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I have been reading this book about philosophy of language by A. Miller": the discussion of Frege and Russell are excellent, using logic symbol to introduce ideas. However, the remaining chapters do use this approach, the author just stops using logical symbols.

So, what kind of branch of philosophy uses symbolic logic as a fundamental tool?

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All philosophy uses logic, but what you've asked suggests that what you really want to know is who uses symbolic logic in drawing out their arguments.

For the obvious reasons, the branch of philosophy that you'll see applying symbolic logic with the highest frequency is the philosophy of logic itself: Russell's Principia Mathematica has enough to make your eyes bleed.

You might also enjoy philosophical treatments of probability, if that's what you're after.

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You can find formalized, symbolic arguments in all of the branches of contemporary philosophy. You'll find more in the philosophy of math than in the philosophy of literature, of course. But I wouldn't be surprised if an aesthetics person didn't occasionally find it useful to use modern logical tools in her arguments. Formal approaches are very common in metaphysics and epistemology, to the point that it would be difficult to understand almost any of the current work being done there without at least some basic knowledge of modern logic.

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I once wrote the Head of Philosophy at Uni of Bristol to ask about the purpose of Russell's symbolic logic because it seemed to me, as a rank amateur with no knowledge of philosophy who had just read a book about it, that it is pointless.

He asked me to tea in his study and we had a good chat. He explained that I was basically correct, symbols offer no advantage over words when it comes to solving philosophical problems, and that symbolic logic was taught to students as mental exercise and so they knew about it, not as a useful philosophical tool.

Forty tears later this is still my opinion and I know of no philosophical 'branches' that rely on it, albeit it is interesting as an attempt to clear up philosophy's endless linguistic ambiguities.

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Well, it depends on what you mean by philosophy. Philosophy is practiced extensively in every field by those who seek to understand the field conceptually. Bertrand Russell is a living example that mathematics stopped being the study of arithmetic hundreds of years ago, and is largely an exercise in logic and philosophy at the graduate level. Computer science has also become largely infatuated in some quarters in inventing and automating logics.

If you love abstractions and formalisms in logic, then your studies in logic will likely take you across these three fields all of which are rather intertwined. Note these days the Aristotelian syllogism is just as "symbolic" as model theory, though less sophisticated.

Philosophical logic studied in Philosophy departments.

Mathematical logic studied in Mathematics departments.

Computational logic studied in Computer Science departments.

You'll find plenty of references on this site from philosophers who enjoy propositional, modal, temporal logics, etc., but if you want something much more abstract, I would start with books like:

Model Theory, 3rd Ed. by Chang Jerome

Computability and Logic, 5th Ed. by Boolos et al.

Both of these provide formalisms in abstractions of natural language logic replete with logic symbols.

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Logic is used in all branches of philosophy except history of philosophy and, as far as I can see, aesthetics. Logic is definitely used in epistemology, metaphysics, ontology, the philosophy of language, and ethics.

However, only a small fraction of philosophers uses logic and even less of them make substantial uses of other broadly-conceived mathematical tools. Since you define "fundamental tool" as one that is always used the answer to your question is thus: Philosophical logic and all "branches" with the attribute formal such as Formal Epistemology. It is, of course, debatable, or perhaps just a matter of taste, whether to count these as branches on their own or not.

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  • How does history of philosophy lack a use for logic? – virmaior Mar 7 '14 at 14:17
  • @virmaior - the OP is asking about symbolic logic (we must assume his modern form : mathematical logic). – Mauro ALLEGRANZA Mar 7 '14 at 14:19
  • Yet the answer does not distinguish between logic and symbolic logic which is major flaw. – virmaior Mar 7 '14 at 14:20

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