The tag has no usage guidance.

learn more… | top users | synonyms

2
votes
1answer
44 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 ...
15
votes
3answers
590 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 ...
0
votes
4answers
156 views

Could it be possible to refute Cantor's findings about multiple infinities on the basis of a radical new concept, that decimals are not numbers? [closed]

[Edit 08 March 2016: Some of my views have changed or evolved since I posted this thread and responded to the posters in it. These have been added to the essay in a new section.] This is a re-post ...
12
votes
9answers
2k 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....
2
votes
3answers
103 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, ...
1
vote
2answers
41 views

How does desire lead to the supernatural?

I Don't understand the following statement (from Pierre Raymond's La Philosophie dans tous ses états): In french: Par le désir, les hommes seraient ouverts à une surnature, disproportionnée comme eux ...
0
votes
1answer
57 views

Infinity recursive simulation on a turing machine? [closed]

Do you think, that it would be possible to run a infinite and recursive simulation of the universe on an turing machine?
4
votes
3answers
115 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 ...
2
votes
3answers
270 views

How does infinity of numbers and of 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 ...
-1
votes
2answers
462 views

If universe is infinite and time is infinite, doesn't that mean that “after-life” exist?

Here is the reasoning... If universe is infinite and time is infinite, then there has to be an instance where our life is 100% simulated (in some computer and such). And there has to be an instance of ...
-2
votes
2answers
65 views

Is an infinity of possibilities is not possible when God is involved?

Within an infinity of possibilities there is a possibility that God exists in all possibilities just as much as there is a possibility that God exists in none of them. This leads to a contradiction. ...
4
votes
7answers
200 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 ...
0
votes
3answers
88 views

Is Pi in Pi? And is 1/3 in Pi? And other numbers? [closed]

Note: According to my high school math teacher, people have seriously gone insane because of musing over stuff to do with infinity, so unless you are fine with going insane, or are sure not to ponder ...
2
votes
4answers
170 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 ...
1
vote
4answers
191 views

Does a beginning imply an ending? (In regards to the universe)

In regards to the universe if it said to have a start (Beginning) does that imply that it will have an end? Are beginning and ends implied when either ones is said to be true of a proposition or can ...
7
votes
5answers
262 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 ...
3
votes
3answers
301 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
votes
3answers
154 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
votes
5answers
687 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 ...
3
votes
5answers
222 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 ...
2
votes
2answers
337 views

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
votes
4answers
248 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 ...
3
votes
1answer
487 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
74 views

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 (...
0
votes
3answers
184 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
134 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
167 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
184 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)
-2
votes
2answers
179 views

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 ...
1
vote
7answers
1k 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. ...
9
votes
4answers
5k 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 ...
7
votes
2answers
3k 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 ...
5
votes
3answers
615 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
308 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 ...
6
votes
1answer
1k 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 ...
-1
votes
1answer
381 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 ...
-3
votes
2answers
2k 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 ...