A Book of Truth: Categories of Things

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Once we have more than one thing, we must naturally group them?

One of the great things that humanity inherited, philosophically, from Aristotle[1] was the concept of the Category. This concept too, reduces the rate of change of human thought. Do you think it strange that after the finest flower of human thought bloomed it slowly withered, tended as it was by a stodgy Roman hand? I believe that the Aristotelian notion of the category hampered philosophical development along epistemological[2] lines. In the West, the Romans tended the garden of human thought year after long year and only produced clones. And even today, we are bound by the straitjacket of Categories. In my mind, the emergence of Set Theory[3] is a perfect example of the problem. Few people think outside the box.

It is paradoxical that as soon as we are outside the box, we begin constructing another. The irony of Schrödinger’s Cat[4] notwithstanding, we need the box to progress just as much as we need to get out of the box to progress. Our inability to resolve the micro and the macro differences of observed phenomena is like our inability to remain outside the Categorical nature of our mind. We’ve learned how to express our thoughts categorically, we see that it works, and we “need” it to keep going in our everyday life.

Some people have suggested that the Category is an accident of the need to use a verb, but this is shallow reasoning – the Category allows us to express a complete thought “verbally” that distinguishes one phenomena from another – but are not gestures, music and myths are every bit as “categorical” as a statement in logic?

Maybe we need fewer statements and more phrases. If we say All S or Some S, must we continue with is P? After all, that’s quite a mouthful even without the predicate. Poetically, we might be OK… All leaves, some acorns and the rain. I could tag on other phrases like of the night or red-throated songbird, and I could keep on painting images with broad, pallet knife stokes enriching the image. Then, even the hint of a verb would become superfluous to the poem – eventually it would even be a distraction. But can we do this with math?

The mind seems to willingly complete a metaphor in poetry, but will the mind stoop for logic or math? Let us say A + bx + 1, 1/x + y, and 2y-x. These phrases beg for completion. Alas, so abstract are the symbols of Logic and math that phrases don’t suffice. So maybe we have to construct a new logic or a new math where phrases do work.

But in many ways, the categorization of things is but one of the many ways in which humans abstract their world. In the next except abstraction is more closely examined.


 

[1] Aristotle was the first to use the term category in philosophy. He adapted "categoria" from the legal language, which meant "accusation," and used it to mean that which is asserted about something. Aristotle distinguished between several types of categories including kind, quality, quantity or size, relation, location, time or date, action, and undergoing.

[2] the study or a theory of the nature and grounds of knowledge especially with reference to its limits and validity

[3] Unlike many mathematical “discoveries” Set Theory was almost entirely the work of one individual, Georg Cantor. Resistance to Cantor’s idea was probably due (subconsciously) to a comfort level with the notion of Categories as defined by Aristotle and by the fact that before Cantor, orders of infinity did not exist. Infinite collections were considered 'the same size'. Hence, they fell into the same “category” no problem, right?

[4] In 1935 Schrodinger published an essay certain conceptual difficulties. A brief paragraph in this essay described the cat paradox.
One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The Psi function for the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts. It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a ``blurred model'' for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

We know that superposition of possible outcomes must exist simultaneously at a microscopic level because we can observe interference effects from these. We know (at least most of us know) that the cat in the box is dead, alive or dying and not in a smeared out state between the alternatives. When and how does the model of many microscopic possibilities resolve itself into a particular macroscopic state? When and how does the fog bank of microscopic possibilities transform itself to the blurred picture we have of a definite macroscopic state.

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