I'm not a philosopher, but it strikes me that the word philosophy is an umbrella term for a wide range of enterprises - some of these would, as per Deleuze, develop new ways of understanding or describing the world. It sounds like you prefer to see philosophy as a creative endeavor rather than one bound by methodologies and mechanistic reasoning.

People seem to pursue the approaches to philosophy that match their dispositions and experience, and these help to form a set of habitual approaches to making sense of the world. I like the idea of philosophy as a way of trying to "undermine" our own habits, but this necessarily suggests that philosophy might need to be different things for different people. What I often observe, including in my own reflections, is that philosophy can serve as a series of elaborate post hoc rationalizations constructed to validate one's affective relationships with the world.

but I do struggle to see how logic can be grouped with epistemology, ontology, metaphysics, morality, ethics, etc. when it is just so distinct from them and uses a completely separate methodology. — Dorrian

On a broadly Aristotelian understanding, disciplined thinking involves rational movement. For example, when we think in a disciplined and structured way, our mind moves from point A to point B. Because every formal domain of study involves this sort of disciplined thinking (e.g. physics, chemistry, history, ethics, metaphysics, et al.), therefore every formal domain of study involves this sort of mental movement from point A to point B.

Logic is the art of this disciplined thinking. The one who possesses the art of logic is able to move from point A to point B securely. Namely, they are able to use their current knowledge in order to produce new knowledge without falling into error. Finally, because every formal domain of study involves rational movement and disciplined thinking, therefore every formal domain of study uses logic to guide that rational movement. This is logic's job. It is not limited to mathematics because mathematics is only one of the many formal domains of study, and the way that mathematicians progress in knowledge will not be identical to the way that other specialists progress in knowledge within their own field.

This is logic's job. It is not limited to mathematics because mathematics is only one of the many formal domains of study, and the way that mathematicians progress in knowledge will not be identical to the way that other specialists progress in knowledge within their own field. — Leontiskos

This gives pause for thought. When I think of progress in math compared to progress in physics, say, the initial step of A to B requires speculation and experimentation, or with math, finding examples. In other words, one must posit the B. After that the mathematician works to logically connect A to B, while the physicist is perhaps more interested with finding counterexamples that would invalidate their theory.

Set theory is closely tied to logic, and lies in an area overlapping mathematics and philosophy. So one might ask whether Philosophy of Mathematics is a part of philosophy. I say it is, but others might disagree.

Once, logic was thought of as setting out rules for rationality. Now it is thought of as setting out the structures we use in our language. When you read, watch or engage in metaphysics or other philosophical discussions, you are for better or worse engaged in an examination of the structure of those discussions, and hence of their logic.

That is, in doing philosophy, you have no choice but to therein be doing logical analysis.

And you can do that analysis either implicitly or explicitly. Doing it explicitly will make your argument clearly, thus enabling a better grasp of what you are saying. Doing it implicitly will leave you open to others explicit analysis and perhaps rejection of your argument.

Studying logic is understanding the tools you use in doing philosophy.

Set theory is closely tied to logic, and lies in an area overlapping mathematics and philosophy. So one might ask whether Philosophy of Mathematics is a part of philosophy. I say it is, but others might disagree. — jgill

I would argue that there are metaphysical considerations that are bound up with mathematics, such that mathematics does have a very broad reach. For example, the reason set theory is so useful in a general sense is because we encounter a world of unitary objects, and set theory provides a basic way to categorize unitary objects. Every kind of thing that we collect into sets has a unitary nature that allows it to be collected in that manner, and this unitary organization is basic to our experience.

Another example might be time. We are temporal beings who move. Indeed, even the rational movement spoken about implies time, where time is itself a way of sequencing this temporal movement according to number. Thus every kind of rational movement will involve progress, this progress can be measured and sequenced, and this will involve mathematics insofar as it involves division and number.

The way I see it, Mathematics and Logic are formal sciences, while physics and chemistry are natural sciences. There are also social sciences, such as sociology.

