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There is no such thing as Infinite outside your heads. This is actually a pattern - a false dichotomy with a pure abstraction produced as an abstract opposite o

by lngnmn 9y ago

There is no such thing as Infinite outside your heads. This is actually a pattern - a false dichotomy with a pure abstraction produced as an abstract opposite or an abstract result of negation of some other concept or a named entity. Applied Hegelian nonsense if you wish. Infinity is a pure abstraction, like zero, but ill-defined (zero is an symbol for a concept of an empty slot, absence or nothing, while infinite is mere a negation of finite). Like many other concepts it might be useful, but usability does not imply existence.

colordrops 9y ago
An orthogonal issue is that most if not all humans have a hard time distinguishing which aspects (all of them?) of their reality are just abstractions.
deleted 9y ago
[deleted]
umanwizard 9y ago
How is "zero" more of an abstraction than "five" ?
- gizmo686 9y ago
  Zero was invented long after the rest of the natural numbers (to my knowledge this is the case in every culture that independently invented zero). At least in the case of the Greeks, its status was somewhat controversial; I am not sure how other societies viewed it once it was invented.
  - johncolanduoni 9y ago
    If we find out some alien race started using positive numbers and zero at the same time, do they then become the same level of abstraction?
- smhost 9y ago
  It would go something like: > Zero is offensive and ungodly. With "five", at least there's something there to abstract. With zero, there's not even anything! How can nothing be something? Cue angry biting of thumbs
- rafiei 9y ago
  Because typically you'd be building `five` out of `zero`, but that's more of an "implementation detail" rather than a property of `five` or `zero`. Examples are numerous: i. Peano Axioms: (Typically) your initial element is 0 and you'll get 1 by applying the successor function to 0 and 2 by applying that to 1 and so on. ii. Von Neumann's definition of Ordinals: {} is zero and one is {{}} and two is {{}, {{}}} and so on. iii. Conway's definition of Surreal numbers: {|} is zero and { {|} | } is one and so on. iv. Church encoding and many more. P.S. I'm not a logician and don't know whether "more of an abstraction" has any well-defined meaning and not just the meaning that might be inferred by a software developer.
nabla9 9y ago
Infinity has been well defined mathematically. Infinity well defined in calculus, set theory and logic. For mathematical object to 'exist' only thing required is logical consistency under the rules used. Mathematical objects don't have other substance or existence than relations to other mathematical objects. Ontological claim that abstract things that "don't exist" by some ontological definition is fine, but it does not mean much. We can't see or think anything concrete. We have never touched anything 'physical' or 'real'. It's all abstract representations in our brains.
- lngnmn 9y ago
  > We can't see or think anything concrete. We have never touched anything 'physical' or 'real'. It's all abstract representations in our brains. This is some sectarian preaching in my opinion. The whole thing including these very Western philosophical sects are possible exactly because something concrete definitely exist. The DNA and the laws which make it stable and the whole life on top of it is the consequence of the fact that something concrete is out there. This, BTW, is an millennia old debate between some branches of esoteric Eastern schools and should, perhaps, be a part of seconady school lectures. As for definitions of infinity, the theoretical possibility of infinite series, infinite small numbers or infinitely many real numbers between 0 and 1 is nothing but mental constructs. There is not a single "concrete" infinity.
- lngnmn 9y ago
  > For mathematical object to 'exist' only thing required is logical consistency under the rules used. This is precisely the rule which establish existence of gods, accelerating time, higher dimensions, and other mental UFOs. Disconnected from reality (from what is) abstract, seemingly consistent logic is what supports all the chimeras. Read some Indian or Tibetan tantras, look at some mandalas - everything is logically consisted according to a particular sectarian logic.
  - Chris2048 9y ago
    > This is precisely the rule which establish existence of gods Can you provide a reference to that? > Read some Indian or Tibetan tantras, look at some mandalas - everything is logically consisted according to a particular sectarian logic. So? "sectarian logic" isn't mathematical logic.

by lngnmn 9y ago

colordrops 9y ago

An orthogonal issue is that most if not all humans have a hard time distinguishing which aspects (all of them?) of their reality are just abstractions.

deleted 9y ago

[deleted]

umanwizard 9y ago

How is "zero" more of an abstraction than "five" ?

gizmo686 9y ago
Zero was invented long after the rest of the natural numbers (to my knowledge this is the case in every culture that independently invented zero). At least in the case of the Greeks, its status was somewhat controversial; I am not sure how other societies viewed it once it was invented.
- johncolanduoni 9y ago
  If we find out some alien race started using positive numbers and zero at the same time, do they then become the same level of abstraction?
smhost 9y ago
It would go something like: > Zero is offensive and ungodly. With "five", at least there's something there to abstract. With zero, there's not even anything! How can nothing be something? Cue angry biting of thumbs
rafiei 9y ago
Because typically you'd be building `five` out of `zero`, but that's more of an "implementation detail" rather than a property of `five` or `zero`. Examples are numerous: i. Peano Axioms: (Typically) your initial element is 0 and you'll get 1 by applying the successor function to 0 and 2 by applying that to 1 and so on. ii. Von Neumann's definition of Ordinals: {} is zero and one is {{}} and two is {{}, {{}}} and so on. iii. Conway's definition of Surreal numbers: {|} is zero and { {|} | } is one and so on. iv. Church encoding and many more. P.S. I'm not a logician and don't know whether "more of an abstraction" has any well-defined meaning and not just the meaning that might be inferred by a software developer.

nabla9 9y ago

Infinity has been well defined mathematically. Infinity well defined in calculus, set theory and logic. For mathematical object to 'exist' only thing required is logical consistency under the rules used. Mathematical objects don't have other substance or existence than relations to other mathematical objects. Ontological claim that abstract things that "don't exist" by some ontological definition is fine, but it does not mean much. We can't see or think anything concrete. We have never touched anything 'physical' or 'real'. It's all abstract representations in our brains.

lngnmn 9y ago
> We can't see or think anything concrete. We have never touched anything 'physical' or 'real'. It's all abstract representations in our brains. This is some sectarian preaching in my opinion. The whole thing including these very Western philosophical sects are possible exactly because something concrete definitely exist. The DNA and the laws which make it stable and the whole life on top of it is the consequence of the fact that something concrete is out there. This, BTW, is an millennia old debate between some branches of esoteric Eastern schools and should, perhaps, be a part of seconady school lectures. As for definitions of infinity, the theoretical possibility of infinite series, infinite small numbers or infinitely many real numbers between 0 and 1 is nothing but mental constructs. There is not a single "concrete" infinity.
lngnmn 9y ago
> For mathematical object to 'exist' only thing required is logical consistency under the rules used. This is precisely the rule which establish existence of gods, accelerating time, higher dimensions, and other mental UFOs. Disconnected from reality (from what is) abstract, seemingly consistent logic is what supports all the chimeras. Read some Indian or Tibetan tantras, look at some mandalas - everything is logically consisted according to a particular sectarian logic.
- Chris2048 9y ago
  > This is precisely the rule which establish existence of gods Can you provide a reference to that? > Read some Indian or Tibetan tantras, look at some mandalas - everything is logically consisted according to a particular sectarian logic. So? "sectarian logic" isn't mathematical logic.