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Thread: The deductive logic of arguments v. mathematical logic

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    Contributor Speakpigeon's Avatar
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    Quote Originally Posted by fast View Post
    Do you have an argument that would be considered sound (“sound” as used by logicians or those that adhere to what you call mathematical logic) that would not be considered valid (the sense of “valid” you use) by you?
    A small collection, yes.

    Quote Originally Posted by fast View Post
    The disconnect between our sense of “valid” that’s been with us for thousands of years and the newfound sense of ‘valid’, the corrupted version through mathematical molestation becomes inconsequential when we deflect away from the implication of the variance between the two when soundness used by logicians is compared to validity used by the layman.
    Yeah, sure, that was my working assumption initially. I'm a very reasonable person and I thought, hey, all these mathematicians, surely they must know what they are talking about! I expected some sort of resolution along the line you're suggesting here. But at some point, I realised that what these people are talking about, that is, mathematical logic, isn't logic, i.e. isn't the logic of human reasoning.

    No big deal, though, just please leave us alone and don't come and lecture us human beings about what arguments are valid and what aren't.

    But no. They have to lecture people. They can't stop themselves. They won't say, Oh, you have a different view on logic? Let's debate on that in a rational and civilised manner! No, instead, wherever I would post something on logic, some intemperate dude would start chiding me as if I was the villainous perpetrator of a hideous crime. Two of them actually completely lost it, going beserk on line! LOL! They sort of don't like ... the contradiction! It makes them explode, I guess.

    Quote Originally Posted by fast View Post
    If I’m wrong, show me an argument I deem sound that you don’t deem valid.
    You're wrong and I won't show anything, but for some of them I found that they were already on Wikipedia, so it's not even a secret and therefore mathematicians know of them, I mean those at least who know their stuff.

    Quote Originally Posted by fast View Post
    I still think language (and not any substantive issue) underlies the conflict. <imagining speakers discussing a topic through prankster interpreters>
    Sure, you do, and that's fine with me, as long as you don't pretend to know that mathematical logic is correct. You just don't know that. Most mathematicians don't even know what it means for a theory of logic or a definition of validity to be correct. They just haven't a clue.

    I'm not here to teach logic. I make an empirical investigation, and it's for all to see. The ones without blinkers.
    EB

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    What I see is analysis at work. They’ve taken a concept (what you call validity) and insightfully separated the structural integrity (or what allows for sensible entailment and implication) from the relevance of truth. They’ve taken a combined, intertwined, symbiotic thing and broken it down into two major component parts.

    However,

    If the house is wet, the house won’t burn down.
    The house is wet.
    Therefore, the house won’t burn down.

    Is that valid? Is that sound?

    The first premise is true, for the particular house in question is impervious to fire, wet or not—and a house impervious to fire, wet or not, will not burn down. The second premise is true because it’s raining on the house and the rain is wet. The conclusion is true for the same reason the first premise is true.

    The structure seems to make sense, but before knowing the reasoning for why the first premise is true, there’s so much doubt because there’s the appearance that the house being wet is somehow relevant when it’s not.

    It goes to show that truth is a requirement for your sense of validity (as it should be with your sense of validity) and are led to think it’s not valid because it appears untrue whereas validity (mathematical style) won’t make for a sound argument unless all premises are true.

    When we use the very same words to convey different things, a convoluted interpretation is bound to ensue. I suppose many mathematicians might not have become so well-versed on non-glossary terms. If all they know is their specific usage and it’s engrained in them, they probably will deny such seemingly uneducated interpretations. They do have a word for your use of validity: “sound.” So, it’s not that they wouldn’t recognize validity—it just goes by another name. Truth must be separated from structure in order to isolate them. They’ve just adopted the term and chizzled away truth pertainment.

    Still, there are arguments that are clearly unsound because of truth alone that you find valid. Right? Curiously right? So, there is still something deeper about your view that I haven’t quite gotten down.

    I recall once you saying something seemingly derogatory about statements including the word “if” and how it factored in somehow—something about needing to be tested against the real world? Kind of like my first premise not sounding particularly probable.

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    Contributor Speakpigeon's Avatar
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    Quote Originally Posted by fast View Post
    What I see is analysis at work. They’ve taken a concept (what you call validity) and insightfully separated the structural integrity (or what allows for sensible entailment and implication) from the relevance of truth. They’ve taken a combined, intertwined, symbiotic thing and broken it down into two major component parts.
    No, it is much less glorified and much more simple. Sort of pathetically simple. The story is that they made basically one unwarranted assumption and one unwarranted hypothesis. That was clearly doomed from the start. The unwarranted hypothesis is well known and seems very reasonable. The unwarranted assumption, well, it's an assumption, they still as of this day don't even know they've made it. They haven't a clue.

