Questions tagged [infinity]

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20
votes
6answers
18k views

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 ...
11
votes
3answers
564 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. ...
6
votes
5answers
1k views

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 ...
7
votes
4answers
354 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 ...
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 ...
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....
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 ...
5
votes
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
votes
8answers
675 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
4answers
512 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 ...
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 ...
12
votes
9answers
840 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 ...
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 ...
4
votes
3answers
379 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 ...
4
votes
3answers
337 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 ...