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Thread: Whence comes logic

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    Contributor Speakpigeon's Avatar
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    Whence comes logic

    Here is your chance to air your views as to whence comes logic.

    As a motivation introduction, I observe that most educated people take logic to be a branch of mathematics, or perhaps whatever mathematicians study that they call "logic" since broadly the beginning of the 20th century. Yet, the first systematic presentation of what humans understand of logical rules was made by Aristotle and that was something like 2,400 years ago, and as far as I know, most intellectuals since have accepted Aristotle's presentation as correct. I'm not aware that anything in mathematical logic shows Aristotle was wrong.

    Whatever the case, is it possible to study anything if there isn't something to study? This suggests logic exists somehow somewhere. But where exactly?

    Traditionally, philosophers see rules of logic as necessary and a priori, rather than contingent and empirical. Putnam argued they could be empirical, taking the example of Quantum Physics to support this suggestion. Yet, even a priori rules have to come from somewhere unless you think God the merciful help us sort out the necessary from the contingent.

    If we all have our own personal sense of logic, why is it most intellectuals agreed with Aristotle's logic (and I would assume most people here)? But if we all have the same logic, how come?

    And where are we supposed to look when we want to produce a method of logic that, somehow, would be correct?
    EB

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    Sapere aude Politesse's Avatar
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    It is a systematic presentation of the fundamental biases and assumptions of one's culture. Hence why people's sense of logic varies rather predictably across cultural boundaries; people who share a cultural background are likely to agree on what "makes the most sense" or "is obvious", whereas people from variant backgrounds are far less likely to agree. Aristotle did not invent his perspective from scratch, after all -- he was a keen observer of how people perceived, named, and made decisions about things, and formalized it all into a package that now only half makes sense to people. (Few people now living read Categories and agree with everything inside, especially where its description of the soul is concerned). Our system of education is heavily based on his presentation, so you would expect most people educated within it to feel some sympathy for his perspective, but this would not follow for every claim, nor would someone unacquainted with the culture built partially on his ideas be likely to find as many points of agreement, aside from those elements actually derived from scientific observation.

    Chasing after a "correct" form of logic is a fantasy; there is no way to confirm or deny someone's basic sense of how the world works, as any test you might devise would produce contested results if the basic assumptions underlying that test and our perception of the results have been biased in different directions. Personally, I just try to figure out what methodology is situationally useful, and leave ontology and the rest of epistemology for after-coffee discussions and philosophy classes.

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    Veteran Member PyramidHead's Avatar
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    I don't have an answer to this question, but it's interesting to me how the act of asking it cannot be performed without utilizing the thing it is asking about. There must already be a pre-existing framework that includes a class of things, of which logic is one member, which are characterized by having "come from" somewhere, such that we can learn about their nature by tracing their origins back to the source. That already involves a range of logical relationships. One of my favorite philosophers has a radical view of logic that rejects the formal/analytical tradition in favor of something more personal and innate, but his work in this field is all in Portuguese for the time being.

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    Contributor Speakpigeon's Avatar
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    Quote Originally Posted by Politesse View Post
    It is a systematic presentation of the fundamental biases and assumptions of one's culture.
    ???

    Logic
    1. The study of principles of reasoning, especially of the structure of propositions as distinguished from their content, and of method and validity in deductive reasoning.
    2.
    a. A system of reasoning: Aristotle's logic.
    b. A mode of reasoning: By that logic, we should sell the company tomorrow.
    c. The formal, guiding principles of a discipline, school, or science.
    3. Valid reasoning: Your paper lacks the logic to prove your thesis.
    Anyway, yours is an extraordinary claim. You would need to provide some commensurate justification to be taken seriously.

    Quote Originally Posted by Politesse View Post
    Hence why people's sense of logic varies rather predictably across cultural boundaries; people who share a cultural background are likely to agree on what "makes the most sense" or "is obvious", whereas people from variant backgrounds are far less likely to agree.
    You think that the following logical expressions would be seen as true or false depending on cultural boundaries?

    1. If it's true that it rains and that I want to pee then it's true that I want to pee. Or, more formally and generally, (A ∧ B) → B.

    2. If he is a liar then I am speaking the truth if I say that either he is a liar or he is an idiot. Or, more formally, A → (A ∨ B).

    3. Living near the Eiffel Tower implies living in France and living in France implies living in Europe, therefore living near the Eiffel Tower implies living in Europe. Or, more formally, ((A → B) ∧ (B → C)) → (A → C).

    I could provide further examples if need be.

    But presumably, that's not at all what you yourself call "logic".

    Quote Originally Posted by Politesse View Post
    Chasing after a "correct" form of logic is a fantasy; there is no way to confirm or deny someone's basic sense of how the world works
    Usually, logic is understood as characteristic of the way the human reasoning works, perhaps the way any kind of reasoning would have to work and so is not understood to be essentially about the world except inasmuch as minds can be said to be a part of the world.
    EB

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    Locic is a set of rules. If the incompleteness theory applies then there can be no absolute proof of logic. To make a long story short you can not in general use logic to prove logic. How would you prove the second set of logic used to prove the first?

    Same with software. The only way to validate software is by empiracle testing. That applies to logic.

    In the early 1900s Hilbert posed a question at a conference. Can all mathematical truths be proven true? I believe the general answer is no.

    So, math including logic is in the end just as empirical as physical science.

