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[–] antiracistMetal 0 points 3 points 3 points (+3|-0) ago
But two raindrops plus two raindrops equals one raindrop.
@peaceseeker @chirogonemd @niggaskissin @sarmegahhikkitha @persiangovernment
[–] chirogonemd 0 points 5 points 5 points (+5|-0) ago (edited ago)
A raindrop is not a proper thing! A thing can be picked out by a number in a way that is non-partitive. The part is assumed in the name raindrop: we must call it a drop of rain. We couldn't ever say "one rain" in the same way we could say "one cat" or "one apple". We must say "one drop of rain". So a raindrop is stuff, not a thing.
Something about the operation of addition over things implies we can 'get our money back'. If I add 2 + 2, this equals 4 and can be expressed as: 2 + 2 = 4 (I never lose my twos, I can always go back over the equals sign).
What persists in the addition of two water drops into a single drop? It isn't the irreducible plurality of water molecules in either drop. Those are gone and we cannot get them back. Only water persists.
Is water a countable thing?
I like the Quinean view of objects which is that an object only ever is the best account we have of the contents of a very specific part of space-time.
I take the addition operation, in purely mathematical terms, to assume that the arrangements of matter in the addends maintain their essential structure across time and across the operation, although they may on average - and from the standpoint of their centers of mass - lose their relative positions as objects in the universe, that is relatively to all other objects in space.
This means that taking two apples and putting them together with two apples in a basket constitutes actual addition in the natural world. We can get our collections of two apples back and their matter is arranged in, more or less, the same way. There is some kind of abstract equation truly existing in nature here. We can "hop back over the equals sign", and get our money back.
That just ain't so with raindrops. There is no way to recover the arrangements of information in our two raindrops and hop back over the equals sign.
I say we aren't adding.
It seems like these things are fuzzy just when we are dealing with things with tricky material arrangements, whose information is undergoing regular, rapid, and comprehensive change - like liquids and gasses. When we refer to a liquid in terms of drops or any reference to them as distinct "masses", there is the distinct feeling that we mean something. To me, there is a definite ontological sense in it. But it isn't particular. There is a higher order concept going on there - I don't know what.
So I guess in my universe there is a definite limit to the amount (and rate) of change that can be taking place in the particular arrangement of information in an object (in the Quinean sense), in order to operate on it like an object.
There is never a case where we can pick out a water, even when we refer directly with "this water here" (say, pointing to a glass), and actually specify an object. By the time we are done with our statement, the spatial-temporal information in the substance has changed radically. Of course, there's a can of worms there. Someone could now claim I change radically in terms of my internal information from moment to moment - what am I?
We can't count liquids and gasses because they aren't things. But this is the best I've got as far as the difference between things and stuff.
It makes me think back to chemistry class and irreversible reactions.
If combining two things is ontologically irreversible, we aren't adding. In other words, I take mathematics to be ontologically non-destructive and this is a big separator between the observable world of nature and the un-observable world of mathematics. There is something very spiritual and significant in this non-destructiveness of the abstract world, something heavenly. Somewhere in there is probably the reason mathematics doesn't reduce to logic. Language is tied to the world, and things die in the real world. Our real actions and operations sacrifice them. Math operations never kill my twos.
My doggie never dies in math land. I just walk back over the yellow brick equals sign and find him there with Adolf.
Nobody asked for this. I'm sorry. I'm autistic and Aztec. I'm Auteztic.
@peaceseeker @sarmegahhikkitha @persiangovernment
[–] PeaceSeeker 0 points 2 points 2 points (+2|-0) ago (edited ago)
I think snowflakes offer a better example than raindrops for emphasising the ultimately non-concrete essence of mathematics, by virtue of the uniqueness of each individual snowflake.
Also, heh, apples.
@antiracistmetal
Also, mathematics aren't reducible to logic and logic isn't reducible to mathematics, it's true. Nor to language.
But all three of these things (mathematics, logic, and language) are reducible to what the Greeks called Logos, and St. John declared, inspired infallibly by the Holy Spirit, that Logos is God.
All this to state the obvious, that the simple and eternal principle of all things is in fact the principle of mathematics, logic, and language.
[–] jackfraser 0 points 1 point 1 point (+1|-0) ago
I enjoyed reading that, thanks
[–] CuckleberryFinn ago
Which is why it's a better habit to think of math as measurement rather than quantity.
[–] antiracistMetal 1 point 3 points 4 points (+4|-1) ago
It's better to think of mathematics as nonphysical/abstract rather than physical/concrete.
It is better to think of math as rational rather than empirical.
So many people conflate math and physics. Not that they think physics is mathematical; but they think math is empirical.
2+2=4 is always demonstrated with appeal to apples.
@peaceseeker @chirogonemd @niggaskissin @sarmegahhikkitha @persiangovernment