You are expecting an assignment whereby the left-side expression takes the value of the right-side because you are used to those higher-ordered languages in computing. The error is not to the 'classic' logic though but to your 'top-down' approach to learning.Logik wrote: ↑Sun Feb 24, 2019 8:11 amMeanings? I am not looking for meaning. Logic is a tool of self-expression.Scott Mayers wrote: ↑Sun Feb 24, 2019 7:05 am Maybe it might help if you stepped back to the simplistic origins of logic, NOT jump ahead to the complex theories that require more intense investigation to determine the meanings implied in those areas?

When you are attempting to express simple ideas Classical logic is fine.

When you are attempting to express complex ideas about a complex reality - you need higher order logic.

There are things I am unable to express in classical logic Like A != A.

If I were to express A !=A I contradict the Identity axiom.

More precisely, every time I express "A != A" a Classical logician (mistakenly) asserts that I have contradicted myself when I haven't.

Speaking different languages is not conducive to communication.

Forcing me to speak your language is not conducive to self-expression.

So I need a logic in which "for all x: x = x" is NOT an axiom.

The code I provided in Python (Lambda calculus - same thing) demonstrates that I have a logic in which A != A is a valid, non-contradictory expression.

The actual logical assumptions from first-order logic are misleading because they confuse 'coincidence' relations to 'equality' and the exclusive-or to inclusive-or.

The general three laws accepted are:

All these are actually implied by any one of them and only spells out different perspectives of the same thing.(1)A law that asserts consistency but often stated as about 'equality'.

A = Abut you need to translate in computers asA == A

(2)A law that asserts,

A or not-Aand

(3)A law that directly asserts no third option that permits

A and not-A......Exclusive Middle possibility such as{A, A and not-A, not-A}excluding the contraction [“con-” (with) “-tra-” (third) “diction” spoken-part]

A more accurate means I believe would/should be to use operators of 'coincidence' (⊙ ) and the 'exclusive-or' (⊕ ) because they explicitly deal with the same term. So the laws might be better written as:

These are all proved within most Boolean systems by simply using the inclusive-or, and, and complement. Then it proves later defines the exclusive or and uses DeMorgan's Theorem to determine theRevised and Clarified Consistency Laws

(1) Law of Consistency

A ⊙ A = 1,

(2) Law of Exclusion, which is just the 'dual' of (1)

A ⊕ A = 0and

The law of excluding the 'middle' term also relates to Aristotle's use of he middle term but is equivalent to the above and the law of non-contradiction implied by both of these but more clearly emphasized by the use of the normal OR operator as

(3) Law of Non-contradiction

A + A̅

**duals**which included defining the inverse of exclusive-or as the 'coincidence operator.

I happen to treat physical reality as due to laws in a kind of Pythagorean sense. Physicists from M.I.T. seem to agree. See those like Max Tegmark or Seth Lloyd for references in general on this. “laws” of reality are just those patterns of a subset of worlds among all possible worlds which happen to be consistent. If anything, we 'discover' math as much as physics but the language we use to express them are itself flexible.Logik wrote: ↑Sun Feb 24, 2019 8:11 amLogic has nothing to do with nature. Logic/mathematics is invented. Man-made.Scott Mayers wrote: ↑Sun Feb 24, 2019 7:05 am All you are asserting is very basic: that you don't trust logic via nature as something based on "consistency" or to the other coinciding assumptions, "the law of excluded middle" and "the law of non-contradiction".

I most definitely do not adhere to the LNC. No constructive mathematician does.

Non-contradiction stays .

[more responses later....this should be at least good for a start.]

EDIT: fixed the color command to make the red letters above appear. needed spaces removed in the command apparently