Subtracting Presuppositions

Follow-up to: Logical Subtraction and Partial Truth

Yablo proposes that (1) the real content of a statement S is what it says as opposed to presupposes; (2) what it says is what S adds to the presupposition π. That is, the real content R = S - π.

How can we tell what's presupposed? Linguists have developed various tests for this, including the negation test: Denying The # of planets is 8 is not thereby to assert There is no such entity or it is not 8. No, whether we assert or deny the claim, this way of talking presupposes numbers either way. So the real content is merely about how things stand concretely so far as the planets are concerned.

Plugging into the formula:
R = S - π
    = 'The # of planets is 8' - 'There are numbers'.

This remainder, the real content of what's said, is true even if the literal statement S isn't (due to the false presupposition). S is merely partly true, but it's true in the part that we care about.

Here's a vital question for metaphysicians concerned with ontological commitment: Are we committed to the truth of our presuppositions, or merely to what we say (i.e. what our assertions add to what's presupposed)? Ordinary talk presupposes all sorts of ontological extravagance: composite objects, numbers, propositions, properties, tensed reality (past/future), mere possibilia, etc. Such talk helps us to convey important truths, some of which may not even be possible to express in less ontologically loaded terms. So it would be nice if we could maintain this talk in good conscience, without thereby committing ourselves to the ontological presuppositions. Can we?

Sometimes, at least, we can knowingly adopt a false presupposition. Yablo mentions talk of 'the King' to denote Harold the usurper. Harold is not really the King, we all know -- the King is locked away in the dungeon. But nonetheless we may use 'The King is coming!' to warn of Harold's approach. This does not commit one to thinking that Harold truly is the King rather than a mere usurper. The false presupposition is adopted merely for sake of communication, and can be safely subtracted to get at the real content of our assertions. Similarly, we may think, for ontological presuppositions. We presuppose that there are numbers in order to more easily describe how things stand in concrete reality. But we may do this while remaining neutral on the question whether the presupposition is really true.

Yablo also briefly mentioned the popular meta-ontological view that various ontological disputes (e.g. whether numbers really exist) are 'empty' or meaningless. He suggests that we have this intuition in cases where the presupposition that X really exists is perfectly extricable from the ordinary claims which rest upon it. We have no trouble simply subtracting away the disputed metaphysical claims, and assessing the concrete remainder. So it seems like the metaphysics isn't really doing anything. That seems to describe my intuitions pretty well, I must admit. But what are the implications for meta-ontology? Can the subtraction method vindicate our deflationary intuitions? Or does it debunk them, suggesting that there is a further question there -- just not one we're typically concerned with in everyday life? Or must we look elsewhere to adjudicate this issue?

Fascinating questions, I reckon. Now if only I could find some answers...