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Questions tagged [infinity]

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4answers
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Is there an alternative to cardinalities that makes proper subsets smaller than their sets?

Cantor defined an infinite set as a set whose subset can be placed in a one-to-one correspondence with its subset. That is, take the set of all natural numbers: {0, 1, 2, 3, 4,...}. From that set, you ...
3
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3answers
67 views

What's the difference between infinite divisibility and infinte extension?

I understand that most people would say that time, such as the time it takes to write this question, is infinitely divisible. But I'm guessing it's unusual to suppose that makes time infinitely ...
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1answer
219 views

Are there any good philosophical arguments for or against Cantor's theorem, other than the ones that Cantor came up with?

I am looking for philosophical arguments for and against Cantor's theorem other than the ones Cantor came up with, if you know any, can you present them or a link to them? I post this in philosophy ...
0
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5answers
201 views

Can infinity have a beginning? [closed]

I have trouble with the mathematical notion of infinity. Example: Consider all of the natural numbers. It has a beginning, therefore it is bordered, therefore it cannot be infinity.
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0answers
25 views

Are there any arguments for why something past-eternal must necessarily be future-eternal as well?

If we assume that something has always existed in the past, what reason is there to assume that it won't perish in the future? I pondered on it and I wondered whether the following argument works: ...
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2answers
1k views

Can you divide the natural numbers in half sequentially? [closed]

My brief stint on SE has been quite interesting because it forced me to make the premises of my inquiry more explicit. I resisted this initially simply for reasons of economy, but economy proved to be ...
1
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3answers
275 views

Is it possible that we are stuck in a loop of endless life?

There are three assumptions for the question. 1) The flow of time is permanent. 2) The universe is repeatedly destroyed and recreated. 3) The initial physical structure of a brain at birth determines ...
7
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4answers
281 views

Is actual infinity physical infinity? Or just the axiom of infinity?

I've always been a little confused on this point. My (second-hand) understanding of Aristotle's difference between potential and actual infinity is this: We all have an intuition of the counting ...
2
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5answers
378 views

Can infinity be defined?

I know that one can look in a dictionary and find definitions for "infinity". Similarly, texts in mathematics will give varying accounts of how "infinity" is treated. So, I am not asking for these ...
3
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4answers
171 views

Is a distinction between actual and potential infinity philosophically significant?

I could use a little exposition on the significance of the distinction. I'm aware that potential infinities have arbitrarily large numbers, whilst actual infinities refer to the number "infinity" ...
1
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1answer
75 views

Can we give a well-motivated distinction between finitary and non-finitary mathematics?

I'm reading up on Hilbert, and wondering if there's actually anything fundamental to his distinction between finitary and infinitary mathematics. His system seems to be an attempt to avoid too much ...
1
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2answers
93 views

Can we assume that there are infinitely many possible states of the world at time t + 1?

I wasn't exactly sure where to post this question, so I decided that it's sufficiently philosophical in nature to warrant its being posted here. I may end up posting it on Mathematics SE as well. I'...
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1answer
209 views

A concept in which an infinite force is also limited

Edit (complete rewrite): OK so I'm completely rephrasing the question. Let's begin with declaring the concept in hand - A is an infinite, willing, creation force. A "wants" to create all the ...
4
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4answers
563 views

What are the best arguments against actual infinity?

What are the best arguments against the coherence of this concept? It seems that a great many people these days take for granted its coherence, but I am not so sure. It seems to me that, at least in ...
5
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2answers
100 views

If we aren't approaching the final theory, does it mean there's an infinite number of natural laws?

A lot say that with every next step we make in science comes always a set of new questions. I think this means there's an infinite number of questions we can ask about the natural laws. And that means ...
1
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2answers
172 views

Has anyone claimed that if time were infintely divisible then events would be mind depdenent?

Has anyone claimed that if time were infinitely divisible then events would not be mind dependent? Obviously, Zeno says something like this, but presumably has been refuted anyway. Can't find anyone ...
1
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4answers
288 views

How many numbers does it take to describe conscious reality?

