William M. Briggs

Statistician to the Stars!

Category: SAMT (page 30 of 32)

A tour through Saint Thomas Aquinas’s Summa Contra Gentiles.

Summary Against Modern Thought: What’s God Like?

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.

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

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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: 10\uparrow 10 = 10^{10} , or 10 billion, where the arrow has replaced the caret, but then 10\uparrow\uparrow 10 , which is 10 raised to the 10 raised to the 10 raised to the 10, etc., 10 times (the arrow iterates the caret) Now that’s a big number! We can write it down all right—Knuth calls it K—but we cannot know it, cannot form a real appreciation for it. It’s too big.

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.

Summary Against Modern Thought: The Last Movement

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.

Previous post.

Recall that the First Way has already been done. Meaning we already have one proof for God’s existence. This is the second, and the good news is that most of our terminology has already been introduced. A lot to do today, but the good news is that this is the last of Chapter 13! But these proofs are all we have. We don’t yet know anything about God except that He’s the Unmoved Mover, the Unchanging Changer. What can that mean? That’s coming.

Chapter 13: Arguments in proof of God’s existence

18 Again, if any two things are found accidentallyi united in a certain subject, and one of them is to be found without the other, it is probable that the latter can be found without the former: thus if white and musical are found in Socrates, and musical without white is found in Plato, it is probable that it is possible to find white without musical in some subject.

Accordingly if mover and moved be united together in some subject accidentally, and it be found that a certain thing is moved without its being a mover, it is probable that a mover is to be found that is not moved. Nor can one urge against this the case of two things one of which depends on the other; because those in question are united not per se but accidentally.

If, however, the aforesaid proposition is true in itself, again there follows something impossible or unfitting. For the mover must needs be moved either by the same kind of movement or by another kind. If by the same kind, it follows that whatever causes alteration must itself be altered, and furthermore that the healer must be healed, that the teacher must be taught, and in respect of the same science. But this is impossible: for the teacher must needs have science, while the learner must needs not have it, and thus the same will be both possessed and not possessed by the same, which is impossible.ii

And if it be moved by another kind of movement, so that, to wit, that which causes alteration be moved in respect of place, and that which moves in respect of place be increased, and so on, it will follow that we cannot go on indefinitely, since the genera and species of movement are finite in number.iii And thus there will be some first mover that is not moved by another. Unless, perchance, someone say that a recurrence takes place, in this way, that when all the genera and species of movement have been exhausted, a return must be made to the first; for instance, if that which moves in respect of place be altered, and that which causes alteration be increased, then again that which is increased be moved in respect of place. But the consequence of this will be the same as before; namely, that which moves by one kind of movement is itself moved by the same kind, not immediately indeed but mediately.iv It remains therefore that we must needs postulate some first mover that is not moved by anything outside itself.

19 Since however, given that there is a first mover that is not moved by anything outside itself,v it does not follow that it is absolutely immovable, Aristotle proceeds further, saying that this may happen in two ways. First, so that this first mover is absolutely immovable. And if this be granted, our point is established, namely that there is a first immovable mover. Secondly, that this first mover is moved by itself. And this seems probable: because what is of itself is always prior to what is of another: wherefore also in things moved, it is logical that what is moved first is moved by itself and not by another.

20 But, if this be granted, the same consequence follows.[18] For it cannot be said that the whole of that which moves itself is moved by its whole self, because then the absurd consequences mentioned above would follow, namely that a person might teach and be taught at the same time, and in like manner as to other kinds of movement; and again that a thing would be at the same time in act and in potentiality, since a mover, as such, is in act, while that which is moved is in potentiality.vi It remains, therefore, that one part thereof is mover only, and the other part moved. And thus we have the same conclusion as before, namely that there is something that moves and is itself immovable.

21 And it cannot be said that both parts are moved, so that one is moved by the other; nor that one part moves both itself and the other; nor that the whole moves a part; nor that part moves the whole, since the above absurdities would follow, namely that something would both move and be moved by the same kind of movement, and that it would be at the same time in potentiality and in act, and moreover that the whole would move itself not primarily but by reason of its part. It remains, therefore, that in that which moves itself, one part must be immovable, and must move the other part.

22 Since, however, in those things among us which move themselves, namely animals, the part which moves, namely the soul, though immovable of itself, is nevertheless moved accidentally, he goes on to show that in the first mover, the part which moves is not moved neither of itself nor accidentally.[19]vii

23 For in those things which among us move themselves, namely animals, since they are corruptible, the part which moves is moved accidentally. Now those corruptible things which move themselves must needs be reducible to some first self-mover that is everlasting. Therefore that which moves itself must have a mover, which is moved neither of itself nor accidentally.