    Logic attributed to Aristotle like language and math evolved over time. That Seaways into how the brain itself works. As of yet no specific answers.

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    Quote Originally Posted by steve_bank View Post
    Locic is a set of rules.
    If that was true, we could not have any proper sense of logic, i.e. something independent of formal training, which seems to contradict our subjective experience and certainly mine. You could not have any logical intuition outside those prompted by whatever formal logic you might have had. This also contradicts recent studies showing that toddlers and animals have logical notions.

    This also contradicts our semantics. We talk of logic as something unique, as opposed to methods of logic, which are indeed many.

    There is something we call "formal logic" and I would agree that formal logic is a set of rules. But logic itself? Where's the proof of that?

    Quote Originally Posted by steve_bank View Post
    If the incompleteness theory applies then there can be no absolute proof of logic. To make a long story short you can not in general use logic to prove logic. How would you prove the second set of logic used to prove the first?

    Same with software. The only way to validate software is by empiracle testing. That applies to logic.

    In the early 1900s Hilbert posed a question at a conference. Can all mathematical truths be proven true? I believe the general answer is no.
    Yes, and that's only a problem for formal logic and for mathematics.

    It's not issue when we consider logic itself because it's not a formal system and we don't have to somehow try to justify it. In this respect, logic is just a fact. You don't need to justify facts. You just have to understand how they come to be.

    Quote Originally Posted by steve_bank View Post
    So, math including logic is in the end just as empirical as physical science.
    I don't see how that follows from what you just said. I think logic is empirical because I see it as a fact of nature, human nature at the very least. We can study logic scientifically just like we can study anything humans do scientifically, even science itself. If it's a problem, there's nothing specific to it. We are limited in our study of nature by what our science allow us to do. We're just as limited in our study of science itself and for the same reason. Basically, we're limited by what we are, which, of course, includes our logical and scientific capabilities.

    Quote Originally Posted by steve_bank View Post
    Logic attributed to Aristotle like language and math evolved over time.
    Only because this is formal logic. Aristotle's logic was already a formal system. A set of rules. Mathematical logic is formally different from Aristotle's formalism, but essentially because it's a calculus (and also because it's just wrong), whereas syllogisms are rules of inference. Look at Gentzen's method. It's really just a generalisation of Aristotle. The rules are formally different, but the logic described is the same. I can look at a syllogism today and have an intuition it's true, much in the same way as people at the time of Aristotle would have had. No change there that would be documented. No evidence of any change.

    I would agree that in principle the logic of the human brain could evolve but I doubt that evolution will produce anything much better than what we already have any time soon.

    Quote Originally Posted by steve_bank View Post
    That Seaways into how the brain itself works. As of yet no specific answers.
    Sure.
    EB

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    Logic is not truth. A valid logical argument or proposition that is contracted according to the rules of logic.

    Same as math. Math and logic are both rule based models. Math and logic constructs can be created according to the rules which can not manifest in reality.

    The end proof of any logical or math construct is empirical demonstration.

    Beyond simple arguments obvious by inspection, using logic arguments to prove logical arguments leads to infinite regression. It is what happens in software testing.

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    Contributor Speakpigeon's Avatar
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    Quote Originally Posted by steve_bank View Post
    Logic is not truth. A valid logical argument or proposition that is contracted according to the rules of logic.
    Yeah, I believe that's true.

    I wonder why people call logical truths "logical truths".

    The real question, however, is whether a given method of logic is true of human logic. If not, what would be the justification for saying it's a method of logic to begin with?

    Mathematicians are at liberty to invent theoretical methods without caring whether those are true of anything. That's the privilege of mathematics. Doing this is certainly a science but not an empirical science. Which is why you have a free range of methods, none true of anything as far as we know.

    Quote Originally Posted by steve_bank View Post
    Same as math. Math and logic are both rule based models. Math and logic constructs can be created according to the rules which can not manifest in reality.
    Not maths and logic. but mathematical theories and logical theoretical methods. And maths and logic are not at all in the same ballpark. Math theories are largely validated by logical rules. You have automatic theorem provers, based on rules of inference which are explicit and accepted as logical truths by all specialists. I'm not sure what's not "manifest in reality" in that.

    Quote Originally Posted by steve_bank View Post
    The end proof of any logical or math construct is empirical demonstration.
    Again, not the same ballpark. Math theories are validated by something not math, i.e. logical demonstration, although most of the time in an informal way.

    The question remains how you validate logical theoretical methods. As I understand it, we only have our intuition to assess a method as good enough. But that's precisely why logic is an empirical science. You have to observe what are the logical intuitions of normally intelligent human beings and build your theoretical method so that it gives the same results as our intuition. This is what Boole, Frege and Russell have done. They checked their method was in line with intuitions human beings have reported since Aristotle. This is what it means for logic to be an empirical science. And as such, any method that looks good at one point, such as standard mathematical logic, may well be found lacking later, such as standard mathematical logic.

    Quote Originally Posted by steve_bank View Post
    Beyond simple arguments obvious by inspection, using logic arguments to prove logical arguments leads to infinite regression. It is what happens in software testing.
    The general principle of Gentzen, the only method of logic that really works, is that you accept the basic rules, called rules of inference, as evidently correct, things which are obvious logical truths like p ∧ q → p. That's what is empirical.
    EB

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