Where does our conception of what is "logical" come from?

[CRSP]

Where exactly do the established laws of logic come from? Are they innate, or are they in some sense learned, passed down from generation to generation? Why, for instance, do the majority of people not accept that there are true contradictions (dialetheia)?

(I suppose the previous paragraph can be surmised by asking whether logic is empirical.)

[phouka]

I believe that the understanding of certain logical concepts - causality, consistency, and such - are learned, but also that our brain structure and the brain structures of all multicellular creatures have been selected by evolution to learn them. If we didn't get those concepts down in very quick sequence, we wouldn't be long for this earth.

From there, the ability to test a statement for consistency, soundness, and completeness, and make judgments based on that is a learned ability of a far higher order, especially when the judgment is contrary to our desires.

Can you give an example of a true contraction?

[Indistinguishable]

I'd say it's ultimately something like a linguistic convention. There is an activity humans engage in under which they use words like "and", "not", and so on in certain ways, and label sentences containing these as "true", "false", and so on according to certain rules. These rules aren't forced upon us, any more than are the rules of chess; they just happen to describe the way most of us have been taught to speak. In this sense, they're just like any other rules of human language or custom.

And, one aspect of these rules is that the label for something like "it's raining and it's not raining" will never be "true"; but this is no more an empirical discovery than that bishops can only move diagonally. If we were playing a different labelling game, the results would be different. But that's not the language-game most of us play most of the time.

[Oliveloaf]

I am going with learned.

Racism seems logical to racists. That can't be innate.

Let's call logic "Quick set" though. Once something(s) is(are) understood to be true, it's tough to change.

[CRSP]

Hmm, not sure that I agree with that, Indistinguishable. For a start, is it really true that the rules aren't forced upon us? Why do philosophy students need to take courses in logic, if these rules are borne of a linguistic convention, that surely they share?

[Liberal]

He's [Indistinguishable is] right. Logic is analytical in nature, rather than empirical. Logic compels.

[xenophon41]

Why do philosophy students need to take courses in logic, if these rules are borne of a linguistic convention, that surely they share?

Two guesses come to mind:

1. Meaning can be communicated quite easily most of the time without strictly following the grammatical and syntactical rules of one's language. Philosophy students generally need to take composition courses as well as logic, because they in fact don't share a common linguistic convention.[/*:m:2sm4yw2c]
2. Linguistic conventions develop organically as complex ideas are introduced into a culture, which means these conventions don't cover all cases and are rarely consistent in application or acceptance.[/*:m:2sm4yw2c]

Edited to fix a spelling error.

[CRSP]

He's [Indistinguishable is] right. Logic is analytical in nature, rather than empirical. Logic compels.

Isn't the debate over the epistemological nature of logic one of the most controversial in philosophy, though? Why do you believe that logic is necessarily analytic?

[susan]

Learned, if we're talking specifics. Some other cultures have different rules of logic that seem bizarre to a Euro-American. Talmudic logic, for example, follows different rules but is nonetheless rigorous. It's more like the witch-weighing scene in Monty Python and the Holy Grail ("If... she... weighs... the same as a duck... she's made of wood").

[Indistinguishable]

One example of why I would not consider logic to be empirical, as such: consider, for example, the distinction between classical and intuitionistic logic, or any other example of differing logical systems. How would one possibly set up an empirical experiment to determine whether or not the law of the excluded middle were valid? What would it even mean? To me, it seems rather similar to attempting to determine, by empirical investigation, whether or not en passant were a valid rule of chess.

Granted, if one has a particular application of logic in mind (i.e., a particular way of interpreting the results of a system of rules as describing some phenomenon), one can determine what system of rules follows; for example, if one decides that propositional connectives should describe the behavior of operations on bitstrings in the familiar way, then the rules of Boolean logic follow. But all this is doing is transferring a description of rules in model-theoretic terms into a description of the same in proof-theoretic terms; if we chose to investigate a different application, we'd get different rules (e.g., investigating the behavior of operations on open sets would yield the rules of intuitionistic logic).

As for why philosophy students should take classes in conventions of logic, it's akin to why computer science students take classes where they learn particular programming languages: even though they generally have a pre-existing intuitive understanding of how to describe algorithms in pseudocode, it is worthwhile for them to learn a highly formalized common standard language, to obviate the ambiguities and differences in interpretation they might otherwise have in speaking in ordinary language, as well as simply to gain experience working rigorously with formal systems. But being taught C++ rather than Java or vice versa doesn't mean one or the other is The One True Language; it's just some particular popular and useful system to investigate. So it is with different systems of logic as well.

[CRSP]

One example of why I would not consider logic to be empirical, as such: consider, for example, the distinction between classical and intuitionistic logic, or any other example of differing logical systems. How would one possibly set up an empirical experiment to determine whether or not the law of the excluded middle were valid? What would it even mean?

I'm not sure that this is what's meant by "empirical", with respect to this debate (i.e. I doubt that anybody is seriously positing the existence of an experiment to settle the debate over the "one true logic", for instance).

