View Poll Results: Do humans have an inherent capacity to decide that a conclusion follows necessarily from premises?

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Thread: Do humans have an inherent capacity to decide that a conclusion follows necessarily from premises?

  1. Top | #41
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    Quote Originally Posted by Speakpigeon
    How could they decide which logic is correct?! I have asked you for a justification that the definition of validity used in mathematical logic was correct, to no avail. There is no such justification. So, they may have arguments about which is correct, but none of them can support their respective claim.
    They try to ascertain which logic is correct by thinking about it, considering different philosophical arguments, etc. It's the way debate about epistemology, metaethics, metaphysics, the philosophy of physics, etc., happen. And to some extent, about how pretty much every other philosophical disagreement happens, and even some scientific disagreements. As for my argumentation, that's a matter for the other thread you started. But I have not replied to that one because I do not want to engage in multiple debates simultaneously, at least not until I'm reasonably confident that the exchange will remain civil.

    Quote Originally Posted by Speakpigeon
    There is just one deductive logic. We all use the same. Whether in our linguistic utterances, our thoughts, in writing, colloquial or formal. What is not deductive logic is mathematical logic. What is funny is that mathematicians use deductive logic like everybody else and somewhat with more rigour, yet they keep up the fiction that mathematical logic is "correct". It's not. They know it's not but they keep pretending. One is reminded of the tremendous capability of human beings for dissembling. That's toeing the party line and nothing else.
    Even if there is one single logic that encompasses the full extent of human language communication, that does not mean that every form of human communication uses the full logic. In particular, in mathematics, we do not use the causal meaning of the conditional - which is one of the but not the only meaning in colloquial language. As a result, the part of logic that applies to that sort of conditional will not be in play in mathematics.

    Mathematical logic is deductive logic, of course. Your claims about pretending, etc., are simply false. I know plenty of mathematicians. I have not found a single one who is pretending and believes that what we're doing is logically corrrect. You simply are way wrong about the psychology of mathematicians.

    Quote Originally Posted by Speakpigeon
    No it's not. Human logic and mathematical logic are mutually contradictory.
    That is not true.

    Quote Originally Posted by Speakpigeon
    Causality, if it exists at all, is a fixture of natural world. As such, there can't be any logical problem with causality.
    Of course. I'm not remotely suggesting that there is. What I'm saying is that the use of the conditional to indicate causality is not present in mathematics. So, whatever the part of human logic that deals with that sort of conditional statements is, mathematical logic is not meant to capture it, and it's not failing for not capturing it. There is another use of the conditional in colloquial speech, which is also in use in mathematics. In the case of that conditional, classical mathematical logic captures our common sense logic.

  2. Top | #42
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    Quote Originally Posted by Speakpigeon
    Your point is irrelevant. Logic does not depend on any formal system and does not depend on language. You are confusing the communicating of the message with the meaning conveyed. Logic is what makes us say what we say when we speak logically but 99.999% of the time we don't even verbalise the logical inferences we make. Indeed, we are not even aware we are making them because, essentially, they remain unconscious. Aristotle pointed at logic, and like most people you're still looking at his finger.
    What depends on language is the capacity to ascertain whether a conclusion follows from premises. It's not present in people who do not even have an understanding of what a premise is, or what a conclusion is, etc., so in particular, it is not present in people who do not have language. This is not to say that when we are making logical inferences, we verbalize it. In fact, much of the logic we do, we do unconsciously. But we do have language. Without language, we can still see patterns, and make probabilistic assessments or moral judgments about things we represent intuitively 'in our heads' about the world. But we cannot even try to ascertain whether a conclusion necessarily follows from premises. That requires language.

    Is there a possible human community in which people do not have language (of the sort relevant in this question), not due to malfunctioning, but just having devised one such language?
    If the answer is 'yes', then it is not the case that the ability to ascertain whether a conclusion follows necessarily from premises is a part of human nature.
    Since there is not enough information to tell whether the answer is 'yes' (at least, I do not have enough information, but if you do, I would ask for relevant links), I reckon we do not have enough information to establish that the aforementioned capacity is a part of human nature.


    Quote Originally Posted by Speakpigeon
    Mathematical theorems are understood by mathematicians using their intuition mostly. Proofs are sketchy indications of the validity of the theorem meant for other mathematicians. They understand each other mostly without using formal logic. Mathematical logic is irrelevant except probably in the few cases where it is misleading.
    The first part is true: Mathematical theorems are understood by mathematicians using their intuition mostly. But our intuition is properly captured by mathematical logic. No, we do not formalize most of the proofs in first-order language (though in some areas, they do), but we do use (intuitively!) the powerful inference kit of mathematical logic. Let me put it in another way: if mathematicians limited themselves to Aristotelian logic, mathematics would be vastly different from what it is. Indeed, Bomb#20 already gave a simple example of a valid inference that Aristotelian logic fails to capture, but it's easy with the predicate calculus. But in mathematics, there are inferences like that, but also far more complicated than that.

