MindForged

What is a non-existent set? If you've defined it, it exists. So that's just the assertion of a contradiction. You don't have to list out all the membe...

I can say that as someone who has studied dialetheism and paraconsistent logic, and has mentioned such to things to friends of mine doing their grad d...

No no, I'm saying that in the thread we could at least agree that sets are a type of collection (the everyday meaning of the words "collection"). The ...

Yeah, that was before we realized the naive comprehension scheme resulted in Russell's Paradox and trivializes the math if you keep the classical logi...

Sex with sex dolls

Yeah that's why I didn't see it as a relevant objection even if it's technically correct. Your points were well made though. *thumbs up*

Sure but that's not really how one gets to infinity in math. It's not like when someone says the natural numbers are infinite they mean they've counte...

Nah it's fine. It's technically not the exact same operation but since it behaves similarly enough I don't know what else to call it (additive operati...

I did not claim that because transfinite numbers have mathematical properties they can have real world referents. I don't see where in the part you qu...

Whatever man, I've said my piece in this thread as many times as I feel like doing anymore. Responses that it's magic or that it's contradictory or th...

It does. Literally every mathematician and any maths student paying attention knows the things I'm saying. #1 is not known to be true and previous exa...

It doesn't behave non-numerically, that doesn't make sense. The normal operations can be performed with such numbers, but that doesn't mean you'll get...

I repeat, you can say that about ANY other kind of number that has a unique property others don't have. It's not a contradiction so the repeated claim...

Obviously they have different properties. Finite numbers are finite, transfinite numbers are infinite. It's like complaining that odd numbers cannot e...

It's not contradictory. How many times are you going to make wild claims with no explanation? How is it not a number? Cardinal numbers are numbers. Tr...

What one quantifies over in logic or places in a set does not commit one to the existence of the thing. If you think modern logic assumes existential ...

It's not an undefined concept, you are out of your mind. Transfinite cardinal numbers are numbers which are infinite. Since wiki wish apparently good ...

They are constructable. I gave an intensional definition of the sets. If you literally mean that "construct" means to individually gather each element...

Again, a total misunderstanding. Stop linking things you don't understand. There's a one-to-one correspondence between the squares and the positive in...

#1 is false because there are lots of infinities, with some being larger and smaller relative to others. The infinity of the natural numbers has a sma...

That's just not true, no axiom in set theory entails this nor in classical first order logic. Objects quantified over are not assumed to exist. The se...

Describing a set is how you populate it with members, e.g. Set "A"={1,2,3}

Why don't we look a bit further than the first sentence, yeah? Sets are not like baskets, I don't need to engage in a temporal process in order to "ma...

Sure, if we just ignore standard mathematics you can believe that.

You have given no evidence of that and you have fundamentally misunderstood many aspects of these issues. Transfinite cardinals and ordinals are infin...

It's not undefined, it is literally defined.

Again, false. Infinity is not a natural number, but there are many kinds of infinite numbers. Namely, those which are the cardinalities of the innumer...

That's just a misunderstanding. Infinity is not a member of the set of natural numbers, so of course there's no natural number of which you can indefi...

They are not on par. Occam's razor is to be used when all else is equal. Denying infinite time is not simple, there's really no independent reason to ...

What annoys me is that bringing Zeno up so much makes it seem like there's no standard resolution to most of Zeno's paradoxes, which is just ignoring ...

I've no clue if she created it, but my grandmother used to say: If you do something stupid, don't do it twice. I suppose I was never good at putting t...

That is saying standard mathematics is incoherent. Standard mathematics incorporates multiple levels of infinity with different cardinalities. It's no...

So you are going even further than limiting infinity in physics and just denying the coherence of standard mathematics.

Putting non-existent things in a set in no way commits one to their existence (goodbye existential import). The set of Harry Potter characters is only...

I didn't make any point regarding physical continuity (if space can even be called physical). I don't think the universe is actually infinite in bread...

It's not "designed" to break this "law", it just doesn't apply and it's perfectly obvious that it wouldn't. These sets aren't conjured, they're the nu...

Nonsense based on what argument? This is what you say but: Like how is the a an actual objection? It's "nonsense because it's useless trivia". Come on...

That's not true, using an infinity is not the same as a singularity occurring in the theory. Space under relativity is treated as a continuum, but tha...

It is a "particular type of set" which distinguishes the finite sets from the infinite ones by means of a relationship that isn't possible for finite ...

Prove it. I've given evidence that we can conceive of the actual infinite by giving a description of it and examples which instantiate it, you just ke...

I'm pretty sure I did in a previous post, but to take sets A set is infinite if it's members can put into a one-to-one correspondence with a proper su...

This is more or less what I use as justification. I wouldn't put it forward as unchallengable or something, but insofar as we accept what our best the...

There's no "constructing" here, space is just infinitely divisible. There's no such thing as a smallest possible distance.

I understand the distinction, you do not understand the point. I'm not talking about the temporal process of looking at ever smaller slices of space. ...

I'm not a Pythagorean, that's just a silly response. Even if I were a mathematical platonist, nothing about that in particular makes me think some asp...

Numbers aren't part of the mind. And besides which, you're contradicting yourself. Previously you said that the mind was finite. But you're saying num...

There's no force to this objection. We're not at an end point. Ignoring our actual universe, if the past were infinite then we would just be at an arb...

Did you miss the word "before"? That was talking about a past series of infinite moments. Premise 2 is the obviously question begging premise. Nothing...

It's an axiom because no one has found any contradiction that is provable from it. The definition of infinity is pretty clear, it's extremely useful i...

I don't see how that's a given. Space is infinitely divisible. Whether or not space counts as a "thing" or not I don't think matters, but it's infinit...