St Bonaventure argues against the eternity of the world in II Sent. 1.1.1.2. First he claims

“that nothing can be added to the infinite. This is manifest per se, because everything that receives addition becomes greater, but nothing is greater than the infinite. But if the world is without beginning, it has lasted into infinity: therefore its duration cannot be added to.”

Since every day adds another revolution of the sun to the world’s duration, this duration cannot already be infinite.

St Thomas presents a basically identical argument in chapter 38 of his Summa Contra Gentiles, but then rejects it:

“There is nothing to prevent an addition to the infinite on the side on which it is finite. On the supposition that time is eternal, it must be infinite on the part of what went before, but finite on the part of what came after, for the present marks the end of the past.”

St Thomas’ assertion might be illustrated by imagining a number line, where 0 marks the present, the negative integers the past, and positive integers the potential future. The negative integers stretch backwards into infinity, but there is a last one, -1; then we come to the present. After this we will continue to move alone the number line into 1, 2, 3, etc. Everything after 0, the present we have picked out, is clearly finite, no matter how many times we add an integer; the infinity lies in the other direction. And our 0 can be taken anywhere along the line we like: there is always some finite number of integers afterwards that can be added to, with an infinity before.

St Bonaventure has heard this argument, but he thinks it doesn’t work. You can’t tell me, he says, that it is on the present side that the “more”, the addition is to be found. Every additional revolution, as soon as it happens, becomes the past and joins the supposed infinity of former revolutions; furthermore, the infinite number of past years would have to be multiplied by a twelve-times infinite number of past months. Therefore even on the side of the past you have an infinite, and something else more infinite, which is impossible.

The second argument Bonaventure proposes relies on the principle that the infinite cannot be ordered. “For every order flows from a principle to a mean; if therefore there is no first, there is no order,” and this applies both to the succession of heavenly revolutions and to the successive generation of animals in a species. St Thomas would reply by insisting that there is no real order to be found in per accidens efficient causes, but only in essentially ordered causes. For Thomas this is enough to invalidate the argument; to show why it is not so for Bonaventure would be to go further into the Seraphic Doctor’s metaphysics than time permits. Suffice it to say, along with Gilson, that for St Bonaventure

“every celestial revolution, instead of following indifferently an infinity of identical revolutions, coincides with the appearance of unique events . . . Every day, every hour even forms part of a series which is ruled by a certain order and of which Divine Providence knows the whole reason.”(Gilson, The Philosophy of St Bonaventure, 174)

To insist on such a worldview at this point when arguing with Averroists or pure Aristotelians would probably seem philosophically indefensible to St Thomas, however much he might agree with it as a Christian; therefore in philosophy he is prepared to do without what to St Bonaventure is an essential but also wholly evident fact about the world. Nevertheless given the assumption that successive events in the universe are really ordered to each other, and not merely accidentally, St Thomas would also accept the argument (see Summa Theologiae Pars 1 art. 46 q. 2 ad 7.)

Bonaventure’s third argument is probably his most interesting and compelling. Like the first one, it examines the notion of an infinite succession of days or years for coherence, but is much more ingeniously constructed. I will give it in full and examine it at greater length than the others.

“It is impossible for the infinite to be passed through; but if the world has not begun, there have been infinite revolutions: therefore it was impossible to pass through them: therefore it was impossible to come up to this one. If you say that they have not all been passed through because there was no first, or even that they can be passed through in an infinite time, you will not escape this way. For I will ask you if some revolution infinitely preceeded today or not. If not: therefore all are finitely distant from this one, therefore they have a beginning. If some one is infinitely far away, I ask about the revolution immediately following that one, whether it is infinitely distant. If not: therefore neither is the first one, because there is a finite distance between the two. If [the second one] is infinitely distant, similarly I ask about the third and the fourth to infinity: therefore no one of them is more distant from today than another one: therefore one is not before the other: therefore they are all simultaneous.”

Let me bring back my illustrative number line of years. 2007 years have passed since the 0 moment, the now of the incarnation. The year before that we will call -1, and before that -2, and so forth. It is perfectly conceivable to extend the line to posit a year -1,285,397; this simply means that 1,285,397 years passed before the angel Gabriel came to Mary. But Bonaventure insists that if the world never began one has to posit a year –(infinity), requiring that an infinity of years passed before that moment. This he denies as impossible.

Thomas would insist that this argument is poorly framed. In Summe Theologiae Pars 1 art. 46 q. 2 ad 6, he says:

“A passing through (transitus) is always understood from term to term. But whatever past day is assigned, from that day to this one there was a finite number of days, which were able to be passed through. But the objection proceeds as though, having posited these extremes, there was an infinity in between.”

In other words, it doesn’t make sense to posit a year –(infinity) because the infinite doesn’t work that way. Pick any number you like and you can say that so many years passed before 0; but any such numer will be finite. Infinity is not a number at all. It simply means that there is always more beyond any point you assign.

