Tarski Undefinability Theorem Succinctly Refuted

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Logik
Posts: 4041
Joined: Tue Dec 04, 2018 12:48 pm

Re: Tarski Undefinability Theorem Reexamined

Post by Logik »

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:

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) }
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.

Code: Select all

self._mortal = choice([True, False]) 
wtf
Posts: 1178
Joined: Tue Sep 08, 2015 11:36 pm

Re: Tarski Undefinability Theorem Reexamined

Post by wtf »

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.

Code: Select all

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.
PeteOlcott
Posts: 1514
Joined: Mon Jul 25, 2016 6:55 pm

Re: Tarski Undefinability Theorem Reexamined

Post by PeteOlcott »

A_Seagull wrote: Thu Apr 04, 2019 4:32 am
PeteOlcott wrote: Thu Apr 04, 2019 4:25 am
A_Seagull wrote: Thu Apr 04, 2019 4:05 am

Well, there are axioms and there are axioms.

Axioms can only define a particular logical system. Any inferences made from those axioms can only be considered to be 'true' within that particular logical system. And it would be an incestuous logical system that made reference to its own truth.
The English language defines all the human knowledge that can be expressed in English and it does this in English.
The English language defines nothing. In any case what has that to do with truth?
The fact that {cats are animals} and thus {cats are not ten story office buildings} is stipulated to be true thus providing semantic meaning to otherwise totally meaningless finite strings.

This is more broadly known as truth conditional semantics.
https://en.wikipedia.org/wiki/Truth-con ... _semantics

There are only two ways that analytical truth is verified:
(1) Some expressions of language are stipulated to be true
(AKA sound deductive inference's true premises)

(2) Other expressions of natural or formal language are
deduced from the above set.
alan1000
Posts: 313
Joined: Fri Oct 12, 2012 10:03 am

Re: Tarski Undefinability Theorem Succinctly Refuted

Post by alan1000 »

Speakpigeon wrote: Thu Apr 04, 2019 5:46 pm PeteOlcott 1 - A_Seagull 0
Popcorn anyone?
EB
One admires the incisive philosophical counter-arguments embodied in comments like "lol" and "popcorn anyone"... I look forward to their next syllables with eager anticipation.
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