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2
votes
1answer
178 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 ...
0
votes
1answer
41 views

Deny the existence of infinities by philosophical means only

Is it possible to deny the existence of infinities in the real world, by philosophical means only? If it makes it easier, I'm mainly interested to deny that we can know an infinite amount of things ...
0
votes
3answers
146 views

Can we claim maths is finite?

By Godel's incompletness theorems we know there are problems that cannot be proven. Is this sufficient to claim mathematics (the set of axioms and theorems) is finite? As a counter-argument, we might ...
3
votes
1answer
89 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 ...
0
votes
2answers
130 views

Is it Possible to have infinite finites

As far as I see, there are only three ways to have infinity apples in the present. they existed eternally they materialized at an infinite rate they were added one apple at a time every second from ...
2
votes
2answers
144 views

necessary conditions for something to be eternal

what are the necessary logical conditions for something to be eternal (i.e. without beginning, always existing)
-5
votes
1answer
95 views

can an infinity be comprised of infinite finites? [closed]

can an actual infinity be comprised of infinite finites? or perhaps infinity is some kind of special "infinite character", a different kind of nature, an "infinite nature", hence an infinite finites ...
-1
votes
2answers
157 views

Changing Universe vs Infinity:

If we accept the idea of a dynamic, changing, evolving Universe (Big Bang Theory), must Infinity remain entirely conceptual? If the Universe is changing and evolving, this necessarily implies borders ...
1
vote
4answers
675 views

One infinity greater than another infinity

Somebody told me this piece of logic: "If we consider in our thoughts something which is actually infinite, and we take a part from it, the remainder will undoubtedly be less than what it was before. ...
7
votes
4answers
1k views

Is infinite regress of logical causation possible? Is infinite regress of logical 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 ...
3
votes
2answers
470 views

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 ...
-4
votes
2answers
152 views

If a machine could theoretically count forever, is that machine counting? [closed]

I was wondering if a machine could theoretically count every second and could survive forever, would it actually be counting? Counting is only possible on finite sets so what would this machine be ...
4
votes
3answers
346 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 ...
7
votes
1answer
232 views

Is there any philosophical significance to the arithmatisation of infinity?

There are two arithmatics of infinity, ordinal & cardinal. I'm going to focus on the cardinal arithmatic as it requires less structure, that is they need less (ie ordinals require the idea of ...
4
votes
1answer
343 views

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 ...
-2
votes
1answer
249 views

What's the relationship between infinity and a dimension? [closed]

When I was reading Kant's Critique, I got the sense that he'd sort of found a formula for calling something a dimension. Space seems to arise out of an infinity of extension. Time seems to arise ...
-5
votes
2answers
580 views

Difference between 'infinite' and 'not finite' [closed]

In a chat on Mathematics.SE about countability of infinite sets, someone responded that regarding the 'counting', infinite in mathematics does not mean uncountable, but means 'not finite'. Can ...