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I got this example from an LLM:

  1. Fix a formal system S. In the LLM example, it uses first-order arithmetic, but I don't see why we wouldn't be able to use ZFC.
  2. Let D be the set of subsets of the natural numbers N which are definable by a finite formula in S.
  3. There are countably many finite formulas, so |D| <= |N|.
  4. Cantor's theorem says that the size of the power set of N is greater than |N|.
  5. Therefore there must be subsets of N which are not definable by a finite formula in S.

If you disagree with this, I would be interested to know.

Take into public ownership.

Do we have any English lawyers here who can comment on whether it may actually be legal to nationalise Adele (the person) under English law? ChatGPT says it may be possible through an act of parliament, but I’m unsure whether I can trust ChatGPT in this case.

Do conceptual frameworks exist outside of language? If so, where do they exist, and how do you define existence in this context?

If facts have truth independent from common language, where do those facts exist, and how do you define existence in this context?

As an example, are you hinting at the existence of facts and truths that are somehow different from the easier definition of formal truths which hold in an assumed axiomatic framework, as happens in mathematics, which itself is a framework of language?

There exist subsets of the natural numbers which are infinite, but which are not finitely definable in first-order arithmetic.

That answers a different question. The empirical success of the equation in question is strong evidence that the theory captures something about the universe, however it does not prove that the proposition exists, or is true, independently of any language or conceptual framework.

Technologies working can test physical predictions. They cannot test the metaphysical claim that facts have truth independent from common language. Simply asserting that they do is the realism that I am disputing.

Also, the proposition in question is made in a certain language, and is not true in all possible languages.

How can we prove that?

“The basic realism of science, then, rests upon the following claim: the Universe is such that facts can be plainly stated within it, even though the facts themselves need not be plain.”

What facts can plainly be stated within this universe? Can facts exist outside the common language within which they are expressed?

Let’s say I bought an NFT for X and later sold it for Y profit. I bought a house with Y. The person who received X bought a car with it, or maybe long in oil futures with X before the Iran war, made Z, and bought a field with the profit. Or maybe he put Z in a couple of bonds and used the resulting return later.

Define useful in a measurable way that does not depend on any specific human’s subjective estimation.

Define intrinsic value in a measurable way that does not depend on any specific human’s subjective estimation.

I feel sad about keeping animals in small confines, away from their natural habitat, but on the other hand, I have come to the subjective conclusion that rights are also subjective.

I wonder what will follow TikTok and Instagram, and how people in twenty years will be reminiscing over the good old days surrounding these services.

Have you considered that the public may be gaining something from the conversations and awareness that arise from the performance of this art? I invite you to move away from evaluating a piece of art simply in terms of the monetary cost to the tax payer.