Monday, December 12, 2011

Quantifying over

In an earlier post I asked whether some men are not men. Intuitively all men are men, and so ‘some men are not men’ is false. Yet if the term ‘man’, occurring in the subject position of a sentence, means something like ‘someone who is, was or will be a man’, and given that Caesar was once a man, but is no longer a man, i.e. not now a man, it seems to follow that some men (e.g. Caesar) are not men, i.e. were men but aren’t now. Thus, counterintuitively, some men are not men. From this we derived the even more puzzling ‘some present events are not present events’. Caesar’s crossing the Rubicon was once a present event. And if ‘present event’ means ‘event which is, or was once, or will be present’, and since Caesar’s crossing the Rubicon is not present, it apparently follows that at least one present event (crossing the Rubicon) is not a present event.

David Brightly, taking the approach of a contemporary logician, helpfully suggests that “we just stipulate in advance which men we propose to quantify over and this bounds what 'some man' may refer to. It could be men alive, dead or alive, living in Midsomer, ever been married, whatever is appropriate, as long as we make it explicit and make appropriate adjustments elsewhere.”

I object that it is a problem either way. If the English word ‘man’ in fact only means presently existing man, it immediately follows that we can’t quantify over men in the 13th century, for there are none to quantify over. Nor were there any. ‘Some man lived in the 13th century’ is false, unless there is a 700 year old man still alive. The question is what the word ‘man’ ranges over. If only presently existing entities, then there were no men alive 10 years except for those alive now, thus very few men who were alive 90 years ago. Census records are all false. There were not 7 million people living in London in the 1920s. More like a few thousand (namely all present Londoners who are old enough to have lived here 90 years ago).

If by contrast we accept that there were 7 million Londoners in the 1920s, we have to accept that most of these, namely the ones who have died, are no longer Londoners. Thus, some Londoners are not Londoners. You can’t escape the problem by specifying ‘domains of quantification’.

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21 Comments:

Blogger Anthony said...

"If by contrast we accept that there 7 million Londoners in the 1920s..."

It is fitting that you forgot the verb :).

5:22 pm  
Blogger Anthony said...

Hmm, according to Stanford Encyclopedia of Philosophy, Brentano, in *Psychology*, says "Some S are not P" means "There is an S and that S is not P". Filling in "men" and "men", we get "Some men are not men" means "There is a man, and that man is not a man". But this is false.

Furthermore, Brentano says (same source) that "All S are P" means "There is no one who correctly judges 'Some S are not P'". Are you denying that all men are men?

http://plato.stanford.edu/entries/brentano-judgement/

5:36 pm  
Blogger Edward Ockham said...

>>It is fitting that you forgot the verb :).

Thanks. Fixed.

5:38 pm  
Blogger Anthony said...

Are you denying that all men are men?

And if so, how can we say that all men are rational animals? Must we say "All men who were men were rational animals, all men who are men are rational animals, and all men who will be men will be rational animals"?

5:40 pm  
Blogger Edward Ockham said...

>>Hmm, according to Stanford Encyclopedia of Philosophy, Brentano

Let's take Brentano according to Brentano, who I quote here.

Admittedly your problem remains.

5:41 pm  
Blogger Edward Ockham said...

>>Are you denying that all men are men?

Of course.

5:42 pm  
Blogger Anthony said...

>> Let's take Brentano according to Brentano, who I quote here.

The categorical proposition "Some man is not learned" has the same meaning as the existential proposition "A non-learned man exists" or "there is a non-learned man".

>> Admittedly your problem remains.

Right. "Some men are not men" becomes "A non-man man exists", which you agree is false, right?

5:54 pm  
Blogger J said...

Brightly's obvious point (living humans vs dead men) re the existential import of "some" has been known, what...500 years or so.

Thats not Brentano's main issue which was about the status of the negation of...whimsical/fictional entities ...say, Pegasus, Hamlet , Gandalf, etc.

7:12 pm  
Blogger Edward Ockham said...

>>Right. "Some men are not men" becomes "A non-man man exists", which you agree is false, right?
<<

Right :(

8:24 pm  
Blogger Anthony said...

>> If the English word ‘man’ in fact only means presently existing man, it immediately follows that we can’t quantify over men in the 13th century, for there are none to quantify over.

"Man" means all men: past, present, and future.

The problem, it seems, is presentism.

9:30 pm  
Blogger David Brightly said...

Let's consider the women called Elizabeth that are or were queens of England. We could call such ladies QQEEs---quondam queen Elizabeths of England. There are two of them: the daughter of Anne Boleyn whom I'll call Liz1 and our own dear queen Liz2. Surely we can talk of the QQEEs. I would like to say 'Liz1 is a QQEE' but I guess that you will say this is false because she no longer exists and cannot be predicated of in the present tense. I say that this is of no consequence. No proposition of the history of England need mention the predicate 'is a QQEE'. Rather it appears to be a kind of 'meta-predicate' used in defining who we are talking about. A careful formulation is rather tricky, I think, involving textual substitution of names into quoted sentences*, so I'll stick to the 'are or were' recipe which everybody understands.

