>Infinite empty space is a form of nothingness.
Infinite empty space is a form of nothingness. There is no such thing as empty space. There's always energy and untestable particles floating through some substrate below our understanding.
Space, Time and Infinity
Re: Space, Time and Infinity
It seems that it all depends on what one means by the word "conceived". Perception is an attribute of living beings, what these beings perceive would be necessarily limited. Space and time could be limits of human perception; for no one could see the totality or a 'thing in itself'.
Space and Time are aspects of reality and we may assume that they belong to the whole that we cannot see directly, so in that sense they do exist as our concepts; just as the colour green exists in my awareness of a green object at the time and place of my perception.
[/quote]
Perception is equivalent to perspective; information available exclusively to a single living entity. There is no thing in itself because all things begin with purpose. Before that it's undifferentiated stuff. We sense, then we distinguish attributes, then we recognise patterns, then we filter for danger, then we filter for interest.
Space and Time are aspects of reality and we may assume that they belong to the whole that we cannot see directly, so in that sense they do exist as our concepts; just as the colour green exists in my awareness of a green object at the time and place of my perception.
[/quote]
Perception is equivalent to perspective; information available exclusively to a single living entity. There is no thing in itself because all things begin with purpose. Before that it's undifferentiated stuff. We sense, then we distinguish attributes, then we recognise patterns, then we filter for danger, then we filter for interest.
Re: Space, Time and Infinity
[quote=Seremonia post_id=201056 time=1430786063 user_id=10861]
We can understand "infinity" in different ways. First, infinity is never ending. Secondly, infinity is "not limited by another thing".
Former, indicates a case where we couldn't hold on it. A never ending implies there is at least one thing which is unreal, in the sense that it has no place wherever possible. Because once you are pointing to the farthest pointer but suddenly it's not the farthest. Never ending, there is no exact place of never ending.
Later, not limited to be consider not limited by another, it makes sense. In the sense that thing could be considered depending upon (limited by) another thing. Or things are not depending upon other things, as not limited by another thing but maybe it's limited by something else.
So, [b]what is infinity?[/b] It's not limited by one thing but on the other side it was limited by something else.
[/quote]
Infinity is a direction, not a destination. It's synonymous with etc. All words that represent infinity (forever, perfect, complete) are subject to the understanding that they're a placeholder for something ineffable.
We can understand "infinity" in different ways. First, infinity is never ending. Secondly, infinity is "not limited by another thing".
Former, indicates a case where we couldn't hold on it. A never ending implies there is at least one thing which is unreal, in the sense that it has no place wherever possible. Because once you are pointing to the farthest pointer but suddenly it's not the farthest. Never ending, there is no exact place of never ending.
Later, not limited to be consider not limited by another, it makes sense. In the sense that thing could be considered depending upon (limited by) another thing. Or things are not depending upon other things, as not limited by another thing but maybe it's limited by something else.
So, [b]what is infinity?[/b] It's not limited by one thing but on the other side it was limited by something else.
[/quote]
Infinity is a direction, not a destination. It's synonymous with etc. All words that represent infinity (forever, perfect, complete) are subject to the understanding that they're a placeholder for something ineffable.
Re: Space, Time and Infinity (numbers & real things)
[quote=Seremonia post_id=202265 time=1431338598 user_id=10861]
[quote="Seremonia"]Well, those (infinitely) many numbers must be considered as real. In the sense, there are real things as much as those represented by infinite numbers in between two pointers (things).[/quote]
What i mean numbers are real is, that it must be considered having relation with real things to be involved in discussion.
[/quote]
All things are a set of attributes and boundary conditions. There are infinitely many pencil concepts.
That doesn't mean any concept is "real" except as a concept. Math is a language and all languages are descriptive. Math describes the relationships of quantity. There are infinite numbers between any two other numbers because we can conceptualise them there as IF we had sufficient resolution to parse them that way. That does not make them "real" in any sense. What are real are the relationships, same as in logic, regardless of how they're applied. You can describe actual relationships between completely imaginary concepts accurately to the extent they correspond to real things.
[quote="Seremonia"]Well, those (infinitely) many numbers must be considered as real. In the sense, there are real things as much as those represented by infinite numbers in between two pointers (things).[/quote]
What i mean numbers are real is, that it must be considered having relation with real things to be involved in discussion.
[/quote]
All things are a set of attributes and boundary conditions. There are infinitely many pencil concepts.
That doesn't mean any concept is "real" except as a concept. Math is a language and all languages are descriptive. Math describes the relationships of quantity. There are infinite numbers between any two other numbers because we can conceptualise them there as IF we had sufficient resolution to parse them that way. That does not make them "real" in any sense. What are real are the relationships, same as in logic, regardless of how they're applied. You can describe actual relationships between completely imaginary concepts accurately to the extent they correspond to real things.
Re: Space, Time and Infinity
[quote=Wyman post_id=202320 time=1431349634 user_id=9673]
[quote]If there are infinitely many numbers, numbers cannot be physical symbols as there are only finitely many symbols. [/quote]
How do you know that? The axiom of infinity assumes that there are infinite sets. What limit is there to the symbols by which we represent the natural numbers? For any n, if you give me the symbol for n, I'll give you n+1 - by induction, there are infinitely many separate symbols.
