Which of the following does having a notion of 'infinite' presuppose?

[Souron]

Yet a concept of 'many things' also means 'one many things' and not 'indistinct if many is many or non-many'. Isn't anything that is conceptualised as being something, viewed as being something because it is set as One?

*

Looking at the above from the point of view of sets: If a set has 'many things', but there was axiomatically no set of 'One thing', then what exactly does a set with many things even mean, and what is it juxtaposed to?
You seem to argue that the antithesis here is between indistinct 'many' and 'infinite', but 'many' is closer to 'infinite' from most points of view than 'one' is, and thus is closer to being the same type/category. Thus it is not practical to use it as the primary juxtaposition, cause one juxtaposes opposites as a basis, and One---Infinite is more of a polarity and of two ends.

The problem with looking at it from the point of view of sets, is that point of view presupposed the concept of knowable cardinality and therefore all finite numbers. Yes that approach will get you infinity from one, but does not show that you need to do it that way.

I'm not talking about the concept of "many" at all, I'm talking about the concept of "more". You don't need all of set theory to have that concept. You need a quantity that is order-comparable, without an upper bound. You don't need to be able to say that one quantity is exactly so much more than another.

Take for example water. You don't need to imagine an atom of water to imagine an infinite ocean. But for "infinite" to describe a quantity of water you do need to be able to compare it to smaller bodies like a puddle and a lake. A puddle is not "one" water". But a if you realize that a lake is bigger than a puddle, you can imagine an even bigger lake. Ad infinitum.

 

[Kyriakos]

The problem with looking at it from the point of view of sets, is that point of view presupposed the concept of knowable cardinality and therefore all finite numbers. Yes that approach will get you infinity from one, but does not show that you need to do it that way.

I'm not talking about the concept of "many" at all, I'm talking about the concept of "more". You don't need all of set theory to have that concept. You need a quantity that is order-comparable, without an upper bound. You don't need to be able to say that one quantity is exactly so much more than another.

Take for example water. You don't need to imagine an atom of water to imagine an infinite ocean. But for "infinite" to describe a quantity of water you do need to be able to compare it to smaller bodies like a puddle and a lake. A puddle is not "one" water". But a if you realize that a lake is bigger than a puddle, you can imagine an even bigger lake. Ad infinitum.

Yet it seems that, inherently and inevitably (regardless of chosen focus at any one moment) a puddle is indeed 'a water', in the same sense that while a cosmos is one, so is a tiny planet in that cosmos, and so is a building there or a room or a speck of dust discernible enough to be isolated for an observer on a wall in that room.
'One' is itself not tied to any volume, although it easily can bound volumes in organised thought. One is most of anything an ability to examine something (even arbitrarily, so it is all the more powerful as a notion) as distinct..

 

[Birdjaguar]

I would say 'one' is not a distinct thing or thought. Rather it is a whole bunch of thoughts. 'One' incorporates the idea of quantity as in "there is one half-eaten apple here, not 5 half-eaten apples". 'One' is a unit for ration comparison, as in "this pencil is one human-foot long". And 'one' incorporates the idea of being whole, as in, "the senate is one in it's decision to support the troops". Other nuanced meanings are possible.

Infinity stems from a concept of induction: if you have some number of things, and you can imagine having more, then you apply the same thinking to the larger group. Realizing that this is an unending pattern gives you the concept of infinity.

That definition of infinity does not require the concept of one. Certainly it does not require all the nuanced concepts that 'one' can mean. You only need a concept that lends itself to induction; that induction does not need to start at one.

I think that K is working with 'infinity' as a concept that is not just a long string of numbers. He is thinking about 'consciousness' and 'being'. Infinite consciousness doesn't leave room for more than 'One'. If there were two such beings, then neither would be infinite. In any case, that is how I see his question and I think they link very nicely.

 

[Kyriakos]

I think that K is working with 'infinity' as a concept that is not just a long string of numbers. He is thinking about 'consciousness' and 'being'. Infinite consciousness doesn't leave room for more than 'One'. If there were two such beings, then neither would be infinite. In any case, that is how I see his question and I think they link very nicely.

Afterall all our conscious patterns, and methods (which can be viewed as fossilised such conscious conceptualisations) are always resting on human thought, which itself does not appear as something axiomatically set - unlike in orders of science, which to varying degrees do rest on axioms in way of ordering a system of thought.

'One' does seem to be, most of anything else, the human ability- and also need- to break things into a point of focus, even if that is arbitrary. In this sense, "One" is primarily the actual point of focus, not any object it is used on.

 

[Souron]

Yet it seems that, inherently and inevitably (regardless of chosen focus at any one moment) a puddle is indeed 'a water', in the same sense that while a cosmos is one, so is a tiny planet in that cosmos, and so is a building there or a room or a speck of dust discernible enough to be isolated for an observer on a wall in that room.
'One' is itself not tied to any volume, although it easily can bound volumes in organised thought. One is most of anything an ability to examine something (even arbitrarily, so it is all the more powerful as a notion) as distinct..

A puddle may be a distinct thing, but it's not a unit of water volume.

