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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.

noviceFedora
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    Does this answer your question? [Difference between logic and mathematics](https://philosophy.stackexchange.com/questions/49566/difference-between-logic-and-mathematics) –  Jul 31 '20 at 13:14
  • These are some other illustrative questions and answers: https://philosophy.stackexchange.com/questions/16119/is-there-still-a-place-in-modern-philosophy-for-qualitative-or-non-mathematical https://philosophy.stackexchange.com/questions/36549/what-distinction-is-there-between-logic-philosophy-of-logic-and-philosophical-l –  Jul 31 '20 at 13:25
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    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 – Logikal Jul 31 '20 at 16:15
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    @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. – noviceFedora Aug 01 '20 at 05:29
  • @noviceFedora, who said there was only Mathematical logic? I clearly stated there are many types of logic. For instance there is Aristotelian logic, Modal logic, Mathematical logic, Fuzzy logic, etc. Perhaps you read my comment wrong? The problem is people don't seem to like to use the full name of the logic they mean. 98 percent of the time today when people say logic they really mean Mathematical logic and not any of the others. Math is popular & that seems part of it. Very few people refer to Philosophy anymore now that there is Mathematical logic. This is the most popular type now. – Logikal Aug 01 '20 at 06:34
  • You know it when the logic is Mathematical logic when there is use of connectives like /\, V, --->, etc. The symbols make it Mathematical. Secondly some of the terminology is used differently than the same terms are used in philosophy. Mathematical logic is math. People should use the full name of the logic system they are referring to but all too common people just say LOGIC. Some people didn't even know the name was Mathematical Logic. They swore it was just called LOGIC. These people did not know there were different TYPES OF LOGIC and there are disciplines that teach logic differently. – Logikal Aug 01 '20 at 06:41
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    @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. – Philip Klöcking Aug 01 '20 at 09:09
  • @Logikal The claim " The symbols make it Mathematical." reveals a complete lack of understanding of what mathematics is. – Arno Feb 17 '21 at 18:18
  • @Amo, you & Philip Klocking have missed my point! My point was that PRIOR to the invention of Mathematical logic there were no logical connectors symbols. Epistemology covered what you people claim as logic. Thus my point was to display why there is STILL a discrepancy with basic terminology Math people use. The words can be identical in spelling & pronunciation but the CONTEXT IS DIFFERENT. I am not a mathematician. I use the terminology in the context of PHILOSOPHY as opposed to Mathematics. Modal logic is another variation of Mathematical logic to Include possibilities over absolutes. – Logikal Feb 17 '21 at 21:27
  • @Logikal Maybe different symbols were used to represent and, or, not in non-mathematical logic but they fell out of use when mathematics started becoming more popular. – noviceFedora Feb 21 '21 at 07:44
  • @noviceFedora, no not at all. Aristotelian logic did not use any symbols. The symbols came with Mathematical logic in the 19th century. Mathematical logic wasn't around in the beginning nor the middle ages. Aristotelian logic is more semantic than mathematics & the purpose is different than mathematics which is kept under wraps & unspoken today. Logic back in the day is now in the topic of Epistemology. This is not identical to modern logic. Aristotelian logic still works. There are just other ways to Express it in symbols. It is still useful. – Logikal Feb 21 '21 at 07:51
  • @Logikal I think you are talking about symbols used in truth tables, although those symbols maybe mathematical, their semantics are similar to the words, and, or and not. These have been used in so called Aristotelian logic from their inception. I don't think mathematics can claim originality in this. – noviceFedora Feb 23 '21 at 08:39
  • @Novicefedora, No not at all reality. Aristotelian logic did not use any symbols for connector whatsoever. There are no AND, OR, IF . . . THEN & NOT. You are confused. Aristotelian logic did not use truth tables. You are part of the math people thinking math = logic. This is & was not the case in deductive reasoning. What philosophy used to call deductive reasoning is now called Epistemology. So there is no correlation to math. What you study is called "MATHEMATICAL LOGIC"--not logic. Deductive reasoning has more rules of inference & stricter rules about propositions than Mathematical logiic. – Logikal Feb 23 '21 at 12:32
  • Part of the confusion comes from people NOT making PROPER DISTINCTIONS. People seem to confuse LOGIC with MATH & DEDUCTIVE REASONING with MATH. People seem to correlate deductive reasoning with MATH as if they are IDENTICAL when they are NOT IDENTICAL. Math uses a small portion of deductive reasoning--not all of it. There are still more concepts & techniques used in deductive reasoning math does not use. So you are likely used to people saying "math is deductive reasoning" where the more accurate saying is math uses a portion of deductive reasoning techniques & concepts. – Logikal Feb 23 '21 at 12:54
  • @Logikal I'm not at all confused between Logic, Math and Deductive reasoning. Even in math, symbols for and, or and not represent semantics found in languages, which predate mathematics. It's just that mathematics assigns symbols instead of using words, but the concept used is still a language concept. For that reason it is part of large branch of logic, of which mathematical logic is also a small part. – noviceFedora Feb 26 '21 at 21:21
  • @noviceFedora, you are likely a math person with your thinking. To call the field LOGIC is what math people tend to do. You saying there is a topic called LOGIC by itself is like me saying CAR is a topic. In reality we know there are several types of CARS. Me stating I study CARS. Okay what kind of CARS? Surely one doesn't mean ALL CARS. Do you expect a mechanic to know the latest foriegn cars? Classic cars, the most popular? Just American? There are distinctions between fields of LOGIC. Each one has a prefix. Why do you think it's okay to ignore the distinction of each prefix before logic? – Logikal Feb 26 '21 at 23:18
  • @Logikal Logic is equivalent to automobiles, Cars is sub-discipline in automobiles. So mathematical logic is a sub-discipline of logic. – noviceFedora Feb 27 '21 at 11:15

