# Is logic part of Philosophy or Mathematics?

Is logic part of Philosophy or Mathematics?

I asked this question "Does programming use logic more or mathematics more" and users on some site insisted that logic was part of mathematics, I checked Wikipedia and it listed logic(symbolic, first-order, formal, etc) as part of Philosophy, not mathematics. So it has to mean logic is part of philosophy, right?

When I look at source code of programs, most of it seems to contain only symbolic logic and first order logic, math is used very sparsely in most programming, there are areas of programming like graphics, cryptography, AI etc where math is used a lot but rest of the programming is only symbolic logic.

– user14511
Commented Jul 31, 2020 at 13:14
• These are some other illustrative questions and answers: philosophy.stackexchange.com/questions/16119/… philosophy.stackexchange.com/questions/36549/…
– user14511
Commented Jul 31, 2020 at 13:25
• Reader do not be mislead. There is no such thing as LOGIC in the sense people today use it.The correct & proper name IS "MATHEMATICAL LOGIC." You can tell by the name this branch of LOGIC is part of mathematics. There are other parts of LOGIC that are NOT MATH. As a matter of fact, there are multiple disciplines that teach a portion of this elusive LOGIC word: Philosophy, Psychology, Rhetoric, Mathematics, Computer Science, etc. All of those fields DO NOT teach the same principles in the same context. There is very little agreement on LOGIC in general. It depends ON WHAT TYPE of logic you mean Commented Jul 31, 2020 at 16:15
• @Logikal I refuse accept there is only "MATHEMATICAL LOGIC", Wikipedia shows Logic as part of philosophy. Not mathematics. Maybe mathematics is using logic from philosophy. Commented Aug 1, 2020 at 5:29
• @Logical You basically just asserted modal logic was not mathematical logic (in your terms). Also, you seem to confuse the language used to convey meaning, which indeed is almost exclusively mathematical in the case of logics these days, with what is meant. Commented Aug 1, 2020 at 9:09

"Logic" is a part of mathematics as well as it is a part of philosophy!

Now, the explanation. I suppose you are well aware of the fact that a term "logic", as more or less any term, can be interpreted differently by any person. But let's put aside the "non-canonical" interpretations...

The term "logic" has an uncertain origin. The Greeks say it was Parmenides (5th century bce) who coined the term. What's certain is that the first system of logic (namely the syllogistic logic, the logic of classes and categories) comes from Aristotle, who was certainly a philosopher, but he was also involved in natural sciences to which he applied his system (i.e. his zoological systematization).

Then were the stoics, who invented the sentential calculus, which, much later, was discovered by mathematicians to be well suited for their metamathematics.

The so called "traditional logic" was certainly considered a part of philosophy.

I'd say that our "philosophy or mathematics" dillema started when George Boole introduced his algebra. It meant that from that moment on logic can not only evaluate mathematical problems, but also can be interpreted in it.

Of course I have to skip many significant breakthroughs and theorems that strenghtened the position of logic in mathematics, I'll just mention here: Hilbert, who wanted to build the whole mathematics solely on logical axioms; Goedel, who proved Hilbert wrong; Tarski, who developed many metalogical guidelines that are well-respected to this day.

The real question here is not: "Is mathematics deducible from logic?", but: "What are the differences between (pure) logic and mathematics?". I'd say that the definitions of terms: "logic", "mathematics", "philosophy" are always the results of some conventions and so cannot be understood unambiguously without more context.

It is a mistake to assume that various academic discplines constitute a partition. Something being part of mathematics does not rule out it also being philosophy, computer science, etc.

I do research in logic. Most of my peers are employed at either CS or maths departments (roughly even split), but there is a meaningful number of people at philosophy departments, too. Of those at CS departments, probably quite a few identify more as mathematicians than as computer scientists (I do). I'd reckon almost everyone identifies as a mathematicians at least to some extent. I don't know how much identification with philosophy there is, but I'd guess much less.

