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Why can’t we eliminate talk of necessity and possible worlds, for talk of analyticity and (non-modal) logical consistency? Has there been any attempt in recent times to do this? I'm not 100% sure, but I think this is what logical positivists believed was correct, and logical positivism as a whole isn’t very popular anymore. But I still don’t understand why this particular view doesn’t come up anymore (or does it?).

As an example, any time I hear of a statement, P, being possible or necessary, I usually rephrase it in my mind as P being consistent or its negation being inconsistent. And if we’re talking about P being metaphysically necessary, I take it to mean it follows logically from some (implicitly or explicitly) assumed laws of metaphysics. If it’s physically necessary, I take it to mean it follows logically from some (implicitly or explicitly assumed) laws of physics. And so on for any other type of necessity. In this way, necessity can be eliminated in favor of formal rules of logic, assumptions (metaphysical, physical, or other), and formal substitution (ex. replacing defined predicates, like “is a bachelor”, with their definiens, “is unmarried, and a man”). An example of this is the problem of evil. Some atheists claim that it is impossible that God is omnipotent, omniscient, and omnibenevolent, and there is evil in the world. In response, theists can put the burden on the atheists and ask for a contradiction to be derived – a modal notion of impossibility (the impossibility of God and evil existing in the same world) is demanded to be shown to be inconsistent (a logical or semantic notion) for it to be properly understood and analyzed. It looks like we try to eliminate modal talk with logic-talk.

But… if this is correct then “possible worlds” aren’t needed. Just (non-modal) logic and unpacking of definitions. What’s wrong with this view?

I know Quine argued against analyticity, but according to page 14, question 4, of this, most philosophers still accept the analytic-synthetic distinction (or at least, it’s not completely dead). Anyways, in Two Dogmas (I don’t have it on hand but I seem to recall) Quine was open to some kinds of formal and explicit definitions as a legitimate kind of analyticity.

Are there any other reasons for rejecting the view that all necessary statements can be analyzed into analytic statements?

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    I made an edit which you may roll back or further edit. You can see the versions by clicking on the "edited" link above. – Frank Hubeny Aug 30 '18 at 19:38
  • I am not sure you define the terms as they were taught. The same words are used differently in different schools of thought and context. The terms originated with Kant. Other philosophers updated the definitions. So don't go by etymology. Here is what I was taught: analytic propositions are either logically neccessary or self contradictory. That is the truth value is based on ideas not science. No sense verification needed just semantics. Synthetic propositions were literally sense verifiable & semantics can't determine the truth values alone. You need knowledge of the world. – Logikal Sep 3 '18 at 22:15
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The OP is very close to Quine's considered view of necessity, as e.g. in Pursuit of Truth:

"In respect of utility there is less to be said for necessity than for the propositional attitudes. The expression does serve a purpose in daily discourse, but of a shallow sort. We modify a sentence with the adverb 'necessarily' when it is a sentence presumed acceptable to our interlocutor and stated only as a step toward the consideration of moot ones. Or we write 'necessarily' to identify something that follows from generalities already expounded, as over against new conjectures or hypotheses. Such utility is local, transitory, and unproblematic, like the utility of indexical expressions. The sublimity of necessary truth turns thus not quite to dust, but to pretty common clay.

Ironically, the demise of necessity-from-analyticity is due not to Quine but to his chief opponent on modal logic, Kripke. Kripke's arguments in Naming and Necessity convinced most that necessity is something distinct from "common clay" shadow of analyticity, at least most modal logicians. One reason is provided by the so-called necessary a posteriori, like "water is H2O". Although water is necessarily H2O, the argument goes, this can only be discovered empirically, not by inspecting the use or meaning of terms. Hence this necessity can not be analytic. What is behind this is the semantic idea that use of some words (e.g. of the "natural kinds" like water) is provisional, it is fixed not by linguistic convention but by independent reference. As a result, the de re ("in things") necessities involved are open to future discovery and can not be reduced to current assumptions only. Kripke's conclusion was that analyticity can not account for such de re necessity. For more on the Kripke-Quine debate see What are the objections to the axioms of modal logic?

Nonetheless, possible worlds semantics, especially its essentialist "metaphysical" versions a la Kripke, are criticized and alternatives are pursued, see Is there modal logic without possible worlds? For instance, Kahle in Modalities Without Worlds writes:

"The ontology explodes. Next to the actual world, one needs additional possible worlds to interpret modalities... If we do not consider nested operators, modal logic does not provide more than a box in front of the derivable formulas. Thus, the power of modal logic is located only in the nesting of operators... In fact, also outside of logic, we are not aware of any practical examples where modal logic or possible worlds semantics helps us to determine a necessary truth, which was not already (explicitly or implicitly) built in by certain axioms or constraints on the variety of worlds".

Forster in Modal Aether argues that continued popularity of the possible world talk with philosophers is based on trading substance for expediency and is therefore misguided. Why is it nonetheless popular? Consider the analogy with classical logic. Its issues with the material conditional, sorites, future contingents, self-reference, etc., are well-known, nonetheless it provides technically simple and hence very handy calculus that is close enough in many situations. Possible worlds play a similar role. There is of course a disanalogy. Classical logic is strictly enforced in (most of) mathematics, which is a major application, modal logic does not have something comparable. The closest thing is formal semantics, where Kripke's causal theory of reference for names and natural kinds had some success, but even there it remains controversial.

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