Definition of 'extensionally meaningful'? And, if you respond with word salad, as you are wont to do, then I can't help you. That's not a definition o...
pi is not a ratio of two rational numbers. pi is the ratio of the circumference of any circle and its diameter. But if the diameter is rational then t...
There's no consideration of intensionality in the illustration. I have no idea what you think you're saying, and, after a number such exchanges with y...
You've described your notion of potential infinity a few times (in another thread especially). And I've replied about it each time. Now, you're coming...
Your analogy betwen mathematics and theology is not apt. One can disprove 'there exists an infinite set' by stating axioms that disprove 'there exists...
The "paradox": Let there be a hotel with denumerably many rooms with room numbers 1, 2, 3 ... Suppose there are denumerably many guests in rooms and t...
As I recall, it's not a perpetually growing hotel. Rather, it's a hotel with denumerably many rooms and denumerably many guests, one to each room. The...
The hotel is not finite. It has infinitely many rooms. ZFC doesn't distinguish among hotels, real or mythical. And the point is not that there is a co...
I know some of the basics of mathematical logic pretty well, but I'm not even within a telescope's distance of being an expert on it or anything other...
Would you please tell me what textbook(s) in mathematical logic is the source of your understanding of the basics of this subject? Then, if I have the...
What? You're the one spreading disinformation, notwithstanding the little touch you give with Latin phrases. You say that set theory claims that a (pr...
There's nothing in the world that doesn't have detractors. So, by your logic, everything is wrong.* Finitism has detractors, so by your logic, there's...
Then you write a post having nothing to do with your quote of me. It still stands that it is disinformation to say that set theory claims that a (prop...
That just takes the conversation back to where we were before. One can have whatever concept of limits one wants to have, including conceiving in term...
That means you understand why it's not such a good idea to post disinformation that set theory claims that a (proper) part is equal to the whole? And ...
Of course. No one says that you have to. A circle is a certain kind of set of points. I don't know what you mean. Yes, and since infinitistic mathemat...
A sequence is a set. And it has a domain, which is a set, and a range, which is a set. An infinite sequence is an infinite set with an infinite domain...
Mathematics, in many branches, is brimming with sets. Analysis, topology, abstract algebra, probability, game theory... Can't even talk about them, ca...
Just to be clear, an infinite set has the same cardinality as some of its proper subsets, but not all of them. No it does not. It means a proper part ...
No. But all complete ordered fields are isomorphic with one another. So all complete ordered fields are isomorphic with the system of reals. I know th...
I don't take it that there is "the" point, but rather many forms of application, engagement and appreciation. Some of them not necessarily that of "pu...
About a meta-metalanguage: What is wrong with this?: Given a language L, and an interpretation M of L, and a sentence P of L: A sentence 'P' is true p...
"Made his name" is not definite enough for me know whether that's true or false. But, of course, Tarski is a giant in mathematics and philosophy, and ...
There is no doubt that the schema has wide and pervasive application and interest throughout philosophy. But in one of the SEP articles it also mentio...
I haven't carefully read that article, but are your own remarks dependent on the article? If so, should we take it that Raatikainen's summary of Putna...
Do you mean this?: Where in Tarski's example is snow denoted by 'snow' and white denoted by 'white'? If not in the example, then how can the schema be...
I need to read the rest of your post carefully, but I am not familiar with people saying: denoted as I guess you mean: denoted by or denotes I am not ...
It might be the case that an ultrafinitist system would not be subject to the incompleteness theorem? I don't know. We'd have to see the system or at ...
With no comment on nominalism, I think you're right that it is cleaner not to drag in 'property'. But my original use of 'property' was not meant in a...
Church says, "A property, as ordinarily understood, differs from a class only or chiefly in that two properties may be different though the classes de...
I might see what you're getting at, but you've not put it in a way that is clear to me. We should take it in steps: (1) Df. An argument is an ordered ...
The standard method is the method of models The notion of 'consistency' is purely syntactical, it does not mention 'truth'. You've added past the defi...
(1) 'finitism' has different senses. (2) Perhaps it is not necessary to have infinite sets for an axiomatization of mathematics for the sciences. It's...
Yes, with that algorithm, at no step is there generated an enumeration of all the natural numbers. But that doesn't prove that there does not exist a ...
How is that substantively different from Thompson's lamp? I already responded regarding Thompson's lamp. / I don't know a theorem of set theory that i...
A sphere has infinitely many points in it. And is there such a thing as a sphere with an infinite radius? If I'm not mistaken the radius of a sphere i...
No, limits use infinite sets. The standard axiomatization of analysis is ZFC. Ordinary modern analysis is decidedly infinitisitic. Maybe you're thinki...
Merriam online has definientia with 'series' and 'enumeration'. (There's another definiens closer to your sense, but I don't think it's common, and es...
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