    The difference between mathematics and empirical sciences is that in mathematics, once you've settled on the axioms, you're unlikely to have any surprise. It's just hard work trying to find out the logical consequences of your axioms. None of your conclusion is likely to contradict your choice of axioms, unless you had been very careless in selecting them. Counterexample, Cantor's theory of sets, which included several contradictions. It must have been a traumatic experience, and you still see today mathematicians insisting intuition isn't reliable. So, when they find a contradiction, what do they do? They just invent a machinerie to encapsulate the contradiction to make it ineffective. It's imagination at work and our imagination is a curse. Mostly, imagination is laziness. It allows you to circumvent the problem without starting all over again. Laziness.

    When scientists realise their pet theory is junk, like for example the jewel in the Crown, Newton's Theory of Gravitation, they grumble and keep looking at nature waiting for someone bright to figure out what the problem is and what might be a "reasonable" solution. Imagination plays a part but mostly not anything you can imagine will do.

    Mostly, there's just one possibility given what you think you know. So, wild imagination is kept in check by the requirement that the theory fit with nature, though this is not so obvious in the case of Quantum Physics and Relativity (and even less in the case of String theory). But, broadly, if anyone thinks they know better, they're welcome to explain themselves. But here, scientists will throw the falsified theory in the junkyard and the redesign the theory from top to bottom. That's the only way.

    Mathematics is an ever-growing fat mass of axioms and theorems. You even have theories which are essentially a repeat of each other! By comparison, science is slim. Relatively easy to do it all over again when the need arise. Two very different world. Logic is science. Not maths.

    In the case of mathematics, who is going to tell them that what they've imagined is wild junk? There's no check and balances. Anything goes as long as it is "logical", and now therefore anything at all goes because logic is "arbitrary" and you can justify any idiot theory by making up a new kind of meaningless logic. Every mathematician their "logic". They don't even bother to keep track of the mess because it's such a mess. It makes me think of the explosion of Protestant Churches because unchecked by the authority of the Pope.

    You can't even make any generality about it, notwithstanding what you just said. But, let's limit ourselves to "classical logic". They haven't analysed anything. Their definition of validity doesn't make sense, which is why some mathematicians invented relevance logic, which is just as pathetic. What you call "sensible entailment and implication" doesn't even exist. You couldn't give an example of that. It is easy. Look at truth-table proofs and try to make sense of why the result is what it is. There's no sense to it. The rules are simple, so you understand the calculation. But there's no sense in it. It just doesn't mean anything at all. Do the exercise. Write the truth tables of all sorts of formulas. And you will see. No sensible entailment and implication. None at all. The only reason they've adopted this calculus is that it seemed to give the correct results. They adopted it because they are mathematicians. No sense at all but apparently the correct results. However, it's not true for all formulas. So, really, nothing at all "insightful". It's plain moronic.

    Quote Originally Posted by fast View Post
    However,

    If the house is wet, the house won’t burn down.
    The house is wet.
    Therefore, the house won’t burn down.

    Is that valid? Is that sound?

    The first premise is true, for the particular house in question is impervious to fire, wet or not—and a house impervious to fire, wet or not, will not burn down. The second premise is true because it’s raining on the house and the rain is wet. The conclusion is true for the same reason the first premise is true.
    Nah, you can't do that. If you consider a particular house, then it's no longer the same argument. In effect, you are smuggling in a new premise, "the house is impervious to fire". You need to analyse the argument as it is, without redacting it.

    If you want an argument with all true premises and conclusion, here it is:

    p1 True;
    p2 True;
    C Therefore, true
    Now you have an argument which is trivially valid and literally doesn't "mean" anything at all, which is what you just called "insightful" and "sensible". But I'm fine with it, as long as you don't redact it. It's valid, but useless, except for methodological considerations.

    Quote Originally Posted by fast View Post
    The structure seems to make sense, but before knowing the reasoning for why the first premise is true, there’s so much doubt because there’s the appearance that the house being wet is somehow relevant when it’s not.
    You don't seem to be aware that "relevance" is precisely the word used by mathematicians doing mathematical logic, not exactly mainstream but still "classical". Why don't you abide by their notion of "relevant" validity?

    Further, I never bought the notion of relevance myself and I now understand why it is... irrelevant. And it is easy to demonstrate why. Very easy.

    So, you are beating a dead horse here. All these notions like "relevance" mathematicians have imagined are just that, imagined. They are not properly justified because to justify them they would need the empirical evidence provided by an investigation of logic as the logic of the human mind, something mostly they think would be suicide.

