Questions tagged [infinity]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
3
votes
0answers
201 views

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, ...
5
votes
8answers
3k views

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 ...
2
votes
0answers
148 views

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 ...
0
votes
4answers
115 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
3answers
114 views

The concept of infinite past [closed]

Is it possible to give an a priori answer to whether or not an infinite past is possible?
2
votes
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 ...
0
votes
0answers
181 views

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
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 ...
2
votes
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 ...
1
vote
4answers
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 ...
2
votes
0answers
123 views

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 ...
2
votes
3answers
87 views

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 ...
1
vote
3answers
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 ...
0
votes
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 ...
5
votes
8answers
2k views

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 ...
1
vote
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 ...
3
votes
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 ...
0
votes
1answer
180 views

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 ...
7
votes
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 ...
3
votes
3answers
156 views

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 ...
-1
votes
1answer
247 views

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 ...
0
votes
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.
1
vote
0answers
42 views

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: ...
-3
votes
2answers
1k views

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 ...
2
votes
4answers
4k 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 ...
7
votes
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 ...
2
votes
5answers
672 views

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 ...
5
votes
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" ...
1
vote
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 ...
2
votes
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, ...
1
vote
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'...
-3
votes
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 ...
4
votes
4answers
1k views

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 ...
5
votes
2answers
109 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 ...
1
vote
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 ...
2
votes
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 ...
8
votes
5answers
1k views

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 ...
6
votes
2answers
1k views

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 ...
1
vote
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 ...
9
votes
11answers
1k views

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 ...
2
votes
3answers
99 views

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 "...
11
votes
3answers
566 views

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. ...
0
votes
6answers
2k views

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!
14
votes
6answers
2k views

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 ...
2
votes
1answer
302 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 ...
23
votes
5answers
3k views

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 ...
-1
votes
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 ...
19
votes
11answers
19k views

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....
2
votes
3answers
791 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, ...
1
vote
2answers
90 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 ...