Logic has been conceptualized in many ways throughout the history of philosophy. Today, what Logic means to the professional logician is very different from what it meant to Aristotle. Most textbooks on modern logic will tell you that logic is the formal discipline that studies the formal aspect of arguments, particularly those which are deductive (however, inductive logic is also a rich field of research and application). In deductive logic, an argument is a series of premises from which a conclusion can be deduced (in inductive logic, an argument is a series of premises from which a conclusion is induced). In a formally valid deductive argument, if all of the premises are true, then the conclusion is necessarily true as well. An argument may be valid and yet it can be unsound. How so? Consider the following two examples. The first one is both valid and sound:

1) If Texans are human beings, then Texans are mortal.
2) Texans are human beings.
3) So, Texans are mortal.

In the following case, we have an argument that has the same formal structure (the structure of a modus ponens), which makes it valid, and yet it is unsound:

1) If Austin is the capital of Texas, then ghosts exist.
2) Austing is the capital of Texas.
3) So, ghosts exists.

Both arguments have the same logical structure. Using propositional logic, that structure is the following one:

1) p → q
2) p
3) q

It is that type of symbolic formulation of the arguments that interests Logic as a formal science. The actual content of the statements, be it the premises or the conclusions of the arguments (i.e., "Texans are human beings", "ghosts exists") are of no concern to modern logic, because modern logic is focused purely on form, just as mathematics is. No doubt, formal logic has applications: in every aspect of human life in which arguments are used, and that includes philosophy and all of its branches (metaphysics, epistemology, ethics, aesthetics, etc.), as well as the natural sciences, as well as political debates, as well as conversations that are had using some ordinary language, such as English or Spanish.

There are many systems of deductive logic, some very simple, like Propostional Logic, others extremely complicated, like Higher-Order Predicate Logic. I myself prefer First-Order Predicate Logic, and I believe that anything that is said in a formal Second-Order language can be reduced to an equivalent expression in First-Order language.

So, to answer the question of the OP: No, Logic as modern logicians understand it, is not a branch of philosophy. Not by a long shot. Philosophers can use modern logic, just as anyone can, for the same reason that anyone can use mathematics, including philosophers: they are universally applicable, because they are purely formal. Logic was certainly a part of philosophy during Aristotle's time, but so was Physics. A lot has happened in both philosophy and logic ever since Aristotle.

I suppose the question I'm asking digs into the question of what philosophy actually is and how to define (personally, I subscribe to the definition laid out by Deleuze and Guattari in 'What Is Philosophy'), but I'd like to hear the insight of the forum on this. — Dorrian

Logic and Philosophy are closely interlinked to each other, even if they are different subjects. Logic can analyze some philosophical concepts, statements and propositions and verify them for validity, truth and falsity.

Philosophy can look into the some of the problems residing in the Logical concepts such as validity, truth i.e. what is validity, what is truth, how does the logical proofs work etc, and establish the definitions and explain the rational process and grounds for the subject.

There are many different types of Logic in use by different subjects. Some folks just rely on the classic propositional logic and formal logic, but they cannot deal with all the problems in the world.

For example, when you say, Today is Thursday. It is only true one day a week. Tomorrow it will be Friday, and the statement will be false on tomorrow and the rest of the week until Thursday returns. Hence you need tense, or temporal logic.

Also the formal propositional logic cannot deal with the epistemic and metaphysical problems such as knowledge, beliefs, inference, reasoning and probability. You need to use Epistemic Logic which uses "K" function for "knows" or "is aware of". Probability Logic uses P for Probability e.g. P(A/B) i.e probability of A given B.

For more flexibility and practicality, high order logic, which can quantify all the elements in the statements (not just the pronouns) with modality which deals with possibility and necessity and probability would be more useful.

Logic is the essence of philosophy. Compare:

Philosophy of science isn't science of philosophy.

Philosophy of art isn't art of science.

Whereas, philosophy of logic is logic of philosophy.

QED

To me, logic seems completely detached and alien to practically every other philosophical discipline. — Dorrian

Try making an illogical argument in any other philosophical discipline and see how far it gets you.