Friday, March 14, 2008

Chad McIntosh defends the Conceptualist Argument


Ilíon said...


Victor Reppert said...

The one I posted seems to be of much more recent vintage.

Ilíon said...

I couldn't remember which of the two blogs is the older (that is, which he abandoned in moving to the other) ... and I didn't think to scroll down to the comments section, which actually has some dates.

One Brow said...

I leave with you the comment I left over there.

These virtues considered, however, fictionalism is perhaps too radical. The most jarring problem is its renunciation of obviously true descriptive states of affairs the truth of which seem to be grounded in certain abstracta like “2 + 2 = 4” or “two entities x and y can have the same shape and size.” For according to fictionalism, such abstracta are merely useful fictions. Indeed, it will be hard to take seriously a view which maintains that propositions such as “4 is divisible by 2”, “Jones believes that [some proposition x]”, or “triangles have three sides” are not just false, but literally truth valueless.

Well, that would depend upon the rules set up to establish the useful fiction, would it not? After all, isn't "useful fiction" in some ways another term to describe a formal system? We would find a fiction where 4 is not divisible by 2 to be not very useful, but that does not impart some sort on inherent falsity, especially since the notions of "true" and "false" are in and of themselves merely useful fictions.

If Tennet’s argument passes, then fictionalism must be false. His argument can be outlined as follows:

(2a.4) There is no possible world such that there are no things that are not self-identical
(2a.5) 0 is the number of such things that are not self-identical
(2a.6) Therefore, 0 exists in all possible worlds

Does Tennet’s argument pass? (2a.4) is self-evidently true, so what support does Tennant give for (2a.5), the argument’s main premise? On the face of it, (2a.5) seems to beg the question against the nominalist by introducing the existence of a number into the premise.

On the contrary, 2a.5 is an instance of the use of a useful fiction to describe a situation, and is true under our usual understanding of 0. It is 2a.6 that introduces the concept of numbers being real, with no justification. 2a.6, without the extra assumption, would read: 0 is useful in every possible world.

The grounds for 2a is completely circular, in that you need the assumption the number is real to derive it.

Wesley Morriston concisely summarizes the problem:

Let m = the number of books in our infinite library, n = the number of odd-numbered books, and o the number of books numbered 4 or higher…
(m – n) = infinity, whereas (m – o) = 4.
n = o (since both n and o are infinite)
It follows that we get inconsistent results subtracting the same number from m.19

The conclusion is that we obviously couldn’t perform such operations in the actual world, so an actual infinite cannot exist.

This argument merely proves that subtraction is not well defined for infinite numbers. Since the definition of infinite is a set that is the same size as a proper subset, this is hardly surprising.

Anonymous said...

One Brow,

See my reply.

exapologist said...

Wow -- that's spooky. Clicking into Chad's blog is like stepping into a Lewisian world where I meet one of my counterparts who remains a believer through grad school. It's like we think all the same thoughts, make all the same moves, read all the same books, have all the same interests,etc. Weird.

Ilíon said...

Wistful for what you chose to discard?

exapologist said...


Anonymous said...

fictionalism is simply a non-rational state of consciousness from any perspective of obervation past or futurist rational reality.

"vision is the science of pure intellect to see mathematic patterns creating new reality in multiple(s) and/or multi-dimensions" - eejames



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