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

[Kyriakos]

This is a poll about your view on which notions (if any) are presupposed as existent in a being's (eg ours as humans) mental world so that a notion of infinite can appear as well in that being's thought or intuition.

Poll question is:

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

Poll options are:

1) Having a sense of 'One'.

2) Having a sense of 'One', but also at least some sense of 'Not One'.

3) Having a sense of anything at all, regardless if a sense of 'One' is there.

4) 'Infinite' is not tied to senses of 'One', or any other similar/following notion (and/or 'Infinite' does not follow from those senses either).

*

My intuition is that the first option is closer to a reality re this question. Since having a sense of 'One' already seems to be a distinction rising from some root that inevitably carries with it its antithetical (in many respects antithetical, not in all) notion of 'infinite'..

 

[Borachio]

Who knows?

But, as far as I remember, my sense of myself as an individual (and hence "One") predates any conception that I may have developed of the "infinite" (if in fact I've ever fully developed such a notion in any case) by quite a large margin.

 

[Kyriakos]

Who knows?

But, as far as I remember, my sense of myself as an individual (and hence "One") predates any conception that I may have developed of the "infinite" (if in fact I've ever fully developed such a notion in any case) by quite a large margin.

An issue with 'One' is that it seems obvious that it is not a notion which does not break into more notions (likely this is true for any human notion anyway). In the Parmenides dialogue there is some claim that 'One' likely means 'One in being' (or 'one in essence', translation is a bit ambiguous, original is En On - Εν Ό&#957, and while One is defined by itself being there distinct from what is not One, Being is also defined as being something in One state (at least in the eleatic view of things..).

I think that 'One' is likely the entire progression of numbers or any volume/change in the first place. This may seem trivial from a point of view (eg the natural progression is just 1, 1+1, 1+1+1,... etc), but if all there is One repeated and combined then what exactly is the infinite tied to?
It would appear that the infinite as a notion is tied to the notion of 'change' at least as crucially as to the notion of 'one', the latter being similar to 'non-change' too in some degree.

 

[bhavv]

Silly philolsopher ...

DEFINE - INFINITE
DEFINE - ONE

Using the terminology that you are thinking of those terms being defined as.

 

[Birdjaguar]

In terms of consciousness, "infinite" carries the notion of oneness, uniformity, and permanence. Two (or more) infinite consciousnesses could not exist without some special definition of infinity that steps outside the normal sense of the word.

 

[Timsup2nothin]

One, two, more than I can count. That is all that is required to grasp the basic concept.

 

[Zelig]

This is a poll about your view on which notions (if any) are presupposed as existent in a being's (eg ours as humans) mental world so that a notion of infinite can appear as well in that being's thought or intuition.

Poll question is:

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

Poll options are:

1) Having a sense of 'One'.

2) Having a sense of 'One', but also at least some sense of 'Not One'.

3) Having a sense of anything at all, regardless if a sense of 'One' is there.

4) 'Infinite' is not tied to senses of 'One', or any other similar/following notion (and/or 'Infinite' does not follow from those senses either).

*

My intuition is that the first option is closer to a reality re this question. Since having a sense of 'One' already seems to be a distinction rising from some root that inevitably carries with it its antithetical (in many respects antithetical, not in all) notion of 'infinite'..

None of the above.

 

[bhavv]

+1 for none of the above.

 

[Souron]

For the concept of infinity you need the concept of "greater than" But you don't necessarily need the concept of one. Concepts of few and many are sufficient prerequisites.

 

[Kyriakos]

For the concept of infinity you need the concept of "greater than" But you don't necessarily need the concept of one. Concepts of few and many are sufficient prerequisites.

The concept of One is not just of the number; it is of any distinct thing or thought. 'Infinity' also is a 'one' in the respect it is not something other (despite being indistinct by nature, it also is distinct from anything finite, thus it is a One next to anything it is not).

 

[bhavv]

That makes no sense at all.

 

[Kyriakos]

That makes no sense at all.

Must be my fault.

 

[Souron]

The concept of One is not just of the number; it is of any distinct thing or thought. 'Infinity' also is a 'one' in the respect it is not something other (despite being indistinct by nature, it also is distinct from anything finite, thus it is a One next to anything it is not).

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.

 

[Kyriakos]

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.

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.

 

[bhavv]

Sorry, but there's no way I can equate the word infinite with having anything to do with the word one.

Your arguments are not even slightly convincing.

 

[Kyriakos]

^Not sure if point is to troll
or just bored?

 

[bhavv]

Infinite = never ending, not one.

 

[Kyriakos]

Infinite = never ending, not one.

The point is that notions such as infinite, or One, or any other notion, are not non-connected dots in the human mind, but rather pinnacles of larger notions which aren't practically used in conscious thought. Much like if a mountain is mostly below water you may now see islands instead, but in reality those all tie in deeper basin.

 

[Perfection]

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

1) Having a sense of 'Bread'.

2) Having a sense of 'Bread', but also at least some sense of 'Not Bread'.

3) Having a sense of anything at all, regardless if a sense of 'Bread' is there.

4) 'Sandwich' is not tied to senses of 'Bread', or any other similar/following notion (and/or 'Sandwich' does not follow from those senses either).

 

[Kyriakos]

Very intelligent. Up to now i was not aware that 1/2= 80/160. 80/160 is an insight on what 1 and 2 is. Afterall 1 and 2 only exist in the fraction 1/2.