Questions tagged [infinity]

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Life and death paradox [closed]

Our lifespans are finite. Our "deathspans" are presumably infinite. Yet, infinity minus (anything finite) is still infinity! By this line of reasoning, we should be dead. But we're alive. So, ...
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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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Is there an alternative to Cantor's 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 ...
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Can the Universe Be Infinite?

Some think that the universe is infinite. To convince one in the creditability of the idea they point mainly at our inability to conceive of its spatial limits. Hence, here, I use 'infinity' (of the ...
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2answers
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Perpetual Division

I recall a story about a philosopher who proposed an idea that everything is essentially perpetually divisible. That is to say, you can divide a whole into two halves and for each half (regarded as ...
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Infinite past with a beginning?

I can conceive of an infinite past with a beginning. I can in fact represent this idea by a simple diagram, part analogical, part symbolic. So, to me, this idea is a logical possibility. I initially ...
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2answers
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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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1answer
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Does infinity in philosophy reduce to philosophy of mathematics?

It seems to me that any modern philosophical investigation of infinity reduces to looking at the mathematical concept of infinity (as introduced by Georg Cantor) and then delving into philosophy of ...
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How should one interpret modern mathematics if one doesn't believe in infinity?

I am an ultrafinitist. http://en.wikipedia.org/wiki/Ultrafinitism I don't believe there is a such thing as infinity. To me, it is obvious that there has to be a largest number; I just don't know what ...
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Is infinite regress of causation possible? Is infinite regress of causation necessary?

For a number of reasons — including perhaps a desire to feel that we have a complete understanding of where we came from, or at least an understanding which is completely sufficient for all of ...
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Infinity in modern integration theory

The Riemann integral itself doesn't work with infinity (±∞) as “endpoints”, you have to take a detour by calculating the integral for arbitrary endpoints ±z and then take the limit for z→∞, which ...
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10answers
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How is it possible for an infinite number of moments to have elapsed prior to now?

In the context of the cosmological argument: How is it possible for an infinite number of equal length moments to have elapsed prior to now? For more context . . I have read several discussions, ...
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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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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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5answers
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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 ...
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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 ...
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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 ...
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242 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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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 ...
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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" ...
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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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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 ...
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What are the necessary conditions for something to be eternal?

What are the necessary logical conditions for something to be eternal (i.e. without beginning, always existing)?
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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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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 ...
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1answer
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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 ...
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1answer
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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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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....
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763 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 ...
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2answers
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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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7answers
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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!
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2answers
444 views

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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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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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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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
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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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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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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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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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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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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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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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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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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 ...
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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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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, ...