Monday, March 26, 2012

On donkeys and deformed thinking

I found the Wittgenstein quotation I was thinking of, which is in the Logic Museum here.
"Mathematical logic" has completely deformed the thinking of mathematicians and of philosophers, by setting up a superficial interpretation of the forms of our everyday language as an analysis of the structures of facts. Of course in this it has only continued to build on the Aristotelian logic.
It's what he says about Aristotelian logic which is the interesting one. There's a school of thought in the medievalist world according to which Aristotelian (scholastic) logic is somehow more faithful to ordinary language than modern mathematical logic. Wittgenstein would clearly have disagreed. I have also been looking at the donkey sophism in Worcester 13 again. The problem is that 'every man's donkey is running' has the form 'every A is B', where A = man's-donkey and B = running. According to Aristotelian logic 'every A is B' and 'every A is non-B' are contraries, they can't both be true at once. But clearly the ordinary language sentences 'every man's donkey is running' and 'every man's donkey is not running' can both be true at the same time, namely in the case where every man has two donkeys, one of which is running and the other of which isn't. It's not a problem for ordinary language at all. But it is a problem for the Aristotelian formalism of the sentence. In that formalism every sentence has two terms, joined by a copula and a quantifier attached to the subject term. It is a procrustean bed which fits our actual thinking very badly, in some cases.

I also noticed this other comment by Wittgenstein in the same place:
The curse of the invasion of mathematics by mathematical logic is that now any proposition can be represented in a mathematical symbolism, and this makes us feel obliged to understand it. Although of course this method of writing is nothing but the translation of vague ordinary prose.
What on earth does he mean by that?

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12 Comments:

Blogger Anthony said...

So according to you, "every man's parent is female" is a true sentence?

I don't agree. And I think if you polled 10 random English speakers, at least 9 of them would also disagree.

"Every A is B" implies "A non-B A does not exist".

6:02 pm  
Blogger Anthony said...

You agree that "every parent is female" is false, right?

6:18 pm  
Blogger Edward Ockham said...

>>You agree that "every parent is female" is false, right?

It's clearly false. But 'everyone's parent is female' is true, on a certain reading (i.e. everyone has a parent who is female).

>> if you polled 10 random English speakers, at least 9 of them would also disagree.

They would disagree in respect of a different reading of the sentence.

8:05 pm  
Blogger Anthony said...

"They would disagree in respect of a different reading of the sentence."

So you agree you are using a sentence which the vast majority of people would not understand in the way you intend it, and you think there's nothing wrong with that?

At the very least you shouldn't say that "clearly the ordinary language sentences...can both be true at the same time". It's not clear at all.

11:57 pm  
Blogger Edward Ockham said...

1. Jane is John's parent and she is female
2. Jean is Jack's parent and she is female
3. Jackie is Joe's parent and she is female
... and so for every man

Thus, every man's parent is female.

7:19 am  
Blogger David Brightly said...

>> Every man's parent is female <<

Interesting example. I tend to side with Anthony but this is a bit more compelling...until you notice that 'is John's parent' etc can be read in at least three ways:

a) 'is a parent of John' (is=indefinite identity not implying uniqueness)
b) 'is the parent of John' (is=definite identity implying uniqueness)
c) 'is parent to John' (is=qualification)

Only the (b) interpretation yields the conclusion. In particular, in (c) 'parent' is adjective-like but in the conclusion it is noun-like. Ambiguity reigns, I think.

8:39 am  
Blogger Anthony said...

That's not how the English language works.

You are speaking a language other than English.

The sentence you are looking for is "Every man has a female parent." This is not equivalent to "Every man's parent is female."

12:01 pm  
Blogger Anthony said...

I think I figured out the construction you are trying to use:

"A parent of every man is female."

12:24 pm  
Blogger Edward Ockham said...

>>The sentence you are looking for is "Every man has a female parent." This is not equivalent to "Every man's parent is female."

I concede that the genitive-nominative construction (John's parent) has an implied definite sense,= 'the parent of John'. This suggests wrongly that John has only one parent, i.e. suggests uniqueness. Latin of course has no definite article.

3:03 pm  
Blogger Edward Ockham said...

>>"A parent of every man is female."

No, that implies that every man has the same parent, and that she is female.

3:04 pm  
Blogger David Brightly said...

>> No, that implies that every man has the same parent, and that she is female. <<

Oh dear. Forget Latin, now we don't agree about English meanings. You read "A parent of every man is female" as

∃p. ∀m. parent (p,m) ∧ female (p)

whereas I see it as

∀m. ∃p. parent (p,m) ∧ female (p)

so we differ in how we order the quantifiers. One nice aspect of the language of predicate calculus is that it is both compact and unambiguous. Compact English/Latin renderings can tend towards ambiguity, I suspect.

I guess your interpretation has the word ordering on its side:

A (parent of every man) is female.

I suspect I reject this reading because I'm influenced by the meaning of 'parent' and know that, in general, several men have no parent in common.

8:35 am  
Blogger Le Master said...

1. Everyone's parent is female.
2. Everyone's parent is male.

Both are still true in the Aristotelian sense; they aren't contradictory. Parent =/= parent. They're simply the same spoken and written word, but they are not the same object.

2:57 am  

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