Questions tagged [infinity]
Use for questions about the properties, nature, or definition of infinitude.
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Is infinity a number?
So I've been on a number of math fora, part of learning some calculus (not much of set theory, no). To my surprise I found what I would describe as strong resistance from some folks against (using) ...
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Is there any major benefit to using NAND in infinitary logic?
In infinitary logic (there's an SEP entry about it), you can have infinitely long conjunctions and disjunctions. But imagine that different logics are like different video games. Usually, to my ...
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Final Steps and Zeno's Paradox
In the SEP article on supertasks, it states that:
Max Black (1950) argued that it is nevertheless impossible to complete the Zeno task, since there is no final step in the infinite sequence. The ...
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Need help understanding how certain mathemetical statements across the landscape can seemingly contradict (e.g. Cantor-Hume vs Euclid)
Here are the main components to my understanding on this issue:
Almost all of math can be given in a foundation of set theory
Different math can seemingly contradict, e.g. in Euclidean geometry ...
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Is the B-theory of time only compatible with an infinitely renewing cyclical reality?
I'm not a mathematician and I may be misunderstanding some aspects of this concept.
According to the B-theory of time, the flow of time is an illusion, and every point in time exists equally. If this ...
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A thought process: understanding infinite density (black hole) from a temporal stance using a hypothetical Ouroboros [closed]
The two main focus questions:
Could a snake theoretically devour itself whole?
Does a black whole actually have infinite density and zero volume?
Everything below is just extra explanatory steps on ...
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Is infinity a concept or a word empty of meaning?
I'm wondering if infinity is a concept.
We know from experience that there are things for which one cannot reach the end. A long way through the space is an example. One cannot reach the end of the ...
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Is there some sort of disconnect between the math we use and our "observed phenomena" in reality?
So my question comes from two questions on this site one of them being my own, How small can we measure space? and Is the (surprising) applicability of mathematics to the physical world a brute fact ...
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What is the state-of-the-art of formal definitions of God?
Isn't the only formal analytic definition of God, that of Cantor's Absolute Infinity?
What is the state-of-the-art of this approach?
Are there other definitions?
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Constructing an infinite interval with a definite starting point given an infinite past [duplicate]
I had a question regarding constructing an infinite interval with a starting point given an an infinite past. I wish to model an infinite past in a non-formal non-rigorous set theoretic manner and was ...
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Has anybody revised Kant's Antinomies of space & time in view of modern physics?
Has anybody updated Kant's antinomies in view of modern physics?
In The Critique of Pure Reason (1781) he laid out the Antinomies of Pure Reason highlighting contradictions in the ideas of time and ...
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Can anything happen at any time right now if there is infinite Possibilities in life?
If we live in a world with possibly infinite realities, and infinite space, doesn't that mean that there is an chance that anything could happen?
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Is learning an infinite loop?
We learn from people who were taught by other people. Those people were taught by other people. Those people were taught by other people.
For example, a professor teaching in a university was once ...
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Completeness in finished system
Gödel's incompleteness theorems addresse formal axiomatic théories.
Incompleteness of arithmetic of natural numbers is an example.
My question is if a theory regarding a finite class of numbers cannot ...
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Is there a philosophical or mathematical proof for "For any observation or claim, there's an infinite number of assumptions we presume to be true?"
Is there a philosophical or mathematical proof for "For any observation or claim, there's an infinite number of assumptions we presume to be true?"
It doesn't seem to make any sense, but ...
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If God is infinite and unchangeable how is there room for the universe? [closed]
If God is infinite and God cannot change, how is there room for the universe?, how could the universe come into existence?
UPDATE:
By "room" or "space" I did not necessarily mean ...
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Can the AC-DC argument against infinitism be defused?
Infinitism is the epistemic theory that claims that justification is only achieved by an infinite chain of non-repeating reasons.
At first, this feels like the "troll" theory of epistemic ...
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What philosophy of mathematics denies the existence of uncountable sets?
Finitism denies the existence of infinite mathematical objects (e.g. quantification over infinite domains is not considered meaningful). Is the position that denies the existence of uncountable sets (...
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Is there a way to prove we live in a universe of infinite or finite “things”?
Sometimes I wonder if science has limits. On one hand; logically no; there will always be something that we don’t understand and when we create new things it leads to other new things. On the other ...
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Isn’t the impossibility of an actual infinite in time almost by definition?
I have seen many philosophers argue that it is not contradictory to suppose that an actual infinite can exist.
But infinite in the future or past means never ending. If it never ends, it never ...
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Does absolute eternality entail timelessness?
Assuming one is committed to the idea that an actual infinite amount of time can never pass, does eternality entail timelessness?
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How to understand the notion of majority when comparing infinite sets?
Suppose I make the argument:
It is very unlikely that in a naturalistic universe, the constants have life sustaining values, since the majority of metaphysically possible universes do not have such ...
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Should proofs of God involve the infinitary language ℒ(∞,∞)?
If God is an infinite being (per Scotus, say), and if no finite number of steps in an argument is adequate to the scope of the divine majesty, then the strictures of monadic theism aside (God as a ...
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Probabilities and Certainties on the Monkey Axis: Yet more about those monkey typists
I was reading with some interest the answers and comments to this question about that familiar, weird and somewhat inhumane infinite-monkey experiment which, somehow, is still generating fresh and ...
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Why would infinite monkeys not produce the works of Shakespeare?
Apologies if this is a very basic/obvious question. I have no training in philosophy, but have been making my way through Peter Adamson's History of Philosophy podcast.
Recently I listened to his ...