    Quote Originally Posted by fast View Post
    It goes to show that truth is a requirement for your sense of validity (as it should be with your sense of validity) and are led to think it’s not valid because it appears untrue whereas validity (mathematical style) won’t make for a sound argument unless all premises are true.
    Nah. You don't get it. It's not and never was a question of the premises being true or false.

    Quote Originally Posted by fast View Post
    When we use the very same words to convey different things, a convoluted interpretation is bound to ensue. I suppose many mathematicians might not have become so well-versed on non-glossary terms. If all they know is their specific usage and it’s engrained in them, they probably will deny such seemingly uneducated interpretations. They do have a word for your use of validity: “sound.” So, it’s not that they wouldn’t recognize validity—it just goes by another name. Truth must be separated from structure in order to isolate them. They’ve just adopted the term and chizzled away truth pertainment.

    Still, there are arguments that are clearly unsound because of truth alone that you find valid. Right? Curiously right? So, there is still something deeper about your view that I haven’t quite gotten down.
    Because I don't explain. Sorry for that but I'm not here to teach logic. I am investigating. Of course some arguments are valid and unsound:

    Trump is a Martian;
    All Martians are presidents;
    Therefore, Trump is president.

    We all know this argument is valid and unsound, yet, our reasons are different from the reason given by mathematical logic.Truth table logic says it's valid because the premises are false, which is just plain meaningless and not at all "insightful" and "sensible". We will all say instead it is valid because the conclusion is necessarily true given the premises. Which makes sense. And it's all formally valid and validity has nothing to do with whether the premises are true or false.

    Quote Originally Posted by fast View Post
    I recall once you saying something seemingly derogatory about statements including the word “if” and how it factored in somehow—something about needing to be tested against the real world? Kind of like my first premise not sounding particularly probable.
    Possibly, but that would be a different context, perhaps the online test where you have to say which cards would need to be flipped over to check whether there is a given implication? Yes, and the test is just wrong, made by people who don't understand logic because they didn't even try to understand it.
    EB

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    I’m beginning to wonder if logic is something that can be taught. Maybe any such teachings would be nothing more than opening our eyes to what we are already innately capable of doing ourselves if only we’d focus more intently. Nay, that’s probably silly. Maybe I can deduce the right answer and fact check it against something. Nay, that might even be sillier. What’s taught might not actually be what it’s said it is. Hell, even facts are about as whimsical as people who use the term. I wonder if our current lexical use of “validity” will one day have that curious word “archaic” next to it—replaced by another usage propagated by our finest nonthinkers.

    on se parle plus tard

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    That is a good question. I think as kids we learn logic and reasoning by immersion like we learn language. It can be taught formally. I had a philosophy class in logic and critical thinking. I don’t think how ro apply logic can be taught, that comes from experience.

    EB conflates the word logic with a generalization of math.

    Mathematical logic is Boolean algebra. It generally maps to formal logic. EB has some imagined logic to math other than common reasoning and logic. Abstract algebra is the other term.

    EB does not grasp what axiomatic means. There are rules and definitions in geometry and algebra, but no logic. We apply algebra and geometry to a problem using general logic and reasoning like anything else. EB thinks math is based on assumptions with no ‘Aristotelian Logic’ as such having no foundation.

    Theory of Computation in CS deals with applying logic to problem solving. Logic trees and graphs, Turing Machines. There are classes of problems that cannot be solved with linear Aristotllian - classical logic.

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    Quote Originally Posted by fast View Post
    I’m beginning to wonder if logic is something that can be taught. Maybe any such teachings would be nothing more than opening our eyes to what we are already innately capable of doing ourselves if only we’d focus more intently. Nay, that’s probably silly. Maybe I can deduce the right answer and fact check it against something. Nay, that might even be sillier. What’s taught might not actually be what it’s said it is. Hell, even facts are about as whimsical as people who use the term.
    We can obviously learn formal logic and it is the only kind of logic we can learn from somebody else.

    But we can also discover our own logic, or rather, the logic, presumably, of our brain, and so to some extent learn what it does, just like we can discover and learn about any of our own brain's manifest capabilities, like memory, perception and such. But maybe that won't get you very far.

    That we are still none the wiser after 2,500 years of Aristotelian logic, not to mention 166 years of dumb mathematical logic, suggests it's a seriously difficult thing to do. Did Buddha say something about it that could help?

    Quote Originally Posted by fast View Post
    I wonder if our current lexical use of “validity” will one day have that curious word “archaic” next to it—replaced by another usage propagated by our finest nonthinkers.
    The word can change as it often did in the past, but validity really just means that an argument is valid if the human brain somehow accepts that the conclusion follows from the premises. It won't go away unless we somehow changed the nature of the human brain, which won't happen soon in any case and probably ever.

    Quote Originally Posted by fast View Post
    on se parle plus tard
    直到你到巴黎來。
    EB

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