How is counting possible?


Preserving passing in time through clever mechanics

Kant: We transcend time by making it objective, by building a model of time, in time, such that the model presents the progression of time with the passing of time. The act of building here can be any action directed at the model that realizes the conceptual process of adding, aka aggregating, aka throwing another rock onto the pile and preserving the pile into the next frame in concept (since the pile as a unity is a concept, and the pile as stuff passes away). Preservation is the condition of addition. Otherwise the receptacle would empty-out due to passing.

A concept is a symbol that distinguishes a rule for constructing an image. In the case of counting, the function of the rule is to aggregate time by counting. To accomplish this, the rule cannot pass away. The virtue of the rule is that it does not continually pass away (unlike images, sense contents, and physical matter). In this regard it is like a ghost.

How can a rule transcend time in this way if its material basis (a living brain) is continually passing? The rule that preserves “meaning”—what preserves it? The inertia of physical form plus mechanical organization around an inner clock (periodic movement attached to a counter).

The interesting thing about making a model of time in time is that the model (its configuration) is continually passing away. A material thing can be a unit only if it is identical over time, which nothing material is. As soon as I say “1” it’s gone—how can I add to it? Here is Kant’s theory.

My goal is to count “1, 2, 3, 4, …”—that is, my goal is to posit (and recognize) a pile of units that is both preserved and ever-growing. Each posit is minimally a marking or a grunting. The grunt or mark is a posited material that signals the positing of a unit. To cognize the number 4, I just follow the procedure “4,” which says

Grunt—and re-grunt the previous series of grunts so that you think of them as a set.

In other words, treat the rule for making GGGG as a rule that makes {GGGG}.

In other words, treat the rule as a unity over.

The magical ingredient which makes counting (aggregating) possible is our ability to mean again. This is what makes math, addition, and number possible. It is also what makes synthesis of external difference—so-called separation, spatial and temporal—possible.

Saying again invents the homogeneous. The rule again is the schema, Kant would say, of qualitative homogeneity. The homogeneous is what fills in the meaning of concepts like “empty space” or “empty time.” How can you add empty to empty? What is the stuff that is both empty and additive? (For if the unit was completely empty, there would be nothing to add.) This is the special nature of pure synthesis.

Theory of number

Grunting like this does not add:

+G [passes away]

+G [passes away]

+G [passes away]

+G [passes away]

Grunting like this also does not add:

+G

+G, +G

+G, +G, +G

+G, +G, +G, +G

In this model, you see that the additive moment is built into the content that is posited. The posited contains the transitive nature of positing in its meaning. So instead of G I have written +G, because the grunt is an act that is put into a domain. There must be receiving for putting. It is on the receiving end that the addition-enabling form subsists. Positing is by nature additive. Every positing into now is additive to some receptacle that presents objectivity. So by +G I mean a grunting that does add.

“[ ]” means preserved ghost. What you “add” to a posit is a pre-posit. Or: adding does not have the form posit, posit—but the form [ ] + posit. Or: the + is only possible if the preexisting again-posit is empty.

So here is how grunting does add:

+G

[+G] +G

[G+G]+G

[[G+G]+G]+G

When I say again while I'm already looking at a posit, then I get addition. Grunt at emptiness, and you get unity. Grunt again at the grunt you just put there. Because you recognize “I made this already-there grunt,” grunting again becomes possible. The identity of coming from the same act they share is the homogeneity that permits the addition.