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If the finite-indefinite-infinite distinction is not exhaustive, does this affect Kant's resolution of the antinomies?
From the modern point of view, infinity comes not only in various flavors (some of which Kant seems to have been aware of), but various sizes. So when Kant talks about conceptions as being too small ...
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Understanding Aristotle's argument of simultaneously and sequentially actualisable potential infinities in response to Atomism
I am reading a book about Aristotle. Aristotle lays out a potential argument against infinite divisibility by the Atomists, that infinite division would leave components of zero-magnitude which could ...
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Does philosophy, based on Archimedean solids, permit an infinite-face prism projecting a fifth dimension of infinite realities from a third dimension?
To quote the MIT work on the Hypershere: 'Considering that the largest Archimedean solid, the hyper truncated icosahedron, has over 14,000 faces, this object alone could contain within it an entire ...
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Do I exist under the aspect of eternity?
Do I exist under the aspect of eternity?
The work of art is the object seen sub specie aeternitatis; and the
good life is the world seen sub specie aeternitatis.
Wittgenstein on the unity of ethics ...
user67104
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How should eternity affect the plausibility of an agent’s existence?
Suppose the concept of God wasn’t eternal. There was some mechanism, perhaps even simpler than God, that gave rise to His existence. Is this more or less plausible than Him eternally existing?
What ...
user62907
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Can a totally ordered set with a last element but no first element exist, or is this contradictory?
Can a totally ordered set with a last element but no first element exist, or is this contradictory? An example of such a set would be a set that is ordered from largest to smallest, with there being ...
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Is there a way to confirm something material is infinite?
Mathematics is full of immaterial examples of infinities. However, is it possible to confirm or prove something material is infinite? Or, can we only conjecture they are?
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If something exists, does everything exist?
Has anyone argued this? I haven't formulated a coherent argument, so I'm just throwing this out there to see if anyone has thought about this already.
Intuitively, I think it makes sense that ...
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Do intuitionists and predicativists have an overly "absolute" concept of infinity?
Sifting through the historical data, I get the impression that intuitionism is not strictly a case of finitism (much less ultrafinitism), but more like "parafinitism". Predicativism, in turn,...
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Finite and infinite temporal duration
I am trying to wrap my head around different philosophical concepts of 'forever'. Correct me if I'm wrong, but I believe there to be three versions of 'forever' in terms of temporal duration:
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How does this theory about infinity compare with known results in "infinity theory"?
I had a conversation about infinity with my friend yesterday and what I left with was a theory about infinity.
HERE goes.
I believe that there are different quantities of infinity because if you have ...
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I have a premise about infinite timeline, how is it?
I think that in an infinite timeline without a start, if such a timeline could exist, the only way things could work is like this:
The only things that can happen are those that already happened an ...
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Applying logic to the question of whether all of existence is infinite or not
Here, I use to exist as generally as possible; if it is an object, it exists; if it is conceivable, it exists; if it is anything, it exists; even the properties and relations themselves exist. ...
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Can an infinite process be discontinuous? [closed]
The question is probably very, very easily answered with basic mathematical facts about infinity. Does it have any bearing on philosophy, what the answer is?
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Is "infinity" simply an accident of brains/turing machines?
As far as I know, no actual "infinity" exists in the universe. For example, the age of the observable universe is thought to be 10 - 15 billion years, while its size seems to be about 93 ...
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Can a backwards infinite regress account for its own existence?
Suppose we have a domain of discourse D with an infinite collection of elements, and suppose that it is the case that the existence of each element x is dependent upon another element y (or collection ...
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Problem with infinity? [closed]
Note: See PART 2 for a better question.
1 kg of matter has infinite number of parts. Infinite number of things together can make an infinite amount of matter. 1 kg is not equal to infinite amount. We ...
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Who came up with the traversing an infinity model of a guy eternally walking on tiles that appear and vanish behind him
I had a debate last year where I got my idea from a scholarly source that I didn't cite at the time. I'm looking to find it again.
As a rebuttal to the idea that an infinity cannot be traversed, this ...
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Can two things or x number of things that are not infinite create infinity?
Can two things or x number of things that are not infinite create infinity? Let's assume that x is not infinity. I am thinking that it's not the case, and there's no paradox here, but I just want to ...
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Is there an alternative to infinity?
We can say that a discrete set with 1 and 2 allows us to count just from 1 to 2 but a sequential set with 1 and 2 allows us to count from 1 to 2 in an infinite way (1.1, 1.2, 1.3 ...) but no man can ...
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If the universe is finite does that nullify Godel's incompleteness, halting problem, and Church-Turing thesis?
I'm not well versed on these topics but they all seem to rely on infinity, mainly infinite recursion or infinite space of mathematics.
If there is no always "next" algorithm, the halting ...
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What is the difference between infinity and endlessness?
Rudy Rucker, author of the book Infinity and the Mind, writes this:
To understand how something can be endless but not infinite, think of a circle. A fly can walk around and around the rim of a glass ...
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If something can’t come from nothing, then has an infinite period of time already passed?
Assuming that something really can’t come from nothing (I know it’s controversial but if it’s true)...
Then at any given point in time (t), something exists and therefore something also existed at t-1....
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Is there such a thing as ωth-order infinitary logic?
I've seen references to ωth-order logic sprinkled (sparsely) throughout my studies, though what properties this has compared to and contrasted with nth-order logics I wouldn't be able to tell you (I'm ...
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Does size become fictional in an infinite universe?
Currently, we don't know if we live in an infinite or finite universe. But let's say, for the sake of argument, that we do live in an infinite universe. So that if we would have a space ship with an ...
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