Of the stuff I would recognize as logic, I'd also recognize everything as mathematics. Some of it is also clearly philosophy, others is also clearly CS. There is certainly also overlap with other disciplines.

Summary: Logic is definitely part of mathematics, but that does not preclude some or all of it also being part of philosophy.

• Amo, it is just dishonest to call discipline "logic" as if this has been the case for thousands of centuries when IT HAS NOT! The discipline is correctly named, "Mathematical logic". It is not "Logic" as you call it. You are using a NICK NAME for the topic that has a formal name: like calling someone "Chuck"who has a government name "Charles". You at least need to mention other fields have been doing logic BEFORE MATHEMATICS. Philosophy & what is deemed Rhetoric today has been around before the choice of logical connectors were even dreamed of. So conceptually there are distinctions. Commented Feb 17, 2021 at 21:38
• Some of the distinctions are within the terminology. Some of the most confused terminology were stolen from Philosophy originally & the context changed. Here are the most confused terminology philosophy students learn as well as so called Mathematical students learn that cause disagreements between students in different departments: tautology, truth, propositions, contraposition, contradiction, syllogism, statement, etc. What I learned was what is NOW deemed Epistemology. What 99.99 percent of humans now deem LOGIC is correctly named MATHEMATICAL LOGIC. The terminology is not identical. Commented Feb 17, 2021 at 21:47
• @Logikal The arguments that rhetoricians use (which can be fallacies or inferred reasoning) cannot be described by mathematical logic? And if so then, is there no underlying logic beyond language and symbols? I ask why I really don't know Commented Feb 17, 2021 at 22:07
• In this way the debate between students in Philosophy & students in Mathematics will go on further until the math side openly owns changing terminology & concepts that have been taught for generations differently. What the math students are being taught is that there was GOD existing and Mathematical logic has been there from the beginning which is FALSE. Mathematical logic was invented in the 19th century which math students apparently are NOT BEING TAUGHT. Aristotelian logic predates Mathematical logic by thousands of years. There are conceptual distinctions being overlooked. Commented Feb 17, 2021 at 22:10
• @Voxywave, ther arguments found in RHETORIC can be transformed into the Mathematical logic just as Aristotelian logic can be transformed. There are still concepts and words being that are not identical though. Now two people using the same words in different contexts is what will confuse some students. This is why we need CORRECT NAMES of what we mean by LOGIC. If the terminology were identical we would not have this issue. Philosophy considers more than form as math & computer science teaches. It is not just about validity which is why I emphasize there is a difference so much. Commented Feb 17, 2021 at 22:17

Yes and no, depending on what you mean by "being part of".

Logic is part of philosophy, but can be applied to various disciplines. When you find logic in philosophy of mathematics, that's just an application of logic, and does not mean that logic is subordinated to that particular discipline. In fact, one may even argue that mathematics itself is an application of logic.

So, is logic part of philosophy of mathematics in the sense that there a significant amount of logic in philosophy of mathematics? Yes. Is logic as a whole a sub-discipline of philosophy of mathematics? Nope.

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– J D
Commented Sep 21, 2020 at 7:16

I like the definition that Wikipedia gives

"Philosophy (from Greek: φιλοσοφία, philosophia, 'love of wisdom') is the study of general and fundamental questions, such as those about reason, existence, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. The term was probably coined by Pythagoras (c. 570 – c. 495 BCE). Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation."

"Historically, philosophy encompassed all bodies of knowledge and a practitioner was known as a philosopher. From the time of Ancient Greek philosopher Aristotle to the 19th century, "natural philosophy" encompassed astronomy, medicine, and physics. For example, Newton's 1687 Mathematical Principles of Natural Philosophy later became classified as a book of physics."

I don't know who said that philosophy was the mother of all sciences but he has my support.

I think the difference between a philosopher and a scientist is that each scientist is specialized in a specific area but even not long ago they were called natural philosophers.