'One' carries much more baggage with it than merely the idea of distinctness. It's a number. A natural number, a rational number, and a real number. It can be used to measure and count. But you don't need to be able to do that in order to conceive of the infinite. There may be a minimal concept that both infinity and one presuppose, but that concept is not the entire nuanced definition of 'one'.

 

[Souron]

I think that K is working with 'infinity' as a concept that is not just a long string of numbers. He is thinking about 'consciousness' and 'being'. Infinite consciousness doesn't leave room for more than 'One'. If there were two such beings, then neither would be infinite. In any case, that is how I see his question and I think they link very nicely.

What's an infinite consciousness? I can easily imagine multiple omniscient beings..

 

[Perfection]

I think that K is working with 'infinity' as a concept that is not just a long string of numbers. He is thinking about 'consciousness' and 'being'. Infinite consciousness doesn't leave room for more than 'One'. If there were two such beings, then neither would be infinite. In any case, that is how I see his question and I think they link very nicely.

Infinite space has infinite room for infinite infinities.

https://en.wikipedia.org/wiki/Hilbe...many_coaches_with_infinitely_many_guests_each

 

[Kyriakos]

A puddle may be a distinct thing, but it's not a unit of water volume.

'One' carries much more baggage with it than merely the idea of distinctness. It's a number. A natural number, a rational number, and a real number. It can be used to measure and count. But you don't need to be able to do that in order to conceive of the infinite. There may be a minimal concept that both infinity and one presuppose, but that concept is not the entire nuanced definition of 'one'.

One does not say that all meanings of One have to be deemed as fundamental or tied to the notion of infinite

And surely 'one' as 'a meter' (measure, unit, etc) is not the only meaning of one, nor the only crucial one. Meters appear, afterall, only if something to be examined with some precision as to its relations to other things is the scope of the work undertaken. But 'One' exists first without any such condition or want. For the same reason that one house has in it (along with other stuff) one room, the one room one bed, the one bed one leech crawling and hanging upside-down from the stained bedsheets of the nastyness the one world has let itself be infested by.


mmmm, what was the topic again? Oh yes, Unity

 

[Souron]

One does not say that all meanings of One have to be deemed as fundamental or tied to the notion of infinite

And surely 'one' as 'a meter' (measure, unit, etc) is not the only meaning of one, nor the only crucial one. Meters appear, afterall, only if something to be examined with some precision as to its relations to other things is the scope of the work undertaken. But 'One' exists first without any such condition or want. For the same reason that one house has in it (along with other stuff) one room, the one room one bed, the one bed one leech crawling and hanging upside-down from the stained bedsheets of the nastyness the one world has let itself be infested by.


mmmm, what was the topic again? Oh yes, Unity

So then we agree that infinity does not presuppose all notions of 'one'. The remaining question is "does it presuppose any?" Here I will concede that you do need some notion of distinctness to conceive infinity. However this notion does not need to be able to distinguish between one object and a handful. You only need to be able to say there is more of something one place than another.

 

[Kyriakos]

So then we agree that infinity does not presuppose all notions of 'one'. The remaining question is "does it presuppose any?" Here I will concede that you do need some notion of distinctness to conceive infinity. However this notion does not need to be able to distinguish between one object and a handful. You only need to be able to say there is more of something one place than another.

Yet how does a human have a notion of 'more of something' if not having in there already a notion of 'something' deemed even generally as one and not more?

ie 'one' not as a meter, as we already agreed, but 'one' as a 'not many'.

And if 'not many' is a prerequisite (or inherent and never lost notional part) for 'many', and 'many' is tied to 'infinite', the latter (infinite) again seems inherently tied to 'one'.

*

Furthermore, "many" is not itself 'distinct' if not tied to a meter, so that would seem to need even more conditions than those we seemed to have agreed to

 

[Perfection]

Consider a light switch.
Either it is On (1)
Or it is Off (not 1)
Anything that can reasonably be said to be able to have a notion of infinity should be able to describe some sort of binary comparison (on/off, true/false, yes/no etc)

So unless you have some nailed down specific definition of one, not one, and infinity I really don't see the point of going further.

 

[Kyriakos]

Consider a light switch.
Either it is On (1)
Or it is Off (not 1)
Anything that can reasonably be said to be able to have a notion of infinity should be able to describe some sort of binary comparison (on/off, true/false, yes/no etc)

So unless you have some nailed down specific definition of one, not one, and infinity I really don't see the point of going further.

Distinct (or in some cases also polar) opposites are often set as the discernible basis of any notion in between them. That is not exactly the question in the thread, though. The question is if 'infinity' rests in a notion of 'one', not as a duality of 'equally fundamental' opposites as in on/off or odd/even or large/small or changeless/flowing (to name a few of main opposites suggested by ancient greek philosophers).

Furthermore, as i noted in the first page of the thread, 'One' and 'Infinite' are not really set as opposites in such manner. (finite/infinite is the obvious duality there, of course).

 

[Perfection]

I'm not saying they're opposites.

I'm saying you can't think without such things. Every formal logical system has values that can be described as True or False (1 and not 1).

Now you might argue that true and false don't constite notions of 1 and not 1 but I haven't gotten a straight answer as to what does.

