I'll believe that he has anything when I see it. Especially, does he purport to offer an axiomatic system? I don't recall, but perhaps he rejects the ...
The philosophy of mathematics is a rich area. (1) Unfortunately, cranks, who are ignorant and confused about the mathematics post incorrect criticisms...
You are egregiously and flagrantly putting words in my mouth. I never said cardinalities don't have size. But I'll say now that cardinalities are size...
That is a good question. We know that, for example, PA and set theory are such Ts. But, putting aside the ambiguity of 'natural' and assuming a genera...
"This sentence is true and unprovable" is not the sentence we prove is not provable in T. Rather, "This sentence is not provable" is the sentence we p...
If T is consistent, then T does not prove both that G is provable in T and G is not provable in G. We prove that if T is consistent then T does not pr...
Curry's paradox has a very technical context. To understand it properly requires being very careful in the formulations. 'X - > F' means "X is false"....
It's even contradictory just to say that x is not x. And set theory does not say there is an x that is not x, nor that there is an x that is x and not...
You are very confused. Yes, you didn't say all others are ignorant. And I didn't say that you said that all others are ignorant. Rather, as now you me...
On some crucial points, you didn't even recognize them, let alone refute them. And when you did attempt to refute points, you failed, as your supposed...
I don't care to say you are "disrespectful", but you are irrational and in bad faith when you skip refutations and explanations given you and instead ...
The cardinality of N = the cardinality of P iff there is a bijection between N and P. There is a bijection between N and P. Therefore, the cardinality...
As I said, the discussion will go in circles given that you skip answers given you and instead just repeat your refuted claims. It's not my mathematic...
The question is not well formed. It is not apparent what "infinitely infinite infinitely infinite infinitely infinite infinitely infinite infinitely… ...
We don't say "using semantic". Rather, we just state the definitions. I stated the definitions in my first post in this thread: https://thephilosophyf...
You know, its a funny thing, but when I don't know much about a subject, I pay attention to people who do know something about it. And especially I do...
We go in a circles, as it is with cranks. The crank makes false claims and terrible misunderstandings. Then the crank is corrected and their error is ...
Whether described as 'picturing an object' or 'positing that there is such an object' my point is that set theory does not mention, describe or posit ...
As that was added in edit, I missed it. Whatever you think of me, or whatever error you think there was in communication, I accurately responded to yo...
Mathematics doesn't mention "all existents" or "set of all things". The heart of your attack on infinitistic mathematics is your own mistaken fabricat...
By definition, a successor cardinal is strictly greater than its predecessor. (By the way, aside from successor cardinals, there are cardinals other t...
G is a sentence in the language of arithmetic. There are many ways to couch incompleteness proofs. Here is one outline: Let T be a recursively axiomat...
'S is infinite' is equivalent with 'S has infinitely many members'. Or as you say: 'the set of natural numbers is infinite' is equivalent with 'there ...
Right, those working in the various branches don't usually concern themselves with the foundations. So use of infinite sets is ubiquitous without conc...
I'm not sure, but I think bread and butter analysis might touch on the cardinality of the power set of the set of reals (?), but I don't have enough i...
Depends on what is meant by 'transfinite math'. 'transfinite' is just another word for 'infinite', and, of course, analysis uses infinite sets. Moreov...
As a connoisseur of cranks and sophists, I beg to differ. This thread is run of the mill in that regard. And there are routinely far more risible igno...
Yes: |- ~X <-> (X -> F) If Y is false then (X -> Y) <-> (X -> F) is true. That's not Curry's paradox. Who does that? You? Did someone previously defin...
It is all-seasonal and perennial I assure you. People spouting hyper-opinionated uninformed and confused misinformation about this subject goes on con...
Of course we prove that there are cardinals of different size. We know the proof well. That doesn't even the least bit suggest that there is a mathema...
What? (1) Whatever jokes you made, you also made the incorrect claim about the size of the set of numbers in the intervals. You still haven't recogniz...
I answered that exactly already. You truly are not in good faith. You make claims about a subject of which you are ignorant. Then when it is explained...
Yes, it's the colloquial part that is so often abused by people who know virtually nothing about the subject. Especially among beginners in the subjec...
And it is fine that the concept is nonsense to you. That is not at issue. But that something strikes you as nonsense doesn't thereby render it nonsens...
(1) There is no object called 'Infinity' in the sense you have been using it. Here is a way to say what you want to say: In mathematics, there are set...
Whether you intend it or not, that is a trollish question. Of course, lines have length. That is implied by my talking about distance. I already expla...
He did it again! He still persists in mischaracterizing mathematics as claiming that there is an "Infinity" that has different sizes. That is after th...
I said nothing about rows and columns. First, you incorrectly objected to taking size as cardinality when you said yourself that the context is mathem...
First, incorrect objection to cardinality. Second, conflating distance with cardinality. Third, citing area when there is no area involved. It's a lin...
Unfortunately for you, you have conflated distance of an interval with the size of the infinite set of numbers in that interval. The distance between ...
In ordinary mathematics the idea of size is formalized as cardinality. I've said that one may propose whatever other concept or alternative mathematic...
Set theory is not standalone in the sense that it has no application outside itself. I am very well aware that that set theory does not account for al...
It makes a real difference. By saying 'infinity' as a noun and then that there are different sizes of infinity is to picture an object that has differ...
Comments