    Also, as I have argued in the other thread, if you mathematical logic were 'wrong' in the sense of failing to capture human logic in the context of mathematics, it would be better than the 'right' logic - i.e., that which captures human logic -, in the context of mathematics. This, however, is a matter for the other thread, so I will refer you to my reply in that thread.

  3. Top | #43
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    Quote Originally Posted by Angra Mainyu View Post
    Indeed, Bomb#20 already gave a simple example of a valid inference that Aristotelian logic fails to capture, but it's easy with the predicate calculus.
    You're making a wrong assumption about Aristotelian logic. I can see why Bomb#20's example is not conclusive. It is in fact very easy to see that Aristotelian logic can prove Bomb#20's example valid. You can't because of your wrong assumption.

    Quote Originally Posted by Angra Mainyu View Post
    Also, as I have argued in the other thread, if you mathematical logic were 'wrong' in the sense of failing to capture human logic in the context of mathematics, it would be better than the 'right' logic - i.e., that which captures human logic -, in the context of mathematics. This, however, is a matter for the other thread, so I will refer you to my reply in that thread.
    Sorry, I don't buy that. I know of incorrect inferences and incorrect proofs accepted as valid in mathematical logic. That's definitely not better. Mathematicians have invented logical rules that do not represent how logic really works. However, being the formalists that they are, they follow, logically, their rules. But their rules being wrong, the results can only include invalid conclusions.

    It is definitely baffling to me that the obvious facts that show mathematical logic is wrong don't seem to register with you or any mathematicians, and indeed with any philosopher. Well, it's just life but there are millions of mathematicians worldwide. What are these people doing? Futile question, I guess.

    Anyway, thanks for going into the detail of your thinking. There's not much else to say. We just disagree.
    EB

  4. Top | #44
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    Well, an innate capacity would imply that most people would be quite good at evaluating simple logical syllogisms and if/then conditionals. Yet, research shows that people are generally quite poor at deductive logic, with the majority of people getting some simple logic problems wrong. This is true if you give people abstract forms of arguments (If p, then q; Not q; therefore not p). Most people will incorrectly say this conclusion necessarily follows the premises and/or will generate that conclusion from the premises. People get better at it if you use real world concepts and relations in place of abstract tokens, but that only demonstrates that people are not using deductive logic to reason about the problems. Also, if you use real world content, people will be even worse if the logical validity of the conclusion contradicts their a priori beliefs about the conclusion. IOW, people generally cannot apply logical reasoning to arguments independent of their a priori agreement with the conclusion.

    Of course, some people are better at logical reasoning than others, and that is partly predicted by measures of general cognitive ability but also by measures of thinking dispositions where some people are more prone to go with their "intuitions" and prior beliefs (aka biases) and others are more able to set their beliefs aside and evaluate what is implied by a set of given claims. The difference between ability and style is the difference between what one can do if they try versus what one is inclined to try to do.

    In fact, more religiosity predicts greater logical errors due to a tendency toward a more intuitive less analytical cognitive style.

  5. Top | #45
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    There seems to be a distinction to be made between inherent capacity and ability....the latter being a matter of education or training.

  6. Top | #46
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    Quote Originally Posted by Speakpigeon
    You're making a wrong assumption about Aristotelian logic. I can see why Bomb#20's example is not conclusive. It is in fact very easy to see that Aristotelian logic can prove Bomb#20's example valid. You can't because of your wrong assumption.
    If you want to show it's valid, please go ahead.
    In any case, I do not need that example, so I will address the rest of your points (though very briefly, because I'm posting the details in the other thread).
    Quote Originally Posted by Speakpigeon
    Sorry, I don't buy that. I know of incorrect inferences and incorrect proofs accepted as valid in mathematical logic. That's definitely not better. Mathematicians have invented logical rules that do not represent how logic really works. However, being the formalists that they are, they follow, logically, their rules. But their rules being wrong, the results can only include invalid conclusions.
    Well, if it were true that some CML-valid proofs (i.e., proofs valid under classical mathematical logic) are not valid, then it would be better of course to know that they're not valid. However, CML would still be better as a means of finding mathematical truth than human logic, and in the context of mathematics at least, we should eschew validity and instead go for CML-validity. The invalid conclusions you talk about would still be mathematical truths, obtained from other mathematical truths by a truth-preserving method (namely, CML). They would be invalid in the colloquial sense of the word 'valid', but then, that is a problem for validity, not for CML (and yes, it would still be a problem for CML if it's believed to match human logic when it does not; but then, the solution is to stop claiming that it matches human logic, but still keep the superior method).


