Sunday, 26 August 2007

Truth and Consequence

Auriol has been leading me a merry dance this month. Besides the disjunction business, he says that verum non sequitur nisi ex vero, i.e. truth only follows from truth.

This principle has to be severely qualified before it can even begin to pass muster. The obvious types of counterexample (‘Grass is blue, therefore grass is coloured’, ‘I have hands and a rhinoceros, therefore I have hands’) can be dismissed if he's talking about formal consequences from one categorical proposition to another. But even then the principle falls foul of the mediaeval insistence on the existential import of universal affirmations, which licenses the inference ‘Every man is white, therefore some man is white.’

Has anyone else come across a similar principle elsewhere?

7 comments:

Ocham said...

A quibble. We should distinguish

(A) If every chimaera is a chimaera, some chimaera is a chimaera

from

(B) If some chimaera is a chimaera, some chimaera exists.

since one might reasonably agree with the categorical proposition (A) but not with the existential proposition (B), i.e. 'existential import' strictly means not (A) but (B).

Indeed, a lot of 13C scholastics (the 'intentionists') held just this view.

But this does not detract from your main point.

Brunellus said...

Just to clarify two points:
(i) since (A) and (B) are hypotheticals, I take it you're talking about the consequent in both cases;
(ii) should "some" in (B) be "every"?

If every chimaera is F has existential import – that is, if (unlike universally quantified propositions in modern logic) its truth requires there to be a chimaera – isn't that enough to license the inference to some chimaera is F?

(I suspect you may be reading something different into my phrase ‘existential import’.)

Ocham said...

Just to clarify two points:
>> (i) since (A) and (B) are hypotheticals, I take it you're talking about the consequent in both cases;

No, the whole thing.

>>(ii) should "some" in (B) be "every"?

Could be, doesn't really matter, since 'every A is B' implies 'some A is B'. The question is whether 'some A is B' implies 'Some A-which-is-B' **exists**.

>>If every chimaera is F has existential import – that is, if (unlike universally quantified propositions in modern logic) its truth requires there to be a chimaera – isn't that enough to license the inference to some chimaera is F?

Again, you need to distinguish the question of whether 'every A is B' implies 'some A is B', which it does in traditional logic, but doesn't in modern logic, from the question of whether such categorical statements imply existential statements. Definition: a categorical statement uses the word 'is' (as the copula), an existential statement uses the word 'exist' (or the verb 'is' secundum adiacens, ie. as a predicate.


>>(I suspect you may be reading something different into my phrase ‘existential import’.)

I may be, but I don't think so. I think you mean that an assertion has 'existential import' if it implies 'some A is B'. Whereas, correctly, a statement has existential import only if it implies an existential proposition. 'some A is B' is not an existential proposition (although it may imply one).

You may find this useful:

http://uk.geocities.com/frege@btinternet.com/opposition/brentanoinnovations.htm

Ocham said...

rats, the link failed. Google

brentano's logical innovations

to get the paper in question.

Brunellus said...

On (i), you surely can't be talking about the whole thing when you say "the categorical proposition (A)", because (A) is not a categorical proposition. It's a hypothetical proposition, that is, a proposition formed from two or more categorical propositions. (At least, so I understand from Shirewood, Burley, Ockham and Buridan.) Hence my suggestion that you were instead talking about the consequents.

In any case, I now see what you're saying. I must say it had never occurred to me that 'some A is B' might not have existential import. Thanks for the article, which I'll be sure to read. (By the way, is anyone bothered by the fact that e.g. 'some man is white' is barely English? Plurals are fine. But the nearest we get to 'some man' is in e.g. 'some guy told me', where it seems to be a variant of 'someone'.)

From a corner of my mind the name Fred Sommers emerges. I'd be interested to hear what you think of him.

Ocham said...

Sorry, I did indeed write

>> with the categorical proposition (A) but not with the existential proposition (B),

meaning of course, the categorical proposition *in* A. I.e. the consequent, as you say.


>> Hence my suggestion that you were instead talking about the consequents.

As indeed I was, sorry.

>>By the way, is anyone bothered by the fact that e.g. 'some man is white' is barely English?

Well there's a lot of English 'translation' of medieval Latin that is barely English. You try and translate in a way that is intelligible, but then you are faced with the problem that the Latin often reflects how they actually *thought*, and so you leave it in a barely intelligible state.

In any case, we do say things like 'some guy is on the phone'.

>>From a corner of my mind the name Fred Sommers emerges. I'd be interested to hear what you think of him.

Quite obviously he was a strong influence.

Other bits and pieces. I got your message on 'Hello World' which I stupidly replied to, despite it is a no reply thing. In summary, thanks for the material which I am reading with interest, and will provide hours of amusement. I've already started on Distinction 8 which is about essence and existence. In fact, there is something truly interesting there because on p. 891 (p. 422 in the pdf) you come across the sentence 'Praeterea, non debet poni superfluum aut aliqua distinctio sine causa, quia frustra fit per plura quod potest fieri per pauciora'. The last phrase (beginning 'frustra') is one of Ockham's famous formulations of 'Ockham's razor'. Note that he never actually said 'entities should not be multiplied beyond &c'. Here, Auriol is giving an identical formulation. But it may be a Franciscan expression, and I think Scotus used it.

On the other piece you sent me, you haven't given me much time to look at it, but I'll try. I've already read it through – note future contingents is not my area at all, but I'll give it a try.

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