Rather, the debate is whether logic stems from some aspect of our experiences with the universe, or whether it's "handed down from God". If it's tied to our experiences in the real world, then doesn't this open up the possibility of "immutable" logical laws being revised over time, as our understanding of the world around us develops (actually, this argument, put forth by Putnam, was what started the debate in the 60's, with his work on quantum logic)?

Further, if you're assuming that our common understanding of logic is borne out of linguistic convention, then aren't you just begging the question? Why was it the case that these conventions arose in the first place? Don't they necessarily arise from an ability to successfully reason, in the real world? That is, a convention that allows a stone age man to deduce where the prey is likely to be, given the conditions, is more likely to survive than one that does not?

[Liberal]

He's [Indistinguishable is] right. Logic is analytical in nature, rather than empirical. Logic compels.

Isn't the debate over the epistemological nature of logic one of the most controversial in philosophy, though? Why do you believe that logic is necessarily analytic?

There are many ways to describe the difference. And people like Indistinguishable will (practically always) give a more learned and formal differentiation than I. But the difference as I see it is in how the rules function.

For the empirical, the rules are in place and we discover them. For the logical, we establish the rules and then squeeze out the implications. That's why I fight so hard on behalf of science, to keep it from becoming analytical in people's minds. Once an Induction Axiom has been adopted by science, science becomes — pardon me — indistinguishable from religion.

(God, I hate this pro-silver or whatever theme. Just a note here to advise you that Black Pearl has suddenly lost the quote, delete, and edit buttons. They just vanished. Please forgive this off-topic note, but you seem to be reading this thread.)

[Indistinguishable]

Rather, the debate is whether logic stems from some aspect of our experiences with the universe, or whether it's "handed down from God". If it's tied to our experiences in the real world, then doesn't this open up the possibility of "immutable" logical laws being revised over time, as our understanding of the world around us develops (actually, this argument, put forth by Putnam, was what started the debate in the 60's, with his work on quantum logic)?

Sure, but I think Putnam was being silly. The existence of applications for quantum logic in no way compels us to revise our language accordingly, for we already knew there were applications for the language as it existed, and for other systems besides. The fact that I sometimes want to play checkers does not conflict with the fact that I sometimes want to play chess. When discussion concerns orthocomplemented lattices, quantum logic is useful; as it happens, modern physics tells us this is a structure which describes many empirical phenomena, and thus there are many situations in which we would indeed want to discuss such things. But there also continue to be many other situations in which we want to talk about, for example, two element sets, in which case Boolean logic becomes a useful language, or open sets, in which case intuitionistic logic is useful, and so on.

Let me put it this way: what are the empirical observations of quantum mechanics supposed to tell us about logic? It can't tell us much about how logical connectives are or should be used in ordinary language: it's not as though the fact that "and", "or", and so on work in a certain way in ordinary language was ever because they were defined in relation to physical phenomena which turned out to work according to certain rules. Rather, these connectives work the way they do in ordinary language because people ordinarily have many natural, not particularly physical, reasons to want to organize their discussions in certain ways (using yes/no questions and so on), and the structure of this organization is reflected in the linguistic structure which arose to express it.

Fine. But then, even if not affecting ordinary language, can the empirical observations of quantum mechanics tell us how logical language should work in more formal or technical language? Well, as concerns this, all the discoveries of quantum mechanics tell us is what the logic of those processes discovered to exhibit quantum mechanical properties is; there continue to be a plenitude of other logics which are more applicable to other purposes. Quantum mechanics isn't telling us what the language of logic is; it's telling us which particular language of logic is applicable to certain problems (in certain ways).

Further, if you're assuming that our common understanding of logic is borne out of linguistic convention, then aren't you just begging the question? Why was it the case that these conventions arose in the first place? Don't they necessarily arise from an ability to successfully reason, in the real world? That is, a convention that allows a stone age man to deduce where the prey is likely to be, given the conditions, is more likely to survive than one that does not?

Well, as I said, if one picks a particular application one intends to model, one can determine what the rules are which describe that application. Classical logic was very useful because, for clear reasons, answering yes/no questions is a common task. Intuitionistic logic is also useful because answering questions about open sets is a common task. We now know that many physical questions concern projections on Hilbert spaces, giving us reason to find quantum logic useful. And so on. But we do not have to decide between these and settle on one, any more than we have to decide between the integers and the real numbers; we just use each as appropriate given the particular task at hand.

[Indistinguishable]

Quantum mechanics isn't telling us what the language of logic is; it's telling us which particular language of logic is applicable to certain problems (in certain ways).

Let me rephrase this: the discoveries of quantum mechanics don't tell us what the rules of logic are; they just tell us which particular system of rules describes, in a certain way, the behavior of certain physical processes. We discover "If you want to interpret the results of your logic as being about phenomenon X using interpretation Y, then you'd better use logic Z". But this isn't a discovery about logic, as such; it's a discovery about phenomenon X. That empirical observations can tell us what the rules of empirical phenomena are is just tautology.

