## Where does logic get its power?

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I like defining things so, logic: A method by which humans go from premise to premise that seems to reflect reality if the premises do. What was the "origin" of logic. Why is it that we are simply born with a "rule for deriving rules" and why does it work so well?

By what is meant by "facts", there can be no such thing as mutually-contradictory or inconsistent facts.

Just by what our words mean, no proposition can be true and false.

The consistency-requirement is inherent in facts and by what we mean when we speak.

For example, in mathematics, you CAN'T be wrong if you follow certain axioms because the axioms DEFINE what being wrong is. However you can never go back and "prove" the axioms you just have to accept them apriori. For example, no one knows why if A=B, B=C then A=C. You can't prove this axiom to be true you just have to accept it. Why is it then that humans can get by using arbitrary axioms that they are born with whose validity they cannot prove?

But that's true of the whole structure of what describably is. Logical relation among propositions. ....abstract implications. It's a basic structural property of the whole system of what describably is, that there's no proof (and usually no reason to believe) that the antecedents of the abstract implications are true.

For example, when I describe my metaphysics, describing the describable world (including our physical world) as consisting of abstract implications, I emphasize that there's no reason to believe that any of the antecedents of any of those abstract implications are true.

A true mathematical theorem is an abstract implication whose antecedent consists (at least in part) of a set of mathematical axioms.

There's no proof of the truth of that antecedent (the axioms, and whatever else is in the antecedent).

(But, as you know, different axiom-systems choose their axioms differently, so that what is an axiom in one system is a theorem in a different system, and vice-versa.)

That's not just how it is in mathematics. It's true in general, in the describable realm, where there's no reason to believe that any of the antecedents of any of the abstract implications are true.

What there describably is:

Worlds of "If".

Instead of one world of "Is", infinitely-many worlds of "If".

Michael Ossipoff
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As to the computer analogy, I think it is flawed just as the brain-in-a-vat hypothesis because they imply a separation between fact/reality and our perception of it. What we perceive is an expression of fact/reality not something disconnected or veiled from it.

An analogy is only that. I think you read more into it than an analogy can usefully support. As for brain-in-a-vat, the most important point in considering it is that we can't know - ever - if it's correct. And this is because the relationship between "fact/reality and our perception of it" is unknown and unknowable to humans. "Fact/reality" = Objective Reality. Our perception shows us (interactive) images of a world - a consistent, testable and comprehensible world - whose relationship to Objective Reality cannot be known. So I don't think we can meaningfully or usefully assert anything about whether these two are separated or not. We don't know. Sadly. Hey-ho! That's life! :smile:
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And this is because the relationship between "fact/reality and our perception of it" is unknown and unknowable to humans. "Fact/reality" = Objective Reality. Our perception shows us (interactive) images of a world - a consistent, testable and comprehensible world - whose relationship to Objective Reality cannot be known. So I don't think we can meaningfully or usefully assert anything about whether these two are separated or not.

Why then are some theories about reality better than others? For example, why is theory of relativity better at making predictions than Newtonian physics?
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Why then are some theories about reality better than others?

Because "some theories about reality" are "better than others"? Don't forget reality is the reference; we just try to curve-fit our data and our theories to it. Some just fit better than others, so they're 'better' (i.e. more useful) than others.

why is theory of relativity better at making predictions than Newtonian physics?

Because its predictions are more accurate in a wider range of circumstances? :chin:
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Because its predictions are more accurate in a wider range of circumstances? :chin:

Sorry, this doesn't answer your question. You asked "why?", but I don't think there's an answer to that. If there is, I don't know it, and can't imagine what it might be. Sorry. :up:
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Because "some theories about reality" are "better than others"? Don't forget reality is the reference; we just try to curve-fit our data and our theories to it. Some just fit better than others, so they're 'better' (i.e. more useful) than others.

So, you said it yourself - some of our theories apparently fit reality better than others. So the relationship between theories and reality is one of "fitting", or correspondence.
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And this is because the relationship between "fact/reality and our perception of it" is unknown and unknowable to humans.

First, I should repeat that we are like children, constantly growing and learning. Therefore, we may not understand everything about the relationship between fact/reality and our perception of it but it is possible to understand some of it. And from the tidbits we understand, it is possible, as some have tried, to infer of the whole, which is one of the applications of logic.

Nature or the laws of nature is that relationship between fact/reality and its many manifestations. Logic, on the other hand, is the expression (or mode of activity) of those laws of nature.

