TonesInDeepFreeze

The question at that point was about Henry Fonda and names for Henry Fonda, not numbers and names for numbers. You objected to my Herny Fonda example ...

I suggest this course of readings, in order: Logic:Techniques Of Formal Reasoning - Kalish, Montague, and Mar Elements Of Set Theory - Enderton (perha...

We must keep in mind that when he says 'proved' it's really 'proved in '. The insightful and witty George Boolos is one of the great writers about fou...

I think the only translation of Godel's original paper approved by Godel is the one in Jean van Heijenoort's 'From Frege To Godel'. Some people who ha...

Like others here, I don't know what he has in mind about division.

Peter Smith's 'An Introduction To Godel's Theorems' is a real good book. I recommend it. But that PDF is only a shorter warmup for the actual book pub...

Rest assured that the Godel sentence G_F is a purely symbolic formula of arithmetic, using symbols like the ones you mentioned, though it is not a uni...

Please, let's stick with one set of letter-symbols, so 'F' rather than 'T'. The Godel-sentence G_F is a formula in the language of number theory. It c...

My points don't depend on whether equality is or is not independent of human judgement. To say that 2+1 and 3 are equal is saying that 2+1 is 3. To sa...

Over many posts, you keep telling me what I think or said, and you're wrong. You're a bane. And you claimed that you asked me a question I didn't answ...

To grasp how exactly it all works and makes perfect and rigorous sense, you really would need to read a book in mathematical logic

When SEP says "true but unprovable" it understood that 'unprovable' is informally brief for 'unprovable in F'. The word 'therefore' is not being used ...

You quoted Wikipedia and put my name on it as if they are my own words. Please don't do that. This discussion is becoming unwieldy with different lett...

I don't recall you asking me such a question. If you did, then please link to the post where you asked it so that I can see the context. Anyway, there...

Wikipedia in general is not reliable regarding mathematics. Much better is the Stanford Encyclopedia of Philosophy. However, possibly that particular ...

Here we go again. Yes, it is the case that G is unprovable in A. And it is the case that G is true if and only if G is unprovable in A. And G is true ...

Put yet another way, without some of the previous simplifications: A is a recursively axiomatizable, consistent, sufficiently arithmetically expressiv...

I'm correcting you; you are wrong. And you're not even coherent. You've got an extra symbol 'T' that makes no sense. You're not even reading what I wr...

If you have a question or a point to make, then please ask it or state it rather than dropping cryptic instructions for me to connect whatever dots I'...

I asked you: You are using teminology and mentioning concepts in the subject, so it seems you've read something somewhere about it. Would you please t...

And don't overlook that your claimed reductio ad absurdum was refuted: https://thephilosophyforum.com/discussion/comment/513487

'S' stands for the successor operation. def: 1 = S0 def: 2 = 1+1 def: 3 = 2+1 The proof in this case is utterly trivial, from the definition of '3'.

You are completely confused about this subject. What is the source you read about this subject? In all these posts about incompleteness, by 'true' I m...

Here by 'provable' and 'unprovable' we don't mean absolutely unprovable (i.e. not provable from any set of axioms) since there are no absolutely unpro...

A theorem by definition is a provable sentence. So what you wrote as the very first line of your argument is a contradiction in terminology. And the r...

Here's a simpified synopsis of the terminology: SYNTACTICAL: 1. We have formal languages. These are sets of symbols. And there are rules for sequencin...

This is explained in any textbook in mathematical logic, usually chapters 1 and 2. Proof concerns just formulas in the language - purely syntactical o...

You are correct. I don't know what you mean.

Then I don't know what relevance you have in mind. G-theories can have finitely many or infinitely many axioms. No, the opposite. First-order logic su...

That is rich from someone who dismisses approaches in ordinary mathematics while insisting on remaining ignorant of understanding their fundamental pr...

This is another instance of imposing your view as if it entails something I said that I did not say. You believe that equality holds based on human ju...

Highly recommended: 'Godel's Theorem: An Incomplete Guide To Its Use And Abuse' - Torkel Franzen Probably the best book ever written for introducing t...

Sincerely, I would like to help you understand this topic and to provide answers, but at many points I don't know what you're trying to say because yo...

So get these straight already: (1) My explanation runs in this order: Determine equality, then it is justified to assert that the terms denote the sam...

You are ignorant of the view in which meaning has at least two components: denotation and sense. Denotation is only part of the meaning of a term. In ...

You mangle nearly everything. (1) Claiming I've said things when I did not say them. (2) Screwing up the direction of my explanation so that your repr...

Where do you find such terminology in discussions of incompleteness? Where did you read such things? Meanwhile, it's better to look at Godel-Rosser in...

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Whatever views you have about the distinction between extension and intension, and between denotation and sense, I gave you more than "vague reference...

This is at the heart of it. The claim that 'Henry Fonda' and 'the father of Peter Fonda' denote the same person is not an argument! It is a conclusion...

That is ridiculously captious and sophomoric. It is deserves all three tropes: red herring, blowing smoke, and grasping at straws. Of course in natura...

You have it backwards again. Mathematics does not prove that objects are equal by showing they share all properties. Rather, we infer they share all p...

What he doesn't understand is that denotation is only one part of meaning. There is both denotation, which is extensional, and sense. 'Henry Fonda' an...

The example was given not so much as an argument but as an illustration for you to understand a basic idea. Ordinary mathematics regards '2+1' and '3'...

You're lying about me again: (1) I didn't make "vague references". Indeed, I posted an explanation of the notion of exentionsality vs. intensionality....

That's correct in an extensional context, but not in an intensional context: Suppose Alice doesn't know that Henry Fonda is the father of Peter Fonda....

I have given you copious explanation. There's no point in me composing more explanation when it is better said anyway at the sources I offered you.

You are not recognizing the distinctions between terms and statements, terms and arguments, reference and inference, extension and intension, denotati...

I addressed that already. The term '2+'1' denotes the value of the function + applied to the argument pair 2 and 1. It denotes the result of any compu...

Two points. (1) You stated falsely about my motivation. (2) You outright fabricated a quote to make me look like I said the exact opposite of what I h...