 

[Kyriakos]

I'm not saying they're opposites.

I'm saying you can't think without such things. Every formal logical system has values that can be described as True or False (1 and not 1).

Now you might argue that true and false don't constite notions of 1 and not 1 but I haven't gotten a straight answer as to what does.

So-called formal logic dates back to Aristotle's 'syllogisms' structure, which indeed has as its aim to construct science only with systems that have at least foundations to be given as true or false. That is not what philosophy always was like, nor what thought is limited by. In fact Aristotle himself presented this move to a system with (axiomatically following) true/false parameters as one with the end to negate the issues with the previous system, the 'dialectic', where things could be true, or false, but also sometimes they could be both true and false.

In his books of metaphysics, Aristotle has suggested as a most resilient basis of the system of logic that:

"Something, at a set time, and in a set manner, can either have a property (eg property A), or not have that property. But it cannot at the same time and in the same manner both have and not have that property".
In fact eleatic and platonic thought always uses that break-up of distinct truth or falsehood for pretty much any quality, if it is viewed from a collapse of a set focal point. Remember the famous socratic phrase that he only knows that he knows nothing, for it meant he knows that only in limited and set context can a system appear to be closed and tied forever to some axioms one identifies in it.

*

As for not having gotten an answer as to what 'one and non-one' is... Yes, you haven't. Thousands of pages have been written on this even 2000 years ago and before. It is not very likely the subject can be examined in depth on CFC, nor to a formal conclusion, and i doubt one such conclusion is to be reached through finite thinking either. But one does not need to know the atomic parts of the atomic parts of the atomic parts of a chair, if he asks to examine if a chair is a basis to have so as to have things like a set of chairs around a table in a living room.

 

[Perfection]

It's not about formal logic systems. It's about any logic system. It's a basic requirement of cognition itself.

Me: "Do you want juice?"
2-year-old: "No"

That's a True/False logical system.

 

[Kyriakos]

It's not about formal logic systems. It's about any logic system. It's a basic requirement of cognition itself.

Me: "Do you want juice?"
2-year-old: "No"

That's a True/False logical system.

You: "Do you want juice?"
toddler: <incomprehensible sounds>
person not speaking english: <vocalised ideograms>
alien: (translation to human speak and english : ) "WTH was that? Where did it come from?!"

etc

Logic is a clear subset of human thought. It is not isolated from the rest, and the rest likely is hugely larger in scope and webs of connections in our mental world that do not tend to become conscious anyway. Take a hint from even the most axiom-based systems quickly leading to non-distinct notions, such as infinity.
(afterall, infinity has been a concept in written down human thought at least since the 6th century BC and Anaximander of Miletos).

 

[Perfection]

Logic is the basis of thought not a subset. Why did the alien ask "WTH was that?" It's because the audio pattern recognition module in its mind returned "match = false". We don't always recognize it as logic because only some parts of our mind are open to introspection but it's the truth.

 

[Birdjaguar]

What's an infinite consciousness? I can easily imagine multiple omniscient beings..

I don't think think that omniscience isn't part of the issue. I agree that there is no reason one could not have or imagine multiple omniscient beings.

Kyriakos will probably have his own thoughts on what 'infinite consciousness' is since he asked the OP question.

What is infinite consciousness to me? It is all in the definitions. For the sake of this discussion, let's assume that consciousness means 'some level of self awareness'.

I would define infinite as 'unending, without limits'.

So infinite consciousness would be an awareness of ones self that has no limits or boundaries and is endless in all directions. I think in that context (which is decidedly mystical) does imply uniqueness or oneness.

If you change the definition of 'infinite' to be related to never ending lines, points, numbers, or other finite (discrete) objects, then you immediately make room for multiple infinities and lose any sense of 'oneness'.

When we choose our definitions (starting points), we usually are also choosing where we will end up or what the possible end points will be.

 

[Birdjaguar]

Infinite space has infinite room for infinite infinities.

https://en.wikipedia.org/wiki/Hilbe...many_coaches_with_infinitely_many_guests_each

I read the link and don't disagree, but the logic only works within the assumed context of the definitions and axioms.

in·fin·i·ty
in&#712;fin&#601;d&#275;/
noun
1.
the state or quality of being infinite.
"the infinity of space"
synonyms: endlessness, infinitude, infiniteness, boundlessness, limitlessness;

2.
MATHEMATICS
a number greater than any assignable quantity or countable number (symbol &#8734.

As I said above, where we choose to begin will limit the paths on which we will travel.

 

[Kyriakos]

Logic is the basis of thought not a subset. Why did the alien ask "WTH was that?" It's because the audio pattern recognition module in its mind returned "match = false". We don't always recognize it as logic because only some parts of our mind are open to introspection but it's the truth.

I do not agree at all that logic is the basis of thought. One also would tend to guess that in the depths of prehistory, back when humans did not even have the first traces of a language, logic was not there, yet thinking always had to be there.

My impression is that logic appeared with time, as a sort of 'only way to go is this one' progression. Afterall, logical thought does have the tendency to protect a thinker against all sorts of psychological pain.