We interact consciously with the many manifestations of fact/reality which we recognise and we attempt to translate the logic expressed into the mental language we possess. It's not that we're incapable, it's just that the job is still in progress (and considering the extensive nature of fact/reality, it may be a perpetual engagement).

When we refer to fact/reality, we always mean the concept not the actual. It's like when astronomers show an image of a galaxy, it's just a model/representation (a decent approximation) but not the actual galaxy. It's the same with our reference to fact/reality - we can conceive of it to a considerable extent even before we experience it. For me, that's one of the utilities that logic presents to us.
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So the relationship between theories and reality is one of "fitting", or correspondence.

We can put it even more simply than that. We create the theories, then test how well they predict the future behaviour of (some aspect of) reality*. The best theories are the ones that best predict.

* - I'm trying not to derail into an objectivity/subjectivity debate, but our relationship with Objective Reality seems to have crept in, and we don't know what that is, or might be. The 'reality' we see in the mental images in our minds may or may not correspond to Objective Reality. We don't and can't know. When I refer to "reality", I refer to these mental images. N.B. I do not assert anything about the source or cause of those images; I define the Apparent World in terms of those images. I define "reality" (i.e. the Apparent World) from within the mind of the human doing the perceiving, because it's what we know. Objectively, all else is pointless speculation.
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It IS entirely ragtag because any rule you choose to use as an axiom is by definition based on no other reasoning.

That is not true, I gave you a perfectly clear reasoning that didn't use the rule. If the Axiom results in trivialism, it cannot be admitted on pain of absurdity and meaninglessness. Avoiding triviality is not arbitrary.

Take the Law of non Contradiction for example. In terms of practical value this law is priceless however it IS an axiom and it IS entirely arbitrary. God could've woken up one day and decided "hey you know what, let's get rid of the law of non contradiction" and created an absurd yet consistent universe.

Using that axiom is not arbitrary. If you take any logic which validates the Argument from Explosion, asserting a contradiction results in triviality: everything becomes true whenever a contradiction is introduced to an Explosive logic. So again, we have a perfectly non question begging reason to adopt Non-contradiction. And no. If a universe "lacks" Non-contradiction (whatever that means) then the universe is necessarily inconsistent. Inconsistent means contradictory, so your claim is just false.

A better example is fuzzy logic. It has no binary truth value but it is still very useful and entirely consistent. You can only say it is not ragtag to the extent that it helps us survive when applied.

The metatheory of fuzzy logic is classical logic. People don't really use fuzzy logic anyway. It might be useful for some applications but as I said, to actually construct the formalism for fuzzy logic you have to apply classical logic in the metatheory.

Why not? This binds our logical systems to practical value, which brings it back to the definition you started your reply with. Now logic requires neither rigor not any specific axioms, it just needs to be useful when applied to the world. It just so happens that rigor is extremely useful when applied to the world so we use that in almost all logical systems

It's not mere practical value, a trivial logic has *no* value because it has completely dissolved the barrier between truth and falsity. A logic which is trivial leaves no mathematical structure because it has no limitations, it is excessively powerful and thus cannot be applied to anything because it literally tells us that every sentence is true. That is a meta requirement which does not beg the question and which is not arbitrary.

Again, you are binding logic to practical value which is exactly what the start of your comment tries to refute.

I'm not binding logic to anything, I'm pointing out a common motivation for why we bother constructing such formal systems in the first place. And I certainly didn't refute that in my first post. As my first post says,

And there seems to be a pretty pragmatic explanation here. If the logic we naturally develop begins failing too often we change our logic until we find one that works. Otherwise we die so there's good incentive.

Practicality plays a role, but it's not the only role.

I'm not looking for a way to justify logic in terms of practical usefulness (because you can justify almost anything that way) or in terms of consensus as a result of practical usefulness. I am looking for a way to justify it that is entirely devoid of practical uses. I think this is impossible but I wanted to see other people try.

I already told you two ways to do this:

There's two ways I can think of how to do this. You justify a deductive logic by means of abduction, a model of theory choice. Whatever logic, in some specified domain, comes out the best on the criterion of theory choice is the correct one for the domain (we can assign them scores basically). That's not question begging, it's using a different type of reasoning.

