.

    (*) for those that actually know their QM: yeah I know that this is not the most general case of superposition, but that is a minor, irrelevant technical detail.

    (**) more technical qualifications: subject to a normalization condition because states are not vectors, but lines, etc. and etc.

  29. G. Rodrigues–I certainly agree with everything you said, and I am certainly familiar with what representations of the state function in Hilbert space entail, but I am confused–what is the point with respect to my comment, preceding and subsequent comments? I ask not to be contrary but to be enlightened.
    Perhaps I should repeat my point about the meaning of “contain”: with Humpty-Dumpty I’ll say
    “when I use a word it means exactly what I choose it to mean, neither more nor less,”

  30. @Bob Kurland:

    I have to confess I am also genuinely baffled by your response. So, in the hopes we both get enlightenment, let me set up some context. In April 17, 2016 at 3:49 PM, after quoting Aquinas thus:

    “Again. Contradiction is included in contraries and privative opposites: for to be white and black is to be white and not white, and to be seeing and blind is to be seeing and not seeing. Hence it amounts to the same that God is unable to make opposites to be simultaneously in the same subject and in the same respect.”

    You ask:

    “Does the quote say that quantum mechanics is not true when it says that a state can contain, by superposition, the spin pointing both up and down?”

    So your use of the word “contain” is directly prompted by what Aquinas is saying, namely the bit “Contradiction is included in contraries and privative opposites”. Your asking whether QM is true is presumably because you think there is, or there may be, some inconsistency between what Aquinas is saying and what QM says. Furthermore, and as can be gleaned from the passage, Aquinas has in mind what we would now call logical inconsistency or contradiction. So an affirmative answer to your question is logically equivalent to asserting the inconsistency of QM. Thus I asked in what sense do you mean that a state “contains” other states. Now you tell me, enjoining none other than Humpty Dumpty, that “when I use a word it means exactly what I choose it to mean, neither more nor less”. Ok, but then what Aquinas is saying cannot be inconsistent with what QM is saying and your original question dissolves to nothing. Am I missing something?

  31. Thanks GR–I’ll stop trying to be cute and explain my problem with the original statement. When I say “contain” I mean “include”. So the state for a spin 1/2 quantized in the + x direction includes as component states spin polarized in the -z and +z direction; these are opposites and contraries as I would understand those terms. So, my question is, given that the quantum mechanical superposition is correct, how should I interpret the Aquinas statement? Could you possibly enlighten me on that? Thanks.

  32. @Bob Kurland:

    “When I say “contain” I mean “include”. So the state for a spin 1/2 quantized in the + x direction includes as component states spin polarized in the -z and +z direction; these are opposites and contraries as I would understand those terms.”

    Yes, there is a perfectly coherent sense in saying they are contraries. Let me put it this way: one state is an eigenstate of a projection operator P corresponding to a proposition, also denoted by P (e.g. if we know that the system is in such a state then we know that P is true of the system), while the other is an eigenstate of the projection 1 – P corresponding to the proposition not-P (e.g. if we know that the system is in such a state then we know that not-P is true of the system).

    “So, my question is, given that the quantum mechanical superposition is correct, how should I interpret the Aquinas statement? Could you possibly enlighten me on that?”

    As I said in my previous post, Aquinas is talking about logical inconsistency or contradiction, so what you are asking me is logically equivalent to asking if QM is logically inconsistent. No, and there is no reason to suppose this — more on this in a moment, but let me hasten to add that I do not make too much of Aquinas use of “included”. I do not know Latin, so it is useless to hunt the originals, but I would say that this is similar to when we say something like “X has property Y” but the verb “has” is quite clearly not being used in the same sense as when we say “X has pink trousers”.

    Back to the main issue; a further problem is that your use of “contain” or “include” does not really make sense except as a figure of speech. A state is not a container of other states, spatial or otherwise. Superposition is a *mathematical* relationship; just that, no need to reify it and suppose there is something more going on. The word “superposition” itself is somewhat unfortunate because it invites picturing a state that can be written as a linear combination of other states, as somehow an actual mixture of those states. But if one means this literally, then it is easy to see that QM is indeed inconsistent.

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