I remember stumbling across Plantinga’s modal argument and going “what?” For convenience of onlookers, here it is in a more digestible form.
Premise 1: Besides our world, there are other “logically possible” worlds.
Premise 2: Some cheeseburgers are totally awesome.
Premise 3: To be totally awesome, a cheeseburger has to exist in all possible worlds, because being “logically necessary” sounds like a totally awesome quality to have.
Conclusion: Therefore, if a totally awesome cheeseburger is possible at all (exists in one possible world), then it exists in all possible worlds, including ours.
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.
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.
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.)
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.
I remember stumbling across Plantinga’s modal argument and going “what?” For convenience of onlookers, here it is in a more digestible form.
Premise 1: Besides our world, there are other “logically possible” worlds.
Premise 2: Some cheeseburgers are totally awesome.
Premise 3: To be totally awesome, a cheeseburger has to exist in all possible worlds, because being “logically necessary” sounds like a totally awesome quality to have.
Conclusion: Therefore, if a totally awesome cheeseburger is possible at all (exists in one possible world), then it exists in all possible worlds, including ours.
(facepalm happens here)
A.k.a., ontology with some bells and whistles.
This introductory philosophy class syllabus links to a statement of the ontological argument by Platinga, if anyone wants to read the argument in the words of the proponent.
the entire enterprise of modal logic seems facepalm worthy to me
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.
Consider my eyes opened.
This is my problem with the modal logics I have encountered—bad or unclear definitions of the modal operators.
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.)
Haven’t read Plantinga and not going to, but ‘possibly necessarily P’ does not imply ‘necessarily P’ in all modal logics.
I agree with Eliezer’s critique of the value of modal logics: 1, 2.
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.