TonesInDeepFreeze

Of course, if one doesn't countenance infinite sets, then one might not countenance the classical notion of convergence to a limit. But that doesn't c...

And we don't do that. The word 'instantiate' has a certain meaning in mathematics. What you mean though - to type out in finite time and space individ...

. Of course, I don't begrudge adding a rubric 'absolute consistency' that way, though I like the term 'non-trivial' better. A set S of formulas is non...

Godel does not use circular reasoning in the incompleteness proof. The proof can be given by means of assumptions no greater than finitistic combinato...

We instantiate them all the time. I instantiated the series in question earlier in this thread.

Then hurry up and take our lunch orders.

A set S of formulas is inconsistent iff there is a formula P such that both P and ~P are members of S. As far as I know, that is the presumed mathemat...

That is not my understanding, which is: Certain paraconsistent systems do not avoid inconsistency; rather they avoid explosion. But, yes, in the seman...

Again, it's not about a sequence "reaching" anything. '.999...' stands for the limit of a certain sequence. There is no "becomming" or "reaching". Sim...

Again, that reflects a fundamental misunderstanding of what '.999...' stands for.

Yeah, you really got that flippant dismissive thing down. Anyway, better that life is too short than it be too long. I have not found problems (though...

I didn't say anything about truth values (semantics) for paraconsistent logics. I am not expert, but, if I am not mistaken, the main point about a par...

Yes, I corrected myself. It's more complicated than I suggested. Indeed, you can see for yourself at the Stanford article. But it's still the case tha...

I don't think it's particularly intuitionistic. Rather, it's that LEM (which is with inclusive-or) is eschewed in intuitionistic logic, while intuitio...

I mistakenly thought you meant 'bridge' in the sense of a connection between the two logic principles. I have no idea about paraconsistent logic used ...

I need to correct that. Usually, paraconsistent logic is attained by not having EFQ. Taking out LNC would be something different. Nevertheless, I stil...

Also, to be able to get intuitionisitic logic.

What do you mean by a "bridge"?

I certainly don't claim to be especially skilled in seeing into the minds of people who are ill-informed about the subject to know how they came to th...

Oh, no, I didn't deliver your desired angle on the subject soon enough, even though what I did say was correct at every point while you persisted othe...

P and ~P are mutually exclusive in classical logic, but not necessarily in other logics, especially paraconsistent logics. To answer your question: (1...

I don't know what you mean by 'a long time ago' relative to the duration of our exchanges. But many posts ago, I wrote: You're blaming me for the fact...

And unprovable from other systems of a certain kind. Systems are not things we look at for being probable or unprovable. Maybe you meant this: That a ...

My posts aren't models of eloquence, but they are, for the most part, articulate and more precise about technical matters than normally found in a cas...

It matters because the 'v' ('or') connective should never have been conflated with exclusive-or. Also, your notion that exclusive-or has an advantage ...

Then the presentation you were subjected to was egregiously errant. I would be on guard about anything else that was offered to you in that presentati...

Classically, LEM and LNC are equivalent, since all logical truths are equivalent. That is, for any logical truths P and Q, we have P <-> Q as a theore...

It's pretty clear that you are not familiar with even the basic concepts in formal logic. To understand the topic raised by the reference to Turing in...

As I've said, it is inconsistent with everything. And again, the point I made to you about LEM is not about what contradicts it, but rather that merel...

Correct.

You only need one. When you have one, you get them all. I have mentioned several times already the principle of explosion. Indeed, it is at the very h...

That is not a good question, because is has a trivial answer: Add any contradiction as an axiom. A better question is: What systems preserve important...

That's not what mathematicians, including Turing, mean by 'inconsistency'. That's not (as far as I can tell) a sense of inconsistency at issue with th...

Inconsistency, in a formal sense, is not a clash between a theorem and the fact that certain people have a different intuition. The context in which ....

That's not the point. '.999...' is informal for SUM 9/10^n And SUM 9/10^n is the limit of a sequence. And that limit is 1. / By the way, when you wrot...

I'll leave my post as it is so that your following self-correction makes sense in context.

That is not a rigorous mathematical proof. However, there is a rigorous mathematical proof that .999... = 1. '.999..' is an informal way of describing...

I am wondering now whether I should have said I accept the following: The consistency of, for example, PA cannot be proven by finitistic means, but I ...

The one we talked about: And I mentioned it most presently only about an hour ago and as you responded to me right after.

You made a general statement about it. You made your own claim about mathematics and mathematical logic. And your claim is incorrect. My point about t...

I have explained more than once already why it is not the case that an otherwise consistent system can be made inconsistent by retracting the LEM. It ...

I have nothing to say about that. Though, while probably not specifically apropos of Wittgenstein himself, one can look up the subject of paraconsiste...

I don't bristle against being corrected on matters of logic. I don't know what scope you have in mind by 'meaning' but I take the LEM in its utterly o...

Of course, you persist petulantly. No, you were not correct. You gave the impression that I had just learned the quote function, which is not correct....

As far as I can think it through, your first paragraph seems reasonable and good added information to my own remark..(Though when I said 'by certain m...

I am well versed in the quote feature, as seen in my many posts in other threads. But I had been experimenting with not using it lately in order to av...

I'm informing you that it is a basic misconception to think that the LEM is a consideration in the way you have claimed. That is not ill will.

It's one consequence not just among many but among all. The supposed connection with the LEM does not hold.

If a system is inconsistent, then the system contradicts every statement in the system, not just the law of excluded middle. So it is pointless to add...

To be clear, Fitch's paradox is not a conclusion that the truth of all statements is known, but rather the conclusion is that it is not the case that ...