Questions tagged [infinity]
Use for questions about the properties, nature, or definition of infinitude.
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Deny the existence of infinities by philosophical means only [closed]
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 (...
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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 ...
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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 ...
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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 ...
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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)?
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Changing Universe vs Infinity: [closed]
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 ...
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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. ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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