Questions tagged [infinity]
The infinity tag has no usage guidance.
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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 ...
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4answers
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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 ...
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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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7answers
305 views
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 ...
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1answer
160 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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1answer
75 views
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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515 views
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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3answers
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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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497 views
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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1answer
288 views
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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8answers
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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
116 views
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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1answer
225 views
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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1answer
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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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4answers
361 views
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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1answer
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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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5answers
923 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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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
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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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4answers
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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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4answers
436 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 ...
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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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8answers
698 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" ...
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1answer
89 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 ...
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10answers
481 views
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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2answers
98 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
267 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 ...
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4answers
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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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2answers
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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
175 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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4answers
380 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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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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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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1answer
363 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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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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3answers
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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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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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If we live in a simulated world, doesn't there have to be a first world that's real?
There are people who believe we live in a world, simulated on a computer. That computer must have been built in either another computer-generated world or a real world (by which I mean a non-simulated ...
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1answer
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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 boy ...
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5answers
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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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4answers
221 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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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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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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2answers
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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 ...
