Mastodawn

@BestGirlGrace Quantity, together with all the emergent properties thereof, is a natural phenomenon and is therefore discovered. Tools operating on those properties, such as notation and terminology, are arbitrary attempts to describe those phenomena and are therefore invented.

Is mathematics the study of quantity, or is it the study of tools for characterizing quantity? A student of anything learns both the tools themselves and that which the tools manipulate.

Quantity is most decidedly not a natural phenomenon.

This is because quantity is a product of Type.
Type, e.g. "a horse" is a human invention along the lines of metaphor.

In reality, every four-legged hoof-haver is a unique being, and certainly not some "exemplar" of some "type".

Without Types, there is nothing to count. Everything is unique. 1 is the only number, and that too is superfluous.

@BestGirlGrace

fool

@androcat Quantity is evident elsewhere than in what our models abstractly deem countable. Distance, for instance. To the extent that this one and that other one are not the same one (and if we can meaningflly speak of uniqueness, then we can on that same basis also speak of distinction), then some distance separates them, and that distance has quantity.

(@BestGirlGrace if this continues should we refrain from tagging you?)

Vx. Princess "size_t queen" Grace

2d ago

@fool @androcat I'm going to bed either way, I don't mind watching.

Again, the same applies. These things are made countable through mental metaphors.

Ultimately every point of our worldly topology is unique. They only turn into "distances" by metaphorically asserting that "distance" even makes sense.

You'll see in ancient texts that the focus was on the way, the path, the road.

And similarly for time. In ancient speech we were using ordinals for time, because each moment was unique, and made sense only in context.
And even that ordinality was an abstraction performed solely to make the unique into something ennumerable.

When I say the uncountability is fundamental, this is historical fact. We didn't always have the technology required for enumerating these things == arithmetic was invented, and its invention required deep changes in how we speak of and conceptualize things.

@BestGirlGrace

@androcat @BestGirlGrace I didn't know Zeno of Elea was on this web site

You can literally track how we invented this stuff by how language changed.

Starting from Types will end up in absurdity, because all of a sudden the specific fish you caught is interchangeable with the one that got away.

That isn't how the world works.

But it is how the game we invented works.

(All logics are essentially games. Logicians understand that, and do not take them overly seriously. After all, almost every logic will contradict almost every other logic)

To put it in a different and more obvious way:

Types are subtractive categories. Actual entities have location, identity and all manner of uniquely identifying traits.

These are subtracted to make them fit the Type.
This loss of information is unrecoverable.

In other words, the Type is most decidedly Not Real.

Even if it means you have to accept that "Horses do not exist".

Countables do not exist.

But we can make games that have countables, and we can sometimes make use of such games for organizing how we think about reality, because sometimes the individuality of entities, while undeniable, isn't relevant to what we are doing at the time.

But only a fool would assert that the abstraction is real because it has utility.

Utility is perpendicular to truth.

@BestGirlGrace

@androcat @BestGirlGrace If you're saying that entities are real and that they are identifiable, then makes them cardinal. You haven't asserted the nonexistence of types at all - rather, you're asserting that there is exactly one type, "entity." And because there's still a type, that brings with it countability.

Go back and re-read everything until you understand it. It's in there.

I have absolutely asserted the irreality of types.

And I have explained why "but types have immense utility" doesn't mean "types are real".

We literally have this entire development as historical fact.

Invention of math == historical fact.

Your viewpoint only makes sense in an ahistorical context, where you assume math as fundamental.

It smacks of mathematical platonism, a much better candidate for Zeno-like folly.

@androcat Leave my argument out of this. I'm talking about your argument. You're the one who showed up suddenly.

You assert that countability is an attribute of types, and types are an element of a model rather than of reality.

However, you also assert the reality of entities; that entities are not a model, but the true reality which models attempt to describe. (Seems to me like it's also a model, but I'll play along.)

You have not shown why countability is not an attribute of entities.