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I know that type of inferences you can make from a given system of axioms depend on what background logic you choose. For example, in some systems of logic, we can do a proof of contradiction but in others we can't. However I think most people would agree that a proof by contradiction is a reasonable way of establishing truth.

What I wish to ask is, how does "correct forms of reasoning" arise in society? Why are most people actually convinced that a method of inference like modus ponens actually work?


Related- Beliving the axioms

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    The laws of logic are not a good reflection of how people reason, and a society does not settle on a set of laws of logic to use. Nov 8, 2022 at 22:47
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    You presume that "society" has produced a correct form of reasoning. This is not in evidence.
    – Boba Fit
    Nov 9, 2022 at 1:43
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    Excellent point: C.D.Broad stated that "induction is the glory of science and the scandal of philosophy". Empirically, modus ponens proves correct (science is the quest for empirical truth). Metaphysically (metaphysics and philosophy seek for deeper truths), you just found that modus ponens could just be a fallacy. Welcome to metaphysics!
    – RodolfoAP
    Nov 9, 2022 at 12:18
  • @Rodolphoap, what are you talking about? If there is a false instance of modus ponens with all true premises can you provide just one for us to see?
    – Logikal
    Nov 9, 2022 at 16:26
  • Just for the record: valid does not mean true or truth in the real world. Rules of inference are not just based on what human leaders think. There are some things that are objectively true without human beings. Rules of inference have been time tested from Aristotle up to now with no false instances. So if you must say how do we know inference rules work towards truth we say because they have never failed yet from the beginning when humans recognized them & named them. Humans noticed these patterns occurred very frequently & the conclusion could be predicted 100 percent.
    – Logikal
    Nov 9, 2022 at 16:31

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By pursuasion. Some of it good, some bad - just look at politics around the world. In certain domains like academia or law courts, we have accumulated rules or guidance based on reasoning about outcomes. It comes down to consensus though, generally.

The Ancient Greek thinkers started formalising thoughts on argumentation in relation to 'loving the truth' rather than just winning debates (rhetoric by sophists), but people shared their philosophy because their case was pursuasive.

Francis Bacon updated the lists of argumentative fallacies in his Novum Organum, and this was much more the start of Modern Science than Newton, who believed in hidden codes in the Bible and dedicated a lot of time to alchemy - all of zero consequence.

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  • purrr -suation? meowww?? Nov 9, 2022 at 9:01
  • +1 but this can be improved: this is basically, an empiricist view, correct, but not sufficient, this immediately triggers the question: what about rationalism? How is such problem addressed in science? Are we pursuaded m-ponens applies to quantum mechanics?
    – RodolfoAP
    Nov 9, 2022 at 12:27
  • +1 but this is basically an empiricist view, which is correct, but not sufficient: this immediately triggers the question: what about rationalism (how are we rationally convinced that m-ponens is (logically) consistent)? Back to the world, how is such problem addressed in science?
    – RodolfoAP
    Nov 9, 2022 at 12:34
  • @RodolfoAP: I regard this answer as about discourse. See 'Can one speak unambiguously of "The" Scientific Method?' philosophy.stackexchange.com/questions/31942/… 'What's an example of a method that isn't Socratic method?' philosophy.stackexchange.com/questions/94597/… & wisdom as the accumulation of tools for decision making: philosophy.stackexchange.com/questions/82325/…
    – CriglCragl
    Nov 9, 2022 at 13:46
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I have the perception that this question has been neglected in the contemporary philosophy of logic. In the history of philosophy, a cartoonish summary of tentative answers would be something like 'We are rational animals because we are created in the image of God. Rational animals follow the laws of Aristotelian Syllogistic. Therefore, we follow the laws of Aristotelian Syllogistic'. A sketch of another possible answer is that following the laws of logic is advantageous from an evolutionary point of view: suppose you are a child in 15000BC in Southwest Asia and your mother communicates you that if you go in a specific part of the forest you will be eaten by lions, but you go there anyway, almost get eaten and when your mother asks you why you did it you respond that you are skeptic about modus ponens and believe modus stultus (stultus=stupid), which goes p, p→ q ⊨ ¬q. This is obviously just a dumb story, but I hope it shows the intuition behind thinking that believing some logical validities is advantageous from an evolutionary point of view.

Fortunately for you, there are not just these vague answers in the current literature. The philosopher Giorgio Sbardolini recently started a research project called 'the Evolution of Logic' to answer precisely this intriguing question and related ones (you can find the webpage of the project at the following link https://sites.google.com/view/giorgiosbardolini/research?authuser=0). He already attempted with Luca Incurvati to answer this question in the case of the logical operator commonly called 'negation'. Their answer is summarised in the abstract of this paper (https://www.journals.uchicago.edu/doi/epdf/10.1086/715140) 'Our hypothesis is that the emergence of expressions for denial, such as the word ‘not’, is an adaptation to existing conditions in the social and informational environment: a specific linguistic form was co-opted to express denial, given a preference for information sharing, the limits of a finite lexicon, and localized social repercussions against synonymy.'.

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  • " localized social repercussions against synonymy.'." what does this mean? Nov 9, 2022 at 21:00
  • Quoting from the paper 'There is a (marked) difference between m and −m, which is perceived overtly, so that any attempt to use m and −m as synonyms triggers a reaction from the social environment: a public fallout, perhaps in the form of a range of disagreeable reactions such as scorn, mistrust, and blame.'. 'm' is to be read as the assertion of something and -m its denial.
    – user63386
    Nov 9, 2022 at 21:38
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How does society decide what styles of argument are valid or invalid for practical purposes?

If valid here means logically valid, then it is not society which decides what arguments are valid, just as it is not society which decides that a tree looks like a tree.

Why are most people actually convinced that a method of inference like modus ponens actually work?

Most people do not understand formal logic and most specialists of formal logic do not understand human logic.

The Modus ponens is essentially the notion of general rule and everyone understands that if it is true that all bats are mammals, then any particular bat is a mammal. This really all there is to it.

All valid arguments have a logic and the logic of each valid argument is a logical truth, which I define as a self-evident logical expression, such as the Modus ponens, the Modus Tollens, the Hypothetical syllogism etc. Nobody decides that these logical truths are true. It is just self-evident. You no more decide that a Modus ponens is true than you decide of what you see. Whatever you see is by definition self-evident, but it is not you who decide what it is.

Since most people, at least people in good mental health, agree that the Modus ponens is self-evident, the Modus ponens has the same epistemological status as an objective fact, and society does not decide of objective facts.

Formal logic did not invent correct reasoning. Rather, humans recognise a correct reasoning when they see one, just like humans recognise light from darkness.

The difficulty, therefore, is not so much to reason correctly but to articulate some formal model of how human logic really works. Logicians have only been able to agree on a rather small number of rather simple logical expressions, such as the Modus ponens, and there is still no consensus on a formal model of human logic.

This absence of a formal model shows that humans do not need to be taught formal logic to be able to reason logically. This has long been known. Plato himself observed that uneducated people were able to give logical answers.

Logical reasoning is convincing because humans are naturally logical. All humans decide that a cat is a cat because it looks like a cat, which is just an application of a general rule, which is itself essentially a Modus ponens.

We are convinced because we are innately logical.

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