Returning to your example, we have two disjoint sets: the ex-Londoners and current-Londoners. The ex-Londoners were Londoners, but are no longer Londoners. The current-Londoners are Londoners. Ordinary usage would tend to say that all these people are Londoners, but as you have pointed out this leads to a degree of trouble. With care over tense the problem vanishes. Am I wrong? And is there a glimmer of an argument against DR in here?

(*) I suspect that the Maverick's paradoxical truthmaker definition that we discussed recently works in a similar way.

9:45 pm  
Blogger Anthony said...

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10:33 pm  
Blogger Anthony said...

>> Ordinary usage would tend to say that all these people [ex-Londoners and current-Londoners] are Londoners

No, I don't think that's right. X is a Londoner implies that X is a current-Londoner. X was a Londoner implies that, at some time in the past, X was a then-current-Londoner.

All Londoners are Londoners is ambiguous, but either way it is true. It could mean (at all times in the past, all then-current-Londoners were then-current-Londoners) AND (all current-Londoners are current-Londoners) AND (at all times in the future, all then-current-Londoners will be then-current-Londoners). Which is true. Or it could mean only that all current-Londoners are current-Londoners. Which is also true.

On the other hand, "All creatures with hearts have kidneys." is, by the latter interpretation, true. Whereas "All creatures with hearts have kidneys.", by the former interpretation, may not be.

10:35 pm  
Blogger David Brightly said...

Ed, knowing that you put these posts together under some time pressure, I tend not to read you too closely. But sometimes much hinges on a close reading. Your first para here is a case in point. You move from 'Caesar is no longer a man' to 'some man is no longer a man' and hence to 'some men aren't men'. But the first inference requires 'Caesar is a man' which your premise emphatically denies. So the argument to a paradoxical conclusion is invalid. That's not to say that there isn't a problem here. I think it appears in its starkest form, as I tried to show in my quondam queens example, if we argue as follows: 'Liz1 does not exist'; therefore 'Liz1 is not an individual'; therefore, by EG, 'some individual is not an individual.' I think this is the argument that's trying to get out. Do you agree? And if so, what's wrong with it?

11:59 am  
Blogger Edward Ockham said...

Thank you for understanding about time pressure – I sometimes omit key bits of an argument. Of course I reject ‘Caesar is a man’, but only because if the present tense ‘is’. I hold that of no once-but-no-longer-existing individual can truly be the subject of a verb in the present tense. Thus ‘Caesar is a man’ is false. However ‘Caesar was a man’ is true, and by conversion ‘some man was Caesar’ is true. So ‘man’ can be use in the subject or predicate position, to range over individuals who no longer exist. But this leads to the paradox that, given the falsity of any present tense statement involving that subject, ‘some man is not a man’ seems to be true.

I think I also agree with you about the argument 'trying to get out', for the same reason.

12:14 pm  
Blogger J said...

actually Aristotle himself was aware of the "existential import" issue (google it yrself), and it was the default position (as was the change issue). It's the scholastics who quibbled over the issue.

Tho' we can say "some Dogs are brown" AND "some Pegasuses are brown". The problem then about...what "exists" not the merely syllogistic.

3:44 pm  
Blogger Anthony said...

>> I hold that of no once-but-no-longer-existing individual can truly be the subject of a verb in the present tense.

That's trivial. No non-existing thing can truly *be* anything.

But the word Caesar is certainly the subject of the sentence "Caesar is dead."

8:41 pm  
Blogger Anthony said...

>> However ‘Caesar was a man’ is true, and by conversion ‘some man was Caesar’ is true.

That's not a proper conversion.

"My girlfriend was a 5 year old." does not convert to "Some 5 year old was my girlfriend."

8:50 pm  
Blogger David Brightly said...

Ed,
Let Ltx denote 'x is/was a Londoner at time t. Let 0 denote present time and negative numbers earlier time. L0x says 'x is a Londoner now'. Then ∃t.Ltx says 'x is/was a Londoner at some time'. Write this as L*x. L* is a 'quondam predicate' with no time argument. L*x is tenseless. It just predicates something of x independently of time. In ordinary English we'd have to use the present tense: 'x is a quondam Londoner' even if x does not exist at present. Does this cast doubt on your principle that no once-but-no-longer-existing individual can truly be the subject of a verb in the present tense?

We can render 'some Londoner is not a Londoner' in two ways: (a) ∃x.L0x∧~L0x, of course false, and (b) ∃x.L*x∧~L0x which can be true. (b) is better rendered 'some quondam Londoner is not a Londoner'. But it's at the price of introducing this untensed predicate L*.

10:16 pm  
Blogger David Brightly said...

Oops, too used to using 'is' tenselessly. Of course we can say 'x was a quondam Londoner' if x no longer exists, meaning 'x was a Londoner at some time'. My second para is OK. I think.

The extension of the '_is a Londoner' predicate varies with time. So the range of individuals that 'some Londoner' covers is not fixed either. Is this elision of the time in ordinary English the source of the problem?

10:35 pm  
Blogger J said...

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11:36 pm  

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