Chalmers, Meta-Metaphysics, Existence, and “Analyticity”

Finally I am going to participate in the INPC 2007 conference on metametaphysics. The list of people there is huge, and I am very excited about it—I hope to finish my paper in time for that!

I have been reading Dave Chalmers’ ‘Ontological Anti-Realism.’ There is a lot of interesting stuff, and I hope we discuss it at length soon in the Meta-Metaphysics e-Reading Group at The bLOGOS.

One thing that surprised me, however, and which connects with the discussion I had here and here, is the following paragraph:

“The absolute quantifier expresses a primitive concept, if it expresses any concept at all. Because of this, it is extremely implausible that ampliative conditionals involving the absolute quantifier, such as ‘If x and y exist, the sum of x and y exists’, or ‘If there are particles arranged heapwise, there is a heap’ could be analytic. It is unlikely that they are true in virtue of the concept of absolute quantification, because that concept is primitive and unanalyzable. It is unlikely that they are true in virtue of the concepts ‘heap’ and ‘sum’ alone, in part because they have logical consequences that do not involve these expressions. And it is unlikely that they are true in virtue of the concepts of absolute quantification and those expressed by ‘heat’ or ‘sum’ together: this combination might at best yield nonampliative analytic conditionals, such as ‘If there is an object made of particles arranged heapwise, it is a heap’, but not ampliative analytic conditionals.” (§7, p. 24)

For him, the conditionals are ampliative

“roughly in that the consequent makes an existential claim that is not built into the antecedent. (That is, the consequent is not a logical consequent of the antecedent, where we take an expansive view of logical consequence such that for example, ‘If x is a father, there exists someone who is an offspring of x’ is a logical truth.)” (§6, p. 18)

With this understanding of ‘ampliative’ it is indeed plausible that ampliative conditionals are not analytic, for being analytic would make them logical truths, in the relevant sense, and thus nonampliative.

The question, of course, is then which reason could be provided for the claim that the relevant mereological statements are not analytic; i.e. are “ampliative” in this sense? And the question is pressing, given that

‘Whenever there are two things, there is something which is a sum of them.’

does seem to be relevantly like related mereological statements such as

‘Whenever something is a proper part of another, there is something that is part of the latter but not of the former.’

‘Whenever two things overlap, there is something that is part of both.’

which, most would agree, are indeed “analytic” (and thus "nonampliative") in the relevant sense.