The set of all real numbers (ℝ) is uncountably infinite, yet all of the general theorems of math, all of the thoughts leading up to them, all of of the particles of the physical universe could be ...
7
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5answers
884 views

Is the axiom of infinity truly an axiom?

I hope I can communicate my concerns effectively, so I can reach an understanding about a topic that I've been reflecting and researching intensely on for a few days. I am thinking about actually ...
8
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2answers
1k views

Are infinitesimals in the Newton and Leibniz calculus potential or actual?

Was reading a bit about history of calculus and its philosophy and stumbled into source of confusion: were infinitesimals in seventeenth century calculus assumed to be actual or potential? Was there ...
1
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1answer
301 views

Support For Empty Room Idea

In an empty room, a person can overcome irrationality such as desire, sustain, and the process of being compelled through long enough introspection. ("long enough" meaning immortality if needed) Are ...
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11answers
803 views

Limitless Space

I know many talked about this, however I am not a professional philosopher, rather a mathematician. In mathematics we have the concept of infinity, so we speak about infinitely big things, we compare ...
2
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3answers
84 views

Can something sensible be said about a world of complete nothingness?

One thought that keeps me up at night is when I start to think about the world "before" the universe existed and "beyond" the universe itself. I know that it doesn't really make sense to speak about "...
13
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3answers
365 views

Do all epistemologies suffer from the “regress of justifications” problem?

Aristotle describes the regress problem in his logical work Posterior Analytics I.2: b5. Some hold that, owing to the necessity of knowing the primary premisses, there is no scientific knowledge. ...
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7answers
2k views

Can there be a “center” of something infinite?

Imagine a plane that's infinitely large. Would there still be a center of it? I feel like there couldn't be one... But something tells me there should be in some way!
2
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1answer
54 views

What is the name of this “paradox” about predictions?

The scenario goes thus: There is a prediction machine which predicts very accurately but always states its prediction, and a boy who always defy what he is told. If the machine predicts that the ...
24
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5answers
2k views

What was Cantor's philosophical reason for accepting the infinite but rejecting the infinitesimal?

I have begun inquiring recently into mathematical aspects of Georg Cantor's theory of transfinite numbers and sets, which he developed between the years of 1874 and 1897. Throughout his theory, Cantor ...
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4answers
201 views

Could it be possible to refute Cantor's findings about multiple infinities on the basis of a radical new concept, that decimals are not numbers? [closed]

[Edit 08 March 2016: Some of my views have changed or evolved since I posted this thread and responded to the posters in it. These have been added to the essay in a new section.] This is a re-post ...
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11answers
14k views

Does the impossibility of an infinite regress prove God exists?

I'm strictly discussing one aspect of God: God as the First Cause. I am excluding all other qualities of God defined by any religion or belief system -- including the notion of God as a sentient being....
2
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3answers
484 views

Finity to Infinity? [closed]

The list of all whole numbers is infinite. Can numbers start from something trivial such as 0, 1 and then reach infinity? As per my understanding, infinity is fully formed, perfectly symmetrical, ...
1
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2answers
70 views

How does desire lead to the supernatural?

I Don't understand the following statement (from Pierre Raymond's La Philosophie dans tous ses états): In french: Par le désir, les hommes seraient ouverts à une surnature, disproportionnée comme eux ...
0
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1answer
72 views

Infinity recursive simulation on a turing machine? [closed]

Do you think, that it would be possible to run a infinite and recursive simulation of the universe on an turing machine?
4
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3answers
305 views

Is Kant's noumenon infinite and in what sense?

In the Critique of Pure Reason (B306) Kant defines noumenon - the thing in itself: If, by the term noumenon, we understand a thing so far as it is not an object of our sensuous intuition, thus ...
7
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5answers
910 views

How does actual infinity (of numbers or space) work?

Is infinity just continuous generation of numbers, or can space be actually infinite? If it is finite can we see it expand if we went to the edge? When I say "I am counting to infinity" does it mean ...
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3answers
2k views

If universe is infinite and time is infinite, doesn't that mean that “after-life” exist?

