TonesInDeepFreeze

I would title it: Problem of finding shortest proof - how complex is it? But I really have to warn that, since I'm not really informed on this particu...

Darn. I need to edit my reply. Can you edit your stackexchange post? (I think complexity class pertains to the problem not the algorithm?) This is bet...

I'm still not sure what your question is. Also, I'm not very informed about complexity, so my own formulation might need correction too. But here's my...

The method I mentioned is brute force. I don't know whether there's a better method.

A machine for ascertaining the length of the shortest proof of a theorem doesn't involve anything like oracles.

If I'm not mistaken, this is not about unsolvable problems. Rather, it's about finding out the complexity of the algorithm for deciding this decidable...

I surmise that he's not asking about degree of unsolvability but about the complexity of the problem. 4.1 Significance of Complexity here: https://pla...

Not 'class complexity'. The 'complexity class'.

No, I addressed exactly the sentence he wrote. What he wrote in that sentence was correct. I am not responsible for addressing other confusions he has...

He said that he thinks PM solves the problem with types but that he might have to look it up to be sure. I said he doesn't have to look it; he is corr...

You seem to be confused. It is correct that PM is one approach to avoiding the paradox. With PM there is no set of all sets.

Why would I want to supply references to a claim that PM allows a set of all sets when I agree that PM does not allow a set of all sets?

You don't need to search. You are correct that PM is one approach to avoiding the paradox.

I have no idea what you mean. I have no idea what you mean. Are you deliberately wasting people's time with remarks you've intentionally prepared to b...

Estimate based on what? I don't see it in the table of contents given in the article on PM in the SEP.

What does "this" refer to there? Set theory can't do a lot of things, but what is it in particular are you saying set theory can't do?

PM addressed complexity classes?

If my attempt was correct, and there are only finitely many symbols in the signature, then, if I'm not mistaken, there is an algorithm to list the the...

I find it interesting as a mathematical question onto itself.

If my previous post is correct, then I take it that your full question is: What is the complexity class of such an algorithm? I don't know. And I'm no...

I find it interesting whether there is an algorithm to compute the least length. I take it we are talking about proofs in the first-order predicate ca...

And by 'complexity' do you mean 'the sum of the lengths of the formulas in the proof'?

That's your edit now. As far as I can guess, you are asking what I already mentioned: Given P, is "What is the length of the shortest proof of P?" com...

(1) You changed my definition of 'L(P)', setting up confusion now as to what is meant by it. I'll stick with my definition. I would add another termin...

For about the fifth time, "completeness of a theorem" makes no sense unless you tell us what you meant by it. Maybe you mean "completeness of a theory...

If P is a theorem, let L(P) be defined by: L(P) = n iff (there is a proof of P in n number of symbols & for all m, if m<n, then there is no proof of P...

Since the U.S. Constitution has been mentioned, it helps to mention what it says: "to form a more perfect union, establish justice, insure domestic tr...

"There is nothing as mysterious as a fact clearly described." — Garry Winogrand

You are very welcome. I fixed some typos (including fatal ones) and added details and more explanation after you replied. If you would like to have ba...

For any relation R, it is a theorem of first order logic that: There does not exist an x such that, for all y, Ryx if and only if ~Ryy. In symbols: ~E...

That only switches the order of the clauses 'I know I'm conscious' and 'because I'm conscious'. That just redundancy, not circularity.

Reasoning requires definitions. You have not provided them. What I'm getting at is exactly the question I already asked: What is your definition of 'a...

That is the second time you've made that false claim. Moreover, I did not couch anything as "counting a quantity".

That is not an answer to my question, and it's gibberish as is the rest of what you've posted in this thread.

What do you mean by a theorem being complete? What do you mean by "determine a QED result for a Turing machine"? / Have you read a book in mathematica...

There is no equivocation or ambiguity in what I said, Your confusions and implacable dedication to remaining ignorant of mathematics and dreadfully mi...

You said the discussion between us reached an end. You were doing better with emoticons.

As if 'obtuse' is seriously "mudslinging". But my remark does bear amendment. It's not that you're obtuse, it's that you are willfully so.

Now you are reaching your true level: emoticons.

Because it's worth pointing out the reason you can't understand the most basic things.

Yes.

Not in logic. And probably not in anything. So what?

There's no reason for me to do that.

Then I don't need your exercise.

Then the moral of your exercise is trivial. It merely highlights what we already know: English pronouns and demonstrative pronouns are contextual and ...

You are utterly obtuse. I miss the point of the numbering because your use of it is not grammatical. Make it grammatical if you would like me to under...

Yes, but that fails with 'this statement' in the mix because 'this' is contextual. Also, you misuse the concept of 'implies'. Each of your posts expre...

I answered your post about the liar. Now you're just flat out ignoring that answer. And, still you are not facing that putting '(1)' between 'this' an...

Again, you miss the point: In "This statement can be negated", 'this statement' denotes "This statement can be negated". but In "This statement can't ...

There is no apparent meaning in placing '(1)' between the adjective 'this' and the noun 'statement'. Now I've said that three times.