An inconsistency in the system such as false / incomplete / contradictory informationLogic wrote:
Do you know what an error is ?
So for a system to be error free it must not contain any of these faults or any others
An inconsistency in the system such as false / incomplete / contradictory informationLogic wrote:
Do you know what an error is ?
Why are inconsistencies errors?surreptitious57 wrote: ↑Sun Mar 17, 2019 12:06 pm An inconsistency in the system such as false / incomplete / contradictory information
Translation of the above without using the word "error".surreptitious57 wrote: ↑Sun Mar 17, 2019 12:06 pm So for a system to be error free it must not contain any of these faults or any others
Logic has to be sufficiently rigorous for it not to be inconsistent or contradictoryLogic wrote:
Why are inconsistencies errors ?
Why are contradictions errors ?
Rigour is "adherence to rules".surreptitious57 wrote: ↑Sun Mar 17, 2019 12:21 pm Logic has to be sufficiently rigorous for it not to be inconsistent or contradictory
What's "logical" is true by definition. It's tautological.surreptitious57 wrote: ↑Sun Mar 17, 2019 12:21 pm Any system that has these errors in it to any significant degree cannot be logical
In a syllogism each premise must be logically consistent with the previous oneLogic wrote:
In what framework have you decided on the correct definition for logic ?
You are not answering the question. You are laying down rules.surreptitious57 wrote: ↑Sun Mar 17, 2019 1:14 pmIn a syllogism each premise must be logically consistent with the previous oneLogic wrote:
In what framework have you decided on the correct definition for logic ?
In a proof each calculation must be logically consistent with the previous one
Logic therefore is about the relationship between different parts of the framework / system
There must be sufficient rigour / consistency within it or else it is rendered invalid / unsound
Those rules would be completely useless in practice because they are too arbitraryLogic wrote:
You could have just as well chosen
in a syllogism each premise must not be logically consistent with the previous one
In a proof each calculation must not be logically consistent with the previous one
I think you have erroneously conflated consistency and rigour with utility.surreptitious57 wrote: ↑Sun Mar 17, 2019 2:05 pm Those rules would be completely useless in practice because they are too arbitrary
A logical system has to be sufficiently rigorous in order to produce effective results
This is only true for certain examples as these laws still apply so are useful for that reasonLogic wrote:
I have SHOWN you a computational logic where neither the laws of identity or non contradiction apply
OK. They have no practical application for me. If you find them useful - use them.surreptitious57 wrote: ↑Sun Mar 17, 2019 2:31 pm This is only true for certain examples as these laws still apply so are useful for that reason
They will only become redundant when they have absolutely no practical application at all
False. Lambda calculus. Turing-completeness. Logics without contradictions.
No I haven't. Proofs compute (Curry-Howard).
I haven't redefined anything. Equality does not have a clear definition beyond the real numbers.
The objective standard for mathematical proofs (Curry-Howard) suggests that you are clearly mistaken.
Bullshit.Averroes wrote: ↑Sun Mar 17, 2019 10:08 am But more importantly in this case, for example, some humans are murderers and some humans are not murderers. Someone who has killed thousands of defenseless women and children is clearly not equal to someone who has not killed any human being. A murderer is clearly not equal to an innocent human being. But according to the redefinition of equality given in the program, a murderer is equal to an innocent human being! This is absolutely unacceptable from both a legal and a moral point of view.
Who cares about set theory? Curry-Howard deals with type theory.
You are translating a Turing-complete system into an incomplete one (set theory).Averroes wrote: ↑Sun Mar 17, 2019 10:08 am While the redefinition expressed in the Python codes given in the OP can be expressed as follows:
Given any x and y, x=y if and only if, there is at least one predicate P and there is at least one predicate Q such that, P(x) if and only if Q(y).
Symbolically: ꓯxꓯy(x=y ↔ ꓱPꓱQ(P(x)↔Q(y)))
Well, actually that's precisely the problem.
The "correct result"? So.... you are telling us that you KNOW what results you WANT logic to produce?