Tarski Undefinability Theorem Succinctly Refuted

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Logik
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Joined: Tue Dec 04, 2018 12:48 pm

Re: Tarski Undefinability Theorem Reexamined

wtf wrote: Wed May 01, 2019 12:46 am You have not convinced me that when we talk about category theory we are talking about the same thing.
What would convince you?

It's an abstract theory. In the abstract it says what it says - it does what it does. How you use it in practice is where it matters (and for fun - I could abstractly interpret the practical aspect via the BHK or Kleene realizability frameworks)

Like this:

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``````B = { being1, being2, ... beingN }
{ b in B | Human(b) } ⇔ { b in B | Mortal(b) }
{ b in B | Divine(b) } ⇔ { b in B | Immortal(b) }``````
Which translates into Python: https://repl.it/repls/ThisBustlingDeal

The universal property of all of the shenanigans above is the 1 bit of information which is all that is required by any binary classifier to sort B into two categories. Irrespective of whether you label them Mortal/Immortal or Divine/Human.

Naturally. Because the set B is generated by a p=0.5 probability function.

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``self._mortal = choice([True, False]) ``
wtf
Posts: 969
Joined: Tue Sep 08, 2015 11:36 pm

Re: Tarski Undefinability Theorem Reexamined

Logik wrote: Wed May 01, 2019 12:26 pm... it says what it says - it does what it does.
I think I'm going to go with ... not convinced that you have any idea what category theory is. It's no great shame. You could say something like, "Cool, I've heard about category theory but don't know much about it. Tell me more." Or even, "F*** you, I don't want you to say anything about category theory."

But trying to bs your way through is silly.
Logik wrote: Wed May 01, 2019 12:26 pm Like this:

Code: Select all

``````B = { being1, being2, ... beingN }
{ b in B | Human(b) } ⇔ { b in B | Mortal(b) }
{ b in B | Divine(b) } ⇔ { b in B | Immortal(b) }``````
That's funny. That's the same snippet you used in the other thread (which I'll be replying to shortly) as an example of an isomorphism. Which it isn't. Nor does this snippet have anything at all to do with category theory.
Logik wrote: Wed May 01, 2019 12:26 pm The universal property of all of the shenanigans above is the 1 bit of information which is all that is required by any binary classifier to sort B into two categories. Irrespective of whether you label them Mortal/Immortal or Divine/Human.
Wow. You just have no idea and you're not doing a very good job faking it.
Logik wrote: Wed May 01, 2019 12:26 pm Naturally. Because the set B is generated by a p=0.5 probability function.

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``self._mortal = choice([True, False]) ``
Which has what to do with anything?

Why not just say, "Oh category theory, that sounds interesting, what is it?" There's no shame in that. You're the one who claims you're reading about HOTT. If so then you'd be interested in category theory. It has a wikipedia entry, you could look it up and at least generate more realistic sounding responses than, "It is what it is."

I don't mean to be giving you a hard time. I'm genuinely startled by your response here. If you asked me, "Prove to me that you know something about orange juice," and I said, "It is what it is and it does what it does," you'd be justified in calling me out on a very lame attempt at trying to bs my way through pretending I know something I don't know. If instead I said, "It's a drink, often consumed at breakfast, made from the pulp of oranges," you'd give me credit for knowing what orange juice is. I hope you can see this.