Philosophy Now Forum

[quote=Skepdick post_id=483684 time=1607359051 user_id=17350]
[quote=Advocate post_id=483681 time=1607358405 user_id=15238]
There is nothing special about dimensions in space. Any attribute that can be measured on a relative scale is a dimension. Leftness/rightness is not distinct from amount of yellowness as far as the variety of pattern it is.
[/quote]
Then you have infinite attributes, and therefore - infinite dimensions.

Relative to "left" and "right" you can also measure a "centre".
Relative to [ left, centre, right] you can measure centre-left and centre-right.
Relative to [ left, centre-left, centre, centre-right, right ]

etc etc. you can always synthesize a continuum.

And you can always invent operators like < which take two arguments, and then x < y can be interpreted as "x is to the left of y".

And so centre-left < right -> True
but
centre-right < centre-left -> False
[/quote]

Those divisions are of a dimension, not dimensions in themselves. A dimension is a scale of understanding from x to y. But that's a quibble. That all arguments can be represented in this way is the important bit. If we could formalize all the other relationships like we do > < = ~, we could really get somewhere. I call that project Spiritual Math.

Advocate wrote: ↑Mon Dec 07, 2020 5:46 pm Those divisions are of a dimension, not dimensions in themselves.

This is Platonism - I don't care for it...

Advocate wrote: ↑Mon Dec 07, 2020 5:46 pm That all arguments can be represented in this way is the important bit. If we could formalize all the other relationships like we do > < = ~, we could really get somewhere. I call that project Spiritual Math.

Computer scientists call it reification.

Expression.

[quote=Skepdick post_id=483687 time=1607359717 user_id=17350]
This is Platonism - I don't care for it...
[/quote]

How does that imply the dimensions are pre-existing things?

Advocate wrote: ↑Mon Dec 07, 2020 5:26 pm There is nothing special about dimensions in space. Any attribute that can be measured on a relative scale is a dimension.

Also.... that's not true.

The Koch snowflake is a ±1.262-dimensional object. Fractal dimensionality is a weird concept for most.

https://en.wikipedia.org/wiki/Fractal_dimension

[quote=Skepdick post_id=483691 time=1607360125 user_id=17350]
[quote=Advocate post_id=483681 time=1607358405 user_id=15238]
There is nothing special about dimensions in space. Any attribute that can be measured on a relative scale is a dimension.
[/quote]
Also.... that's not true.

The Koch snowflake is a ±1.262-dimensional object. Fractal dimensionality is a weird concept for most.

https://en.wikipedia.org/wiki/Fractal_dimension
[/quote]

It's a ratio. That means some part of the way between x and y, even if we don't know precisely what x and y are. You wouldn't say grey was a .5 dimensional thing.

Added reification to https://docs.google.com/spreadsheets/d/ ... Wy_X2Kbneo