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Hi Dan,

Interesting post. I'm not sure I'm quite following the entire line of thought, so maybe you can clarify something for me a bit. Here are two premises of Sider's argument:

(1) If a numerical sentence is indeterminate for semantic reasons, then some semantically simple expression of that sentence is precisifiable, i.e., not entirely precise.

(2) No expressions of numerical sentences are precisifiable, i.e., every semantically simple expression is entirely precise.

(1) and (2) together entail the negation of what you're arguing for, so I take it that you're denying one of them. But I can't quite tell which one it is -- could you elaborate a bit?

Dan Korman

Hi Jason,

The sparse borderliner will say that it's (1) that's false. This is actually a pretty natural way to go for someone who embraces a sparse ontology on which sentences aren't necessarily isomorphic with the states of affairs they represent as obtaining.

By denying (1), I'd have to give up the theoretical machinery available to most linguistic theorists for deriving the precisifications of a sentence from the precisifications of its constituents. But I take it that doesn't show it's not a linguistic theory; only that it's not a standard linguistic theory.

Is it therefore worse than standard linguistic theories? Well, they both have their costs. The nonstandard one is less powerful. The standard ones can't accommodate borderline composition.

Irem Kurtsal Steen

I think we knew what the candidate meanings would be all along--this view clarifies that. What we don't know is how come a numerical sentence is indeterminate between these two representations when it has no non-logical parts that can be blamed for it.

Mama Africa

great! thanks very much for sharing!

Kenny Easwaran

It almost sounds to me like you're denying composition at all! You're replacing it with talk of simples being "arranged objectwise", which you then say is a vague expression. If the only facts are about the simples and their arrangements, then it seems that you're saying there are no composite objects.

Dan Korman

Irem --

The sparse borderliner has to deny a certain inheritance principle about vagueness, i.e., that a sentence is vague only if some expression in that sentence is vague. I take it that this is what’s worrying you. I’m not sure how best to motivate denying this principle. Here are a couple (highly controversial!) examples that might be used to motivate denying the principle. First example: suppose that one says ‘there is no beer left’, and the context makes it clear that there is a tacit restriction to *cold* beers. And suppose that there is one beer left which is borderline cold. This sentence would then (arguably) lack a determinate truth value as a result of vagueness, but the vagueness would (arguably) not be the result of any expression *in* that sentence. (NB. The word ‘cold’ does not appear in the sentence.) Second example: ‘The sentence “Paul is bald” is true’, where Paul is borderline bald. The sentence (arguably) lacks a determinate truth value as a result of vagueness, but (arguably) no expression in the sentence (including ‘true’) is vague. I don’t expect everyone to be moved by these examples; there’s a lot of wiggle room.

Mama Africa -- thanks!

Kenny --

I was hoping that the sparse borderliner can play the same sorts of games that other sparse theorists sometimes play (though I admit that I don’t know much about how those games are usually played; I’ve spent too much time in the Platonic heavens, not worrying about nominalist hell!). I imagine that there are plenty of people who want to be relatively sparse about which properties, facts, and propositions exist, and yet in the same breath want to accept ordinary claims that, taken at face value, commit them to these things. For instance, they’ll accept that wisdom is a virtue even though they deny that ‘wisdom’ names some entity. Similarly, my sparse borderliner wants to pound the table and insist that of course there are tables, and that some things neither definitely do nor definitely do not compose tables, and yet weasel his way out of ontological commitment to such entities as *facts* or *propositions* about tables. You probably have a better sense than I do about the range of strategies that one might employ here, and how well they carry over to this case.

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