Nagase

I don't think it's helpful to concentrate so much on the name of the principle, in this case. The name comes from a time when the separation of syntax...

No, since disjunction is inclusive. A few posts ago I described a system in which you have a truth-value glut (i.e. a proposition being true-and-false...

Why is it a bad example? In any case, it helps to distinguish between: semantics, which is how we interpret our system, from syntax, which is concerne...

It may be useful to introduce some distinctions. Let's call the principle of weak bivalence the idea that there are only two truth-values, and the pri...

Yes, as far as I know, most readings of bivalence include an explicit clause such as "but not both". Also, note that, in my formalization, B can be (f...

Here's an easier example than fuzzy logic. Suppose some statements are true (T), some statements are false (F), and some statements are both true and ...

Yes, that's it. On the other direction, note that intuitionists generally uphold bivalence, but they reject excluded middle.

There are a couple of options, here. One way is to employ a weaker meta-theory, say primitive recursive arithmetic, and simply talk about what ZFC can...

It's very rough, but yes, that's the gist of it. Incidentally, this is a very good bare-bones summary of both theorems.

Technically, to say "This statement is unprovable". But what is remarkable is that the fanciness consists in showing (i) isolating a class of interest...

Bold emphasis mine. The bold part is the difficult (or, at least, tedious) part. As I mentioned, we need to show that T proves that Con(T) -> G, which...

No, that's not exactly right. The first theorem states that, if T is a theory strong enough to capture all the primitive recursive functions, then, if...

I already did it, in my last post. What part did you find troubling?

I'm glad you found my reply useful. Well, the whole point of the first Critique is to argue against this idea, that is, to argue that there re synthet...

Bold emphasis mine. Yes, that is obviously absurd, but it's not what is going on here. The bold part is employing modal reasoning (can only exist), wh...

But this has nothing to do with the original suggestion, which involves just names and not descriptions. It also does not mention names being "bound b...

The first sentence is incorrect. ZFC can formulate a truth predicate for PA in such a way that a formula from PA is true iff ZFC proves that the natur...

One problem with construing the quantifiers substitutionally is that you will need a denumerable language if you're working with the natural numbers, ...

Actually, that's pretty straightforward: 1. premise: A 2. premise: ~A | 3. Assumption: A (assumption for ->-intro) | 4. ~A (p2) 5. A -> ~A (->-intro)....

Actually, you can derive contradictions in a natural deduction system if you have inconsistent premises. That just shows that you have an inconsistent...

Suppose I gave you $1. Does that mean I also thereby gave you the number 1?

But (using my previous notation) d(4, 0) is not a "problem", it is a functional term, so it requires no "solution". Suppose I define a function f on t...

The natural with addition and multiplication. The theory of the natural numbers with addition (also known as presburger arithmetic) is actually comple...

I don't see the problem. Let d(x, y) be the result of dividing x by y, i.e. d(x, y) is the unique z such that y*z=x.. Then it's true that d(x, y) is u...

I don't see why they are facile. Given a language L = {+, *, 0, 1} and the normal axioms for the natural numbers, we can define am unary predicate E(x...

A couple of comments: (a) When reading Kant, it is often useful to take a look at his historical predecessors in order to understand how some of his d...

Well, I personally think (1) is clearly wrong; there need be no "magical thinking" or "social constructivism" involved in the thought that unfair port...

I'm not saying that (alleged) libel is sufficient for harm, either. What I am saying is that when it constitutes harm, then there's no magic involved....

As I said, I don't think this does justice to the complexity of Aristotle's metaphysics, for a couple of reasons. First, I'm not even sure it makes mu...

But when they do determine that a case of alleged libel is unlawful, they presumably are not engaging in magical thinking.

One does not need to be in favor of libel laws in order to recognize that it (libel) constitutes harm.

I'm trying to understand your position here. I'll be direct: why do you think that the fact that libel constitutes harm does not require magical think...

I know this is not the topic of the thread, but I don't agree with this characterization of Aristotle (I think he's a much better reader of Plato). I ...

My primary concern is to point out that your claim is dubious. You asserted that magical thinking is a necessary condition for believing that unfair p...

I don't see how I'm using your statement "selectively" in my argument (if anything, it seems that you're the one who's using it "selectively" here). Y...

No "postmodern irony" (?), just the logical conclusion of an argument using your premise: (1) Only "social constructionists" believe that there could ...

Indeed. That's why those people who drafted libel laws are all "social constructionists".

Thanks for the warm welcome! I don't have the details, but if I'm not mistaken he did own a lot to Frege, as it's clear for anyone who reads the TLP. ...

You seem to be on some kind of tirade against classical logic. But this has nothing to do with what I asserted, namely that Gödel's theorems don't ass...

Unfortunately, I can't understand how your reply has any bearing on what I said...

That's not quite true. Socrates apparently read other philosophers such as Anaxagoras, Gorgias, Parmenides, etc., and Plato, aside from reading those,...

And I'm saying that no question is begged. If I say "If John is decapitated, then he will die", I'm not "begging the question" as to whether John was ...

But Gödel's theorems do not state "classical logic is true". They state "if we assume classical logic and some other conditions, then there are some m...

Look, here's the fact of the matter: Gödel's theorems do not assume classical logic is true. They are about classical logic. If your logic contains co...

And my assertion is that the theorem does not beg the question you're saying it begs, namely that classical mathematics is true, because it does not a...

I quite frankly don't see how you could give this reading to what I said. What does it mean to say that classical mathematics is "commutative"? Some c...

Emphasis mine. If that is the heart of the matter, then it can be quickly be made to rest, since that particular claim is not what Gödel's theorems ar...

Actually he was a physicist by formation. In any case, you may do whatever you like, but the point is that scientists don't often proceed in the way F...

I would say that that Feynman quotation is incredibly naive in our post-Kuhnian age, but no matter. Gödel didn't assume that classical mathematics was...

I was wondering about that. Who's posting under ModBot? Paul?