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Post by xxxxxxxxx on May 5, 2022 22:39:19 GMT
1. All logical systems require axioms.
2. These axioms are unproven except through the proofs in which they are used.
3. The proof justifies the axiom and the axiom justifies the proof.
4. Proof and axiom, as circular, thus become interchangeable: a proof is an axiom and an axiom is a proof.
5. This interchangeability, as equivocation, results in obscurity as it is self-referencing therefore the axiom is no longer the axiom and the proof is no longer the proof as both become indefinite.
6. Axioms/proofs are only that which are accepted to deal with this indefiniteness, thus logic requires intuition.
7. Intuition thus expands the circle of axiom=proof to axiom=proof=intuition.
8. However intuition is not universal as the axiom=proof would not have to be taught if it where such.
9. In the equivocation of "axiom=proof=intuition" the intuition not being universal necessitates the axiom/proof as not universal.
10. This absence of universality necessitates a multiplicity of logics, all of which may not agree.
11. This absence of agreement in logics results in the axiom of "Logic" being obscure yet logic was used to deduce this.
12. Logic=no logic
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Post by Eugene 2.0 on May 10, 2022 4:00:27 GMT
Well, partially your arguments work, but there's something really funny. I guess making such a mistake is explainable: anyone who tries to defeat or to disprove logic ends with nothing or with bunch of contradictions.
Axioms – is a stable part, and any theorems – are not stable. So, to make an inference is to make non-stable to be stable with the stable.
Actually, we can skip that stability, but one thing must be important: some axioms are chosen freely, or without proof. That's why you can trust them only believing in them. This point ruins all the idea of logic, but nobody can prove it since for proving something one has to use logic.
There's a way of skipping it and to justify logic, but this requires usage of modalities. Unlike truth/false dichotomies the modal logic uses accepted/unaccepted. For example, if a system S is acceptable, then it's impossible that it has or contains falsely.
So, how we suppose to prove logic or to trust it? It can be done with thing by thing examination, i.e. checking all the possible axioms. If we've checked them, and no other axioms left, and if we've made all the inferences, then our logical system is acceptable.
By checking all the axioms we open the gate to logic without using the trust or the belief. We just know all the possible axioms, and we know all the inferences from them.
It's quite similar to the total knowledge of everything: if one has got such a knowledge, then only what one lasts to do is to calculate or to choose.
But there's also one big point that protects logic from any brute objection. The thing is that axioms can be similar or alike. If among all the possible axioms only 100 are different, while the other ones are just repeating the previous, then we've got 100 axioms and ∞ epigones or clones of them.
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Post by xxxxxxxxx on May 11, 2022 22:58:16 GMT
Well, partially your arguments work, but there's something really funny. I guess making such a mistake is explainable: anyone who tries to defeat or to disprove logic ends with nothing or with bunch of contradictions. Axioms – is a stable part, and any theorems – are not stable. So, to make an inference is to make non-stable to be stable with the stable. Actually, we can skip that stability, but one thing must be important: some axioms are chosen freely, or without proof. That's why you can trust them only believing in them. This point ruins all the idea of logic, but nobody can prove it since for proving something one has to use logic. There's a way of skipping it and to justify logic, but this requires usage of modalities. Unlike truth/false dichotomies the modal logic uses accepted/unaccepted. For example, if a system S is acceptable, then it's impossible that it has or contains falsely. So, how we suppose to prove logic or to trust it? It can be done with thing by thing examination, i.e. checking all the possible axioms. If we've checked them, and no other axioms left, and if we've made all the inferences, then our logical system is acceptable. By checking all the axioms we open the gate to logic without using the trust or the belief. We just know all the possible axioms, and we know all the inferences from them. It's quite similar to the total knowledge of everything: if one has got such a knowledge, then only what one lasts to do is to calculate or to choose. But there's also one big point that protects logic from any brute objection. The thing is that axioms can be similar or alike. If among all the possible axioms only 100 are different, while the other ones are just repeating the previous, then we've got 100 axioms and ∞ epigones or clones of them. Logic self-negates through self-referentiality thus logic results in contradiction. The totality of parts, with logic being applied to the relative parts, has no comparison as it is self-referential. The total, as logical, is logic self-referencing thus self-negating. |
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Post by Eugene 2.0 on May 12, 2022 5:51:21 GMT
Well, partially your arguments work, but there's something really funny. I guess making such a mistake is explainable: anyone who tries to defeat or to disprove logic ends with nothing or with bunch of contradictions. Axioms – is a stable part, and any theorems – are not stable. So, to make an inference is to make non-stable to be stable with the stable. Actually, we can skip that stability, but one thing must be important: some axioms are chosen freely, or without proof. That's why you can trust them only believing in them. This point ruins all the idea of logic, but nobody can prove it since for proving something one has to use logic. There's a way of skipping it and to justify logic, but this requires usage of modalities. Unlike truth/false dichotomies the modal logic uses accepted/unaccepted. For example, if a system S is acceptable, then it's impossible that it has or contains falsely. So, how we suppose to prove logic or to trust it? It can be done with thing by thing examination, i.e. checking all the possible axioms. If we've checked them, and no other axioms left, and if we've made all the inferences, then our logical system is acceptable. By checking all the axioms we open the gate to logic without using the trust or the belief. We just know all the possible axioms, and we know all the inferences from them. It's quite similar to the total knowledge of everything: if one has got such a knowledge, then only what one lasts to do is to calculate or to choose. But there's also one big point that protects logic from any brute objection. The thing is that axioms can be similar or alike. If among all the possible axioms only 100 are different, while the other ones are just repeating the previous, then we've got 100 axioms and ∞ epigones or clones of them. Logic self-negates through self-referentiality thus logic results in contradiction. The totality of parts, with logic being applied to the relative parts, has no comparison as it is self-referential. The total, as logical, is logic self-referencing thus self-negating. But at the end your argument against logic doesn't work. Why so? Just think about it: - you're denying logic or saying that logic ends in contradiction - anyone can ask you: how did you know that? with what did you do this? - the answer can be with or without logic - if you never used logic, then there is no certain about your answer - if you had used logic, then logic isn't contradictory (at least in your case). |
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Post by xxxxxxxxx on May 12, 2022 17:21:44 GMT
Logic self-negates through self-referentiality thus logic results in contradiction. The totality of parts, with logic being applied to the relative parts, has no comparison as it is self-referential. The total, as logical, is logic self-referencing thus self-negating. But at the end your argument against logic doesn't work. Why so? Just think about it: - you're denying logic or saying that logic ends in contradiction - anyone can ask you: how did you know that? with what did you do this? - the answer can be with or without logic - if you never used logic, then there is no certain about your answer - if you had used logic, then logic isn't contradictory (at least in your case). If I use logic to contradict logic then the logic is self-negating. An example of this would be: The law of excluded middle applied to the law of identity and the law of non-contradiction, either the law of identity is true or the law of non-contradiction is true. Either way one of the laws negate through this self-referentiality. Because of the "or" function of excluded middle a decision must be made between the two laws (identity and non-contradiction) however before the decision is made both laws are simultaneously true and false until the potential of one existing is actualized, this is the contradiction. |
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