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The way ZFC navigates around Russel's paradox is by adopting the axiom of restricted comprehension [1]. Here's a thought experiment: What happens if we allow f
by ukj 6y ago
The way ZFC navigates around Russel's paradox is by adopting the axiom of restricted comprehension [1].
Here's a thought experiment: What happens if we allow for unrestricted comprehension [2] ? What happens if we say 'Contradictions exist and they are empirical. What do they mean?'
The upside is that you attain "unrestricted comprehension" (In the English, not Mathematical sense) with the miniscule downside of having to navigate around contradictions from time to time.
Contradictions exist - if they didn't I wouldn't be able to contradict myself when I want to. I wouldn't be able to trigger exception-handlers in your brain when I want to.
How you handle that exception is a matter of choice.
I like the Dialetheist solution [3]. Basically the Axiom of Unrestricted comprehension is akin to practicing the Principle of Charity.
[1] https://en.wikipedia.org/wiki/Axiom_schema_of_specification https://en.wikipedia.org/wiki/Axiom_schema_of_specification
[2] https://en.wikipedia.org/wiki/Axiom_schema_of_specification#Unrestricted_comprehension https://en.wikipedia.org/wiki/Axiom_schema_of_specification#...
[3] https://en.wikipedia.org/wiki/Dialetheism https://en.wikipedia.org/wiki/Dialetheism
- magnio 6y ago> Contradictions exist - if they didn't I wouldn't be able to contradict myself when I want to. Huh, I haven't thought about it that way. Very interesting.
- frutiger 6y agoCan you provide an example of you contradicting yourself?
- ukj 6y agoI don't exist. Or the Philosophical cliche... I freely believe in the absence of free will. Scott Aaronson has discussed this in more detail: https://www.scottaaronson.com/democritus/lec18.html https://www.scottaaronson.com/democritus/lec18.html
- frutiger 6y agoIs that a contradiction or a lie? Genuine question: is there a difference between the two? Edit: I read the article (and I’m not sure I was able to follow it completely) but it seemed to mostly be about free will, and not people making contradictions (or lying).
- ukj 6y agoGood question/intuition. You are correct in that I am appealing (exploiting?) the Liar's paradox [1]. The gist of which is that the truth-value of the proposition is undecidable. You could interpret my statement as a performative contradiction; or you could interpret it as a lie, but a far more interesting a conversation would ensue if you simply ask me "Why do you say that?" Which is why I said that it's up to you on how you choose to handle the exception (which I have intentionally triggered in your brain). The way I would prefer you to interpret my intentional contradiction is to see it for what it is. I am engaging in cooperative multi-tasking [2]. I am yielding control by triggering an exception. Your turn to steer the conversation. [1] https://en.wikipedia.org/wiki/Liar_paradox https://en.wikipedia.org/wiki/Liar_paradox [2] https://en.wikipedia.org/wiki/Cooperative_multitasking https://en.wikipedia.org/wiki/Cooperative_multitasking