Here is the reasoning... If universe is infinite and time is infinite, then there has to be an instance where our life is 100% simulated (in some computer and such). And there has to be an instance of ...
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2answers
118 views

Is an infinity of possibilities is not possible when God is involved?

Within an infinity of possibilities there is a possibility that God exists in all possibilities just as much as there is a possibility that God exists in none of them. This leads to a contradiction. ...
3
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7answers
618 views

How can one determine, and justify, that something is infinite?

Can infinite things be measured and known? Imagine you stood on a long rope, and in the distance, you see that the rope continues past your vision. The further you walk on it, the more rope seems to ...
1
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3answers
160 views

Is Pi in Pi? And is 1/3 in Pi? And other numbers? [closed]

Note: According to my high school math teacher, people have seriously gone insane because of musing over stuff to do with infinity, so unless you are fine with going insane, or are sure not to ponder ...
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4answers
273 views

Countable additivity

Graham Oppy writes in »Philosophical Perspectives on Infinity«: Without countable additivity, it seems – for example – that we must lose the result that an arithmetic sum of an infinite series is ...
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4answers
374 views

Does a beginning imply an ending? (In regards to the universe)

In regards to the universe if it said to have a start (Beginning) does that imply that it will have an end? Are beginning and ends implied when either ones is said to be true of a proposition or can ...
12
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7answers
623 views

Are infinities in physics (or in any other materalist philosophy) actually possible?

Aristotle made a distinction between infinities that were in potential (dunamis) and in actuality (energia); and stated that actual infinities did not obtain in the physical world. This is the basis ...
3
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3answers
485 views

Are ordinal or cardinal infinities theories for real?

There are a number of notions of infinity in mathematics that are respectable. One of the first is 'the point at infinity' to the line or plane; but one can argue that this is a spurious infinity as ...
4
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3answers
308 views

Does the concept of infinity mean we have already 'been'?

A memory that frequently inhabits my consciousness is that of a lesson taught by my religious education teacher in senior school. He likened the conditions and occurrences that resulted in the ...
4
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5answers
739 views

Why is mathematics fond of infinity, but dismissive towards partially (un)defined operations?

One main reason why the law of excluded middle can fail is that some operations are simply undefined in some contexts. This doesn't even mean that they are undefinable in principle, it just means that ...
4
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5answers
359 views

Infinity and the universe [closed]

"If the universe (not in matters of space-time but in the context of scope) is truly infinite, and the true raw potential of everyone's imaginations are truly infinite (removal of environmental ...
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2answers
2k views

If there are infinite realities, do realities exist in which there are no infinite realities?

I don't have any experience with physics. I am just very interested to know whether or not this might be possible.
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6answers
502 views

Hilbert Grand Hotel vs. Cantor: Can we postpone the solution into infinity?

We can accomodate infinite amount of people into an Hotel with infinite rooms. Next, we can add extra infinitude of people. (See Hilbert's paradox of the Grand Hotel.) Obviously, the trick is just to ...
3
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1answer
830 views

The possibility of impossible

While thinking about the possible and impossible I came into the following conclusion. Some people say that nothing is impossible. But by saying that "nothing is impossible" they automatically ...
0
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1answer
97 views

Deny the existence of infinities by philosophical means only [closed]

Is it possible to deny the existence of infinities in the real world, by philosophical means only? If it makes it easier, I'm mainly interested to deny that we can know an infinite amount of things (...
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3answers
227 views

Can we claim maths is finite?

By Godel's incompletness theorems we know there are problems that cannot be proven. Is this sufficient to claim mathematics (the set of axioms and theorems) is finite? As a counter-argument, we might ...
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1answer
205 views

Is there a finitistic set theory, and if there is, is it provably consistent?

ZFC is the mainstream set theory. It has an axiom of infinity which claims that there is at least one infinite set. Now suppose like Aristotle, we object and say that there are no actually infinites ...