Every horse is living

Here is a translation of a question by Jean Buridan which has some affinity with our earlier discussion about men who are not men.  Reading what he says, it is clear that he would resolve our difficulty by rendering 'some men are not men' into 'some things which are men, are not men', which is clearly false.

Does a Common Term Suppositing with a Present Tense Verb Supposit Only for Presently Existing Things?

Sorry for the strange title but it is a literal translation of one of the questions (Latin: Utrum terminus communus supponens verbo de praesenti supponat tantum pro praesentibus) in Scotus’ Questions on the Perihermenias, and I am struck by the increasing resemblance between the discussion going on here, and the discussions on the same subject going on in the late 13th century in Oxford and Paris. In my last post, I discussed the slightly paradoxical syllogism

(1) No y is identical with Caesar
(2) Some x was identical with Caesar
(3) Some x is not identical with any y

to which David Brightly objected that

For (1) to be true it's clear that the range of the quantified expression 'no y' cannot be all men who ever were. Rather the present tense 'is' modifies the quantifier 'no man' restricting the ys in (1) to the presently existing men. Similarly in (2) the past tensed 'was' modifies the quantifier 'some x', restricting the xs to the men who ever were, ie, no restriction at all.

Well that’s true, and that’s one solution proposed by some of the scholastics, who thought that the present tense of the main verb of the sentence restricts (Latin: restringit) a common term like ‘man’ to suppositing (i.e. ranging over) presently existing men (praesentibus).

What’s wrong with that solution is the present tense that we have to use when we say what things are in the domain or range of quantification. David says that using a verb in the past tense allows the quantifier it to range over all the man that ever were. The problem is the implied present tense of the ‘ranging’. How is it that the quantifier ‘ranges’ – present tense – over past men, men who longer exist? Surely it can’t. Nor can the domain now ‘contain’ all such men. It used to contain them, but now it doesn’t. So the second premiss (2) cannot be true. There cannot be any x that was identical with Caesar, because however wide the domain or range of quantification, the domain exists in the present. It has to exist in the present because we say that it is the range of our quantification, and to say that we must use the present tense.

Anthony is closer when he says that the real problem is presentism, but there are problems with presentism also, which I will talk about later.

Clarification

David Brightly has rightly questioned whether my argument is valid:

Caesar was a man
Caesar is not (any longer) a man
Some man is not a man

It's not, unless our domain of quantification consists only of men.  But I can easily restate the argument

No y is identical with Caesar
Some x was identical with Caesar
Some x is not identical with any y

I don't see any way round that.  Of course, some x was identical with some y (for y = Caesar, where the verb "=" has past tense).  And perhaps we could read the existential quantifer as tensed - there was an x such that x is not identical with any y.  But there's no way we could make any sense of it in standard predicate logic.  Moreover, the standard way of understanding quantification as a kind of relation between variables or open sentences or predicates on the one side, and objects on the other, makes no sense either.  For example, logicians say that the predicate "- was an emperor" is satisfied.  Is satisfied?  Or was satisfied?

Presentism and truthmaking

Anthony, who occasionally asks some very good questions (I'm sorry I don't have time to address them all), asks in a comment to this post whether my position on truthmakers is inconsistent with my presentism. I'm not sure exactly where he is coming from, but I agree there may appear to be an inconsistency when I use singular terms like 'Socrates' to refer to non-present, and therefore non-existing individuals.

I explained this a while back. See this post and the posts it links back to. The verb 'refers to' is, I claim, a logically intransitive verb. This concept I have tried to explain to the Maverick on many occasions, with little apparent success (smiley face icon).

Priscian's Institutiones Grammaticae

Priscian's Institutiones Grammaticae now available (Latin version only) in the Logic Museum annex. I had ignored Priscian before, thinking of him as a grammarian. Which he is, mostly, but there are interesting philosophical and logical insights in this enormous work. Such as that the present time is that of which part is past, part is future (Book 8, p. 414). Scotus uses this to explain how a sentence in the present tense (e.g. "Robert is just passing through the door") may be true even when the event it refers to may just be over.

