## Anything Can Be Postulated

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### Anything Can Be Postulated

Any proposition can be a postulate.

Let p be a proposition. It is logically necessary that p is permitted to be a postulate. It is logically necessary that the proposition "p is true in the actual world" is permitted to be a postulate.

If p is a postulate, then: p is true and no contradiction exists.

Proof. It is given that p is a postulate. Then by definition of postulate, p is true.

Assume some contradiction exists. Then there is a contradiction. Discharge the assumption. It is thus proved by contradiction that it is not true that some contradiction exists. So, no contradiction exists.

By conjunction introduction, p is true and no contradiction exists. This concludes the proof.

Since the proposition "p is true and no contradiction exists" is true at all times that p is a postulate, there is never a problem with p being a postulate.

In the proposed debate "The Absolute Russell Set Exists," which I recently cited on social media and is located at http://www.debate.org/debates/The-Absol ... -Exists/1/, I, Paul E. Mokrzecki, postulated the existence of the absolute Russell set. The proposition "the absolute Russell set exists" can be postulated without contradiction and thus without trouble.
Paul E. Mokrzecki
browser32

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### Re: Anything Can Be Postulated

Self reference can drive people up the wall, as in the case of Cantor. The true implication is inherent in the paradoxical structure of language, which is and isn't reflective of reality (consciousness) at the same time.

This is so simple and complex at the same time , that such notion , to be proposed seeks a set boundary , which does not exist.

I would like to connect this concept to the notion of transparency somehow, using by example the Moebius Strip

I may be way way off or near to some connectivity , in an interconnected world, but in a naive , intuitively real way.

Reasoning from effects to affects is just such an incalculable method.perhaps the postulated place of mathematics stands on an intuitive , rather then on a theoretical basis, is this why Frege was so impressed by Russell's

An allowence must be made to the introductory phase of this search, with an eye to a minimal view to a mathematical background.

Note: even the seemingly contradictory all inclusive set of -rational-irrational must (logically) contain it's/IT's self.

On that premise, (proposition), how can self reference be inferred?

If so, that would clear up a lot of necessary contradiction to seek Enlightement.

Note: Don't let it throw You, for daring to begin thusly, especially by ignoring/attending to ME/me.

Your proof is topical.- akin to a Moebius demonstration.

A lot of profundity can be had from these postulations , coming on the heels of existentialism, the difference between eidectic and phenomenological reduction, the further regress into the Naturalistic Fallacy, and even the paradoxical nature of Descartes' Cogito.

Even the political near sightedness that Trumpism has exploded unto humanity, but in that sense, the rightness or wrongness of that posture has become blurred to HIS advantage, or, the world's?

The paradox is at once clearly understandable and muddy like a can of worms.

Is it or not fitting to these times?
Meno_
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### Re: Anything Can Be Postulated

Meno_ wrote:On that premise, (proposition), how can self reference be inferred?

It's unclear what you are asking there.

In the case of the absolute Russell set, the set both is and is not an element of itself.

Proof. Let R be the absolute Russell set. As I claimed in the proposed debate I cited in the opening post of this thread, R is an element of R if and only if R is not an element of R.

Assume R is not an element of R. Then R is an element of R. So, there is a contradiction. Discharge the assumption. It follows by the proof by contradiction method that R is an element of R.

Assume R is an element of R. Then R is not an element of R. So, there is a contradiction. Discharge the assumption. It follows by the proof by contradiction method that R is not an element of R.

So by conjunction introduction, R is an element of R and R is not an element of R. This concludes the proof.

Since the absolute Russell set both is and is not an element of itself, a contradiction exists. According to ex contradictione quodlibet, every proposition is implied by a contradiction. So, all propositions are true. It follows by definition of trivialism that trivialism is true. Trivialism is hence a logical consequence of the postulate that the absolute Russell set exists. So, "self reference," whatever you mean by that, can be inferred from trivialism.
Paul E. Mokrzecki
browser32

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### Re: Anything Can Be Postulated

Of course implication is the key between the the proposition and the postulate, and it rests not on the logical ground but on the intuitive -statistical ground. That is trivial to say the least and highly complex at the same time, and yet it is topical, and therefore referential.

I was aiming for a non referential , dynamic relationship, not trivial .

But I guess that may exceed the boundary and scope , not to mention the preparedness for such.
Meno_
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### Re: Anything Can Be Postulated

But no matter, discovered Your philosophy forum article, and try to read that, and go from there.
Meno_
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### Re: Anything Can Be Postulated

This post includes another proof that if p is a postulate, then: p is true and no contradiction exists.

Proof. It is given that p is a postulate. So, by definition of postulate, p is true. It's a basic truth that: some contradiction exists or no contradiction exists.

Assume no contradiction exists. Then by reiteration, no contradiction exists. Discharge the assumption.

By disjunction elimination, no contradiction exists. So by conjunction introduction, p is true and no contradiction exists. This concludes the proof.
Paul E. Mokrzecki
browser32

Posts: 218
Joined: Fri Jun 03, 2011 1:25 am

### Re: Anything Can Be Postulated

browser32 wrote:This post includes another proof that if p is a postulate, then: p is true and no contradiction exists.

Proof. It is given that p is a postulate. So, by definition of postulate, p is true. It's a basic truth that: some contradiction exists or no contradiction exists.

Assume no contradiction exists. Then by reiteration, no contradiction exists. Discharge the assumption.

By disjunction elimination, no contradiction exists. So by conjunction introduction, p is true and no contradiction exists. This concludes the proof.

This proof is not trivial and better then the latest explanation, and I appreciate the entropic elegance. The latter is even more patently significant , so I can not go there until I can connect the two. Therefore it is the word implication which further decay the referentiality of meaning. This simple exposure is the basis of the extraordinary logical difference that logical positivism has revealed.
Meno_
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### Re: Anything Can Be Postulated

There's a difference between claiming that a proposition is true and postulating that a proposition is true. A claim that a proposition is true is not always true, but a postulate that a proposition is true is always true.

If a proposition is not considered to be a postulate, but a person claims the proposition is true, then the person could be wrong. However, if a proposition is considered to be a postulate, and a person claims the proposition is true, then the person is right.

If it is considered to be a postulate that "trivialism is true," and a person claims a proposition, then since the claim is implied by trivialism, the person is right. If I consider it to be a postulate that the absolute Russell set exists, then every claim I make is correct.
Paul E. Mokrzecki
browser32

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