Reminded by an article posted about by @Rhysy, I came to think of the difference between difference and similarity (or vice versa) - I think I've already written about how this difference (or indeed similarity) is like a reversible sweater. The two concepts are intrinsically two sides of the same coin, and anything that can be described as similar to something else can also be described as different from that same thing.

But I am not sure I have really written about abstractness, which might be an oversight, considering how much opinions I have on the matter.

My taxonomy if abstraction is really very simple (if black-boxy), and also quite predictable, if you know me at all:
Abstraction is the act (or its product, because english is like that), of inductively deriving a pattern from a bunch of observations, or a bunch of ideas, and maybe of bunches of things too abstract to name. In simple terms, there are measuring points from which we abstract their relation, like an extrapolation.

In this taxonomy, arithmetic is an abstraction from counting, which again is abstracted from the idea that things are not unique (vis a vis my oft-mentioned threeness piece https://medium.com/@ansugeisler/threeness-25185def6ab7 ).
Math, or at least its starting seed, is in turn an abstraction from arithmetic, and what a can of worm that is...

The post that stirred up this train of thought was about whether wasps can be said to have an abstract concept of "sameness" just because they can be shown/trained to react to instances of "same".

The connection to Set Theory seems unavoidable. "Sameness" does not belong to the set of "Same", nor does "Same" belong to the set of "Sameness". In my taxonomy of abstraction, I put it this way: A relation between individual measuring points doesn't include the measuring poinnts. Similarly, although the measuring points embody the relation, the relation is not a part of the measuring points.

#philsophy #math #science #arithmetic #AtMePls