Questions tagged [infinity]

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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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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 ...
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Is there any philosophical significance to the arithmetization of infinity?

There are two arithmetics of infinity, ordinal & cardinal. I'm going to focus on the cardinal arithmetic as it requires less structure, that is they need less (i.e., ordinals require the idea of ...
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1answer
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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 ...
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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 ...
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3answers
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What is the difference between an Ordinal number and a Cardinal number?

I'm trying to understand the real difference between an Ordinal and a Cardinal, especially in relation with transfinite cardinals. The stuff on Wiki is a bit too complicated. Can anyone make it simple ...
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2answers
112 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 ...
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2answers
176 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 ...
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6answers
643 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 ...
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4answers
447 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 ...
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4answers
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Cantor and infinities

I know we have accepted Cantor's ideas a long time ago and many mathematicians use sets and infinities without ever realizing that thinking about sets and infinities intuitively fails, because there ...
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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 ...
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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 "...
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7answers
1k 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 ...
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7answers
2k views

One infinity greater than another infinity

Somebody told me this piece of logic: "If we consider in our thoughts something which is actually infinite, and we take a part from it, the remainder will undoubtedly be less than what it was before. ...
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227 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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1answer
350 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 boy ...
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2answers
92 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 ...
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3answers
833 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, ...
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1answer
91 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?
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3answers
406 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 ...
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5answers
762 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 ...
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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. ...
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3answers
663 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
411 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
461 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 ...
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3answers
668 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 ...
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3answers
351 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 ...
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5answers
458 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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1answer
103 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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247 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
223 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 ...
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233 views

Is it Possible to have infinite finites

As far as I see, there are only three ways to have infinity apples in the present. they existed eternally they materialized at an infinite rate they were added one apple at a time every second from ...
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2answers
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Changing Universe vs Infinity: [closed]

If we accept the idea of a dynamic, changing, evolving Universe (Big Bang Theory), must Infinity remain entirely conceptual? If the Universe is changing and evolving, this necessarily implies borders ...
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1answer
703 views

What's the relationship between infinity and a dimension? [closed]

When I was reading Kant's Critique, I got the sense that he'd sort of found a formula for calling something a dimension. Space seems to arise out of an infinity of extension. Time seems to arise ...
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1answer
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Why is infinite regress a problem for ontological explanations?

Suppose some ontological theory creates an infinite regress. Take, for example, Platon's concept of ideas, and then there must be some connection between idea and its actualisation, and then this ...
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2answers
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Difference between 'infinite' and 'not finite' [closed]

In a chat on Mathematics.SE about countability of infinite sets, someone responded that regarding the 'counting', infinite in mathematics does not mean uncountable, but means 'not finite'. Can ...

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