Three worlds for the NeoKantians, under the sky:

In which I attempt to clean up some hopelessly tangled terms.

We humans have three distinct worlds that we track beliefs about.

World 0) There is (we must assume) the objective world, which we can't access, but which we (must) presume forms the causal basis for our sensory input.

World 1) There is our subjective world, which we form inductively from our sensory input. It is not "mere opinion", but rather each person's entire world. It is the polar opposite of solipsism to acknowledge that we are confined to this level, we do not create this world on a whim, nor with any kind of freedom: It is our map of how the world seems to behave. There are as many World 1s as there are subjects.

World 2) There is the social (quasi-real) world, in which we negotiate with other subjects all manner of things, which become very real indeed, but not in the ontological sense. Morality, Truth, Math, etc. they are all born at this level, NOT at the objective level, hence there can never be objective morality or objective truth. These are, however, concepts that largely function as if real, and which we are forced to acknowledge as real because we are social beings. The only part of these concepts that can be said to be objectively existing is the conditions in whatever parts of the objective world make up the basis for what we (in world 2 and 3) call our brains.

As can be imagined, a lot of what people think is objectively true is just World2 stuff. The English Language, for instance, only really exists in the World1 instantiations, the idiolects. But abstracting from and negotiating with other speakers (that's how we learn the language in the first place), we project an "underlying" English Language. That, however is the polar opposite of objective - it's an abstraction, and hence it is non-real.

Threeness

There's something strange about numerals.

Think about it for a moment: What is the threeness of three apples? Where is it located?

How about the threeness of four apples? Did it stop existing? Or is it there still, as a three-plus-one-ness? Is there then a three-minus-two-ness of one apple?

Part of the strangeness is linguistic.

"Three men" involves a noun and an adjective. The adjective is singular, but forces the noun to be plural, because the noun phrase as a whole denotes a plural reference. 

This is not always the case. In Finnish, a numeral adjective doesn't force a plural. In Finnish the numeral forces the partitive singular. What is partitive? Well, English has a partitive plural in the sentence "She is one of our best lawyers", where "of our best lawyers" is the partitive - it denotes an entity (our lawyers) from which a part has been taken away (making "of" the partitive clitic marker of English). In Finnish this would simply be "Hän on parhaimpia lakimiehiämme" (she/he is best.of.plur lawyers.of.ours). The finnish way to say "Three apples" is "kolme omenaa" - which is "three apple.of", no plural required. 

So, Finland uses a metaphor where there is a conceptual (almost platonic) "apple" from which can be carved any number of instantiations.
There are also languages where a threeness is expressed with a verb. Imagine if you would say "The artist was threeing at the fair" and mean "there were three artists at the fair".

Threeness in categories and types

Returning a bit: What is a plural reference? It's a number of entities/objects that have been deprived of their dissimilarities. Take "three men". It's not Bob and Joe and Allen anymore.
No, it's "three men", no identity to any of them.

This is how we construct types. We take stuff and throw it together in a big pile according to a single parameter (in this case HAS_A_PENIS), then we abstract from that piling some kind of average non-exemplar (in this case MAN).

It's a non-exemplar because it's not a real entity. There isn't a man that coincides with MAN. We make a vector out of real entities, dropping all their real properties that don't fit our reason for grouping them.
And because we lump Bob and Joe and Allen together, violate their identities by insisting on using only the vector, we are able to speak of their threeness. This is important. Threeness is not a property of Bob, nor of Joe, nor of Allen. It is a property of the annihilation of their features.

Incidentally, this is part of a weird sexualization of our society. Why are we even referencing people's innies or outies in contexts where these body parts aren't relevant to anything? We can't easily even talk about people without gendering them. What if people don't like being seen as a disembodied penis or vagina? What if they're of the belief that there's more to them than their coincidental reproductive organs? Too bad, huh?

Imagine; we live in a world where one can hack off people's faces and reduce them to conceptual non-particulars... simply by assigning them a type and putting a number in front of it.
It wasn't always like that. When that linguistic ability evolved, it most likely caused a revolution in the society it was invented in. It is the basis of armies and economy, after all. Of bulk and grossness.

The only linguistic calamity that can rival it is likely the time when people started doing the same thing to units of time. From being distinct places in time, of which were only used ordinal numbers (on the sixth hour of the fourteenth day), they became a commodity,  to be bought and sold like animal carcasses at the market. Three days. Think of the first day, the second day and the third day. Then chop off their faces and limbs and drop them on the counter. Three carcasses of time. Their order no longer discernible.

Few metaphors are more intensely violent and violating than the ones which allow us to use numbers.

#threeness