Matt_Simpson comments on Welcome to Less Wrong! (2010-2011) - Less Wrong

42 Post author: orthonormal 12 August 2010 01:08AM

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Comment author: Matt_Simpson 12 August 2010 07:14:27AM 0 points [-]

the entire enterprise of modal logic seems facepalm worthy to me

Comment author: Oligopsony 12 August 2010 07:26:27AM 4 points [-]

Modal logic is actually quite useful. If modal realism turns you off you can just accept it as a language game (which any sort of formal logic is going to be.)

The non-sequitur in Plantinga's argument, as presented by cousin it, is P3. (Plantinga's own argument is a bit more subtle, and its ultimate error is in eliding between different meanings of the term "possible." He successfully shows that under formal logic if possibly necessarily x then necessarily x, and then ascribes possible necessity to God because God is one of the most few things that often is argued to be necessary, and that God seems like the sort of sufficiently abstract thing that it might be necessary. But this isn't the sort of possibility that's germane to formal logic.)

Comment author: false_vacuum 03 February 2011 06:05:31AM 1 point [-]

Haven't read Plantinga and not going to, but 'possibly necessarily P' does not imply 'necessarily P' in all modal logics.

Comment author: cousin_it 12 August 2010 09:59:59AM 0 points [-]

I agree with Eliezer's critique of the value of modal logics: 1, 2.

Comment author: thomblake 12 August 2010 02:31:51PM 2 points [-]

Eh. He didn't really show they're not valuable, just that they haven't reduced the notions they work with to something other than black boxes. Modal operators can mean all sorts of things, aside from "possibility" and "necessity", and black boxes are fine as long as they work properly - if you need to know what their internals look like, that's just a project for some other formalism.

Comment author: fiddlemath 12 August 2010 03:24:22PM *  3 points [-]

I understand that when folks say "modal logic" in this context, they're generally referring to model logics that implicitly quantify over poorly-defined spaces. However, that's not what all modal logics are like, and so I hate to see them maligned with a broad brush.

Consider, say, dynamic logic, which I actually use as a tool in my research on program analysis. When my set of "actions" are statements in a well-defined programming language, I can mechanically translate any dynamic logic statement into a non-modal, first-order statement. I almost never do this, because the modal viewpoint is usually clearer and closer to the way we actually think about programs.

Equivalently: you can use whatever logical operators you like, if you can define the operator's meaning without reference to the operator. It can help you say what you're trying to say, rather than spending all of your time with low-level details. It's like a higher-level programming language, but with math.

Comment author: Matt_Simpson 12 August 2010 11:47:23PM *  1 point [-]

I understand that when folks say "modal logic" in this context, they're generally referring to model logics that implicitly quantify over poorly-defined spaces. However, that's not what all modal logics are like...

Consider my eyes opened.

Equivalently: you can use whatever logical operators you like, if you can define the operator's meaning without reference to the operator.

This is my problem with the modal logics I have encountered - bad or unclear definitions of the modal operators.