24 It is clear that, in accordance with his hypothesis, some self-mover must be everlasting. For if, as he supposes, movement is everlasting, the production of these self-movers that are subject to generation and corruption must be everlasting. But no one of these self-movers, since it does not always exist, can be the cause of this everlastingness. Nor can all of them together, both because they would be infinite, and because they do not exist all together. It follows therefore that there must be an everlasting self-mover, that causes the everlastingness of generation in these lower self-movers. And thus its mover is not moved, neither of itself nor accidentally.

Again, we observe that in self-movers some begin to be moved anew on account of some movement whereby the animal is not moved by itself, for instance by the digestion of food or a change in the atmosphere: by which movement the mover that moves itself is moved accidentally. Whence we may gather that no self-mover, whose mover is moved per se or accidentally, is always moved. But the first self-mover is always in motion, else movement could not be everlasting, since every other movement is caused by the movement of the first self-mover. It follows therefore that the first self-mover is moved by a mover who is not moved, neither per se nor accidentally…viii

30 The Philosopher proceeds in a different way in 2 Metaph. to show that it is impossible to proceed to infinity in efficient causes, and that we must come to one first cause, and this we call God. This is how he proceeds. In all efficient causes following in order, the first is the cause of the intermediate cause, and the intermediate is the cause of the ultimate, whether the intermediate be one or several. Now if the cause be removed, that which it causes is removed. Therefore if we remove the first the intermediate cannot be a cause. But if we go on to infinity in efficient causes, no cause will be first. Therefore all the others which are intermediate will be removed. Now this is clearly false. Therefore we must suppose the existence of a first efficient cause: and this is God.ix

31 Another reason can be drawn from the words of Aristotle. For in 2 Metaph.[22] he shows that those things which excel as true excel as beings: and in 4 Metaph.[23] he shows that there is something supremely true, from the fact that we see that of two false things one is falser than the other, wherefore it follows that one also is truer than the other. Now this is by reason of approximation to that which is simply and supremely true. Wherefore we may further conclude that there is something that is supremely being. And this we call God.x

32 Another argument in support of this conclusion is adduced by Damascene[24] from the government of things: and the same reasoning is indicated by the Commentator in 2 Phys.[25] It runs as follows. It is impossible for contrary and discordant things to accord in one order always or frequently except by someone’s governance, whereby each and all are made to tend to a definite end. Now we see that in the world things of different natures accord in one order, not seldom and fortuitously, but always or for the most part. Therefore it follows that there is someone by whose providence the world is governed. And this we God.xi

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iA circle can be accidentally red or yellow and still be a circle, etc. A thing is not defined by its accidents.

iiAquinas created this argument in ignorance of our modern educational system, of course. But he’s still right.

iiiYou can change quantity, mass, color, place, and the like, but there are not an infinite number of changeable qualities.

ivDon’t loose sight of the main example, the stone moved by the stick moved by the arm moved by the muscles, etc., all in the here and now. This movement cannot be circularly caused.

vWe’re starting to hone in on (but have not reached) the idea that there can be only one Unmoved Mover, and not an assemblage of them. Not gods, but God.

viYou cannot potentially and actually be in Cleveland simultaneously. Aquinas is speaking ontologically, not epistemologically. And this reminds me that we have to, sometime soon, introduce Jaki’s criticisms of complementarity.

viiWe’ll also do this more later. But, for now, the soul of the animal is its form. Things are composed of forms and substances or matter. Clay, a substance, can be in the form of an ashtray (eek!) or (say) a model car. Speaking loosely, and later correctly, the soul animates the substance. The souls of plants are lesser than the souls of animals, which in turn are lesser than the souls of men. Like I said, this is only a crude introduction. Let’s stick here to the argument of movement, else we will be arguing that of which we have incomplete information.

viiiYou may feel buried after these last two paragraphs. Slow reading is in order. Again, Aquinas is leading us to why there can be only one Unmoved Mover. There’s no getting around that this last proof is rather dry—I even leave out some discussion about movement of heavenly bodies—but it dots all the Js and crosses all the Xs.

ixHere it is in a compact form! This is the elevator proof. Pretty, too.

xI don’t think Aquinas expected this snippet to be convincing in itself, but included it as an augment to main argument. Here’s a good article from Swinburne on the argument from the beauty of design, and another by Williams on beauty.

xiAnd this sketch is cruder still. It’s doubtful that it, in this telegraphic form, would convince any moderns. I’m not expert enough in Medieval history to know why Aquinas included it, which audience he had in mind.

