Historically, yes there is. But they’ve both been replaced by modern global math, whose formalism is largely shaped by classical western math, so many people get the idea that math is just somehow intrinsically “culture-free” or “essentially western”. Culturally specific philosophical/religious/literary disciplines have been more successful in maintaining their separate disciplinary identities in academic perceptions of their subjects.
Note that I’m not trying to claim that, say, pre-modern Chinese or Indian mathematicians got different answers from Greek ones when computing 2+2 or something like that. But various mathematical concepts had different levels of salience in the different traditions. E.g.:
primality: very big deal in Greek mathematics, not treated in Indian or Chinese.
numerical approximation: generally considered suspect in Greek mathematics because of lack of rigorous proof and/or geometric representation of magnitudes, but explored in great detail in Indian math.
And so on and so forth, excuse hijack.
Huh, so did an undergrad advisee of mine some years ago. Simultaneously.
He thought it was an interesting experience but found it tricky to remember which notation conventions he was supposed to use on which exam.
The real point is that there are many logics, all perfectly valid. There is 3-valued logic where there is one intermediate value. For example, the set of mathematical statements can be divided into proved true, proved false, and unknown. Even if you can show that no proof can exist, it does not follow that it is false.
Then there is a logic in which the truth value of something can be any real number between 0 (false) and 1 (true). That one is close to, but not quite the same as fuzzy logic. You can logics in which the truth values are not totally ordered.
The point is that {0,1}-valued logic is perfectly consistent and that is what your professor was teaching. And you could have learned that one, even if you didn’t accept it personally. Each logic has its own area of applicability.
I studied logic in the departments of philosophy, mathematics, and computer science. There was, at least for me mostly only a matter of emphasis between them, and lots of repetition of the basics, and also repetition of some of the more advanced stuff.
Some of this depends on the interests and biases of the individual lecturers.
All three would cover the basics of boolean algebra, and cover Church through to Gödel. But the emphasis placed on each and the implications differed.
I was about 19, had been mostly taught not to argue with teachers, and just wanted to pass the course. These days, sure, I’d have argued.
I actually did try arguing the issue with a different professor, in a different class though in the same department, a year or two later. I got up and went to the door of the room and stood there with my feet and lower body outside and my head and upper torso inside and said “Am I in the room or out of the room?” and he said “Don’t be trivial.” The specific example was trivial but the issue wasn’t; but again I was clearly not going to get anywhere arguing about it.
Was this understood in USA undergrad philosophy programs in the early 1970’s?
That was basically what I did; well enough to pass the class, anyway.
And if it had been presented in that fashion, I would have had no issue with it. But it was presented entirely as ‘this is what logic is, there are no other options.’
And of course, there’s the phenomenon that all wiki-links lead to philosphy: click on the first substantive link in the lead of any wiki article; click on the first substantive link in the wiki article that opens; keep doing, and eventually you will land on the wikipedia article on “Philosophy”.
(Ironically, the article on “Getting to Philosophy” is an exception to the rule, since it ends in an endless loop of communication - language - classical language - Latin)
I was a math major at a small liberal arts college in the 90’s, and the first thing that my advisor informed me was that I could get out of my humanities/philosphy requirement by taking two logic courses, which were cross referenced both as math and philosophy.
The first class was sentential logic and was taught by the philosophy department. If found it extremely easy and fun, since I’d been reading Smullyan since age 12, but many of my classmates who were coming from a philosophy background struggled. I think it culminated in the proof of completeness for sentential logic
The second course “mathematical Logic” was an upper division class taught by the math department but fortunately for my graduation requirements was still cross referenced with philosophy. It was much more dry and complex, defining formal systems and resulting in Goedel’s incompleteness theorem. I think everyone taking that class was a math major.
Rolling my eyes at the dumbass academic advisor at a liberal arts college whose only “advice” to a young undergraduate math major about fulfilling a humanities/philosophy requirement was how to “get out of” it.
Why was the dumbass even teaching at a liberal arts college if he opposed the fundamental liberal arts college principle of encouraging students to engage seriously with intellectual disciplines beyond their own major fields? Or did he just assume that a math major wouldn’t have the breadth or intellectual curiosity to benefit from studying a humanities subject?
[checks forum] Oh, right. Well, time for me to shut up and leave I reckon.
It occurs to me that there is a difference between logic to a philosopher and to a mathematician. To a philosopher, logic is a psychological commitment. To a mathematician, all kinds of logic are worthy of serious study, even if they give different results.
If you don’t accept excluded middle, that is a philosophical statement. A mathematician is perfectly happy to consider logic with and without excluded middle. Or with and without choice. The results are different, but all are valid within the axioms you choose.
There is a sequence that can be described that appears to expand indefinitely, but this cannot be proved or disproved in basic Peano arithmetic, using ordinary finite induction. To be precise, it is a method of generating sequences and what cannot be proved is what happens to all such sequences. Using a tiny fragment of transfinite induction (up to \epsilon_0) it is trivial to prove that all such sequences eventually end in zeroes, contrary to their eary growth. So if you accept only finite induction, the question cannot be answered.
What the hell has put a bee in your bonnet Kimstu.
It wasn’t as if that particular requirement was the only exposure I was going to have to non-STEM while I was there. I still took 3 semesters of humanities, 5 semesters of psychology, 2 semesters of linguistics, as well as the math physics and yes logic, Why was he teaching in a liberal arts college probably because he preferred teaching math students who were interested in the theoretical side of mathematics, and learning for it s own sake rather than just "How can I pass the class to get an engineering degree because I hear that is where I can make the most money. "
For the record the English students were told that if they wanted to they could take natural science to get past their physical science requirement, and language courses to satisfy their math requirements. There is nothing particularly evil about letting your advisees know about their options, and no that wasn’t the only thing he told me, nor actually probably the first, I just said it was because it makes the story flow better.
