1
The first philosopher said everything is water. True as a metaphor in the sense that everything is continuous. Single things exist no more distinctly than waves. This troublesome objective existence of things became one of philosophy's themes.
My interest: not how things are unreal, but precisely why and how some minds invent them. Things are a product of a certain class of mind with a particular use as a presumption about the mind's reality. They aren't just lying unambiguously out in the universe for any mind to instantly and perfectly perceive. Then what precisely is the best method for a mind to believe or doubt a thing?
2
Here, by thing I don't mean a sound or a color, but a persistent object, e.g., a tree—what we imagine to cause sensations. The mere segmentation of a sense, 2 kHz vs. 1-10 kHz vs. 1-100 kHz, is less interesting. When a mind thinks of a thing, it expects only one of it to exist in any instant. In this sense, you think of yourself as a thing.
3
Humans tend to feel that things are real while types are inferior imaginary abstractions, that type or thing is a basic dichotomy of thought where every idea must refer to one or the other. The reverse is true.
4
What is a type? A set of attributes—red, heavy, tall—that may match no, one or many objects. Human is a type. Human is a subtype of mammal because the attributes of mammal are a subset of human's.
5
How do we know that an idea refers to a thing and not a type? There could be an identical you elsewhere. You would think there is only one thing in the Universe with all those attributes, except location, but now your thing is a type—but you don't know it. We can be certain that a type is a type but not that a thing is a thing. Since thing is uncertain, it mustn't be an axiom. We're left only with types. Beliefs in things are routinely wrong and must be revised. Beliefs in types are useless at worst.
6
What use are things? Things are used like types except for the presumption that only one match can exist at a time. What use is that assumption and where would we get it from? If you believed x was a thing, and you believed x was in front of you, then you can assume that x isn't anywhere else. This exclusivity needn't be limited to space. Imagine that a light is on. If you rightly think of the light as a thing, you can safely disbelieve that the same light is off.
Things are negative associations between types, expanding a mind's knowledge of its Universe and the mind's effects on it. These inferences seem trivial only because your mind constantly relies on them. They're so important that your mind could not leave them to your narrow consciousness. At bottom, such inferences can only be learned, which only a powerful mind can do. Our minds learn these associations from experience: When there was an x here there was never an x elsewhere.
7
A mind thinking of a mind can forget that what is a thing to itself may not be to the other. Though a thermostat can never believe in more than one temperature at a time, the temperature isn't a thing to it because the temperature sense opaquely enforces this exclusion. The thermostat's mind doesn't know that if it were to sense a new temperature it should disbelieve the old.
8
Given the rewards of belief in things, the presumption of them unsurprisingly appears in the languages invented by human minds. For most purposes, this simplification costs us nothing, but when a mind wants to define a mind in such a language, even if the language is, in principle, capable of defining anything, the bias of the language misleads.
Example: natural languages divide proper nouns from common nouns, definite from indefinite articles, nouns from adjectives. Few thinkers do serious work in these languages but their prejudices tend to survive translation.
9
Faith in the reality of things, encouraged by our minds, reinforced by our languages, breeds paradox. Things are a useful presumption, but nothing beyond absolute certainties can be at the bottom of any system that we hope to be universal. The ultimate assumption of things distinct from types influences natural language—English, German—math, logic, philosophy and computer programming. A paradox in a tool that you already know to be a useful fiction is unpleasant but inevitable. Paradoxes in the base are intolerable.
10
Mathematicians are fond of sets with elements, like types and things. What of a set that contains itself? Worse, what of the set of sets that don't contain themselves? Mathematicians side-stepped these problems by complicating the distinction. Deep minds must admit these statements because they're useful. We want statements that can refer to themselves and we want minds that can see nonsense and see through it.
In a mind, a set would only exist so far as the mind applied the set's type to matching forms. In the case of a paradoxical set that a mind can't even build, instead of complicating axioms, make a simple robust mind that, if it can't see the pattern, can at least notice and demote the looping process, favoring parallel acts of thought that are reaching ends.
Math is a means for minds. Systems are only sets of blocks for building models analogous to a mind's universe. Loose systems, such as types and things, might offend our taste because their syntax allows odd statements, but a language maker must design for more than isolated aesthetics, seeing the context, the class of mind that will apply them.
11
Instead of imagining a type as a collection of existing things, see each as an intersection of unique experiences. Every featherless biped you saw seemed mortal, so the type men would include mortality, though not blue eyes. A type isn't primarily defined by its members but by the test of membership. The test defines the type. You can know a type's test, but you can't know all its members in the Universe. Its members vary with changing experience.
12
Think of a set as a form built by matching one form to other forms. If a mind believes in an inference from one form to a similar form, the mind maker simply engineers it to not follow that simple loop more than once, defending the mind from many paradoxes.
13
First-order logic divides things from predicates. Statements about predicates—red is a color—become impossible without resorting to tricks, such as reification, or more complex higher-order logics. If a mind wants to make statements about predicates, it simply shouldn't use a system that assumes predicates aren't things.
Is a vs. is. If you eliminate things, then saying the sky is blue is similar to saying blue is a color. Blue is part of a generalization of various experienced skies. Color is general to various blues. Blue is a subtype of color. Sky is a subcategory of blue.
14
Object-orientation dominates computer programming. Classes and instances instead of types and things. Programmers get away with this because computers mechanize our conscious level of thought. The objects in a software system have strong objective existences using unique identification numbers, etc. The system fails and misleads when the programmer must handle real ambiguous objects.
15
Axioms are to systems as rules are to a game. I think it unwise to afford an axiom to the idea of things when a mind's universe may contain none or when belief in them may be useless. Cutting an axiom, an ultimate distinction, such as things, solves puzzles and simplifies deep understanding, though for convenience the use of that distinction must be rebuilt above the foundation of a mind.
16
Any system—mind, language, physics, philosophy—advances by cutting axioms. Example: code is data. The remaining axioms represent deeper patterns, giving greater leverage.
In physics, Newton invented a single model for the whole Universe by removing the distinction between Earthly and Heavenly physics. In a computer program, cut an axiom to ease improving speed and reliability. In any case, fewer axioms with the same power are likely to be more expressive: simpler parts can form more combinations.
Comments