The Absolute Russell Set Exists

Philosophy Forums Science, Technology, and Math
41

There is a principle that we are seeking a consistent framework for mathematics. You are entitled to desire an inconsistent framework, but that seems pointless.

If you think 11 is the largest prime, we’re done. Actually we are done. You haven’t said anything new in quite a while.

You greatly misunderstand proof by contradiction. But if you enjoy typing Latin phrases, by all means enjoy yourself.

I would agree. But “not necessarily useless” is not the same as “We should adopt inconsistent mathematics.” The latter would be counterproductive.

You should not assume I have not looked at your other online work. I’ve seen the nudes, I’ve seen the restraining order filed against you. What of it? If you have something to say, say it here.

Whatever that word salad means.

If you reject the concept of mathematical proof, we’re done. Which we are.

All the best.

42

Through ex contradictione quodlibet, every inconsistent framework for mathematics is consistent.

Inconsistency, by its very nature, coexists with consistency.

I am telling you the objective truth. 11 is the largest prime.

I’m afraid you may have misinterpreted my paragraph there. I intended its first sentence only to be exclusively about proof by contradiction. The rest of that paragraph, including its last sentence about a proof of ex contradictione quodlibet, is about general proof. The last sentence of that paragraph provides evidence for my claim of the second sentence of that paragraph.

I strongly disagree with your claim that I “greatly misunderstand proof by contradiction.” I assure you I understand proof by contradiction. It’s clear I use proof by contradiction myself. In my post at viewtopic.php?p=2699066#p2699066, which I have now cited for the fifth time in this thread, I invoked two proofs by contradiction.

Notwithstanding, by ex contradictione quodlibet, a contradiction implies its own nonexistence. Also, by the law of noncontradiction, there is no contradiction. With no contradiction, there is no proof by contradiction.

It’s clear from the proofs I’ve given in this thread alone that I have not rejected the concept of mathematical proof.

43

I do not agree that were done. Mathematical proof is contingent, not necessary to demonstrate the law of inconsistency.

Simply, the presumption fails, rather the holding the principle ,form the simple reason of the failure of self evident truths.

Nowhere is this more evident then in the proof of God argument where , the quality of perfection of god, is part of his existence. Without the quality of perfection God would not be god.

And lack of existence would detract from his perfection, therefore his non existence would lead to contradiction.

Therefore the presumption of his existence is necessary to avoid contradiction. This was all Russel was saying , as anyone who declared certain inalienable rights.

No rights are inalienable , to found a perfect union, this is what is at the base of the great Trump debate.

Trump is using this contradiction to bring back certain expired assumptions.

Logic through language leads to contradiction, where, the pseudo consistency presents false meanings .

The search for meaning is tainted from the get go.thisnisnwjubtjen genesis of meaning has become such an important part of philosophical study, which could not separate reason from meaning.

By saying thus I hope I don’t end up in the trash in of intentions where its sometimes falsely claimed that the man in the middle between antithetical claims , both hold ing. a union of antagonistic attitudes.

44

Of course I did not unilaterally declare the thread to be finished. I couldn’t do that if I wanted to. Rather, I said I’m done responding to the OP, having nothing more to say.

Meaning unclear.

Self-evident truths from the Declaration of Independence?

This is Saint Anselm’s famous proof of the existence of God. It leads to the interesting question of whether or not existence is a predicate.

Russell was saying nothing of the sort. Russell pointed out that Frege’s unrestricted set formation leads to a contradiction. Anselm’s proof of God has absolutely nothing to do with this.

Back to the Declaration.

The phrase “perfect union” of course famously appears in the preamble to the US Constitution.

Has nothing to do with anything.

Perhaps you can give an example.

Word salad.

I can agree with that. Just as the writing of history often says more about the present than it does about the past. Nevertheless we make the effort.

If you say so. What does that word mean please?

Earlier I said I would make a good faith effort to take you seriously even if not literally, but this latest post of your makes that difficult. You’re either trolling or running a poorly-executed chatbot.

It’s difficult to take your post seriously. Surely it’s fair for me to say that. I was going to ask if perhaps you are not a native speaker of English, but even that doesn’t account for the strangeness of this post.

45

Fair.I’m not even going to try to defend the above,it was very late and try to pull things together,

. albeit unsuccesively.

The merit of my argument , nevertheless, as tenuous, has redeemable featured.

