A method by which humans go from premise to premise that seems to reflect reality if the premises do. — khaled
1) What was the "origin" of logic.
2) Why is it that we are simply born with a "rule for deriving rules" and why does it work so well?
3) Why is it then that humans can get by using arbitrary axioms that they are born with whose validity they cannot prove?
4) And why is it that despite the fact that many axioms fit that description, that only very few work?
5) Again, where does logic get it's reality-reflecting power? — khaled
Is there any metaphysical basis for logic or are humans just stuck with a certain type of hardware — khaled
Broadly, logic refers to the rules of correct reasoning — MindForged
Is there any metaphysical basis for logic or are humans just stuck with a certain type of hardware? — khaled
However you can never go back and "prove" the axioms you just have to accept them a priori. — khaled
Gödel said that every non-trivial (interesting) formal system is either incomplete or inconsistent:[1] There will always be questions that cannot be answered, using a certain set of axioms;
[2] You cannot prove that a system of axioms is consistent, unless you use a different set of axioms.
Those theorems are important to mathematicians because they prove that is impossible to create a set of axioms that explains everything in maths.
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. — khaled
Why is it that we are simply born with a "rule for deriving rules" and why does it work so well? — khaled
So, my view is that you can't explain logic - logic is what explains — Wayfarer
We both seem to have reached the conclusion that logic is: "A rule for making rules that is based off of ragtag collection of intuitions that we are born with strung together which helps us survive". You said that we are not born with logic and that we change it periodically to help us survive which I totally agree with but then that would be putting logic on the same "correctness" level as lunacy. They are both based on primordial intuitions, just that the followers of one survive and the followers of the other perish. — khaled
The problem is, there are countless potential ways to formulate such rules and there is no meta-rule about how to do this for which there are no alternatives, at least none that I can see. — khaled
The main goal for this discussion was to get people to think about such a meta-rule (A method for choosing logical axioms) for which there is no alternative. A "common ground" across all possible systems of logic if you will. Question 4 was supposed to be a trick question because what defines "work" IS the axioms of logic. You can't get an answer to "what works" without knowing something that works and you can't know what works without knowing the answer to "what works". It seems to me that the only way to develop a logical system is to pull yourself up by your bootstraps (beg the question) and I'm looking for someone to convince me otherwise
It's not ragtag, that would suggest the rules are arbitrary. — MindForged
So there's one "meta-rule" right there: the axioms cannot on pain of absurdity result in the system degenerating like so — MindForged
This is mistaken, I believe. When I referred to a logic "working", I was speaking extra-logically — MindForged
That will be a common ground across logics that are actually used — MindForged
This is why I tell people to find me this axiom that is entirely indisputable without resorting to arguments from practicality — khaled
What I'm trying to find in this discussion is an axiom that escapes this, an axiom everyone MUST accept — khaled
Now logic requires neither rigor not any specific axioms, it just needs to be useful when applied to the world. — khaled
My definition of fact/reality is that which is; that whose value is absolute; the indisputable, the undeniable, and in that sense, it describes that which remains even when everything else ceases. — BrianW
You wouldn't have access to the concept of "physical reality" if all you can ever see is a 2D computer screen. — khaled
Is there any metaphysical basis for logic or are humans just stuck with a certain type of hardware — khaled
Humans being humans, many of them would choose not to accept it anyway — Pattern-chaser
because an argument against identity would automatically refute itself — litewave
I want something completely self evident and irrefutable. — khaled
True, but it would also refute every other argument with it. It's like an intellectual suicide bomber. You can refute the principle of identity, refute your own refutation and still be perfectly consistent in a state of eternal "I don't know". That's what the phyrrhonean skeptics did and I believe their position is the most valid and unassailable in philosophy. — khaled
The best way to conceive of fact/reality is as a union of principle and potential. If we try to confine it with a form, then it defines its own limitation and ceases to be absolute. — BrianW
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