What kind of logic questions or discussions belong on this site?

Question

I'm someone with a sincere interest in logic and I self-study the subject. For example, I'm now reading Gensler's Introduction to Logic, and Language, Proof and Logic, and testing out ideas on my own.

If we were to divide the topic of logic between philosophical logic and mathematical logic, then my interest is definitely more about philosophical logic, as my interest is in reasoning generally, and I get bored with literature that discusses formal languages for their own sake, and any kind of calculus that doesn't seem to represent actual human reasoning. That said, I definitely study formal ("symbolic") logic.

So my question is about a perceived split between the philosophy and mathematics stack exchanges. I get a sense, browsing this site, that many logic questions are at least more welcome on the mathematics stack exchange. There are statements to the effect that logic questions are only welcome here if they are only about philosophy of logic, to which to my mind is more narrow than philosophical logic. I worry about moving my questions to the mathematics stack exchange because I hate to see answers that aren't about substantive reasoning, but about irrelevant calculi and vacuous truths (e.g., proposition P is true in system S because the axioms say so).

I should try to clear up the distinction between philosophical logic, philosophy of logic, and mathematical logic, and I would welcome answers that help to clarify this, or provide a more authoritative view. But I would say that philosophical logic and mathematical logic should be contrasting terms, and while they share the aims of logic, and the systems of logic, they just employ logic for somewhat different purposes. Philosophical logic would be logic that is used for philosophical reasoning, and we could also include reasoning generally so long as it isn't too specialized or technical. It would be, for instance, hard to find interest in term logic in the mathematical stack exchange, yet discussions about term logic, in itself, is not a topic of the philosophy of logic.

In fact, there is a great deal of logic that would neither be appropriate for the mathematics stack exchange, nor could it be plausibly be considered philosophy of logic. A good example of this are older forms of logic which have fallen out of fashion in the mathematical community. I would almost call this the history of logic, except much of this logic is commonly used in every day reasoning, such as the Aristotlean syllogisms, but this is rarely formalized these days. This logic has more interest for philosophers, because philosophers are more likely to read historical texts where these out of fashion systems of logic are to be found.

So I suppose I argue that more logic should be acceptable on this stackexchange than what constitutes philosophy of logic proper. I would even suggest that any discussion should be acceptable here so long as it isn't strictly mathematical logic: Logical reasoning about mathematics that isn't philosophy of mathematics, nor logic that is specialized for use in mathematics.

Answer 1

The question of which parts of logic belong to mathematics and which parts belong to philosophy is a question that is not even settled in the community of professional mathematicians and philosophers, and there is little need to settle it here. I personally know many logicians — some in mathematics departments and some in philosophy departments — who find it difficult to say whether their work is mathematics or philosophy. And is such a categorization important anyway?

My impression is that there are a large number of philosophers who are interested in all parts of logic, including the technical parts, and able to answer logic questions of all kinds; similarly there are mathematical logicians who are able to answer both philosophical questions and technical questions about logic.

Certain parts of logic that are quite commonly studied by philosophers, such as much of modal logic, are essentially mathematical in nature and easily can fit in with mathematics or with philosophy.

I would also take issue with your suggestion that philosophical logic must not be involved with the technical parts of logic. Some of the most exciting current work in the philosophy of set theory, for example, is concerned with aspects of the most technical methods in set theory — forcing and large cardinals — and the area needs philosophers who are knowledgeable about those methods.

In the end, I believe that many logic questions could be asked either here or on the mathematics sites. If you ask a logic question here, it seems that you are more likely to get an answer with a greater level of philosophical gloss, with philosophically oriented examples, for example; and if you ask on the math site you will get an answer with greater level of mathematical gloss and mathematical examples. So my advice is to ask in the forum that appeals to you. But don't shy away from asking technical logic questions here, since there are people here who are interested and can answer.

In any case, if you ask here, and find that you want a more mathematical answer, then you can still ask again over there.

Answer 2

What kind of logic questions or discussions belong on this site?

The line I've taken before is basically that we have a mathematics stack for pure maths; questions here really should have something interesting to do with philosophy of math or at least fairly pure logic (which is naturally of professional interest to many philosophers.)

It strikes me that it may be a little ambiguous perhaps because there's a lot of 'native' experience here around logic and mathematics. That said, most of the Q&A tagged mathematics and logic isn't "just" math/logic, but really about philosophy of math or philosophical implications of logic.

Note that I'm certainly not expert enough to comment closely on the material itself, but judging from 30,000 ft my sense is that a large majority of it is definitely a better fit here than over on maths. But that's really the line in my mind: whether a question is really about mathematics at it's core (and so belongs on their stack) or whether it has significant philosophical context/interest/motivation (and so belongs to us!)

If you're in doubt whether a question is 'pure' enough for us, please feel free to bring it up on chat or in meta and we can work out the line together for particular cases.

Answer 3

I am speaking as a scholar of medieval philosophy and logic. I am not expert in mathematical logic, although I know enough to get on in conversation, much as I know French.

'Logic' used to mean a subject which was split into three parts according to the 'operation of the intellect' that they studied. The first operation is the apprehension of simple ideas or 'terms', such as 'Socrates', 'man' etc, what they mean, how they signify and so on. The classic text on this was Aristotle's Categories. The second operation was the combination of simple terms into propositions like 'Socrates is a man', how such propositions are true or false, how contradictories, contraries etc are related in the 'square of opposition'. The third operation was reasoning or argumentation, where propositions are combined together into arguments. The classic form of argument was of course the syllogism.

The focus of Aristotelian logic was natural language, and on questions like truth, reference, signification, identity and existence as well as argument, validity and inference. 'Logic' as traditionally understood was much closer to what we now call 'philosophy of language' or 'philosophical logic'.