### The Concept of Logical Consequence

So this is just an advertisement with a bit of philosophy in it.

How would you explain necessity to the uninitiated? Here's (roughly) a way I've done it in the past: in terms of nested necessities of increasing strength. Small circle encompasses the technological possibilities. Bigger: Nomological possibilities. Bigger: Metaphysical possibilities. Bigger: Logical possibilities. Then necessity is specified in the usual way: blah necessity is truth in all blah possibilities.

Now for a question: Which do you care the most about philosophically? The merely technologically possible is boring and laws of nature are only a little more interesting than that. Metaphysical possibility is the thing. But what about logical possibiliy? I think in one respect it's lame. So a non-lame respect is trying to figure out the limits of the logically possible. That has to do with correct accounts of logical consequence. But here's the lame way: To say that P is logically possible is merely to say P has a model in which it's true. But what's that mean? Well it means (roughly) that there is a way of interpreting the non-logical constants that is consistent. Big whoop. This seems like it amounts to saying 'Oak is a type of metal' is logically possibly true simply because there's a language in which that sentence is true. (Since interpretations are in the business of hooking up the formulas to the domain(s) in different ways.) Not very illuminating.

Russell said that logic was just as concerned with the world as zoology, but with its most general features. I think that's basically correct but does not seem borne out by what counts as logical possibilities. It's really the metaphysical possibilities that do that. That's because metaphysical possibilites "hold fixed" meanings and vary worlds as opposed to holding fixed formulas and varying ways of hooking that formula to the world(s). (In fact we caution that the latter approach is an elementary mistake in thinking about metaphysical possibility.) But that's what logical possibility does.

Just recently I discovered John Etchemendy's 1999 book, The Concept of Logical Consequence. The book argues (basically) that logical possibility should be pursued in the manner in which we pursue metaphysical possibility and in fact the Tarskian tradition amounts to a mistake. This strikes me as a very deep and important issue. I suspect that y'all might sympathize so I thought I'd pass along the recommendation.

How would you explain necessity to the uninitiated? Here's (roughly) a way I've done it in the past: in terms of nested necessities of increasing strength. Small circle encompasses the technological possibilities. Bigger: Nomological possibilities. Bigger: Metaphysical possibilities. Bigger: Logical possibilities. Then necessity is specified in the usual way: blah necessity is truth in all blah possibilities.

Now for a question: Which do you care the most about philosophically? The merely technologically possible is boring and laws of nature are only a little more interesting than that. Metaphysical possibility is the thing. But what about logical possibiliy? I think in one respect it's lame. So a non-lame respect is trying to figure out the limits of the logically possible. That has to do with correct accounts of logical consequence. But here's the lame way: To say that P is logically possible is merely to say P has a model in which it's true. But what's that mean? Well it means (roughly) that there is a way of interpreting the non-logical constants that is consistent. Big whoop. This seems like it amounts to saying 'Oak is a type of metal' is logically possibly true simply because there's a language in which that sentence is true. (Since interpretations are in the business of hooking up the formulas to the domain(s) in different ways.) Not very illuminating.

Russell said that logic was just as concerned with the world as zoology, but with its most general features. I think that's basically correct but does not seem borne out by what counts as logical possibilities. It's really the metaphysical possibilities that do that. That's because metaphysical possibilites "hold fixed" meanings and vary worlds as opposed to holding fixed formulas and varying ways of hooking that formula to the world(s). (In fact we caution that the latter approach is an elementary mistake in thinking about metaphysical possibility.) But that's what logical possibility does.

Just recently I discovered John Etchemendy's 1999 book, The Concept of Logical Consequence. The book argues (basically) that logical possibility should be pursued in the manner in which we pursue metaphysical possibility and in fact the Tarskian tradition amounts to a mistake. This strikes me as a very deep and important issue. I suspect that y'all might sympathize so I thought I'd pass along the recommendation.