4 Answers4

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"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.

k-wasilewski
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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.

Arno
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  • 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. – Logikal Feb 17 '21 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. – Logikal Feb 17 '21 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 – Voxywave Feb 17 '21 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. – Logikal Feb 17 '21 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. – Logikal Feb 17 '21 at 22:17
  • @Logikal Maybe, just maybe, if 99.99% of the people use words in a particular way, then its you and not them who is wrong about what words mean? – Arno Feb 18 '21 at 08:55
  • @Amo, You are still missing the point. It is like if the word triangle all of a sudden was MODIFIED or changed to mean a geometric shape with 72 sides now while we recall it used to mean some thing different. My point is STILL the math people are refusing to acknowledge there was a field called Philosophy that originated the terminology & someone modified what already existed for their own purposes. You have never heard of the discrepancies between Philosophy & Mathematics students? It is a real thing that has existed for years. You could look into this yourself. It is not me making claims. – Logikal Feb 18 '21 at 15:07
  • @Logikal Is your point that you feel that modern philosphers are somehow the "rightful heirs" of the logicians of yore, and resentful of modern logic being so mathematical? – Arno Feb 18 '21 at 15:29
  • @Amo, I am not resentful. I think it is the mathematicans that are being dishonest. It is not the case the terminology was invented by mathematicians & these words have always meant what people take them to mean today. That is a lie or misleading at best. There is no such thing as LOGIC. We have too many types of LOGIC that have different purposes to use ONE single shortcut name. The correct name is "Mathematical logic" & using any other kind of cover up tactic is deceptive. You are not using Aristotelian logic which is the original type. Why be deceptive & deny words were modified in math? – Logikal Feb 18 '21 at 15:37
  • This answer has the form "I am an authority, my experience is X, conclusion: yes". Not even an opinion, pure _ad auctoritatem_. – RodolfoAP Feb 19 '21 at 05:32
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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.

Sam
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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.

Voxywave
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