Hooray! We are finally done with Chapter 13! But not entirely done with motion.

[18] 8 Phys., l.c.
[19] 8 Phys. vi.
[22] D. 1a. i. 5.
[23] D. 3. iv. 27, 28.
[24] De Fide Orth. i. 3.
[25] Text 75.

Summary Against Modern Thought: Contingency & Necessity

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.

Previous post.

The First Way is in the bag. And now we continue, fresh as it were, with the Second Way. But since this introduces what are unfamiliar concepts to some, we again slow down. But have no fear: after this chapter, we can again speed up, because most of the terms will by then be familiar.

Chapter 13: Arguments in proof of God’s existence

16 We have thus clearly proved both statements which were supposed in the first process of demonstration whereby Aristotle proved the existence of a first immovable mover.viii

17 The second[16] way is as follows. If every mover is moved, this statement is true either in itself or accidentally. If accidentally, it follows that it is not necessary: for that which is accidentally true is not necessary.i Therefore it is a contingent proposition that no mover is moved.ii But if a mover be not moved, it does not move, as the opponent asserts. Therefore it is contingent that nothing is moved, since, if nothing moves, nothing is moved. Now Aristotle holds this to be impossible,[17] namely, that at any time there be no movement.iii Therefore the first proposition was not contingent, because a false impossibility does not follow from a false contingency. And therefore this proposition, Every mover is moved by another, was not accidentally true.iv

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iMost things you know are contingently true. It is true (supposing) that your car is in your driveway, but only because you bought a car and parked it there. The universe did not require you to buy this car. Not everybody has a car (Yours Truly does not). Propositions which are contingently true can be imagined false. I can easily imagine you too do not have car. No rules of logic would be violated were that to be so.

A necessary truth is that which cannot be other than true. A necessary truth cannot be imagined false. Here is a necessary truth: “A thing cannot both exist and not exist simultaneously.” It is impossible to imagine, or more properly to think of, a thing existing and not existing at the same time. Logic cannot be violated.

When speaking of contingency, some speak of “possible worlds”, as if the world in which you do not own a car is, somehow, brought into existence by your imagining you do not have a car; a sort of milky idealism. Or that this “possible world”, simply because it can exist, actually exists; perhaps part of a multiverse or one of the “many worlds” where all events occur.

But this thinking mixes up the existence of a thing with the knowledge of the thing. Ontology is not epistemology. Things can exist without your, or anybody’s, knowledge. And you can have knowledge (or rather can think) of things that do not exist, like conservative sociologists or the Starship Enterprise. The latter does not come into existence just because it can be imagined.

Now some say of necessity that nothing occurs “at random” or “randomly”. But this is to make the same mistake. Randomness isn’t a thing. It therefore cannot be a cause. Best way to think of this is to substitute “ignorance” every time you see random. If the sentence is still sensible, then the author has a proper understanding; if not, then not.

iiIf it is only contingently true that “no mover is moved”, it can be imagined that “it is false that no mover is moved.” And you have to love the next two sentences.

iiiSome highlights from Aristotle (following the footnote):

…Now the existence of motion is asserted by all who have anything to say about nature, because they all concern themselves with the construction of the world and study the question of becoming and perishing, which processes could not come about without the existence of motion.

It is not always asserted by some readers here, but let that pass. Continuing, we see that talk of “infinite possible worlds” is not a new invention. (I added extra paragraphs for readability.)

But those who say that there is an infinite number of worlds, some of which are in process of becoming while others are in process of perishing, assert that there is always motion (for these processes of becoming and perishing of the worlds necessarily involve motion), whereas those who hold that there is only one world, whether everlasting or not, make corresponding assumptions in regard to motion. If then it is possible that at any time nothing should be in motion, this must come about in one of two ways…

…Motion, we say, is the fulfilment of the movable in so far as it is movable. Each kind of motion, therefore, necessarily involves the presence of the things that are capable of that motion. In fact, even apart from the definition of motion, every one would admit that in each kind of motion it is that which is capable of that motion that is in motion: thus it is that which is capable of alteration that is altered, and that which is capable of local change that is in locomotion: and so there must be something capable of being burned before there can be a process of being burned, and something capable of burning before there can be a process of burning.

Moreover, these things also must either have a beginning before which they had no being, or they must be eternal. Now if there was a becoming of every movable thing, it follows that before the motion in question another change or motion must have taken place in which that which was capable of being moved or of causing motion had its becoming.