    Quote Originally Posted by Speakpigeon
    It is definitely baffling to me that the obvious facts that show mathematical logic is wrong don't seem to register with you or any mathematicians, and indeed with any philosopher.
    That is another matter. Of course I disagree with you, but the argument I'm making in this context is under the assumption that you are correct about that.
    In other words, here I'm saying that if CML is wrong as you claim, then it is a tool superior to logic as a means of finding mathematical truths, and we should keep using it. But all of these are arguments for the other thread, and in fact I have given much more details over there, so I will not repeat more points here.

  7. Top | #47
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    Quote Originally Posted by DBT View Post
    There seems to be a distinction to be made between inherent capacity and ability....the latter being a matter of education or training.
    Yeah, but if a "capacity" does not entail an actual ability unless it is developed, then it seems it is not an "inherent" capacity.

    I said no to the OP, for the reason detailed in my post. Certainly humans have a capacity to develop the ability to reason logically, b/c that would only require a single person being able to reason logically .

  8. Top | #48
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    Quote Originally Posted by ronburgundy View Post
    Well, an innate capacity would imply that most people would be quite good at evaluating simple logical syllogisms and if/then conditionals. Yet, research shows that people are generally quite poor at deductive logic, with the majority of people getting some simple logic problems wrong. This is true if you give people abstract forms of arguments (If p, then q; Not q; therefore not p). Most people will incorrectly say this conclusion necessarily follows the premises and/or will generate that conclusion from the premises. People get better at it if you use real world concepts and relations in place of abstract tokens, but that only demonstrates that people are not using deductive logic to reason about the problems. Also, if you use real world content, people will be even worse if the logical validity of the conclusion contradicts their a priori beliefs about the conclusion. IOW, people generally cannot apply logical reasoning to arguments independent of their a priori agreement with the conclusion.

    Of course, some people are better at logical reasoning than others, and that is partly predicted by measures of general cognitive ability but also by measures of thinking dispositions where some people are more prone to go with their "intuitions" and prior beliefs (aka biases) and others are more able to set their beliefs aside and evaluate what is implied by a set of given claims. The difference between ability and style is the difference between what one can do if they try versus what one is inclined to try to do.

    In fact, more religiosity predicts greater logical errors due to a tendency toward a more intuitive less analytical cognitive style.
    I agree generally that most people are not very good at formal reasoning. However, most people are not very good at singing from a score either, yet most people can learn to sing. Most people are not very good at writing and reading, yet most people can talk and understand other people talking and most people can learn to read and write. I think any research on our logical capabilities would need to make that distinction.

    By inherent capacity, I mean a natural capacity. We all display this capacity each time we understand what people mean from what they say. Our brain is wired to use rules and using any rule correctly is a logical capacity. We need first to learn the rules themselves, or rather our brain needs first to integrate the rule in its processing of the information but this is the result of learning. Definitions are rules. Learn a new word, say "diorite", and from this point you'll understand what anyone using this word will mean with it, or at least assume that's what he means. People can't speak a language unless they somehow learn it but I think we would all agree we have a natural linguistic capacity, whether it is derived from a more general capacity I don't know but we have that capacity. We all learn a language but we don't all learn formal logic, and indeed very few people do. Formal logic itself is just one of the many things we can do that require a logical capacity. Think of even being a racist. Being racist is basically having somehow memorised a rule saying all people of that ethnic group are cheats or murderer or whatever and then going on to apply this rule to any fellow of that ethnic group. Same for sexism and any discrimination. So, even being an idiot requires a logical capacity.

    I would also agree that most people don't use formal logic to reason but that's really only because most people don't reason at all. Ask people why they do stuff and you'll see what I mean. Indeed, most of what we do we do it without reasoning about it first. We just do it. Reasoning is for "intellectuals". Indeed, most people dislike people who argue their views. But even intellectuals don't reason at all about most of what they do in life, including the stuff that can be very important. Reasoning is generally rather costly in terms of time and energy unless you're used to doing it and that's generally because it's part of your job. And you can only reason about stuff that has already been formalised. Logic itself is a good example of that.

