The Instigator
holla1755
Pro (for)
The Contender
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Open Debate

The Absolute Russell Set Exists

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Voting Style: Open Point System: 7 Point
Started: 4/4/2018 Category: Philosophy
Updated: 9 months ago Status: Challenge Declined
Viewed: 335 times Debate No: 112321
Debate Rounds (3)
Comments (4)
Votes (0)

 

holla1755

Pro

The absolute Russell set exists. A thing is a member of the absolute Russell set if and only if it is not a member of itself. The existence of the absolute Russell set implies a contradiction because, as is fairly self-evident, the absolute Russell set is a member of itself if and only if it is not a member of itself. The contradiction can be used in a proof by contradiction to conclude that the absolute Russell set does not exist. Additional context is available at pages 432, 433, and 434 of Language, Proof and Logic (1999, 2000, 2002, 2003, 2007, 2008) by Jon Barwise and John Etchemendy, and at https://en.wikipedia.org....

Argument 1. Postulate that the absolute Russell set exists. As previously mentioned, the absolute Russell set is a member of itself if and only if it is not a member of itself. So, there is a contradiction. Through the principle of explosion, there is not a contradiction. Since there is not a contradiction, no contradiction can be used in a proof by contradiction to conclude that the absolute Russell set does not exist. Any contradiction that exists does not actually exist because no contradictions exist. The postulate never runs into trouble because there are no contradictions. Therefore, the absolute Russell set exists. This concludes Argument 1.

As Barwise and Etchemendy suggest in chapter 15 of their aforementioned textbook, the claim that the absolute Russell set exists has been historically strong. As they suggest on pages 433 and 434, the claim is granted by the Axiom of Comprehension. As Barwise and Etchemendy suggest in chapter 15, the Axiom of Comprehension was itself intended to be an intuitive truth. It is intuitive that given any set, the set either has the property of being a member of itself or does not have the property. The claim that the absolute Russell set exists is too strong to be false.

One might attack Argument 1 on the basis that it implies trivialism. Trivialism is not bad. I was recently promoting trivialism in an online thread located at http://www.ilovephilosophy.com...; I have previously cited that thread on social media. Regardless of whether trivialism is true, no contradictions exist. So, the postulate that the absolute Russell set exists can not be contradicted.
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Debate Round No. 1
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Debate Round No. 2
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Debate Round No. 3
4 comments have been posted on this debate. Showing 1 through 4 records.
Posted by philochristos 9 months ago
philochristos
So. . .who actually does shave the barber, then?
Posted by canis 9 months ago
canis
Change it a bit and it will be an easy win..
Posted by canis 9 months ago
canis
A thing is a member of the absolute de loise set if and only if it is a member of it.
Posted by canis 9 months ago
canis
Not if you ask De Loise.
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