Eodnhoj7 wrote:It can be true and false at the same time in different respects considering "sat" is past tense referencing a different position in the time line. The cat may have got up, during a seperate part of the same time line. In these respects the cat both sat and did not sat, relative to the length of time measured. …

There is no time in Propositional Logic.

The proposition is actually neutral considering it exists if and only if it continues to progress in definition. As the proposition is non-localized, as in not existing within a set of further localities, it observes a retro-gressive potential statement. Let me elaborate that point....the cat may have sat potentially within "x" period of time, but unless the proposition expands further it is only a potential statement. Because it is potential it maintains both possibilities simultaneously. …

Only in your barking world where time is a factor in Propositional Logic(PL).

Propositional logic only works if the definition of the propistion continually expands.

No, PL works because there are things or states of affairs, declarative sentences and Reason.

Propositional logic is a framework of rules, which exist as limits, that exists as a synthesis of axioms. …

What limits?

There is no measurement in PL.

The problem of "choice" comes along, as the axioms which necessitate Propositional Logic either:

1) Where chosen as a beginning point of measurment, admidst other possible axioms, hence an element of randomness was involved by the application of choice. …

There is no 'problem of choice' in PL, the axioms came from logical deduction from the idea that if there is a P then there can be a Not P, etc.

2) Because these axioms exist if and only if they relate, they inevitably result in a form of circular reasoning (as argued above) which contradicts their form and function. One axiom, as each law is an axiom, exists if and only if they relate to further axioms. …

The only relation is logical deduction.

This form and function is contradicted as they are required to observe a dualism of "being or non-being" but require a third neutral median of "either/or" which exists between "is" and "is-not". Even then the propostion, as evidenced by the Cat example above, must continually replicate itself if it is to be truly justified. …

No it doesn't, it just requires there to be a cat sitting on a mat.

3) These axioms of Propositional logic leads to further axioms, such as those of intuitionist logic, with Propositional logic existing if and only if it extends to these further axioms. It is does not extend to these further axioms, it is not continually justified, it also circulates through itself and contradicts itself. …

You have in no way shown that the axioms of PL contradict themselves and you won't because they don't.

An apple is an apple observes the apple exists through replication across time and space. Logic follows this same course of definition, as this replication allows "the apple" to exist through various different positions in the argument, hence not just tying the argument together but Replication observes an extension across the argument.

What it observes is that there is an apple.

"A = A " tends toward "A","A" and "equality" as things in themselves. They exists if and only if:

1) There exists "A", which exists if and only if there is "equality" and a seperate "A". …

No, P exists if there is a P.

2) There exists "equality", which exists if and only if there are seperate "A"'s. …

No, 'equality' exists if you can substitute the term with no change in truth value.

3) Rehash of point 1 with second A as premise.

4) These existences of A, equality, and A are directed through eachother and alternate …

Really no idea what you are talking about?

All of this is depending upon the beginning point of measurement, however the fact that the definitions require a form of alternation to exist, a medial term is necessary. …

There is no measurement in PL. What does 'medial term' mean?

And what is memory but the replication of events in the minds, as a frequency, conducive to a form of symmetry. X event is replicated "Y" times across the mind as a form of memory, hence is structure in itself dependent upon symmetry. …

But the event does not depend upon there being a mind.

Logic exists "because there are things and states of affairs"...what does that mean? If that is the case I am logical because I exist. …

No, if you exist then Logic applies to you as Logic(at least PL) comes from there being things or states of affairs.

P - You exist

¬ P - You don't exist.

(P v ¬P) - You exist or you don't exist.

¬(P ^ ¬P) - You can't exist and not exist.

P = P - You exist if and only if you exist.

There can only be a P in the first place if P replicates itself, hence P exists if and only if there are multiple "P"s.

There are 7 P's in the above sentence. P exists as a letter and a letter exists if and only if it conveys a thought through sentence. The sentence exists through the letter, however the letter must exists in seperate postions within the sentence simultaneously if the sentence is to exist...hence the P must replicate if it is to exist.

You seem to not understand that "P" is a variable?