    I also agree that there are biases, essentially emotional ones. Once your committed to a particular belief, you will ignore logical arguments to the contrary. However, there's a good reason for that. Logic is garbage in, garbage out. Whatever the validity of the argument, we still don't know whether the conclusion is true simply because we don't know whether the premises are true. So, people are in fact correct to dismiss even valid arguments. And, most people don't know about the formal distinction between valid and sound, they just dismiss the argument wholesale, and again, that's the correct attitude to take. Logic isn't used for discovering the truth. Logic is used to believe the conclusion that follows from a prior belief. If I know your beliefs, I can move you to act logically in accordance with them by using a valid argument. If I know you believe in God and that God asks believers to help their neighbours, I can argue you should help your neighbour. But it won't work if you don't believe in God to begin with. And whether God exists or not is entirely irrelevant. What matters is what you believe is true.

    Most people don't use formal logic but all use their inherent logical capacity. Suppose some people are talking about Obama. After ten minutes someone may say, "Well, politicians are just liars". And that's it. Whether you agree with this "rule" and whether you think Obama is himself a liar, indeed irrespective of whether you like or dislike Obama, you will understand what the guy actually didn't even spell out, namely that he meant that Obama is a liar. That's a logical inference and yet, although they will understand what the guy meant, no one present will need to think about it. They will just know what the guy meant without having to think about it. That's entirely intuitive and people don't learn formal logic. They're not even aware they made a logical inference. You yourself don't even understand, given what you say here, that you are making precisely this kind of inference all the time without having to think about it. So, we all have this inherent capacity because without it we could possibly even begin to understand each other.

    So, intuition is not to blame. Indeed, we have people trained in formal logic being systematically wrong about whole classes of inference because the formal logic they learn is wrong. As of today, our best logic is our intuitive logic. The brain is a natural. You just need to learn to listen to it and make the distinction between the logical validity of your intuition and the assumptions you make without even realising it. If you're wrong, the likelihood is that some of your assumption are wrong.
    EB

  9. Top | #49
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    Quote Originally Posted by ronburgundy View Post
    Quote Originally Posted by DBT View Post
    There seems to be a distinction to be made between inherent capacity and ability....the latter being a matter of education or training.
    Yeah, but if a "capacity" does not entail an actual ability unless it is developed, then it seems it is not an "inherent" capacity.

    I said no to the OP, for the reason detailed in my post. Certainly humans have a capacity to develop the ability to reason logically, b/c that would only require a single person being able to reason logically .
    So a child that doesn't develop a language because he has nobody to talk to him has no inherent linguistic capacity? Then nobody has any linguistic capacity and then how come we all speak some language? You think you don't have an inherent linguistic capacity?
    EB

  10. Top | #50
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    Quote Originally Posted by Speakpigeon View Post
    Quote Originally Posted by ronburgundy View Post
    Quote Originally Posted by DBT View Post
    There seems to be a distinction to be made between inherent capacity and ability....the latter being a matter of education or training.
    Yeah, but if a "capacity" does not entail an actual ability unless it is developed, then it seems it is not an "inherent" capacity.

    I said no to the OP, for the reason detailed in my post. Certainly humans have a capacity to develop the ability to reason logically, b/c that would only require a single person being able to reason logically .
    So a child that doesn't develop a language because he has nobody to talk to him has no inherent linguistic capacity? Then nobody has any linguistic capacity and then how come we all speak some language? You think you don't have an inherent linguistic capacity?
    EB
    You said earlier:
    Quote Originally Posted by Speakpigeon

    We can be incapacitated. It's actually not true that humans have two legs and one nose because some people miss those. Do the British people speak English? Well, no, because not when they're in deep sleep or in drunken stupor. We cannot vote in elections since many people literally can't decide who to vote for.

    Please understand "inherent" to signify that it is in our nature. We have two legs because of our nature but some will be missing one or two because of the imponderables of life.

    I guess whatever capacity we have as individual human beings is best explained by the fact that human beings have inherent capacities due to their nature. I wouldn't want to have to explain the fact that we can communicate with each other using sophisticated languages by leaving our DNA out of the picture.
    Indeed. But on the other hand, say, a capacity to swim is not part of our nature by that standard. Indeed, if a human lives in a mostly deserted area and never finds a body of water where she could swim, she will not learn how to swim, but very much unlike the human who lacks one or two legs, there is no malfunctioning in the person that does not know how to swim.
    In fact, historically one can find entire communities of humans who cannot swim, with no malfunctioning at all. Of course, the same cannot be said about legs.

    What about language?
    I do not know. I do not think anyone knows. I already explained why that matters when it comes to the capacity of ascertaining whether a conclusion follows necessarily from premises.

    Still, that is a side issue. Even if it's not an inherent capacity, it may well be (and it's quite probable, I'd say) that there is only one human logic in colloquial languages - at least, for humans who happen to have that capacity, even if not inherently. This is why I think the question about an inherent capacity is not the right one for the intended task.

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