Another way would be to pick a very weak logic which contains principles no one disputes but which does not contain principles under disagreement. Whatever that logic ends up being, it would have to, for example, have a conditional which satisfies Modus Ponens. That will be a common ground across logics that are actually used. Either of these means suffice.

That's how you justify logical systems without begging the question or being entirely arbitrary.
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oh I'm fine with there being nothing like that trust me but I highly doubt everyone is. This post was supposed to bring together both the theists and scientific reductionists vs the prospect that there is no absolute in reality. A more interesting question however is: WHY is there no such absolute. In reaching the conclusion: "There is no axiom that everyone must accept" we have used axioms in our reasoning (one of those being "logic works" for example, if you don't have that you can't go anywhere). Those axioms might have been wrong. Therefore it is impossible to rule out the possibility of an objective reality. This the difference between a pyrenean skeptic and a normie skeptic. The normie skeptic uses axioms to reach the conclusion that objectivity does not exist except by consensus. The pyrenean skeptic does not know whether or not to even use axioms. He is in an eternal state of "I don't know" about everything.
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no. Ask a pyrenean skeptic "Do you know that you don't know" and his answer would be: No. Perfectly consistent
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Avoiding triviality is not arbitrary.

Why not? Why should we avoid triviality?

Inconsistent wasn't the right word here sorry. I meant feasible

The metatheory of fuzzy logic is classical logic. People don't really use fuzzy logic anyway

People do use fuzzy logic in many many applications such as "facial pattern recognition, air conditioners, washing machines, vacuum cleaners, antiskid braking systems, transmission systems, control of subway systems and unmanned helicopters, knowledge-based systems for multiobjective optimization of power systems, "
Source: first site that pops up when you look up fuzzy logic uses.
Not only that, but the fact that fuzzy logic shares some axioms with classical logic does not in any way indicate that those axioms are to be shared by all systems of logic. That is a genetic fallacy.

I'm not binding logic to anything, I'm pointing out a common motivation for why we bother constructing such formal systems in the first place

Yes and the common motivation you pointed out was: So the system doesn't blow up. But as for why the system SHOULDN'T blow up you've given no answer. You've simply asserted "the system should not reach the point of triviality" but you've never said why and the only reason I can think of is practical uses.

Practicality plays a role, but it's not the only role.

Oh really? What else plays a role?

Another way would be to pick a very weak logic which contains principles no one disputes

The fact that no one disputes them is no proof of their validity.

Whatever logic, in some specified domain, comes out the best on the criterion of theory choice

What are the criterions of theory choice? Because as far as I know that's a matter of opinion and practical utility. One might choose to use the most elegant theory, the most accurate theory, the easiest theory to use, etc. https://en.m.wikipedia.org/wiki/Theory_choice
The criterion of theory choice are, guess what, purely practical
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yayy someone who agrees. However, as I've pointed out in other comments, in order to reach the conclusion "logic is based on antecedent axioms that are unprovable" you have to use a few axioms yourself to get there which are ALSO antecedent and unprovable. It's a self referring problem. So one now has to doubt the antecedent axioms that got him to doubt antecedent axioms. oof help
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no. Ask a pyrenean skeptic "Do you know that you don't know" and his answer would be: No. Perfectly consistent

If it's consistent, what's the problem? Logic is intact.
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I never said there was a problem but people have always told me there was. I just wanted to see them demonstrate it in this post. None have so far
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Why not? Why should we avoid triviality?

Because triviality is incoherent. It dissolves all conceptual barriers, prevents any kind of analysis or understanding, leaves the resulting mathematics without any structure at all. It is true absurdity.
People do use fuzzy logic in many many applications such as "facial pattern recognition, air conditioners, washing machines, vacuum cleaners, antiskid braking systems, transmission systems, control of subway systems and unmanned helicopters, knowledge-based systems for multiobjective optimization of power systems, "
Source: first site that pops up when you look up fuzzy logic uses.

Incorrect. With the exception of knowledge based systems (e.g. SQL), all those examples use the Boolean logic which is just a physical implementation of classical propositional logic. Don't bother with Google search results that don't go into any specificity, those things you mentioned are based on classical computers, they utilize classical logic.

Not only that, but the fact that fuzzy logic shares some axioms with classical logic does not in any way indicate that those axioms are to be shared by all systems of logic. That is a genetic fallacy.

