1. A quantity is a specified amount of something. It has a limit. The infinite is that which has no limits and so cannot be quantified. Therefore, not a quantity as not quantifiable.
2. Infinity is not limited to numbers (because it has no limit). if you say infinity is only a number you have broken the law of none contradiction as you have put a limit on something defined as having no limits. Therefore, infinity contains numbers but numbers do not contain infinity as numbers are limited to number.
This is just... no. Look, even if I take your definition of quantity, I can easily show infinity is a quantity. Take the set of Natural Numbers (o, 1, 2, 3...). In set theory, the concept of "size" is formalized as what is known as "cardinality". The cardinality (size) of the set of Natural Numbers is infinity, specifically aleph-null. QED. You can say the Natural Numbers have "no limit" in the sense that it can always get bigger, but that doesn't mean it's impossible to quantify. — MindForged
A better way to think about it is there are different kinds of infinite numbers, some larger or smaller than others — MindForged
No one is contradicting themselves saying there are infinite quantities. — MindForged
You can separate out the odds and evens similarly and end up with ω+ω = 2ω. — fdrake
You can add 1 to any real number, so infinity isn't a real number. Infinity is a concept. — GreenPhilosophy
Nothing to prevent you from adding 1 to infinity. — tom
Yes there is. If it is Infinity then it should already contain the 1 you’re attempting to add to it. If it doesn’t contain that 1 being added then it’s not infinity, as it is limited to not containing the 1 you are adding. This means what you are calling ‘infinity’ is not limitless at all and so not worthy of the title. — Mr Phil O'Sophy
Seriously, you can even add infinity to infinity. Plenty of cases where that happens in mathematics. — tom
I understand that mathematics uses the concept of multiple infinities. I’ve been exposed to the idea before. — Mr Phil O'Sophy
I’m saying that I fundementally disagree with it. What ever they are adding is more worthy of the title ‘indefinite’ than infinity. — Mr Phil O'Sophy
As I said before. If you try to have more than one infinity then you create a problem. — Mr Phil O'Sophy
Infinity is boundless, without limit, Etc. — Mr Phil O'Sophy
If you have two infinity’s, A & B, then you are saying that in order to add infinity A to infinity B that A does not contain B. Which is to say that both A and B are limited or bounded to A and only A or B and only B — Mr Phil O'Sophy
This making two infinity’s then leads to the logical conclusion that it is an indefinite number; an undisclosed amount that is limited to not containing that which you wish to add to it; not an infinite quantity as the mathematitions like to insist. — Mr Phil O'Sophy
You have never studied mathematics — tom
Indefinite in number, you say. — tom
You haven’t actually confronted my rebuttal, only used an appeal to authority fallacy a kin to ‘the mathematitions disagree with you so you’re wrong’. — Mr Phil O'Sophy
So it would appear that I understand the problem more than you do, unless of course you can demonstrate why i’m wrong, which so far you haven’t. — Mr Phil O'Sophy
Simply agreeing with authority without actually confronting the argument being made against it ad infinitum is not itself an argument. — Mr Phil O'Sophy
Yes I have. — Mr Phil O'Sophy
Please feel free to actually deal with the argument. I’m genuinely interested to hear a counter argument, which you have failed to offer so far. — Mr Phil O'Sophy
The thing you missed here is the unspoken inference you make. The cardinality of the set of Natural Numbers is not infinity (which is defined as having no limits) as by referring to Natural Numbers you are limiting it to Natural Numbers alone. You are not including anything which is not a Natural Number, it does not include different colours, shapes, texture etc. It is a concept limited to that which is considered a natural number.
You can say that the numbers have no end.. or could go on forever.. or go on indefinitely.. but you cannot refer to them as infinite as you contradict yourself by describing them as such. As they are limited... to Natural Numbers. I am aware that mathematicians are fond of using the word infinite, but I would argue that its an illogical thing to do. As I think I have sufficiently shown.
No because then you're not talking about the infinite any more.
Consider the following:
1. There are two infinite numbers, A and B
2. A is not B, and B is not A.
3. A is larger than B.
this isn't a description of something without limits. You are specifically saying that A is limited to A and does not include B. And that B is limited to B and does not include A. These are limits.
You can say it has no limits in one specific sense but has limits in others, but then you are not referring to the infinite or to a limitless thing anymore.
You are if you are saying this thing has no limits when it defined within the specific limits of Real or Natural numbers as in the examples you gave. You are therefore saying that this thing is both limited and not limited simultaneously. Which is a contradiction. It cannot be A and ~A.
I'm of the opinion an actual infinity cannot exist. I feel strongest about the impossibility of an infinite past, because that would entail a completed infinity: how could infinitely many days have passed?
That doesn't imply the philosophical analysis is wrong, it just means that we don't know of any particular limits
My opinions are consistent with the dominant opinion among philosophers prior to Cantor's set theory, but that doesn't seem like a very good reason to believe an actual infinity exists in the world.
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.