As I said above, you're aptly showing the people pushing this are the ones out to make a political point and skew things through the lens of their own...
Whenever I see these sorts of threads or discussions on the internet, I immediately know these people have not looked much into the sokol hoax (and it...
That's not what I said, I said one's goals cannot be reached by pure logic. The axioms one adopts can be done so rationally (non-arbitrarily), as I ga...
You might well reject the PSR as a metaphysical principle (as most scientists do) while still doing as Hume suggested and retain it as an Epistemic pr...
To even apply that logic programmatically, one is going to be using a computer operating with a two-valued logic. What I'm saying is that it's not rea...
I just explained why. A trivial theory loses ALL meaning, it's literally meaningless and without structure. It can't be used for practical or theoreti...
How does it have anything to do with practicality? If you apply a trivial logic to purely theoretical problems (pure mathematics, for instance), it's ...
Because triviality is incoherent. It dissolves all conceptual barriers, prevents any kind of analysis or understanding, leaves the resulting mathemati...
That is not true, I gave you a perfectly clear reasoning that didn't use the rule. If the Axiom results in trivialism, it cannot be admitted on pain o...
No it doesn't. You're confusing the listing of the mapping with me populating the set. These numbers are already part of the set. When you say "the na...
It's not ragtag, that would suggest the rules are arbitrary. If the rules allow us to survive and understand the world, then the justification for acc...
This doesn't seem like quite the right definition of logic. Logic can refer to many things, and the scope or domain of logic has changed over time. Br...
You have got to be kidding me. Both the left and right contained 4 and 6, your just had to continue the mapping a few more spots. (4 & 6 appeared on t...
This is what happens when you don't realize that Even numbers exist, are a proper subset of the naturals, and are provably the same size as the natura...
This is what happens when you don't understand math. At all. I mean, it's almost like numbers such as 0.5 exist. Aside from people who insist on stupi...
How? It doesn't matter if the numbers I chose arbitrary, we're talking about whether it's infinite or not. Because there are numbers greater and small...
By unbounded I meant there was not in principle a final member which the array could reach. In practice is irrelevant, we're talking about abstract ob...
You did not give any counterargument here that the real between zero and one are either finite or unbounded. I gave an argument for why it was both, a...
Great argument, about your usual standard in this thread. I continue to be amazed by the questions asked here. It's not an assumption if you can prove...
In math, counting in understood rigorously, e.g. one-to-one correspondence. I'm not talking about the temporal process that people do. That has absolu...
Utterly irrelevant. They have a specific magnitude, they are demonstrably greater than 0 and lesser than 1. The length of their decimal expansion has ...
Yeah I mean constructivists have issues with Choice, but constructivism has a lot going for it, and it's been around about a century now so that's not...
Good luck doing that without the rigorous mathematical understanding of infinity as opposed to the vague colloquial understanding. Infinite sets can v...
A set is defined by said rule applying to the objects in question. It has nothing to do with the process of collecting things. The properties in quest...
I gave a rule that populates members of a set, I do not literally gather abstract objects and place them somewhere. You're using a colloquial usage of...
As you point out, we lose quite a lot of mathematics by dropping the Axiom of Infinity. And to me the foregoing arguments for doing so are ridiculous ...
That's not the debate I was asking for in the OP. It was whether the words themselves have inherent meaning that straying from is necessarily changing...
This is what I'm talking about. "Infinity" in the context of limits might mean something else (emphasis on "might"), but calculus still uses multiple ...
Ehh, I think the issue there is what the brain does cognitively when we think about words is that we've already internalized "this means that because ...
Infinite sets are not indefinite, why do you keep saying this as if it's an obvious fact that I've conceded? Every object that's a natural number will...
Sure but I'm assuming that none of the other users here are doing constructive mathematics. In classical, standard mathematics, what I said is complet...
This is why you don't quote Wikipedia, especially when it's not a topic you're familiar with. The infinity referred to there is not a number. Limits d...
The number of natural numbers is the infinite cardinal aleph-null. Ergo, by your definition it's a quantity. QED. "How could it?" How could it not? It...
You aren't making sense. I just told you the difference. I already walked your through the informal proof, but not once have you actually acknowledged...
You should have specified what you meant by difference. I assumed you were asking how such sets were any different than a purportedly infinite set, so...
Because that's what the numbers are called. http://en.wikipedia.org/wiki/Transfinite_cardinal. Further, your comment that they have no "distinct" card...
OP has been arguing against the coherence of infinity, including infinite sets. Qlso, I have repeatedly mentioned the transfinite numbers. I am talkin...
An arbitrary quantity of elements referred to as a whole and which gain membership in said whole by means of sharing a common property we pick out or ...
I forget, are mathematicians doing math or philosophy? Worse, most philosophers who actually study maths too will employ the mathematical definitions ...
Um, no. Literally you're entire argument is that "collection" and "set" are necessarily finite because of the definition your use. Your argument is wi...
If space is a thing, it's not the same as the natural understanding of a thing. That's what I was talking about. You're other point wasn't what I was ...
They don't produce two different concepts. The extensionally defined set {3,5} and the intensionally defined set "odd numbers which are greater than 1...
It's not a label for two different concepts, it's two ways of defining instances of the same concept. Intensionally defined sets are not incomplete, a...
A set is not a list. A list can contain members of a set. The set of real numbers is unlistable (uncountable), but it's still a set. Listing out the m...
Cantor's set theory did fall into numerous paradoxes because of the naive comprehension scheme. It was, as you said, ZF that avoided them using the se...
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