# Questions tagged [infinity]

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### Is infinity an imperfect and unsubstantial epiphenomenon of the finite?

To my mind the concepts of the finite and the infinite are equally mysterious. But recently I was surprised to encounter the view that infinity may be something different from what I have ...
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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 ...
6k views

### 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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### Where does Schelling discuss the "bad" or spurious infinity?

I read in my Hegel Dictionary that Schelling also discusses a version of the "bad infinity" and gives as an example the repayment of debt by issuing more debt at the Bank of England. I just ...
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### What is the difference between Zeno's "Dichotomy" and Richardson's "Coast of England" paradox?

We assume, though I believe it can be debated, that Zeno's "Dichotomy" paradox is apparently "unreal." We can treat any given distance as the sum of an infinite regress of smaller ...
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### Why is mathematical induction so applicable in mathematics?

Mathematical induction is a way to give finite proofs for (some of the) claims that concern infinitely many objects. For this reason it can be thought of as an approximation of the ω-rule. However, ...
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### Does science require the exclusion of the "infinite"?

And if so, are there any interesting implications? According to the storyline, Galileo launched modern science by declaring the necessity of rendering physical events countable. What is countable must ...
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### Did Augustine try to prove God's existence using Set Theory?

Some time ago I heard a professor of mine describe Augustine's Confessions as an attempt to prove God's existence using set theory. I didn't get a chance to ask him more of what he meant, and ...
164 views

### Is infinity really infinite if we can encode it in a finite number of bits?

I'm asking this question because in some programming languages there is an object defining "infinity", which behaves as the mathematical infinity (e.g. it is indefinite if you multiply it by ...
1 vote
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### The concept of infinite past [closed]

Is it possible to give an a priori answer to whether or not an infinite past is possible?
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### Is it possible to flip a coin an infinite number of times and never land on tails?

If I would flip a coin an infinite number of times would it be possible to never land on tails? In other words if there's an infinite number of chances of something happening is it still possible for ...
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### Is it possible philosophically that the entire cosmic void with one or more universe/s inside it will stop exist eternally?

As a conscious agent who suddenly appeared in this cosmic void as a child to my parents and got a consistent memory since about the age of 3; With time I have learned of the question "why is there ...
1 vote
204 views

### Does human conciousness "prove" that God exists?

I'm aware this question assumes our universe isn't an infinite regression. The logic is as follows: A is the source of everything. B exists. B came from A. Therefore B is an attribute of A. A being ...
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### Stack vs. Queue Brainteaser [closed]

So I have a thought in my head I was wondering if anyone could offer wisdom on, and excuse me if this is a silly question or is not philosophical in nature. The question is basically this: Let's ...
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### Would it be logically possible that the Universe has a beginning in time but an infinite amount of time has elapsed since this beginning?

Imagine that the Universe had a temporal beginning but no temporal end. At the beginning the Universe has a finite size, and as time passes its size increases exponentially. And the number of ...
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### Is this general argument against immortality valid?

I found the following argument here (although the paper is about a different topic): A General Argument Against Immortality: The method of Theory Confirmation can be applied to the question of ...
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### Do questions of Infinite regress, uncased cause and nothingness just point to our limits?

A lot of debates and conversations with theists seem to end up with the "ultimate" questions where the questions themselves seem to me to be conceptual/linguistic/psychological dead ends. Infinite ...
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### Theology of set theory

Absolute space and time are said to emanate from Aristotle. The Church acted as custodian of these concepts from early on up to recent times. I am thinking about another issue, namely that of ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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. Considered the ...
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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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### 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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### 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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### 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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### 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 vote
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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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### 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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### 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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### 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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### 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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### 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 ...