I did not say that. First off, I wasn't talking about the axioms of fuzzy logic, I was talking about the metatheory: the language/logic within which you construct the logical system in question. For fuzzy logic, it requires assuming classical logic. Other logics (e.g. Intuitionistic logic and paraconsistent logic) can avoid this classical assumption in their metatheory, but fuzzy logic cannot.

But as for why the system SHOULDN'T blow up you've given no answer. You've simply asserted "the system should not reach the point of triviality" but you've never said why and the only reason I can think of is practical uses.

I did answer why, repeatedly. It becomes completely incomprehensible *in principle* and loses any possible use towards anything, whether practical or theoretical. That's why triviality is, in logic, also referred to as absurdity. It has no structure to it, it's just the arbitrary entailment of every sentence.

Oh really? What else plays a role?

Theoretical virtues: simplicity, fruitfulness, adequacy to the data, lack of ad hoc elements, unifying power, etc.

The fact that no one disputes them is no proof of their validity.

You asked for their justification. Validity is a separate notion that requires already making assumptions by which validities can be derived. If no one can agree on any assumptions (which never actually happens) then the conversation is over, there's no common ground to work from. Assumptions are necessary.

What are the criterions of theory choice? Because as far as I know that's a matter of opinion and practical utility. One might choose to use the most elegant theory, the most accurate theory, the easiest theory to use, etc.

I listed them earlier in this post. And they're not just practical utility, you yourself just mentioned how they make theories more elegant, which is not necessarily a practical thing. And it's certainly not a matter of opinion. A theory which has equal explanatory power to another theory but which makes an extra ad hoc assumption is a worse theory because it contains an assumption that is not needed to explain the data. It would not be mere opinion to point out that flaw, it's just the truth.
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I did answer why, repeatedly. It becomes completely incomprehensible *in principle* and loses any possible use towards anything, whether practical or theoretical.

That is a practical consideration. As I've said before all of your explanations as to why we should avoid triviality are practical explanations. If triviality one day proves to be a more useful form of logic we will switch to that.

Theoretical virtues: simplicity, fruitfulness, adequacy to the data, lack of ad hoc elements, unifying power, etc.

All of these are practical virtues. They are virtues because they are useful. I don't mean practical as in used in physics, I mean practical as in both theoretically and physically applicable

If no one can agree on any assumptions (which never actually happens) then the conversation is over, there's no common ground to work from. Assumptions are necessary.

Yes and the problem I'm having is that there is no reason for anyone to agree on assumptions that is not itself an assumption
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That is a practical consideration. As I've said before all of your explanations as to why we should avoid triviality are practical explanations. If triviality one day proves to be a more useful form of logic we will switch to that.

How does it have anything to do with practicality? If you apply a trivial logic to purely theoretical problems (pure mathematics, for instance), it's just as useless (due to its incoherency) as it would be in practical matters because it forces you to derive every sentence as a theorem so you end not getting a answer that can be understood in principle. It cannot be more useful because it asserts that everything is true. There is no possible circumstance or theoretical issue where that assumption is a more useful, because no possible state of affairs or problem which can be answered or understood by recourse to pointing at every sentence.

All of these are practical virtues. They are virtues because they are useful. I don't mean practical as in used in physics, I mean practical as in both theoretically and physically applicable

No they are not, they are literally theoretical virtues, properties of theories. People, due to practical necessity, make arbitrary assumptions all the time. In science, or whatever other field, that's a black mark on a theory. You are just labelling random things "practical" with no explanation. These virtues apply to theories in pure mathematics as well, and by definition pure math has no known application to physical reality or practical use (otherwise it becomes part of applied mathematics).

Yes and the problem I'm having is that there is no reason for anyone to agree on assumptions that is not itself an assumption

Except for avoiding triviality, except for practical use (or even practically necessity), except for understanding the structure of the actual world, except for developing good theories as opposed to bad ones, etc.
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I'm not advocating triviality here. I am simply stating that you cannot explain why triviality is to be avoided without appealing to theoretical or practical uses. Why should we have a consistent theory of mathematics? Why should we have an understanding of the natural world? Why should we seek the answers to theoretical problems? I'm not saying we shouldn't do any of these things, I'm pointing out that to have an understanding of the natural world/ to have a consistent mathematical theory, etc cannot be justified without begging the question. You have to set these things as goals first before you discriminate against triviality/ other systems of logic. And there is nothing in classical logic that can be used to justify itself or to frown at triviality. The statement "A=A" is not ontologically different from the statement "A!=A" and there is no proof of either statement therefore one cannot be used to justify itself or devalue the other. It's just that the people that thought A!=A died and the ones that thought A=A lived. Ultimately, logic is based on consensus between homo sapiens and there is nothing in the consensus of homo sapiens that leads one to believe a proposition is true.
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I really don’t think you can appeal to evolutionary biology in support of logic, as I tried to explain in my initial response.