Plainly St Bonaventure just doesn’t accept St Thomas’ principle that “even though the infinite does not exist at all if it is actual, it can exist successively” (from On the Eternity of the World Against the Averroists), or at least not in the same way. For him this is nothing more than an evasion. Perhaps what he has in mind can be clarified by adding a future arm to our number line. Until now I have only contemplated the past leading up to the present; I either assigned the past a negative number and labeled the present 0, or I assigned 0 to some point in the past and counted the finite number of years following it up to now. But I can project into the future and postulate that if today is 2007, there will be a 2008, and a 1,285,397. In fact I can postulate that there will be no final year but that the world will continue forever, that whatever number I choose there will be a corresponding future year, and more after that. In this sense we can say that the future is infinite, even though the world will never reach a single particular year that itself is infinitely distant from this one.

It seems that in St Thomas’ view the past and the future are the same in this respect, while in St Bonaventure’s view they are fundamentally different. Neither the past nor the future exists in the way that the present now does, since

*now*they are not, but since time moves in a definite direction their nonexistence is not of the same kind, and from the vantage point of the present we cannot look indiscriminately either way. The future is in potency as not yet having happened, and this potency is infinite, because more can always happen. But the past is not in potency but in the state of

*already having happened*. There is no potential for more past once the present has passed away, except by adding on to it from the future end of the line, converting potential future revolutions into actual present ones and the completed past ones. We speak of it in the perfect tense because, while not having simultaneous being with the present, nevertheless it has a kind of unalterable completion. It has the status of

*having been*the present, and so every past now must have been passed through to come to the present now. In the imagination we can always extend the future arm of the number line further and say that there can always be more years. But this is a different operation from extending the past arm backwards and saying that there can always have been more years. If future years are like promissary notes, past years are like debts which have already been paid to reach the free and clear state of the present. Thus Bonaventure insists that it makes no sense to wave one’s hand at an infinitely and indefinitely distant past without relating it to the present. Either some given past year has an infinite distance from the present, or it doesn’t. If not, then the past is finite. But if it does, then since that infinite distance cannot have been traversed, it must really be a kind of simultaneous eternity with no real relation to the present at all, a year which was never passed through to reach the present, a year that the world now cannot count as having once experienced as part of its journey to reach the present now. We have then the finite number of years that the world has passed through, and the unreachable infinity of time somehow lying behind them which we can never reach by counting back, and which were never passed through on the way forward. In other words, we have a finite past which is really past, and an infinite one which is not past. Bonaventure will agree with Thomas that a passing through requires going from term to term; but he rejects as contradictory the notion of apst which, not having been passed through, was never a present, and thus cannot serve as a term marking the distance between then and now.

If Bonaventure rejects Thomas’ principle that, while there cannot be a simultaneous infinite in act, there can be a successive one, it is because he thinks that this still implies the admission that there can be an actual infinite of some sort or other. Stretching it out in time does not eradicate its actual character; but the infinite can only exist potentially. Bonaventure draws out this implication in his fourth and fifth objections. . . .

## 10 comments:

Mr. Sullivan:

Thank you kindly. You have given me much to ponder, and I haven't had time to ponder it yet, but I will set to doing so promptly when I have more leisure to do so. :)

Thank you very much for posting this!

Thank you very much. I am teaching Medieval Philosophy, and your essay clarifies many points and explains Bonaventure in a way that makes him make more sense than I thought he had.

David Lukens

David (and other anonymous), I'm glad you found it helpful.

This is a really good post. I've never understood Thomas' reply to that argument "whatever bygone day we choose...". It seemed to miss the point. The thoughts of Bonaventure you have laid out here give precision to my own cogitations on the matter.

Having said that, I would agree that it is not a good idea to argue for God's existence by starting with the fact the world had a beginning etc since the arguments do not require, are not affected, by the eternity or non eternity of the world. The less variables / premises you need to establish or defend to make the argument the better.

Cool beans, thanks. Nicely presented.

Michael, thank for this post (even if I'm writing 5 years after the post). The third argument of Bonaventure is objectively solid because for the past to exist, it had to first past through the present. In which case no moment could be infinitely distant from the present moment - if the past were "infinite" then this would mean that there are moments not measurable from the present, something which is impossible if it passed through the present moment. All past moments have to be a finite distance from the present moment; therefore, there has to be a first moment - a beginning. Your example (humorous, but true) of debts and promissory notes was most helpful!

If you or someone respond to me, I'd like to dialogue more on the subject of finite or infinite time/space. If no one responds, then I know that no one has enough

timeto write on this subject ;-)Mr. Sullivan - yes I am another one highly interested in this debate. I'd like to discuss over email if you have time. My email is clansullivan at hotmail dot com.

Sorry to "grave-dig" this post but I only just summed on it.

Any chance of a discussion on how Hilbert's hotel paradox fits in with this treatment of infinity?

Sorry! "summed" should have read "stumbled".

Predictive text plainly is a false prophet!

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