A couple of remarks: 1) The logical positivists were influenced by the Neo-Kantians, but weren't themselves Neo-Kantians. So Neo-Kantian worries do no...
Just to be clear, I'm not saying that Popper is irrelevant or whatever. It's just that popular accounts of science tend to portray him as being the be...
First, I would like to dispute that "fallibilism" is any better criteria of significance than verificationism, or even that it is mainstream today. It...
Incidentally, I don't think boundary policing ("Is philosophy a science?") is much helpful. Philosophy is whatever is practiced at philosophy departme...
I'm happy that my posts have been helpful, though I'm not too sure if I'm representative of academic philosophy---I'm finishing my PhD in a third-worl...
I take it that there are two ways of interpreting your objection to the use of formal systems. One is a ban on the significance of formal systems tout...
You said that the sentence "This sentence is not false" was meaningless. I then asked, supposing it meaningless, why it is meaningless. Notice that th...
A bit of both, I suppose. I'm following Scharp (and Ripley's account of Scharp), here (this is not meant as an endorsement of his position, I'm just t...
I don't have much to add besides what I have already mentioned in my first reply to you. Take arithmetic, for instance. It is not difficult (though it...
Let us suppose you are right and the Liar is meaningless. This raises the question: why is it meaningless? Let us suppose, for definiteness, that the ...
In his book (p. 81), Scharp mentions that the following triad is inconsistent for a logic L: (i) L accepts modus ponens and conditional proof; (ii) L ...
Self-referentiality may seem like a problematic concept, but Gödel, Tarski, and Carnap have shown that it is possible to construct a self-referential ...
If a theory is such that: (i) it has a reasonable proof system (i.e. one can check by an algorithm whether or not a sequence of formulas is a proof) a...
If by G you mean the Gödel sentence, then, yes, the algorithm will miss it. But that's because the algorithm lists all the theorems of PA, and the Göd...
Yes, there is a proof of the consistency of PA, though whether or not it is finitistically acceptable is debatable. Gentzen proved that the consistenc...
I'll be very explicit, then: there is, in fact, an algorithm that lists all and only the theorems of PA. This algorithm therefore provides an exhausti...
I think you are focusing too much on the fact that theoremhood is not strongly representable in PA, with the consequence that you are ignoring the fac...
A couple of observations: (1) First, note that the theorem, in the form I stated, is a bit more general, since it does not rely on any specific unprov...
Well, proof is relative to a system of axioms. That is, we usually define proof, relative to a theory T, as follows: a sequence of statements A1, ...,...
There would only be a contradiction if Gödel claimed that his own theorem was unprovable. Fortunately, he was not an idiot, and therefore did not clai...
There is no contradiction. One can hold that proof is necessary to establish truth, yet hold that it is not necessary for truth (cf. my point about un...
You seem to be confusing knowledge with truth. Obviously, to establish a proposition as true, I need to, well, establish as such. And, in mathematics,...
(1) Gödel (well, Gödel, Church, Tarski, Rosser, etc.) showed a bit more than what you are implying. He showed that, for any consistent system containi...
I don't think Löb's theorem supports the constructivist position. That's because truth is generally taken, prima facie to obey the capture and release...
In my (philosophy) department (here in Brazil), undergrads are generally introduced to the basics of logic or formal reasoning, say through Priest's A...
Refer to my reply to for a clearer sketch of why truth is not provability, and which has nothing to do with G or whatever. And, again, you're evading ...
Let me put it this way. Suppose truth were equal to provability (or even just extensionally equivalent). Then any algorithm for enumerating all the th...
Let us suppose that everything you say is true. This still does nothing to address two facts: (1) the set of true formulas is not arithmetically defin...
Unfortunately, from the fact that provability is sufficient for truth, it does not follow that it is necessary for truth (in general, being a sufficie...
There is a better proof of Gödel's theorems that considerably clarifies the situation. It relies on two other theorems: (1) Gödel's proof that the set...
(1) I'll give two examples that I think can be illuminated by considering economic models. Consider what is generally taken to be Smith's doctrine of ...
For Kaplan, the two utterances of "Bob" that you described are not occurrences of the same word, but of different words that just happen to share the ...
(1) On idealization: yes, I do think it is a successful strategy in most, if not all, sciences. Note that idealization is not used (just) to isolate a...
A couple of points: (1) First, I'd just like to second 's claim that Priest (and most dialetheists I know) does not claim that all contradictions are ...
I think the two discussions (about economics, about punishment) are a bit different, perhaps in the direction gestured at by . In the case of rational...
I don't understand. Consider two actual (in contrast to potential?) circles on the Cartesian plane, say, one described by x^2+y^2 - 1=0 and the other ...
I don't personally think there is any property that is common to every two pair of objects (except in a gerrymandered way), but let us leave this to t...
Again, from the fact that some (perhaps all) universals, like "circleness" (the universal), are abstract, it does not follow that every abstract entit...
It seems that you are confusing abstractness with being a universal. Some may defend that universals are abstract (but not all do: some people defend ...
Well, for starters, I think that you vastly overestimate philosophy's impact on the world. The revolutions you cite were definitely not the "direct co...
Well, I thought that you wanted your principle as a solution to a problem described in the OP. If the relation between them is irrelevant to you, ok, ...
Yes, we use folk psychology all the time in interacting with other people (interestingly, this is now studied under the heading of "theory of mind" an...
But then, how can he justify that what is beyond the physical cannot be perceived? Surely this a metaphysical claim about the nature of whatever it is...
Well, according to you, he is saying that what is not perceivable is not physical, which seems a pretty strong connection between perception and reali...
Sure, but Hume is not denying that some things can be perceived, nor he is denying that there is a connection between perception and reality. So, agai...
I strongly recommend reading Kenneth Mander's papers in The Philosophy of Mathematical Practice, edited by Paolo Mancosu (you can easily find the volu...
You asked about whether we can scientifically study people's minds, with the specific challenge that we somehow do not have access to the inside of pe...
I don't see the relevance of the principle to the problem. If something can't be perceived, then no one can perceive it, so, ipso facto, there will be...
Some of these ideas are captured by modal logic, especially counterfactual logics (cf. Lewis's theory of causation, for instance). But I'm not sure wh...
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