To suppose, on the other hand, that these things were in being throughout all previous time without there being any motion appears unreasonable on a moment’s thought, and still more unreasonable, we shall find, on further consideration. For if we are to say that, while there are on the one hand things that are movable, and on the other hand things that are motive, there is a time when there is a first movent and a first moved, and another time when there is no such thing but only something that is at rest, then this thing that is at rest must previously have been in process of change: for there must have been some cause of its rest, rest being the privation of motion…

We went as as this for two reasons: (1) Aquinas was not pulling his assertion about Aristotle out of thin air, and that Aristotle’s assertion is true, and (2) for the phrase “rest being the privation of motion”. This is a tease, but the concept of privation will become important for us. For instance, evil, as it will turn out, is privation of the good. But let’s not get distracted by this today.

ivSince we’ve already done a lot, without really have done much, we leave this phrase hanging in the air, as it were. We’ll pick up with it again next week. Very little was proved this week, except Aristotle’s small proposition.

Next installment.

[16] [8 Phys. v.] [17] 8 Phys. i.

Summary Against Modern Thought: Non-existence Of Infinite Causal Chains

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.

Previous post.

Here’s what was proved so far: (1) that some things move and others change, and that (2) whatever is in the process of being moved or being changed is being moved or changed by another. Utterly unremarkable assertions; but both the backbone of science, even though some scientists pretend to be skeptical of causality. There is a world, nay a universe, of difference between our knowledge of a cause and of the existence of a cause. Poor Jaki spent his career reminding people of Heisenberg’s fallacy of equivocation. “Poor” because, for whatever reason, people cannot keep in mind the difference between epistemology and ontology. Once more I beg you to read the stone being moved by the stick being moved by the arm being moved by the muscles etc. example. Today we reach the end of the First Way. Next week we begin the Second way.

Chapter 13: Arguments in proof of God’s existence

4 This argument contains two propositions that need to be proved: namely that whatever is in motion is moved by another, and that it is not possible to proceed to infinity in movers and things moved…

11 He proves the other proposition, namely that it is impossible to proceed to infinity in movers and things moved, by three arguments.i

12 The first[10] of these is as follows. If one were to proceed to infinity in movers and things moved, all this infinite number of things would necessarily be bodies, since whatever is moved is divisible and corporeal, as is proved in 6 Phys.[11]ii Now every body that moves through being moved is moved at the same time as it moves.iii Therefore all this infinite number of things are moved at the same time as one of them is moved. But one of them, since it is finite, is moved in a finite time. Therefore all this infinite number of things are moved in a finite time. But this is impossible. Therefore it is impossible to proceed to infinity in movers and things moved.iv

13 That it is impossible for the aforesaid infinite number of things to be moved in a finite time, he proves thus.[12] Mover and moved must needs be simultaneous; and he proves this by induction from each species of movement. But bodies cannot be simultaneous except by continuity or contact. Wherefore since all the aforesaid movers and things moved are bodies, as proved, they must needs be as one movable thing through their continuity or contact. And thus one infinite thing would be moved in a finite time, which is shown to be impossible in 6 Phys.[13]v

14 The second argument[14] in proof of the same statement is as follows. In an ordinate series of movers and things moved, where namely throughout the series one is moved by the other, we must needs find that if the first mover be taken away or cease to move, none of the others will move or be moved: because the first is the cause of movement in all the others. Now if an ordinate series of movers and things moved proceed to infinity, there will be no first mover, but all will be intermediate movers as it were. Therefore it will be impossible for any of them to be moved: and thus nothing in the world will be moved.vi

15 The third argument[15] amounts to the same, except that it proceeds in the reverse order, namely by beginning from above: and it is as follows. That which moves instrumentally, cannot move unless there be something that moves principally. But if we proceed to infinity in movers and things moved, they will all be like instrumental movers, because they will be alleged to be moved movers, and there will be nothing by way of principal mover. Therefore nothing will be moved.vii

16 We have thus clearly proved both statements which were supposed in the first process of demonstration whereby Aristotle proved the existence of a first immovable mover.viii

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iIt is utterly absolutely painfully crucial that you understand what is meant by this. Aquinas means here-and-now, or at-this-very-moment causation. The stick moves the stone here-and-now, your arm moves the stick here-and-now at-this-very-moment, your muscles move your arm here-and-now at-this-very-moment, simultaneously. Your muscle and other cells here-and-now at-this-very-moment move, and so on down to something. Some first unmoved mover. It is this here-and-now at-this-very-moment chain which cannot proceed here-and-now at-this-very-moment to infinity. Update See YOS’s clarification on “instantaneous” movement/change below.

