FOM: Frege hath said it (logical priority)
finn.spicer at kcl.ac.uk
Fri Mar 8 04:00:41 EST 2002
On 7/3/02 10:25 pm, "Dean Buckner" <Dean.Buckner at btopenworld.com> wrote:
> Argument: a discussion in which reasons are put forward in support of a
> proposition. One such reason can be "Aristotle hath said it" (and who
> argued that?)
> Here is my argument again.
> 1. Children from an early age (before 2) grasp the concept of "other"
> (here's one foot, point to the other)
> 2. For there to be one thing and for there to be another thing, is for
> there to be two things.
> 3. To grasp that there is one thing & another thing, is to grasp there are
> two things (even though can't grasp how to use the word "two")
> 4. (so) Children under the age of two can grasp something like the concept
> of number
> 5. But can they grasp Hume's principle? this is to understand not only the
> concept of "same number", but to grasp a particular condition attached to
> there being the same number
> I can see plenty of things to challenge in this, so please challenge it. No
> more Aristotle, no more Frege. They would not approve.
Here's an objection: 4. does not follow from 3. It is not in general true
that when a child grasps some particular concept, then the child must also
grasp a more general concept, and so the claim needs special defence in this
instance. Such a defence might be perhaps by arguing that the particular
concept is part of a system of concepts that exhibits a local holism,
grasping one, the child grasps them all. This holism might well be the case
for grasp of the concept of 2. Perhaps there is a 2-concept which one grasps
as part of grasping a cluster of concepts - those of the other small numbers
. But this 2-concept might not be the only 2-concept; the holistic 2-concept
might be that 2-concept which corresponds to a mastery of word 'two', while
other 2-concepts do not correspond to this mastery (that there are such
different 2-concepts is implied by premise 3., while that premise explicitly
says that there is no such mastery).
So what would be required to get 4. from 3. is an argument that the concept
ascribed in 3., despite not being one delivering a mastery of the word
'two', exhibits a local holism which includes grasp of a number concept.
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