When you’re asking why such thing as the law of identity holds, you can’t avoid a circular argument, because in order to explain why anything is the case, the mind needs to be able to grasp such things as the law of identity.

I think what you’re grappling with, in very high-level terms, are the ‘transcendental arguments’, which are that ‘X is a necessary condition for the possibility of Y—where then, given that Y is the case, it logically follows that X must be the case too.’ ‘X’ here is ‘the ability to recognise logical propositions’, and ‘Y’ refers to the existence of logical propositions. So, in this case, in order to know that there are logical propositions, you must be capable of knowing what what a logical proposition is. And understanding why we know such things, is a much more complicated issue, I think, than is assumed when you analyse the problem in terms of adaptive necessity.

The statement "A=A" is not ontologically different from the statement "A!=A"

How does ontology come into it? It’s a question of semantics. Because A! Is a different symbol to A, then there’s no reason to assume it means the same, unless you designate the exclamation mark as meaningless.
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I'm not advocating triviality here. I am simply stating that you cannot explain why triviality is to be avoided without appealing to theoretical or practical uses.

I just explained why. A trivial theory loses ALL meaning, it's literally meaningless and without structure. It can't be used for practical or theoretical purposes. That's been my repeated explanation, it's not a practical justification.

Why should we have a consistent theory of mathematics? Why should we have an understanding of the natural world? Why should we seek the answers to theoretical problems? I'm not saying we shouldn't do any of these things, I'm pointing out that to have an understanding of the natural world/ to have a consistent mathematical theory, etc cannot be justified without begging the question.

If the theory isn't consistent and Explosion is valid, then the theory becomes meaningless and thereby cannot be used for anything practical or theoretical. And you don't have to have an understanding of the natural world. But then no one will want to communicate with you in any capacity so it's a pointless conjecture. All you're really doing is asking "But what if I wasn't interested in that?" A question which is of no interest to anyone but yourself. I've already justified having a non-trivial theory above, you just keep misrepresenting or ignoring what I say.

You have to set these things as goals first before you discriminate against triviality/ other systems of logic. And there is nothing in classical logic that can be used to justify itself or to frown at triviality.

If your point is that there's no necessity in having any particular goals then you're shifting the goal posts and are in fact doing exactly what I just said: You're complaining that there's no purely logical reason to have some goal or other. That's a matter of what interests you, but good luck finding people who have no interest in having a non-trivial understanding of the world or who completely dissavow all meaning of everything whatsoever (otherwise known as trivialism). It has nothing to do with self-justification, that's a fool's errand. It doesn't exist.

The statement "A=A" is not ontologically different from the statement "A!=A" and there is no proof of either statement therefore one cannot be used to justify itself or devalue the other. It's just that the people that thought A!=A died and the ones that thought A=A lived. Ultimately, logic is based on consensus between homo sapiens and there is nothing in the consensus of homo sapiens that leads one to believe a proposition is true.

Um, they are ontologically distinct. "A!=A" provably leads to a contradiction, and thus (in Explosive logics) it entails triviality (total meaninglessness). We can sensibly speak of objects which lack identity (see Non-reflexive logic), but it has nothing to do with negation. If you have non-self-identical objects they are ontologically very different than self-identical objects, surely this difference is obvious? One has the property of self-sameness and the other kind of object lacks that property, they are qualitatively different. The reason Identity wins out is that even if we take into account the possible existence of objects that lack ontological individuation, any object we actually deal with practically and in mathematics do have identity, so it just makes sense to preference that. Quantum objects lacking identity just won't be relevant to almost anything else ever. And besides, QM is rather new so prior no one really could conceptualize how an object could even lack an identity. So yes, that was a good reason to hold to it if one seems to find it impossible for it to be otherwise.

They could be wrong, sure, but unless you can give good reason why they are (or why they could be) wrong then you might as well just make fart noises. Simply objecting to something is not a reason to consider that thing is incorrect.
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I really don’t think you can appeal to evolutionary biology in support of logic, as I tried to explain in my initial response.

