5/23/2011

A question about necessary truths and non-referring terms

Someone must have already thought about this. If you know who, I'd appreciate a reference.

In our Kripkean era, most philosophers hold that sentences like 'Hesperus=Phosphorus' and 'Cicero=Tully' are necessarily true, if they are true. In other words, if these two sentences are true in our world, then they are true in every possible world (accessible to ours).

But I'm not so sure about this received view. In other possible worlds, Venus does not exist, and therefore in those other worlds the names 'Hesperus' and 'Phosphorus' lack referents. But on most standard semantics for non-referring names, 'Hesperus=Phosphorus' will NOT be true. (For the free logic cognoscenti: that sentence will be false on a negative semantics, truth-valueless on neutral semantics, and truth-valueless on a positive supervaluational semantics. It could only be true on a positive, inner-domain/ outer-domain [roughly Meinongian] semantics.) In short: 'Hesperus=Phosphorus' will be untrue on 3 of the 4 extant semantics for non-referring names.

So, if we want to maintain that 'Hesperus=Phosphorus' is necessary if true, then it looks like we're stuck with only unpalatable options:
(i) accept the roughly Meinongian semantics that makes 'Hesperus=Phosporus' true in possible worlds where Venus does not exist.
(ii) Say that Venus exists in all possible worlds accessible from ours.

But I would rather accept that 'Hesperus=Phosphorus' is NOT a necessary truth, than accept either (i) or (ii).

7 Comments:

At 23/5/11, Blogger tristanhaze said...

I have thought about this, but I don't know of a reference.

Whatever we say about its necessity, it seems clear that 'Hesperus is Phosphorus' has the property that its negation is subjunctively impossible - the property that it could not have been otherwise.

It seems natural enough that people use 'necessity' for this property, even if it doesn't fit exactly with the standard explication of necessity in terms of truth in all worlds.

If one wants to retain an explication which quantifies over possible worlds, perhaps one could say that a proposition is necessary iff it is true in all worlds where its putative referents exist - this being analogous to the qualification Kripke puts on his rigid designation thesis about proper names.

 
At 23/5/11, Blogger Aaron Boyden said...

Wouldn't a Kripkean be more likely to say that the propositions are necessarily true, than that the sentences are? I'm not sure that a sentence involving non-referring terms could express the same proposition as a sentence involving referring terms (even if they're in different possible worlds); some would say the sentence involving non-referring terms doesn't express a proposition at all. I'm not proposing this as a solution to the problem (as it obviously isn't), but I'm not sure you've located the problem in the right place in your description here. And non-referring Millian names are generally puzzling; this seems to be just one instance of that. I don't know if he gives a satisfying solution to your problem exactly (I'm not sure what a satisfying solution would be), but I know Nathan Salmon has worked on this more than a bit.

 
At 23/5/11, Blogger Greg Frost-Arnold said...

Hi Tristan --

A couple thoughts:
1. You say:
"Whatever we say about its necessity, it seems clear that 'Hesperus is Phosphorus' has the property that its negation is subjunctively impossible - the property that it could not have been otherwise."

First, note that (i) the negative semantics for free logic would disagree with that (since every sentence of the form 'a=b' is false if at least one of a,b is non-referring). (ii) Someone who accepted neutral free logic AND thought negation is 'external' would also disagree with you (external negation = if p is neither true nor false, then ~p is true).

Second, I don't personally feel inclined towards the negative semantics or neutral semantics+external negation. But I think there is a difference between a sentence that is necessarily true, and a sentence whose negation is necessarily not true. For that latter will describe any truth-valueless sentence, if we use 'internal' negation.

You also said:
"If one wants to retain an explication which quantifies over possible worlds, perhaps one could say that a proposition is necessary iff it is true in all worlds where its putative referents exist."

But then I think 'c exists' will be a necessary truth, for all names c.

Hi Aaron --

I think switching the discussion from sentences to the propositions expressed would be fine. I take it that one motivation/ reason folks have for accepting the neutral or supervaluational positive semantics is precisely because sentences containing non-referring names do not express truth-valued propositions -- perhaps because such sentences do not express any proposition whatsoever, or because such sentences express partial propositions. One more small point: Frege (no Millian) thinks that sentences with non-referring NPs are neither true nor false either. But your general point is a good one: using anything about the semantics of empty names as a premises is usually not a good/fair dialectic approach, since those semantics are so contested.

And you're right that Nathan Salmon is probably the best person to go to for stuff on this: he's written so much on direct reference, and he's worked on empty names too. So thanks for that idea.

 
At 23/5/11, Blogger Greg Frost-Arnold said...

And a note to myself: after some googling, it looks like free quantified modal logic uses inner-domain/ outer-domain semantics. See e.g. Giovanna Corsi, "A Unified Completeness Theorem for Quantified Modal Logics" JSL 2002 (pp. 1483-1510).

 
At 23/5/11, Anonymous Tristan Haze said...

(Comments aren't working with my Google account. Now trying with Name/URL.)

Hi Greg,

'But I think there is a difference between a sentence that is necessarily true, and a sentence whose negation is necessarily not true.'

I don't disagree with this - my fault for not making that clearer. I just wanted to say that it's understandable why people naturally use 'necessity' for the latter property (at least before they've reflected on the distinction).

As for my comment:

'If one wants to retain an explication which quantifies over possible worlds, perhaps one could say that a proposition is necessary iff it is true in all worlds where its putative referents exist.'

And your reply:

'But then I think 'c exists' will be a necessary truth, for all names c.'

Good point. So it probably isn't advisable to unify things in this way. But still, I think we can have the proper conception of necessity, and also the "necessity" which attaches to identities (necessary non-truth of internal negation). And of course, in a modal logic, one could define a special operator for this.

Also, I admit this may generate problems for really hardcore Millianisms, but I think that's bound to happen anyway. (Of course, this is no argument.)

 
At 24/5/11, Blogger Greg Frost-Arnold said...

A further bibliographic note to myself:
David Efird's MS "Necessary Existence and The Semantics of Quantified Modal Logic" deals with a lot of closely related material in great detail, and has a direct discussion of exactly this point on p.35.

Efird takes exactly the line I suggest here: there are no necessary truths about contingently existing entities.

 
At 24/5/11, Blogger tristanhaze said...

Hi Greg,

'But I think there is a difference between a sentence that is necessarily true, and a sentence whose negation is necessarily not true.'

I don't disagree with this - my fault for not making that clearer. I just wanted to say that it's understandable why people naturally use 'necessity' for the latter property (at least before they've reflected on the distinction).

As for my comment:

'If one wants to retain an explication which quantifies over possible worlds, perhaps one could say that a proposition is necessary iff it is true in all worlds where its putative referents exist.'

And your reply:

'But then I think 'c exists' will be a necessary truth, for all names c.'

Good point. So it probably isn't advisable to unify things in this way. But still, I think we can have the proper conception of necessity, and also the "necessity" which attaches to identities (necessary non-truth of internal negation). And of course, in a modal logic, one could define a special operator for this.

Also, I admit this may generate problems for really hardcore Millianisms, but I think that's bound to happen anyway. (Of course, this is no argument.)

 

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