The Absolute Russell Set Exists

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Re: The Absolute Russell Set Exists

Postby wtf » Wed May 02, 2018 4:11 am

browser32 wrote:
Jakob wrote:This leads me to question the sincerity of the OP of this thread.


I'm unsure why that would be.


Jakob is graciously assuming you are sane.
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Re: The Absolute Russell Set Exists

Postby browser32 » Wed May 02, 2018 7:15 am

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.

browser32 wrote:A conditional statement with a necessarily false hypothesis is only vacuously true, and treats the false hypothesis as true, yielding a contradiction that by ex contradictione quodlibet implies and does not imply everything. So, such a conditional statement is true and false simultaneously.


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.
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Re: The Absolute Russell Set Exists

Postby Fixed Cross » Thu May 17, 2018 3:54 pm

browser32 wrote:
Jakob wrote:This leads me to question the sincerity of the OP of this thread.


I'm unsure why that would be.

If any proposition can be treated as a formal truth statement, where does that leave the faculty of discernment?
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Re: The Absolute Russell Set Exists

Postby Fixed Cross » Thu May 17, 2018 5:05 pm

The absolute Russell set exists.

Proof.

Lemma. If a statement is false, then it materially implies some contradiction exists.

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.
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