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On the theme of Russell's paradox:

Does the set of all sets that do not contain themselves contain itself?

And the Barber's paradox:

Does a barber who shaves all men who do not shave themselves shave himself?

Can we formulate a similar regarding self-consciousness?

For example, are there any legs to a paradox of the following composition:

There are two types of thoughts:

1) Thoughts which are about themselves

2) Thoughts which are not about themselves

Is a thought which is about all those thoughts which are not of themselves a thought about itself?

If this is flawed, how is it flawed, and can you improve on the paradox to make it not flawed?

Thanks

  • These are paradoxes of self-reference, they have nothing to say about anything in particular, consciousness or something else. It makes no difference if it's sets, barbers or thoughts, if it can refer to itself it can be folded into a paradox. – Conifold Oct 24 '19 at 23:15
  • Russell's paradox led mathematicians to abandon naive set theory and start upon axiomatic set theories which are much less intuitive, so why do you say that paradoxes have nothing to say about anything in particular? Regardless, the question is about whether the paradox suggested is in a logically valid form. I.e. is it coherent. – Bonj Oct 25 '19 at 9:56
  • Yes, mathematicians had to develop formal theories that block or limit self-reference. Set theory is just one example, there is nothing specific to sets about the idea. And the prototypical self-referential paradox of Epimenides was known long before set theory, naive or otherwise. Your version mimics Russell's so closely that it is not even really about thoughts, "thoughts about X" can be replaced by any "classes containing X". So yes, it is fine. – Conifold Oct 25 '19 at 15:59
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It seems to me this is a useful paradox in the sense that where it arises we know we must be thinking incorrectly. But as phrased it seems easy to overcome. I feel there is a more interesting and real paradox underlying this one.

It is not thoughts that think. If you drop this idea and rephrase the paradox then it might have more bite.

  • @Bonj It is hopeless. The bit about the two types of thoughts is OK. The conclusion is nonsensical. There are indeed two kinds of thoughts, but the conclusion introduces a third kind: A thought of a thought of a thought?! Doesn't make sense. I would say that thinking is not transitive, unlike inclusion or containment. – Speakpigeon Oct 24 '19 at 19:36
  • I've clarified the proposed paradox somewhat, it no longer suggests a third type of thought. The question is whether (2) is a member of (2). – Bonj Oct 24 '19 at 20:45

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