I never did lol. Its more like evolution of ideas rather than biology. So for example evolution from "the earth is flat" to "it ain't"
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You're complaining that there's no purely logical reason to have some goal or other. That's a matter of what interests you, but good luck finding people who have no interest in having a non-trivial understanding of the world or who completely dissavow all meaning of everything whatsoever (otherwise known as trivialism). It has nothing to do with self-justification, that's a fool's errand. It doesn't exist.

Yay you agree. I was simply pointing out that which axioms you choose to adopt cannot be determined without the use of other axioms so you ultimately end up with an arbitrary logic. The only reason the law of identity holds as you've said is because
A) not having it would result in an incoherent and absurd system of logic and
B) a system of logic has to be coherent and consistent

My point is you cannot get A from B nor B from A and so one should just admit that they're both arbitrary because they are. You justify A using B then claim that everyone has B. While that is true, I'm trying to find a way to get B that does not rely on consensus, pragmatism or arbitrariness (thus the title of the discussion: where does logic get its power. So far you've clearly shown that everyone has B but I'm asking WHY everyone has B and you cannot use an answer that refers to C if C is also as arbitrary as A and B)

I think we disagree on the meaning of arbitrary. I use it to mean "has no proof"

Also what's that whole paragraph about QM? What does QM have to do with anything
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The metatheory of fuzzy logic is classical logic. People don't really use fuzzy logic anyway. It might be useful for some applications but as I said, to actually construct the formalism for fuzzy logic you have to apply classical logic in the metatheory.

[Fuzzy logic] is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. — Wikipedia
Fuzzy logic simply introduces grey to an otherwise black-and-white scenario. It is implemented using "classical" (Boolean) logic, because that's what it was created for. In its most recent incarnation, fuzzy logic allowed programmers to code for decision-making that is not limited to two truth values, but exists on a spectrum where TRUE and FALSE are merely the extremes, not the only possible truth-values.

In circumstances where truth-values exist on a spectrum, people do use fuzzy logic.
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as I've pointed out in other comments, in order to reach the conclusion "logic is based on antecedent axioms that are unprovable" you have to use a few axioms yourself to get there which are ALSO antecedent and unprovable. It's a self referring problem. So one now has to doubt the antecedent axioms that got him to doubt antecedent axioms.
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In my previous reply, I told why I don’t think logic has that problem. It just comes down to a consistency-requirement. Need it be proved that there aren’t mutually contradictory or inconsistent facts, or propositions that are true and false?
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That consistency requirement is built-into your experience-story, because any definite yes/no matter is, tautologically, one way or the other, and that doesn’t need proof.
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What I was saying that the describable world, including our own physical world, consists of systems of abstract implications, and that our own physical world consists of a complex system of inter-referring abstract implications about hypothetical propositions about hypothetical things (with the many consistent configurations of mutually-consistent hypothetical truth values for those hypothetical propositions).
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…and that there’s no reason to believe that any of the antecedents of any of the implications are true. I suggest that they’re false.
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In my other reply, I made a false analogy between that and the mathematics axioms. As you’d surely agree, no one would say that the axioms of the number-systems are in doubt, even though they’re stated as unprovable axioms.
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You mentioned an axiom that, if A = B, then B = A. I don’t think that has to be regarded as an unsupported axiom. Instead, just say that, for some un-ordered set containing two elements, both elements are the same as eachother. That’s all that need be said. This asymmetrical wording “A = B” as opposed to “B = A” is just a writing-convention (because we write in a line) that makes it look like two different or separate statements, when they’re both just ways of saying: “The elements of that un-ordered set of two elements are the same thing.” The illusory problem results from the fact that we write along a line, always writing one thing before another thing.
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Likewise the additive commutative axiom: Just speak of combining the two numbers. The apparent need to write one number before the other is just a consequence of our writing in a line. That matter of the order in which the two numbers re written is an unnecessary artificial concern. So the commutative axiom for addition is obvious too. The algebraic symbolic language for addition is intended to model the cardinality of the union of two sets whose cardinalities are known.
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Of course with some other element-sets and operations, such as some groups and their operations, commutativity doesn’t apply, because it’s a different kind of an operation, an asymmetrical one in which the two elements it’s applies to don’t have identical roles or treatment.
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Anyway, the matter of the number-system axioms and the more general matter of the antecedents of the abstract implications that I spoke of aren’t the same. But, as I said, a true mathematical theorem is an abstract implication whose antecedent consists, at least in part, of some mathematical axioms.
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My main point in my other post was just that, because of the not-necessarily-true (probably false, I’d say) antecedents of all those abstract implications that I claim are the basis of our physical world, then having to just accept axioms in mathematics, and have only implications based on an unproven “if “, doesn’t sound so bad, when one considers that that’s just the way things are throughout the describable world. So mathematical theorems’ conclusions (or consequents) are a matter “if “ like everything else in the describable world.
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Michael Ossipoff
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Need it be proved that there aren’t mutually contradictory or inconsistent facts, or propositions that are true and false?

