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I've done some personal research on formal logic, but I was wondering how philosophers today actually use it to, say, develop an argument.

The most relevant example I can think of is Plantinga's modal ontological argument; but other than that, a lot of what I've seen so far is simply the use of formal logic to rephrase or make more explicit the nuances of certain phrases (e.g. "Paul is son of x and Elmer is son of y and x is colleague of y" (Word and Object)).

What are some of the ways philosophers use formal logic apart from clarifying ordinary language?

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    Apart from phil of math and phil of logic, not many. As you said, very few philosophical arguments have been fully "formalized". See e.g. Gödel's ontological proof. – Mauro ALLEGRANZA Dec 4 '17 at 7:54
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    Philosophers depend on formal logic for any progress at all. Usually they use the dialectic and proceed by making reductio arguments against theories to defeat them and in this way zero in on theories that stand up to analysis. Philosophy would be impossible without formal logic so perhaps I'm not understanding the question. . – PeterJ Dec 4 '17 at 12:32
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I agree with @PeterJ's comment to a point, but believe NO "meaningful" theories stand up to analysis. Given the justification for any "meaningful" theory, I believe one or both of the following must be true:

  • The justification contains a logical fallacy

  • You can show the theory is logically equivalent to statements that "reasonable" people would reject

More specifically, a "meaningful" theory is one that addresses real-life issues, not pure abstraction.

"Reasonable" people reject statements such as "it's OK to kill innocent babies for no reason".

A fun application of my belief is arguing with people on social media: you can show that all arguments either contain logical fallacies or, when logically extended, are equivalent to statements that the arguer abhors.

  • Sorry, are you really saying all meaningful theories are founded on fallacy or can be reformulated into a form reasonable people would reject? I'd like a source on that please. – Canyon Dec 6 '17 at 20:24
  • @Canyon I said "I believe" so I'm not claiming a source, but I'd be happy to debate with you (either in a chat room here or see my profile for contact info) – barrycarter Dec 7 '17 at 21:24
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It may be possible to say that first order logic is also used in modal logic for at least analysing the way that modal statements seem to behave.

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