Ed Feser (who not uncoincidentally, since I’ve stolen many of my ideas from him, today wrote on a similar subject) has taken great pains in his many books and articles to teach that this per se chain of here-and-now at-this-very-moment causes exists here-and-now at-this-very-moment, that everything is happening at once. His experience has been that this teaching does not stick. Why? Who knows. But since it is so, I remind you we are not talking about accidental chains of causation, such as when one rock falls off a hill into another, and the second rock then hits a third, and so on. No no no no. We are talking about how movement or change in the here-and-now comes about. Meditate on the example until it is clear in your mind before continuing.

Or watch Feser’s terrific lecture on the subject.

iiAll of Aristotle’s Chapter 6 may be found here. The stick is a body, and so is your arm, and so are your cells, the chemicals, the electrons and neutrons, the quarks, the strings (if they exist) and whatever, if anything, is “below” them. Notice that Aquinas and Aristotle use a proof by contradiction. They assume there exists an infinite here-and-now chain.

iii Here-and-now at-this-very-moment!

ivSweet, no? If there did exist an infinite chain, and because we certainly see things move or change in finite time, this entire infinite chain would have to move not only in finite time, but at this moment, here and now (have we memorized this yet?). The proof immediately follows.

vAristotle proves even more than his: his book 7 may be found here. Anyway, it is clear that if we have an infinite here-and-now chain of objects, the whole thing must itself, here-and-now at-this-moment, move. And that is not possible in finite time. Worse, this would have to be the case for everything everywhere that is in the process of being moved or changed. That’s a lot of chains and lots of infinite movements! Since it is absurd that these infinite chains can move in finite time, yet things are moved or changed in finite time, the chains must not be infinite.

viIf the here-and-now chain is finite—this is an assumption, arguendo—and the first element is removed, the later parts also cannot move, which is obvious. Now I don’t think people understand how big infinity really is. It is not just big, nor even BIG, but horrifically huge. An infinite chain would have more than a googol of elements, which is 10100; it would have more than a googoplex of elements, which is 10googol. If you were to keep doing that operation, namely taking 10 to the power of the last result, and continuing once a second for a whole day, you still would not have got close to infinity. You would still be infinitely far away. But the, to us humans anyway, unimaginably long chain would have only just got started! Just to use your arm to move a stick to push a stone.

An infinite chain is one which never stops. It goes on and on and on and always on some more. If infinite chains existed, there would not and could not be a first element. How, then, would the whole thing get started? Answer: it could not. It would be impossible—not unlikely, but impossible.

I think people believe infinity isn’t all that big because of mathematical analysis, and used in many areas of science. In analysis we regularly and somewhat glibly call on infinity. We say some function converges (perhaps) “O(n2)”, meaning as the number of elements grows, the finite function gets closer and closer to its infinite cousin. We plug in n = 20 or even n = 100 and see that the function is “settling down”, i.e. approaching some obvious value, and we think, “Ah, infinity and n = 100 aren’t that far apart.” However useful an approximation our function at some finite number of elements is, it is never the real value of the function at infinity. Taking approximations as reality and not just as approximations is a common, though not usually painful, fallacy.

It’s a killer here, though. When we are talking movement or change, we cannot have an approximation. We must needs have the whole chain. Stopping at the first (say) 100 elements just won’t do. If we remove a link, the chain cannot pull. And if we do have an infinite chain, there will be nothing to give the chain impetus. Without a first mover, nothing can happen. The chain thus cannot be infinite.

viiThe rock is being moved instrumentally by the stick, which is being moved instrumentally by the arm, and so forth. The principal unmoved mover sets off the whole shebang. I think we get it by now.

viiiLet’s review. We proved the premises in this First Way:

Whatever is in motion is moved by another: and it is clear to the sense that something, the sun for instance, is in motion. Therefore it is set in motion by something else moving it. Now that which moves it is itself either moved or not. If it be not moved, then the point is proved that we must needs postulate an immovable mover: and this we call God. If, however, it be moved, it is moved by another mover. Either, therefore, we must proceed to infinity, or we must come to an immovable mover. But it is not possible to proceed to infinity. Therefore it is necessary to postulate an immovable mover.

The premises being true, and the argument valid, the conclusion must also be true. And therefore it would irrational to deny it. But why God as the unmoved mover? Why not call the immovable mover the Higgs Field Driver or whatever? Well, we haven’t fleshed this part of the proof out yet, so our modern scientistic suspicion is natural.

As a hint—and only a hint—there cannot be more than one immovable mover, one unchangeable changer. There must be something which exists which acts to sustain everything. Stay tuned!

Next installment.

[10] 7 Phys., l.c.
[11] L.c.
[12] 7 Phys. i. ii.
[13] Ch. vii.
[14] 8 Phys. v.
[15] Ibid.

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