Philosophy Stack Exchange
Philosophy Stack Exchange

Questions tagged [infinity]

109 questions
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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 our purposes — there is a strong tendency to suppose…
Niel de Beaudrap
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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 captured the so called actual infinity and thus…
L.M. Student
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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. For the scope of this question God could be…
Lynel Hudson
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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 world). If it has been made in another…
Deschele Schilder
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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 for me?
Zerub Roberts
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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. Others think there is, but that all truths are…
Geremia
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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 of Kants antinomies of time and space. It has…
Mozibur Ullah
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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 problem goes away for example doesn't it? Is a finite universe…
J Kusin
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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 infinity in mathematics, specifically set theory with…
J. Dunivin
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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 them, we label and order different kind of…
Euler_Salter
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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 numbers 1, 2, 3, 4, ... The idea that "there's always…
user4894
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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 ordering whereas cardinals do not). Cardinal…
Mozibur Ullah
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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 can form a subset of all even numbers: {0, 2, 4,…
jshthng
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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 connection must have an idea, etc. One could then…
Tommi
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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 thought that nearly everyone should be able to do…
Speakpigeon
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