[/quote]
To any symbol i can add "plus the number of digits in pi." This cannot change the reality of it but it does illustrate that the reality of it is meaningless in the limited context humans can operate within. There are not infinite symbols because minds are finite.
[quote]If there are infinitely many numbers, numbers cannot be physical symbols as there are only finitely many symbols. [/quote]
How do you know that? The axiom of infinity assumes that there are infinite sets. What limit is there to the symbols by which we represent the natural numbers? For any n, if you give me the symbol for n, I'll give you n+1 - by induction, there are infinitely many separate symbols.
[/quote]
To any symbol i can add "plus the number of digits in pi." This cannot change the reality of it but it does illustrate that the reality of it is meaningless in the limited context humans can operate within. There are not infinite symbols because minds are finite.
-
commonsense
- Posts: 5196
- Joined: Sun Mar 26, 2017 6:38 pm
Re: Space, Time and Infinity
If I understand you correctly, I am hearing you indicating something not entirely unlike the following: numerals are symbols which stand for mathematical concepts. Of course concepts are distinct from reality even when they are concepts of real things.surreptitious57 wrote: ↑Mon May 11, 2015 10:50 am Numbers are not real as they are mathematical symbols and mathematics is abstract by definition
Now there are real numbers but the word real in that context means some thing entirely different
And so talking of numbers in a real sense is completely meaningless for they do not exist in reality
I should add that in mathematics there is a term, “real number”, which refers to a particular mathematical concept. One must be careful to discern which kind of real the writers here are referencing.
-
commonsense
- Posts: 5196
- Joined: Sun Mar 26, 2017 6:38 pm
Re: Space, Time and Infinity (numbers & real things)
My take on this matter is that real numbers reference real things while unreal numbers do not.Seremonia wrote: ↑Mon May 11, 2015 11:03 amWhat i mean numbers are real is, that it must be considered having relation with real things to be involved in discussion.Seremonia wrote:Well, those (infinitely) many numbers must be considered as real. In the sense, there are real things as much as those represented by infinite numbers in between two pointers (things).
It’s been quite a while, so please correct me if I’m wrong, but the square root of negative 3 is an unreal number. Or have I got it mixed up with irrational numbers? Oh well, now I suppose I’ll just have to reread some math.
-
commonsense
- Posts: 5196
- Joined: Sun Mar 26, 2017 6:38 pm
Re: Space, Time and Infinity
Why do you think there cannot be infinite symbols. As long as the universe expands there should be enough space for another distinct symbol, no?Lawrence Crocker wrote: ↑Mon May 11, 2015 12:55 pmIf there are infinitely many numbers, numbers cannot be physical symbols as there are only finitely many symbols.surreptitious57 wrote:Numbers are not real as they are mathematical symbols and mathematics is abstract by definition
There cannot even be a symbol (which must be of finite length) for the typical transcendental number.
That no abstract entities exist needs to be argued. What it is for pi to exist is something different than for pies to exist, but that is not enough to show that pi lacks existence.
SORRY! I had not read your reply to others on this subject. Never mind what I wrote here.
Last edited by commonsense on Mon Sep 28, 2020 9:11 pm, edited 1 time in total.
Re: Space, Time and Infinity
[quote=commonsense post_id=473519 time=1601323478 user_id=14610]
[quote="Lawrence Crocker" post_id=202303 time=1431345312 user_id=10843]
[quote="surreptitious57"]Numbers are not real as they are mathematical symbols and mathematics is abstract by definition
[/quote]
If there are infinitely many numbers, numbers cannot be physical symbols as there are only finitely many symbols.
There cannot even be a symbol (which must be of finite length) for the typical transcendental number.
That no abstract entities exist needs to be argued. What it is for pi to exist is something different than for pies to exist, but that is not enough to show that pi lacks existence.
[/quote]
Why do you think there cannot be infinite symbols. As long as the universe expands there should be enough space for another distinct symbol, no?
[/quote]
Symbols are mind bound. Minds aren't infinite.
[quote="Lawrence Crocker" post_id=202303 time=1431345312 user_id=10843]
[quote="surreptitious57"]Numbers are not real as they are mathematical symbols and mathematics is abstract by definition
[/quote]
If there are infinitely many numbers, numbers cannot be physical symbols as there are only finitely many symbols.
There cannot even be a symbol (which must be of finite length) for the typical transcendental number.
That no abstract entities exist needs to be argued. What it is for pi to exist is something different than for pies to exist, but that is not enough to show that pi lacks existence.
[/quote]
Why do you think there cannot be infinite symbols. As long as the universe expands there should be enough space for another distinct symbol, no?
[/quote]
Symbols are mind bound. Minds aren't infinite.
Re: Space, Time and Infinity
Yes. If they are more than concepts in the mind then they would have to be infiniie or finite, and as you say neither idea works. All that is necessary in philosophy is to follow the logic. It does not endorse realism.