Praesens tempus est cuius pars praeteriit, parsque futura est

Snow in London

Alan Rhoda has been defending the idea that there must be some necessary connection between the present and the future in order for propositions about the future to be true or false. I restate his argument as follows. A true proposition depends on what exists - a 'state of affairs' - for its being true. The state of affairs that makes the proposition true at some particular time must exist also at the same time. Accordingly, it cannot be true now that there will be snow in London tomorrow, unless this truth 'supervenes upon present reality', i.e. there is some existing state of affairs which makes this proposition about the future true. Which is absurd. Why should snowing in London tomorrow be logically connected with any state of affairs existing today?

The mistake lies in his assumption that what makes a proposition true at some time must exist at that same time. Certainly there is a connection between truth and existence. This was recognised by the scholastic philosophers of language. Unumquodque sicut habet esse, ita et veritatem "As each thing is in respect of being, so it is in respect of truth", taken from Aristotle Metaphysics book 2 (993b 31). A proposition signifying that some state of affairs exists, is true or false depending on whether that state of affairs exists or not.

A corollary of this is what I shall call the Adequacy Principle: that the state of affairs signified to exist by the proposition can be no more (and no less) than what makes the proposition true. Otherwise, suppose a proposition signifies the existence of more than what is required to make it true, e.g. suppose that it signifies the existence of X and Y, but Y alone is sufficient to make it true. Then so long as Y exists, the proposition will be true, even if X does not exist, and even though the proposition signifies that X does exist. This is impossible, therefore a proposition can signify the existence of absolutely no more than what is sufficient to make it true. (A similar argument proves that a proposition can signify the existence of no less than what is necessary to make it true, but that is not relevant here).

From the Adequacy Principle it follows that a proposition in the future tense, signifying that some state of affairs Y will exist, depends for its truth on the future existence of Y, and nothing else, particularly nothing else in the present. The proposition 'It will snow in London' can be analysed as

* Snowing in London will be the case

which signifies that the future state of affairs 'snowing in London' will exist. It signifies no more than that, in particular, it does not signify that some state of affairs X exists now. Why should it? It may be that some present state of affairs (large cold front sweeping in from Siberia) will be the cause of the snow. But the proposition in the future tense has nothing to say about cold fronts.

Scotus on future contingency

I mentioned in this post last year that I was working on Scotus' discussion of the problem of future contingents, in his Questions on the Perihermenias, and I said I would discuss it in the future. Alan Rhoda's post on 'alethic openness' has finally got me round to doing so. Alan writes:

For a proposition to be true, what it represents as being the case must
correspond to reality, to what is the case. Likewise, for a proposition to be
true now, what it represents as being the case must correspond to present
reality, to what is the case now. [my emphasis]

Scotus discusses a claim very similar to this in Book I of the Questions, qq 7-9. He disputes the claim apparently made by Rhoda above, namely that the truth of a proposition about the future must correspond in some way to 'present reality'. He writes:

It must be understood that a proposition about the future can be understood to
signify something in the future in two ways. So that the proposition about the
future signifies it to be true now that something in the future will have to be
true [verum esse habebit] (for example, that ‘you will be white at a’ signifies
it now to be in reality so that at time a you will be white). Or it can be
understood that it signifies now that you will be white then: not that it
signifies that it is now such that then you ought to be white, but that it
signifies now that then you will be white. For to signify it to be [the case]
now that you will be white at a, signifies more than to signify that you will be
white at a.

It rather hangs upon what Rhoda means by 'true now'. Scotus argues for something like a redundancy theory of future truth. A proposition that says that S will be P so is (now) true iff it will be P, and false if it will not be P. If you mean by 'is now true' something like 'something exists now in reality that makes the proposition true' then Scotus would disagree (and so probably would I). If you mean that 'now' simply indicates the present tense of the 'is' in 'is true', then this is harmless and trivially true.

I think Scotus puts this very neatly, and we do have to take seriously his claim that "to signify it to be [the case] now that you will be white at a, signifies more than to signify that you will be white at a."

See also my discussion of rain tomorrow.

The Frozen Present

I am translating Scotus' questions on Aristotle's On Interpretation (the Peryhermenias) and have reached the part where he discusses the problem of future contingents. Scotus' take on this is interesting and I will discuss it in a future post. Meanwhile I am reading around the subject. I dusted off Gilbert Ryle's Dilemmas, which was one of the first philosophy books I read, a discussion by Prior in a paper called 'It was to be', and older discussions by Boethius, Abelard. Today it is Aquinas. He writes (in his commentary on the Peryhermenias, I l 15. n2).

