Friday, April 06, 2012

Subsumption and subordination

Maverick dedicates his post here to me, saying that I like “sophisms and scholastic arcana”. Yes, and Fregean arcana too, Bill, heh heh. His post is about the odd-looking inference

Man is a species; Socrates is a man; ergo, Socrates is a species.

Note that the scholastics would have resolved this by treating the conclusion as a reduplicative proposition: Socrates insofar as he is a man, is a species, but never mind that. Maverick goes on to discuss the ‘modern’ Fregean treatment of propositions like ‘man is a species’. According to Frege, a universal proposition like ‘every man is an animal’ has a fundamentally different form from ‘Socrates is an animal’. In the former, one concept is subordinated to another: the concept ‘man’ is said to be subordinate to the concept ‘animal’. In the latter, the individual Socratres is subsumed under the concept ‘animal’.

Fregegives some very bad arguments for this in his famous essay ‘On Concept and Object’, but I won’t discuss those now. For the moment, here are two arguments against his view.

1. Argument from obviousness. It is obvious that ‘every man is animal’ does not say that one concept is subordinate to another, for the simple reason that it does not say anything about concepts at all. What it says is that every man is an animal. Thus, Socrates is an animal, Plato is an animal. It is talking about every man, not about some concept.

2. Frege’s position requires taking on the absurd idea of ‘object dependence’, i.e. that the meaning of a proper name depends on the existence of some object referred to. I discuss this at length here, with reference to another less well-known essay of Frege's*. Briefly, if we allow that a proper name N can be meaningful and empty, there must be some relation which holds between the name and its referent when its referent exists, and which fails to hold when there is no referent. But then a proper name is not essentially different from a common name like ‘man’. We can say ‘there are no men’ if nothing falls under the meaning of ‘man’, and we can say ‘there is no Socrates’ if nothing falls under the meaning of ‘Socrates’. Frege correctly rules this out as inconsistent with the concept-object distinction. In summary: the distinction between ‘subordination’ and ‘subsumption’ implies and is implied by the object-concept distinction. And the object-concept distinction implies and is implied by the position that the meaning of a proper name is object-dependent.

*Though I note that Maverick mentions this essay, at second-hand, in his book here.

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7 Comments:

Blogger Jason Hills said...

Excellent discussion. Very clear.

4:56 pm  
Blogger David Brightly said...

Against (1): 'every man is an animal' is the extensional counterpart to the intensional 'a man is an animal' and this is equivalent to 'the concept Man is subordinate to the concept Animal'.

Against (2): The argument here appears to be that on the background assumption that there is an object-concept distinction then a certain further assumption, A, leads to a contradiction, namely, that there is no object-concept distinction. Hence this further assumption A must be false. Your claim is that A is that there are (or can be) meaningful empty proper names. If this is right then it looks as if Frege, wishing to maintain the O-C distinction, is forced to adopt the view that there can be no meaningful empty names. But I say that the assumption we have shown to be false is the conditional

'if (we allow that) a proper name N can be meaningful and empty, [then] there must be some relation which holds between the name and its referent when its referent exists, and which fails to hold when there is no referent'

This isn't obviously true and your own well-argued position on reference is that though there can be meaningful empty names there is no such reference relation. That is, the assumption is indeed false.

11:16 pm  
Blogger Anthony said...

I have to go with equivocation on man:

def 1: an individual human
def 2: the human race

Also, there is a missing article. A man is an animal. Not "Man is an animal." Man is a species. Not "A man is a species." Socrates is a man. Not "Socrates is man."

As usual, this is probably much more ambiguous in Latin, with its lack of articles.

12:40 pm  
Blogger Edward Ockham said...

>> the intensional 'a man is an animal' ... is equivalent to 'the concept Man is subordinate to the concept Animal'.

Is this a definition of 'intensional'? In which case, prove that 'every man is an animal' has an intensional meaning, i.e. is equivalent to "the concept Man is subordinate to the concept Animal"

>>This isn't obviously true and your own well-argued position on reference is that though there can be meaningful empty names there is no such reference relation. That is, the assumption is indeed false.
<<

Yes, correct. I was merely arguing for the enemy here.

12:46 pm  
Blogger David Brightly said...

>> In which case, prove that 'every man is an animal' has an intensional meaning, i.e. is equivalent to "the concept Man is subordinate to the concept Animal"<<

If the concept Man is subordinate to the concept Animal (intensional, about concepts) then in every possible world and context an instance of Man is an instance of Animal. Hence every man is an animal (extensional, about objects).

But there is no equivalence. From the extensional 'every man is a bald-thing' it does not follow that the concept Man is subordinate to the concept Bald-Thing. It may just happen to be the case that in some context and world every individual that falls under Man also falls under Bald-Thing.

I have a critique of Bill's original post here. I imply there agreement with Anthony that articles offer valuable clarification of meaning.

3:54 pm  
Blogger Edward Ockham said...

Hmm. This requires the assumption that there are 'concepts', i.e. objects that bear some semantic relation to common nouns. And the relation 'falls under' such that an individual 'falls under' the concept signified by 'man', iff that individual is a man.

OK. But my original claim was that 'every man is an animal' does not say that every individual falling under the concept 'man' also falls under the concept 'animal'. Understanding 'every man is an animal' does not require understanding what 'concepts' are.

5:32 pm  
Blogger David Brightly said...

>> This requires the assumption that there are 'concepts', <<

Yes. I had been wondering how long it would take us to backtrack to the point of abandoning concept talk.

>> Understanding 'every man is an animal' does not require understanding what 'concepts' are. <<

Perhaps, but once we realise 'a man is an animal' is true even when there are no men or animals we aren't far off.

11:13 pm  

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