Contradiction on the naive logical level, contrasts with the later, more expanding scientifically based level. Here, ordering of sets , based on types- qualities, expressed through adverbs, rather then verbs, ( where verbs are prone to express the duality of exisyence.

adverbs qualify, through modified, not primary logic, deliniations of meaning, consistently and subtly, shading the extreme inclusive/exclusive logic through language. The grey area has a limited backward look into the inception of such language, and philology. can not trace the origin, in an exclusive set of membership.

Political ambiguity and contradiction then, are present in politics, Trumpism, St. Anselm, and even the Declaration of Independence utilize the progressive languages, whereby the logical nuances are exemplified.

Such declarations of basic rights, do not express the coming ambiguity between the coming inherent contradiction between rights of life, liberty and the enjoyment of life, in light of the non comprehension of factors of Capitalistic accumulation which may (and did) work against such prematurely ideal constructs, and hence when political scientists talk of a Constitutional Crisis, it is not too far a stretch to interpret. these in terms of absolute exclusivity. versus inclusivity between them, and the emergence of modified conceptual grey areas.

Logically, duality has been more based on intuitive levels of understanding, such as Kant brought into recognition .However, it is the correctness of such premature deliberations, that became a sort of foreseeable development, upon which Hegel, Marx, came to create their own developments.

Logic through the evolution of language, which finally reveals the actual contradictory experiences of living these logical. contradictions meaningful. bear them out in realitu5

Yes my English is not primarily of native origin but.acquired secondarily , so it plays into the differential systems between the logical systems.

That Hungarian, my first, is a very unique language type (I’ve heard it said) thanks for noticing.

Other than this I have nothing to add, and I brought Anselm, into the discussion , fully understanding the significance of his failure. Mixiing what now has been seen as two different kinds of systems of logic, literally exemplifies the two languages I am at times conflating. Incidentally Hungarian being the more literal language,not that this alone makes the difference

Finally, I’m not adverse to be found wrong, with differences of opinion of varying phonetical and grammatical systems of thought.

46

If you’re saying that ambiguity exists in society and in language, I completely agree.

That’s exactly why we use formal logic and math as realms where ambiguity is eliminated. Logic and math aren’t the same as the contradictions of the world. But that doesn’t mean that logic and math are somehow tainted by the confusion of language and the world.

47

Perhaps my brushstrokes were leaving too broad a trace in implying that the very basis of the use of logic that has created the very contradictions through language, as useful as they appear within themselves.

You may laugh, but the most obvious being is Hegel’s systemic logical approach in forming reality through the logical adaptation of language as the mirror of reality speaks for itself.The question then becomes not that logic is wrong, but it can misrepresent reality by assuming that it can systematically apply its methodic dual aspect to order , types of dual functions to semantic usage.

Is this a case of finding fault with either language or logic, or, is it based on the assumption that dual , contradictory thinking is due to the construction of the structure of the brain itself, wherein duality is merely a functional processing of the physiology of the brain?

Either assumption is exctrinsically factual, but intrinsically conflated, which leads to paradoxical contradiction.

In another form the question manifests not as the etymology of the brain, nor the functional use of the adaptive uses of the brain. It appears convincing to say that the latter has more inclusive features.

The example of the human thought occurring, when in the face of an impending attack by a superior and enhanced attack, most humans will automatically have the thought ,based on a sudden appraisal, that the fight-flight dilemma is not a contest, and this after experiencing countless instances, will result in a logical sequence, by inserting types of characteristics which deter.one whether the action required I’d fight or flight from the threatening situation.

This very primitive almost instinctual act, is not really that, and is more a basis of logical systems then the dual aspect morphology seems to imply.

This is more ‘absolutely’ true, then the idea that an early sequence can be discovered post ex facto.

This is why the mind , not the brain, sets up very early absolutes, in terms of no exclusive use of thought.

It simply doesn’t mean that it has no priority or inclusive function in the process. It took millennia to find out that unraveling this fallacy would take many twists and turns, meanwhile the stage of reality upon which these changes were really utilized , cost unbelievable losses in both lives and material.

The eidectic reduction of logic is demonstrationable exclusive of logic itself, therefore pertinent and necessary to this discussion., in my opinion.

48

I wondered how to read this
then I read this previous thread.

