It is a discussion about infinity but it really does belong on one of his threads.
I gave my reasoning for why I distinguish between the semi-infinite and the infinite. If someone wants to make a distinction between these two semantics by calling one infinite whilst calling the other truly infinite, that’s also fine in my opinion. But when no distinction is made between the truly infinite and that which is not truly infinite, then I think confusion can occur.
Existence is the set of all existents. It is also a meaning. It is also an existent. Its quantitative capacity is infinite, and by this I mean, the quantity of things it encompasses is infinite. So as a set it encompasses an infinity of things, hence why it semantically qualifies as being the infinite set, and why it is also a number. Alternatively you can put it this way:
Infinity = a number
The infinite set = the set that encompasses an infinity of things (the set of all sets: Existence).
Yes I think that’s what I meant. Maybe I should say the set of all existents instead of the set of all sets. But they both amount to the same thing. Existence, the infinite set. The universal set.
Yes, I see it as the largest number. And yes, I see the cardinality of the set of all things as being equal to infinity.
To be fair, I did not focus on the OP beyond the fact that it is about infinity. So to that end, I will stop discussing infinity and semi-infinity here.
Infinity is not a noun. It’s a verb. It’s a process. If infinity were a thing it’d have borders.
CR,
Your need for god to exist is clouding your judgement.
Who are you talking to? If you’re talking to me, you are needlessly repeating yourself. That’s not welcome.
I see.
Whether it should be a noun or not - whether their definition is precise or not - is totally irrelevant to the fact that in English “infinity” is a noun.
Actually, proofs are made through definitional logic that is self evident.
Since the computer doesn’t know what self evident is, it runs in vague circles.
Ask the computer if it is ambiguous for beings whether their consent is being violated in a visceral manner… (self evident to each being)
There are also inferential proofs, say, the counting numbers… even though we can’t count them all, we still know it’s a well ordered set through deduction and inferential proof (we infer evident proofs)
lol @ the consent stuff
That is pretty fucking funny.
The math stuff was gibberish too.
It literally tried to explain infinitely adding 3 to something forever and gave this as an example:
2+1=3, 2+2=4
This AI has been short circuited many times now.
That isn’t what it was doing. It only said 3 because it started with that and then immediately went to four. It was just writing an infinite series while talking about sets
" 3= 1+2… 4=2+2" [You can continue it: 5=3 + 2, 6= 3+3, etc)
[b]
1 and 2 does make 3, you know that right? 2 and 2 do make four. So it was correct…
So how was it short circuited?
[/b]
I already said it!!!
Before it added that set, it set up its example as adding 3 forever …
That example has NOTHING to do with adding 3 forever!!!
It short circuited.
It doesn’t know what it’s talking about.
Everyone knows what an inferential well ordered set means, even if they don’t know the TERM.
The part where the machine stated something like “that’s besides the point” was actually the WHOLE point.
Again, a malfunction.
Well technically it can’t malfunction because it is not following a program. It’s simply producing thoughts in an open-ended way. If I ask it the same thing again, it gives a different response; it doesn’t repeat itself. (Also you seem a little defensive of your human superiority)
Maybe I should mention that I have it configured to spit out a paragraph or two at a time. If I want more response, I just re-input the same prompt again. So there was a cut-off between
The axioms of math can be inferred, but that’s not the point of this discussion, because it is also well-ordered (like anything, it is an ordered, finite set of axioms. But again, that’s not the point of this discussion). In an infinite mental model where we can imagine what it means to add 3 to a number…
And
3= 1+2… 4=2+2… and so on. It goes on forever.
Those are two different trains of the thought it was having.
So I will re-enter and let it continue that first train of thought to prove it to you:
We have laws though.
These are immutable.
The law of otherness (in order for something to distinguish itself, there must be something besides it that exist).
That never changes in existence.
Or the self evident law of consent violation… if any being in all existence is having their consent violated, the work is not done.
I have a couple more laws, but I’ll leave it there.
I don’t want to get into a long mathematical debate about “we don’t know what the rules are but we can still do it”. That’s insightful but also hand waving.
^ pretty sure it just inferred how perspective works
Does the machine understand that otherness does not require dichotomies?
What is “completely false”?
I think GPT needs a software update. An axiom is a logical premise. It is a stated foundational assumption used as a building block for further logic reasoning - such "because [axiom] is true - this reasoning must be true - logic. Premises are a part of logic - axioms are a part of logic - maths is entirely logic - an only verified as true when logically deduced or axiomatically defined as an assumed immutable logic premise (a place to start).
Axioms cannot be proven. They are the initial assumptions - expected to be true. Axioms are not proven - but granted - “self-evident”.
“A mathematical proof - is a proof - of a theorem”? Since a theorem is a proven idea you are saying that a “maths proof” is a proof of a proven idea. 
And if “1+1=2” is a theorem then it is already proven by other maths propositions (such as the basic maths proposed language definitions - “2” is defined to be “1+1”).
I don’t think “established” has anything to do with proof. And “demonstrate” means either logical syllogism or empirical evidence. A demonstration can serve a logical proof - “If we see it - it is true - We saw it - therefore it must be true.”
Certainly it can. The simple logic is that in maths -
- 1 can always be added to any value
- a greatest value is a value that cannot be added to
- therefore it is impossible to have a greatest value
- the definition of “infinite” is “having no greatest value”
- therefore a value can be infinite.
A “tautology” -
Logical truths are statements that are consistent with other accepted truths. Their “truth value” is merely that they are consistent with whatever has already been accepted as true - therefore are also “existentially true”.
I agree - but we aren’t talking about the physical world in this thread - only the logic (the consistency) within maths.
Update GPT’s software, mate. 
The program also has another thing it doesn’t understand… it knows the law of otherness, but doesn’t realize the paradox… the particle/wave problem; the perceptual acuity problem.
1 by itself is non existence… the otherness law.
So how do we add 1+1 to equal 2? Well the plus sign is an otherness as an operator, and equals is an analogy… so you have 4 1’s embedded in a 2 equality.
Let’s look at it from another way…
(0+1) (otherness) + (0+1) otherness = 2
But!!!
Let’s take another otherness…
(2+1) + (2+1) = 6, 12 or 2 or 24!
That’s called number theory.
See observor, when I read a criticism like that I can only conclude one thing. You don’t seem to understand what the point is: that it can be wrong, is a good thing. Because being wrong is often the side effect of thinking originally- of thinking in general, which is what this thing is doing, as opposed to calculating or simply looking something up in a database. That it can be ‘wrong’ is one of its greatest powers. If you just want the dictionary definition of a word like axiom, use a dictionary. This is a neural turing machine that needs 500GB of RAM just to boot up.
In fact, check this out. I just asked it: “What is being incorrect a side effect of?”