Sorry I should of said:

- A point has zero length according to maths definition
- But according to my intuition, a point must have non-zero length — Devans99

Do you suppose there's a reason why points are zero-dimensional?

How would we define distance? The beginning/end of one point to the beginning/end of another point? Why not just consider the beginning/end as zero-dimensional points?

Do you suppose there's a reason why points are zero-dimensional? — TheMadFool

I find the concept of a dimensionless object difficult - it has no extents so it cannot have any existence - how can any sound reasoning performed with a non-existent object - assuming its existence (in order to reason with it) leads straight to a contradiction?

How would we define distance? The beginning/end of one point to the beginning/end of another point? Why not just consider the beginning/end as zero-dimensional points? — TheMadFool

Well the concept of 'measure', as alluded to above by @softwhere, seems to be math's answer. But measure theory does not seem (from my very limited knowledge of it - ?) to provide a justification for treating a point as dimensionless (or that there are infinite points on a line segment).

To define distance in a conventional sense is to have a unit of measure and a zero dimensional point is not a valid unit of measure - if we say a point has zero length and try to use it as a measure, then the measure of all line segments, no mater what length, is UNDEFINED.

I'm not even sure it is correct to say the beginning/end of a line are points - points don't exist - so would the line even have a beginning/end?

I don't think measure theory has much to do with this. But maybe it does. A non-measurable set is not a triviality. A point on the real line simply corresponds to a specific real number. In the complex plane, a point corresponds to a specific complex number. If you don't accept Cantor's conclusions that the real numbers cannot be "listed" (counted) then you are destined to wander through a metaphysical jungle. Remember the suggestion: If you come to a fork in the road, take it. :cool:

Well the concept of 'measure', as alluded to above by softwhere, seems to be math's answer. But measure theory does not seem (from my very limited knowledge of it - ?) to provide a justification for treating a point as dimensionless (or that there are infinite points on a line segment). — Devans99

The important thing to grasp is that math doesn't ultimately work with mere intuitions of what a point 'really' is. Such intuitions can guide the construction of a formal system, but the math itself is a definite formal system. That's why serious finitists and contructivists offer new exact systems. If it isn't a system that's as a dead and machinelike and trustworthy as the rules of chess, then (roughly) it isn't math. Because then it isn't a 'normal discourse.'

This is why a person has to learn to read and write actual mathematical proofs to really know what math is. So I encourage you to get a book on proof writing and reading. It will be fascinating, and your criticism will have more relevance.

I find the concept of a dimensionless object difficult - it has no extents so it cannot have any existence - how can any sound reasoning performed with a non-existent object - assuming its existence (in order to reason with it) leads straight to a contradiction? — Devans99

I did a cursory reading of Euclid's definition of a point: "that which has no parts" which I suspect alludes to points being zero dimensional.

The usual way points are expressed in Cartesian plane is by an ordered pair (a, b) which to me means points are intersections of lines, in this case the lines x = a and y = b.

Lines are not dimensionless, they have length, so shouldn't be a problem for you. After all you seem to have an issue with the dimensionless and lines have a 1 dimension viz. length. However, lines don't have width i.e. lines have one and only one dimension which is their length. This won't be a problem for you either since even though lines lack a width, lines have a dimension, length.

Now, consider the intersection of two non-parallel lines. They intersect on their widths and not their lengths. Such intersections being points can you now see how points can be zero-dimensional?

To me the past is a deducible concept without referencing external realities — Devans99

This expression sounds very anti-realist to my ears. Namely that the past is deducible i.e. in some sense a living construction out of present sense-data and current activities, as opposed to being an inductively inferred and immutable hidden reality that cannot be observed.

The conceptual distinction between the inductive inference of causes from effects versus the deductive 'construction' of effects given causes seems to lie at the heart of disagreements between the realist and anti-realist. The latter wants to bring these two concepts much closer together by interpreting causal induction constructively as a generalised form of deduction.

- I have thoughts, these thoughts from a causal chain. The present exists, there are thoughts that I am no longer having, so the past exists. There are thoughts that I will be having so the future exists. I can label each thought with an integer. Assuming a past eternity, then the number of thoughts would be equal to the highest number. But there is no highest number, so a past eternity is impossible? — Devans99

Yes, the realist thinks of "past eternity" metaphorically in geometric terms, as an infinitely long line beginning at, say, zero and ending at positive infinity at the "the present", which obviously cannot be constructed. The anti-realist can reverse this metaphor by labelling the present with zero, and considering the past to be 'created on the fly' as and when evidence of the past becomes available.

And of course, you presumably mean that you have present thoughts which you interpret as being 'past-indicating' and present thoughts you interpret as being 'future-indicating'. Although recall that an appearance per-se does not refer to either the past or future, as exemplified by a randomly generated image that by coincidence looks historical. And recall that we can doubt the veracity of our memories if we judge our present circumstances to contradict them. So we cannot make an immediate identification of appearances, memories, thoughts or numbers with points on a physical-history timeline.

Yes, the realist thinks of "past eternity" metaphorically in geometric terms, as an infinitely long line beginning at, say, zero and ending at positive infinity at the "the present", which obviously cannot be constructed — sime

I class myself as a realist but a finite realist, which I consider to be a more 'materialistically real' proposition than a realist who believes in actual infinity - for example of past time:

- If time has a start then it was 00h:00m at the start of time and current time is given by elapsed % 24
- If time has no start then it is UNDEFINED and all current times are also UNDEFINED, so no time

So we cannot make an immediate identification of appearances, memories, thoughts or numbers with points on a physical-history timeline. — sime

So you would hold that even the temporal succession of old thoughts followed by present thoughts followed by new thoughts could be an illusion?

Thoughts are constantly happening so that leads one to have an ever expanding history of thoughts. You hold that even that ever expanding history could be an illusion?

It is hard to argue against such a viewpoint. Denying the evidence of the senses as real is one level of anti-realism. Denying the veracity of our own thought is another level of anti-realism. The second seems impossible to counter logically?