Omne quod est necesse est esse quando est, et omne quod non est necesse est non
esse quando non est. Et haec necessitas fundatur super hoc principium:
impossibile est simul esse et non esse: si enim aliquid est, impossibile est
illud simul non esse; ergo necesse est tunc illud esse. [my emphasis]

I.e. everything that is the case, is necessarily the case, when it is the case. This is because (he argues) it is impossible that the same thing should be the case, and not be the case at the same time. At first sight his argument seems absurd. It is sunny now. Might it not be sunny now? Of course. And this doesn't involve supposing a contradiction, because although 'it is sunny' is true now, to suppose that it were not sunny now involves supposing that 'it is sunny' is not true now. So no contradiction is involved. Aquinas seems to be confusing the possibility of its being p, but being possibly not-p, i.e.

possibly( p and possibly not-p)

which does not involve a contradiction, with the possibility of being p and not-p, i.e.

possibly( p and not-p)

which does involve a contradiction.

Or does he mean something else? Is he denying the sort of 'instantaneous counterfactual' that we take for granted in modern philosophy? In everyday life, we take it for granted that the realisation of any possibility takes time. Might it not be sunny? Only if the clouds pass in front of the sun. But when the clouds pass in front of the sun, it will not be now, and the qualification 'when it is sunny' no longer applies. Time must pass in order to realise the possibility. Perhaps this is the meaning of Aquinas qualification 'when it is p' (quando est). This would be consistent with Augustine's view that God cannot change the past, because would be to turn what was the case, into what wasn't the case. For the same reason, he cannot change the present. For if it took take time to do that, it would no longer be the present. If it did not, this would be turning what is the case, into what isn't. See The Frozen Past.

The Frozen Past

Most scholastic philosophers, with the exception of St Peter Damian, say that God cannot change the past.

St Thomas includes it on his list in Summa Contra Gentiles (II. 25) of what God cannot do (Deus non potest facere quod praeteritum non fuerit). In
On Eternity he says that the proposition that the past did not exist contains in itself a contradiction. For which reason Augustine says in the book against Faustus [xxvi c.5] 'Anyone who says "If God is omnipotent, let him bring it about that those things which happened, did not happen", does not see that he says 'If God is omnipotent, let him bring it about that those things which are true, are false in that very thing by which they are true' [PL 42, 481.].

The problem with this is that it is a logical argument, and for that reason it applies to the future as well as the past. Paraphrasing Augustine, 'The Future' means 'those things which will happen', and God cannot bring it about that the Future will not happen they way it will, otherwise we have the contradiction that those very things which will happen, are not those very things.
Yet we are more tempted to say that God could change the future. The future is not frozen in the way the past seems to be. But if this being frozen is not a logical being, what is it?

Ockham on Past and Future

The latest exhibit in the Logic Museum is a parallel Latin English translation of Ockham's theory of past and future tenses, in chapter 7 of book II of his Summa Logicae. Find it here. It is connected with the discussion going on below concerning the problem of supplying truth conditions for past and future tense propositions.

Rain tomorrow

"There is some actual state of affairs which constitutes its now being the case that it’s possible that it rain tomorrow"

But is this actual state of affairs is the same state of affairs as the state of affairs which will obtain when it rains tomorrow? This seems to be the argument.

1. A statement must be true or false, and so there must be conditions under which it is true.

2. To state the conditions when a given proposition is true, is to say what IS the case, if it IS true. Merely to state the truth conditions is to specify something that exists now.

3. Thus statements about the future can be reduced to statements in the present tense. For if the truth condition obtains, the statement that it obtains, is true now. If it does not obtain, the statement that it does not obtain, is true now.

But why should the truth conditions be in the present tense? I agree that a proposition like 'Tom thinks it will rain tomorrow' says something about the present. It says that Tom has a certain thought, right now, in the present. Similarly 'the weather forecaster says it will rain tomorrow' says something about what the person on the TV says, now. Likewise 'It is causally determined that it will rain tomorrow'. Similarly also for 'it is possible that it will rain tomorrow', which says something about the speaker's present state of knowledge.

But 'it will rain tomorrow' doesn't say anything about the present. 'It will rain tomorrow' is true if and only if it WILL rain tomorrow.