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? — khaled
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? — khaled
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. — BrianW
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. — Pattern-chaser
Why then are some theories about reality better than others? — litewave
why is theory of relativity better at making predictions than Newtonian physics? — litewave
Because its predictions are more accurate in a wider range of circumstances? :chin: — Pattern-chaser
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. — Pattern-chaser
And this is because the relationship between "fact/reality and our perception of it" is unknown and unknowable to humans. — Pattern-chaser
So the relationship between theories and reality is one of "fitting", or correspondence. — litewave
It IS entirely ragtag because any rule you choose to use as an axiom is by definition based on no other reasoning. — khaled
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. — khaled
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. — khaled
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 — khaled
Again, you are binding logic to practical value which is exactly what the start of your comment tries to refute. — khaled
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. — MindForged
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. — khaled
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. — MindForged
Avoiding triviality is not arbitrary. — MindForged
Inconsistent means contradictory, so your claim is just false. — MindForged
The metatheory of fuzzy logic is classical logic. People don't really use fuzzy logic anyway — MindForged
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 — MindForged
Practicality plays a role, but it's not the only role. — MindForged
Another way would be to pick a very weak logic which contains principles no one disputes — MindForged
Whatever logic, in some specified domain, comes out the best on the criterion of theory choice — MindForged
Why not? Why should we avoid triviality? — khaled
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. — khaled
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. — khaled
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. — khaled
Oh really? What else plays a role? — khaled
The fact that no one disputes them is no proof of their validity. — khaled
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. — khaled
I did answer why, repeatedly. It becomes completely incomprehensible *in principle* and loses any possible use towards anything, whether practical or theoretical. — MindForged
Theoretical virtues: simplicity, fruitfulness, adequacy to the data, lack of ad hoc elements, unifying power, etc. — MindForged
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. — MindForged
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. — khaled
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 — khaled
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 — khaled
The statement "A=A" is not ontologically different from the statement "A!=A" — khaled
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. — khaled
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. — khaled
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. — khaled
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. — khaled
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. — MindForged
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. — MindForged
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.[Fuzzy logic] is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. — Wikipedia
.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.
Need it be proved that there aren’t mutually contradictory or inconsistent facts, or propositions that are true and false? — Michael Ossipoff
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 — Michael Ossipoff
"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 — khaled
any definite yes/no matter is, tautologically, one way or the other (not both), and that doesn’t need proof.
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. — khaled
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. — khaled
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) — khaled
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. — MindForged
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