"I don't think anybody ever claimed Boole's algebra would somehow be unrepresentative or untrue of human logic." - Don't say that in front of intuitionists, they'll tear it to pieces. In particular, lots of people have taken issue with the material implication connective.

Relevant for two approaches to logic : Jean Van Heijenoort, Logic as Calculus and Logic as Language (1967) as well as J.Hintikka, Lingua Universalis vs. Calculus Ratiocinator.

Most human beings also have geometric, mechanical, ethical, etc., capacities, logic is not that special. Logically consistent and applicable to the real world does not amount to "somehow true", witness instrumentalism. Applicability is task-specific, there are many "logics". Boole's algebra of logic was both limited and crude as an account of natural reasoning, Gentzen was arguably much closer. Ramsey talked of "human logic" in a different sense, he is taken as a precursor of epistemic logic. To make for a substantive answer you need to unpack "somehow true". True how? Applicable to what?

The closest thing I can think of that's still going strong today is certain parts of modal metaphysics, where some philosophers hold that modal logic is a theory of the nature of necessity and possibility. [Williams' Modal Logic as Metaphysics is a good example of this.

@Kevin Yes, but whatever the claim, you'll find somebody to disagree with it. But, OK, I'll rephrase...

@Conifold "humans also have geometric" Sure, I didn't claim human logic had anything supernatural about it. I think of it as akin to a sense of perception like vision etc. We study vision empirically, so we can study logic empirically. I certainly do.

@Conifold 'Logically consistent and applicable to the real world does not amount to "somehow true"' Sigh... Did I say that?! Please take more time to understand what I said.

@Conifold "logic is not that special" Please read again. I didn't say logic is special compared geometry. I said it's a special case among what mathematicians usually work on.

@Conifold 'you need to unpack "somehow true"' No I don't. Either there are "mathematicians whose work on logic should be seen as not only mathematical but also avowedly scientific in the sense that they would try to produce a theory of logic explicitly presented as somehow true of human logic" or they aren't. All words in there are in the dictionary.

You put too much faith in dictionaries, "should be seen", "avowedly scientific", "somehow true", "human logic" are vague buzz-phrases that do not mean much. Hintikka, Priest, Ben-Yami, Girard, etc., all profess to present something "somehow true of human logic", nay, something that reflects it better (in some respect) than the competition. But you speak of "human logic" as if it was a single thing. If your analogy is to vision you should be looking into experimental psychology, not products of anecdotal self-introspection by mathematicians, and expect an array of hazy partial models instead.

@Conifold "Hintikka, Priest, Ben-Yami, Girard" Not interested in vacuous suggestions. Scientists have often been very explicit about science as the correct method for investigating nature. That's my standard for "explicitness". We know what they claim they are doing. I've read a few books about logic, by mathematicians or philosophers, looking specifically for that sort of thing. I spent 45 days on it. Didn't find anything. I still don't know what mathematical logic, according to its practitioners, is supposed to be about. Mathematics, yes. Logic, yes. Is that human logic? They don't say.

@transitionsynthesis I would agree generally that mathematical and philosophical logics seem obviously at least inspired by human logic but so was curved space geometry and the complex numbers. But I'm looking for explicit claims that the logic they are working on is not just inspired by human logic but is meant to be a model of it. Any of them ever claimed that the mathematical definition of validity was equivalent to that given by Aristotle, do you know?

By 'human logic' do you mean the way people actually make inferences?

@Eliran Not quite. I see human logic as an empirical fact and as such it should be investigated scientifically. Aristotle did a good, empirical, job, and we can all do it to some extent but only if we try. Sure, we make mistakes but we do whatever we do and we still do good science, so why not a science of logic. There are complex reasons that we don't, not least that Descartes successfully trashed logic in the eyes of the first empiricists. Also philosophers running in circles. And mathematicians not much interested in the philosophy or the science of it.

You're not really answering my question. A scientific study of what exactly? What is the phenomenon to be empirically investigated? You need to say more than 'human logic' because it's unclear what you mean by that.

@Eliran Whatever inferences most people make probably won't get us very far. But there's no other source. Aristotle probably looked at what other philosophers were doing. Other logicians uncovered more logical truths beyond Aristotle's syllogisms. That's empirical data. Any logic has at least to prove those valid.

The closest thing I can think of is Lukasiewicz and other Polish logicians in 1920-1939. My sense is that these guys thought they were developing the correct theory of logic, making genuine scientific discoveries that outstripped Aristotle, the Stoics, Frege, etc. These were all logicians who were also philosophically oriented, having studied with people like Husserl and Twardowski. This was a time when mathematical logic and philosophy were not nearly as insulated as they are now in university departments.books.google.com/books/about/…

Have you read Priest's or Girard's manifestos, or is this just a rant sight unseen? You are not the only one passionate about "true logic", and yore is not the only place to look. Look below, are you happy with the answer you got? Either you get your act together and approach this without rigid preconceptions and golden age dreams about Aristotle, and take the complexities of the subject seriously, or you will consign yourself to online rants. A modern account will have as little to do with Aristotle's logic as it would with his physics.

@Conifold LOL. You're not even in a bad mood, right? My piece is not a rant. I framed my question according to my view of things, based not on an unbridled imagination but on a very long standing interest in logic. So, you're welcome to prove me wrong but you'd need to focus on the substance of my question rather than on this poster. It is ridiculous of you to suggest as you clearly do that unless I've read all the books on logic, expressing my view is some sort of outrage.

@Conifold I have no preconception on Aristotle I'm not ready to drop. I change my thinking on him on a day-by-day basis. Still, he at least got something right and that was 2,500 years ago! I don't see for now anything wrong with his logic. It's human logic, i.e. correct, and his presentation of the principle of validity is the best I know of. All a bit short on details but again, that was 2,500 years ago. Aristotelian logic is the only correct expression of human logic I'm aware of. How many mathematicians, nay, logic experts, have worked on this exactly do you think?!

Count the number of I-s and my-s above, self-reliance is good only up to a point. There has been a lot of developments in 2000 years, and you are not giving yourself enough material for productive thought by filtering it through a self-imprinted archaic template, if "Aristotelian logic is the only correct expression of human logic" your are aware of. Changing only your thinking of him is running in a hamster wheel. And it is a shame. Because you do show freshness of thought that could be more aptly applied if you drop the idea that "human logic" as a unified block is a meaningful expression.

@Speakpigeon - I share your view that Aristotle's logic models human reasoning. I've never seen the need for another logic either in metaphysics or ordinary life. Problems arise for it only where rigour is not observed.

@PeterJ Yes, and the beauty of it is that most mathematicians don't even use formal logic. However, rigour is indeed a concern. Leibniz wanted a method to help rigour in philosophical dispute just as Frege wanted a method to help more rigour in mathematical proof. And Aristotle's syllogistic isn't a model of human logic at all. Maybe I should ask a question about this.

@Speakpigeon - It would be a good question. I see no evidence that A's method does not model human thought, and I might ask it myself to see if there is any. .