Saturday, September 29, 2007

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.


Blogger Brad said...

The nomological possibilities are only marginally more interesting than the technological possibilities, philosophically speaking? As a philosopher of science, this is where I get off the train.

11:05 AM  
Blogger Chris Tillman said...

Haha, sorry Brad. That was mostly directed at non-phil-sci metaphysicians. No offense intended.

1:17 PM  
Blogger Joshua said...

I agree that metaphysical possibility is more interesting than many of the other kinds of possibilities. Though, I am a bit confused about a couple of things. Specifically, I am confused about your discussion of logical possibility. Are you arguing for the conclusion that

(A) Logical possibility is less interesting than metaphysical possibility.

and using the premise that logical possibility is merely having a model?

Or are you suggesting that

(B) logical possibility is something other than merely having a model.

and pointing to Etchemendy's book as a place where one might find an argument for (B)?

9:17 AM  
Blogger Chris Tillman said...

My impression is that according to the standard view, logical possibility is having a model. And that is not very interesting. Etchemendy's book argues that logical possibility is not really truth in a model under an interpretation. His view, basically, is that in looking at variance we should not look at variance under interpretations (a la Tarski) but rather invariance in extension under variation in circumstances (a lot like how most people think of metaphysical possibility). That is still loose, but does that help?

11:22 AM  
Blogger Joshua said...

I am going to suppose that you agree with Etchemendy that logical possibility is roughly variance of circumstance given an interpretation. I guess nothing in your post indicated that you agree to that extent, but it will make it easier to ask my question.

I take it that you think that metaphysical possibility is something less than variation in circumstance given an interpretation. This is because (insofar as I understand the variance in circumstance talk) it looks like a variant circumstance is one in which your mother is not your mother. But, I know that you think it is metaphysically impossible for your mother to fail to be your mother. So, this gives me reason to believe that you think that logical possibility is something wider than metaphysical possibility but narrower than mere truth in a model. Is this a correct assessment of what you are thinking?

1:22 PM  

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