Questions tagged [infinity]

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23
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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 ...
20
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6answers
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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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11answers
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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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6answers
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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 ...
12
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9answers
866 views

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 ...
11
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3answers
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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 ...
11
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3answers
572 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. ...
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11answers
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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 ...
8
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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 ...
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11answers
1k views

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 ...
7
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4answers
366 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 ...
7
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1answer
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Why is infinite regress a problem for ontological explanations?

Suppose some ontological theory creates an infinite regress. Take, for example, Platon's concept of ideas, and then there must be some connection between idea and its actualisation, and then this ...
7
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4answers
440 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 ...
7
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2answers
469 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 ...
6
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5answers
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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 ...
6
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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 ...
5
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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 ...
5
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4answers
1k views

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 ...
5
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8answers
719 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" ...
5
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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 ...
4
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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 ...
4
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5answers
454 views

Infinity and the universe [closed]

"If the universe (not in matters of space-time but in the context of scope) is truly infinite, and the true raw potential of everyone's imaginations are truly infinite (removal of environmental ...
4
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5answers
758 views

Why is mathematics fond of infinity, but dismissive towards partially (un)defined operations?

One main reason why the law of excluded middle can fail is that some operations are simply undefined in some contexts. This doesn't even mean that they are undefinable in principle, it just means that ...
4
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3answers
341 views

Does the concept of infinity mean we have already 'been'?

A memory that frequently inhabits my consciousness is that of a lesson taught by my religious education teacher in senior school. He likened the conditions and occurrences that resulted in the ...
4
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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 ...
4
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1answer
52 views

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 ...
4
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2answers
338 views

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)?
4
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3answers
381 views

Is Kant's noumenon infinite and in what sense?

In the Critique of Pure Reason (B306) Kant defines noumenon - the thing in itself: If, by the term noumenon, we understand a thing so far as it is not an object of our sensuous intuition, thus ...
3
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3answers
648 views

Are ordinal or cardinal infinities theories for real?

There are a number of notions of infinity in mathematics that are respectable. One of the first is 'the point at infinity' to the line or plane; but one can argue that this is a spurious infinity as ...
3
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1answer
1k views

The possibility of impossible

While thinking about the possible and impossible I came into the following conclusion. Some people say that nothing is impossible. But by saying that "nothing is impossible" they automatically ...
3
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1answer
45 views

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 ...
3
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3answers
158 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 ...
3
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7answers
1k views

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 ...
3
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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 ...
3
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0answers
205 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, ...
3
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4answers
400 views

Countable additivity

Graham Oppy writes in »Philosophical Perspectives on Infinity«: Without countable additivity, it seems – for example – that we must lose the result that an arithmetic sum of an infinite series is ...
2
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5answers
677 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 ...
2
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6answers
606 views

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 ...
2
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4answers
397 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 ...
2
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3answers
797 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, ...
2
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1answer
219 views

Is there a finitistic set theory, and if there is, is it provably consistent?

ZFC is the mainstream set theory. It has an axiom of infinity which claims that there is at least one infinite set. Now suppose like Aristotle, we object and say that there are no actually infinites ...
2
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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.
2
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7answers
316 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 ...
2
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10answers
494 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, ...
2
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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 "...
2
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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 ...
2
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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 ...
2
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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 ...
2
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1answer
310 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 ...
2
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0answers
149 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 ...