Yes. Or else you'd never know it was true. All you'd have is an intuition that just happens to work very very well and I'm trying to ask where that intuition came from

have only implications based on an unproven “if “, doesn’t sound so bad, when one considers that that’s just the way things are throughout the describable world

I know. It wasn't intended to "sound bad" I'm not trying to slander science and math. I'm just wondering where all of these basic axioms came from (axioms such as "there aren’t mutually contradictory or inconsistent facts, or propositions that are true and false"). They clearly are not provable but they work so damn well it's a miracle.
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"Need it be proved that there aren’t mutually contradictory or inconsistent facts, or propositions that are true and false?" — Michael Ossipoff

Yes. Or else you'd never know it was true. All you'd have is an intuition that just happens to work very very well and I'm trying to ask where that intuition came from

Here's something that I said:

any definite yes/no matter is, tautologically, one way or the other (not both), and that doesn’t need proof.

A tautology just tells another way of saying the same thing. Such a statement is its own proof, and needs no other proof.

Michael Ossipoff
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To even apply that logic programmatically, one is going to be using a computer operating with a two-valued logic. What I'm saying is that it's not really an interval of truth values, it's more of a formal trick since in the semantics of fuzzy logic those values disappear, leaving only truth and falsity.
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Yay you agree. I was simply pointing out that which axioms you choose to adopt cannot be determined without the use of other axioms so you ultimately end up with an arbitrary logic.

That's not what I said, I said one's goals cannot be reached by pure logic. The axioms one adopts can be done so rationally (non-arbitrarily), as I gave two means by which to do so.

The only reason the law of identity holds as you've said is because
A) not having it would result in an incoherent and absurd system of logic and
B) a system of logic has to be coherent and consistent

My point is you cannot get A from B nor B from A and so one should just admit that they're both arbitrary because they are.

Then as I said you're just pointing out an is-ought distinction. The ought has nothing to do with the logic itself, it regards the normativity of logic. And unless you completely disavow all normativity your argument really seems besides the point. Even just considering the logical formalism itself, a trivial logic is without use or understanding in any circumstance. Everyone rightly assumes you care about what the words you say mean when you use logic because otherwise your communication would be ineffective.

You justify A using B then claim that everyone has B. While that is true, I'm trying to find a way to get B that does not rely on consensus, pragmatism or arbitrariness (thus the title of the discussion: where does logic get its power. So far you've clearly shown that everyone has B but I'm asking WHY everyone has B and you cannot use an answer that refers to C if C is also as arbitrary as A and B)

A & B are the norm precisely because there would be no point in having one without the other. If you don't care about being coherent at all there'd be no reason to construct a coherent logic, and vice-versa. I've given non-arbitrary, non-pragmatic, non-consensus answers. Recourse to models of theory choice (abduction) is not arbitrary nor any of the others characteristics you mentioned.
• 141

Let's define pragmatic here just to make sure we're on the same page: Accepted for a reason that is not logical proof

That's not what I said, I said one's goals cannot be reached by pure logic. The axioms one adopts can be done so rationally (non-arbitrarily), as I gave two means by which to do so.

How can you reach axioms to adopt without starting with certain axioms. Logic requires premises. You can't reach a conclusion without premises. I am pointing out that there is a near infinite number of premises you can start with. Both methods you have highlited adopt certain premises themselves.

For the first, using a model of theory choice, you'd have to choose WHICH model to use. That cannot be determined by the models themselves. There are multiple theoretical virtues such as elegance, accuracy, complexity, number of assumptions, etc. You only pushed the problem one step back so now instead of deciding what premises to base my logic upon I know have to decide which criteria to use to decide which premises to base my logic upon. You ultimately still need an arbitrary pivot.

The second is literally the definition of consensus based logic.
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