This leads me to question the sincerity of the OP of this thread.

49

I’m unsure why that would be.

50

In fact , to post scripitively answer Jacob’s problem with the issue of sincerity with the opus, the impression I get is not consistent with the concept of sincerity, but the phenomenal eidectic reduction to naive realism, which does entail the implausability of retaining a root of meaning, where types having been lost, retaining only formal logical arrangements.

Positivism thus is absolutely concerned with interpreting present meaning with the reduced one, and the absolute set consists as ground to it.

Browser’s intention is to show that naive formal , absolute meaning does end in a logical absolute contradiction. at that absolutely reduced logical level, where the existence and the non existence of even of that : vis. of the absolute Russell set exists absolutely.

Browser’s demonstration of the absolute Russell set as existentially-phenomenologically reduced, can not delineate between existential/non existential difference on that level, since it belongs to a prior level, a-priori.

It took me a while to understand that logical notation, can not differentiate on an other level which .can encompass
that difference.

Hence the contradiction is supposed to entail the compilation of necessary truths.

So the absolute is really not absolute, except in the logical format of its formal description.

That existence is not a predicate on that level, the contradictory nature of the existence of absolute sets can not be described, , it only can be. demonstrated postscriptively , within the the language used.

I think Browser knows the paradox that the title of the forum implies
Its not insincere, but a showing of the paradoxical nature of the proposition…

The liar’'s Paradox literally tries to figure a way out of the paradox, insincerity and lies are the very essence of the argument.

51

Jakob is graciously assuming you are sane.

52

This post includes a third proof that the absolute Russell set exists. The third proof invokes an idea that was used in the second proof, but is simpler and more direct than the second proof. The idea is expressed in the following quotation from the argument for Postulate 2 in the second proof; the second proof is located at viewtopic.php?p=2699904#p2699904.

Third Proof.
Premises: s is a statement. Under the assumption that “s and it is not true that s,” s is true. It is not true that: under the assumption that “s and it is not true that s,” s is true.
Conclusion: The absolute Russell set exists.

Statements (Reasons)

  1. s is a statement. (Premise)
  2. Under the assumption that “s and it is not true that s,” s is true. (Premise)
  3. It is not true that: under the assumption that “s and it is not true that s,” s is true. (Premise)
  4. Some contradiction exists. ((3) is the negation of (2))
  5. The absolute Russell set exists. (Ex contradictione quodlibet)
    This concludes the third proof.

Premise (1) is a prescribed description of s. Each of premises (2) and (3) is evident by itself.

53

If any proposition can be treated as a formal truth statement, where does that leave the faculty of discernment?

54

Note: If there is a statement “A”, and if it is known that this statement “A” can be proven false, this produces the implication of a far broader statement than the mere denial of “A”.

The capacity to indicate the falsehood of a statement implies a lot more than the truth or falsehood of that statement.
An implication is a power. All sets are origins of powers. x is the power to be identified as x, so x is always a set. Sets underlie indicators, integers and all positives.

55

Every proof by contradiction of the nonexistence of the absolute Russell set includes a temporary assumption that implies, regardless of whether the assumption is in effect, the absolute Russell set exists.

Fourth Proof. Consider a proof by contradiction of the nonexistence of the absolute Russell set. Name the proof p. As my post at viewtopic.php?p=2699066#p2699066, which I have now cited six times in this thread, allows me to infer, under p’s assumption that the absolute Russell set exists, the absolute Russell set is an element of the set. The linked post also allows me to infer that it is not true that under p’s assumption that the absolute Russell set exists, the absolute Russell set is an element of the set. So, there is a contradiction. Thus, through ex contradictione quodlibet, the absolute Russell set exists. That concludes the fourth proof.

Every proof by contradiction that the absolute Russell set does not exist thus becomes a part of a proof that the set does exist.

56

Right. And semiological interpretation has bearing unto the general critique of Russell, as his notion of sense data is absolutely reducible toward absurdity, an infinite reduction.

The question pertains to Ayer as well, as to a behavioristic model.

The set theory as a substantial concept, between identity and difference strung between two infinite reductions of sense and meaning.

This relatedness , one, a set belonging to its own set and exclude it at the same time.

Time is of relevance here, one as simultanity, within measurable limits.

As long as it can be measured, it can be differentiated.

Is there a point of absolute non discernment, thus absolute identity?