Anyway, on re-read, I see that the question of the thread is less "Where does Logic come from?" and more "Where does our conventional logic come from?". For this, as I said, I don't believe the answer has anything to do with physics, empirical observation, or so on; it just has to do with the fact that people often want to discuss the answers to yes/no questions, and thus the structure of operations on yes/no answers has become integrated into our usual logical language (giving us such things as negation for switching 'yes' and 'no', conjunction and disjunction for combining them with a bias towards either 'yes' or 'no', and so on). And then such logical rules as double negation elimination, the law of noncontradiction, the distributivity of conjunction over disjunction, and so on simply follow as consequences of this (because of the properties of the given operations on {yes, no}). It has little to do with any empirical observations; it's just drawing out the consequences of the interpretation of the logical language.

[Indistinguishable]

Er, I want to change the last two lines to: "And then properties of the resulting logical system (e.g., the validity of double negation elimination, the lack of true contradictions, the distributivity of conjunction over disjunction, and so on) simply follow as consequences of this (following from the properties of the given operations on {yes, no}). It has little to do with any empirical observations; it's just drawing out the consequences of the motivating application/interpretation of the logical language."

I should plan my posts out more before submitting them, instead of after...

[prr]

the label for something like "it's raining and it's not raining" will never be "true"

I'm sorry, could you clarify what you mean by this? You're not saying that "it's raining and it's not raining" will never be true, are you? Because that statement is not only the truest statement I can think of, but it's necessarily true, as in "At any given moment on this planet,..."

[CRSP]

Indistinguishable, interesting series of posts. I'm not sure at what point we start disagreeing, here, so I'd like to clarify:

I think there's two issues with Putnam's claims: one is the question over where the rules of logic come from, and two is Putnam's (implicit) logical monism, i.e. that classical connectives are really special cases of quantum connectives. I've reread your posts a few times, and I think a lot of the objections are aimed at the second claim (correct me if I'm wrong). That is, Putnam states we should revise "conventional logic", due to discoveries in quantum mechanics, in favour of quantum logic. You disagree, stating that conventional logic is a good tool for answering yes/no questions in ordinary discourse, and that quantum logic is fine for answering questions about quantum mechanics (and a host of other specialised logics are tailored for other domains).

Is that a fair summary? If so, then I agree with you.

[Indistinguishable]

Yes, I think something like that is a fair summary. I did begin to realize, as I noted near the end of post #14, that I had gone off too much on the question "Is logic empirical?" and missed that the real thrust of the thread was "Where exactly do the established laws of logic come from?".

As I said, I think the established laws of logic by and large simply come from the algebraic properties of the two element set. We think of propositional questions as having either a yes or no answer, and so we have the ready means to craft complexes out of these propositions in a manner corresponding to operations on {yes, no}. Logic springing forth from the traditional truth tables, basically, even if no one ever sat down and wrote it out like that.

As for prr, sure; the sentence I gave was a poor example, what with its implicit spatial deixis (meant to be coordinated between the two clauses). Pretend it was something more like "It is raining [at my house] and it is not raining [at my house]".

[erislover]

I have a lot to say on this topic. The ideas behind logic specifically and mathematical reasoning more generally interests me greatly. A post I made some time ago, which I would some day like to revise and expand, is here.

What I like best is Indistinguishable's comment: "I'd say it's ultimately something like a linguistic convention." I think it is completely a linguistic convention used to represent, communicate, describe, etc, certainty. (Not the subjective feeling of certainty.)

One example of why I would not consider logic to be empirical, as such: consider, for example, the distinction between classical and intuitionistic logic, or any other example of differing logical systems. How would one possibly set up an empirical experiment to determine whether or not the law of the excluded middle were valid? What would it even mean? To me, it seems rather similar to attempting to determine, by empirical investigation, whether or not en passant were a valid rule of chess.

The confusing aspect, though, is that the applicability of a game is, in a way, an empirical investigation; and further, the derivation of special grammars may also be done in tandem with empirical investigation (the logic of the subatomic world).

For example, I have said elsewhere: "[F]rom a contradiction—it is often said—all propositions can be proved. This is not a testament to the 'bedrock' nature of such proposition which we hold to be inviolate, but to the nonsensical nature of their denial—that is, we have not created a language game where denial of this proposition is a legal move. But that says something about us, not about the proposition." And the creation of such a language-game would often go hand in hand with an empirical investigation: it is the domain of the language game itself, however ill-defined. ("Pure math" pursuits are worthy of a completely separate discussion which I almost certainly don't have time for right now.)

Let me rephrase this: the discoveries of quantum mechanics don't tell us what the rules of logic are; they just tell us which particular system of rules describes, in a certain way, the behavior of certain physical processes.

I'm not even sure they tell us that. We have some phenomena we strive to describe in a systematic way, and come up with some formalism for it. Did the formalism "come from" us or the phenomena? I could think of several answers to the question depending on what was meant by its asking. In some ways, logic doesn't "come" from anywhere. In others, it comes from the phenomena. In still others, it "comes" from us.

Logic comes from nowhere: meaning, there is no innate logical sense that some have and others lack, or which we all happen to have, or whatever.

Logic comes from phenomena: we seek to understand what rule guides phenomena, so the phenomena serve as the cause of logical reasoning (it motivates us to understand)

Logic comes from us: we seek to understand what rule guides phenomena; the phenomena are not our creation, but logic is our interpretation of it.