NUMBERS: POSITIONAL NAMES OF CONSTANT RELATIONS. MATH: THE SCIENCE OF MEASUREMENT OF RELATIONS BY THE USE OF CONSTANT RELATIONS. EXTENSIONS OF ORDINARY LANGUAGE
Numbers are names. All nouns are names. Numbers evolved as positional names.
We use many positional names: none, one, and some, short medium and tall; small, medium, and large; front, middle, and back; right center and left; port and starboard; daughter, mother, and grandmother;
Numbers differ from nouns only in that we produce them by positional naming. Whereas early positional names varied from one two and many, to base ten, or base twelve, or in the twenties, or sixties, each which increases the demand on the human mind; the decimal system of positional naming
Positional names are produced by a series of consistent operations. We call those series of consistent operations ‘functions’. By analogy we (unfortunately) called all such functions numbers: a convenient fiction.
Because of positional naming all positional names (numbers) are context independent, scale independent, constant relations, descriptively parsimonious and closed to interpretation.
So unlike other nouns (names), they are almost impossible to misinterpret by processes of conflation (adding information), and are impossible to further deflate (removing information).
Any other information we desire to add to the noun,( by which we mean name, positional name, number) must be provided by analogy to a context: application.
Numbers exist as positional names of constant relations. Those constant relations are scale independent, context dependent, informationally parsimonious, and nearly impossible to conflate with information that will allow for misinterpretation or deception.
As such, numbers allow us to perform DEDUCTIONS that other names, that lack constant relations, scale independence, context dependence, parsimony, immutability, and incorruptibility do not. Because deduction is possible wherever constant relations, parsimony, immutability, and incorruptibility are present.
As such, numbers serve as as a method of verbal reasoning within and beyond the limits of human imagination (cognition), short term memory, and ordinary reason.
Numbers then are simply a very clean set of nouns(positional names), verbs (operations and functions), including tests of positional relations (comparison operators) that allow us to describe, reason and discourse about that which is otherwise beyond our ordinary language, and mental capacity.
As such we distinguish language, reason, and logic from numbers and measurement, and deduction both artificially and practically. Since while they consist of the same processes, the language of numbers, measurements, and deductions is simply more precise than the language of ordinary language, reason, and logic, if for no other reason that it is nearly closed to ignorance, error, bias, wishful thinking, suggestion, obscurantism, deceit, and the fictionalism of superstition, pseudorationalsm, pseudoscience.
Unfortunately, since to humans, that which allows them to perform such ‘seeming miracles’ that are otherwise beyond comprehension, must be justified, we invented various fictionalisms – primarily idealisms, or what philosophers refer to as platonisms – (mythologies) to explain our actions. To attribute comprehension to that which we did not comprehend. To provide authority by general rule to that which we could only demonstrate through repeated application. So mathematics maintains much of it’s ‘magical language’ and philosophers persist this magical language under the pseudo-rational label of ‘idealism’ or ‘abstraction’. Which roughly translates to “I don’t understand”.
Perhaps more unfortunately, in the 19th century, with the addition of statistics and the application of mathematics to the inconstant relations of heuristic systems: particularly probability, fiat money, economics, finance, banking and commercial and tax accounting, this language no longer retains informational parsimony, and deducibility, and has instead evolved into a pseudoscience under which ignorance, error, bias, wishful thinking, suggestion, obscurantism and deceit are pervasive.
Math is a very simple thing. It’s just ordinary language with positional names that allow us to give names and describe transformations to, that which is otherwise beyond our ability to imagine and recall, and therefore describe or reason with.
Like everything else, if you make up stories of gods, demons, ghosts and monsters, or ‘abstractions’ or ‘ideals’ you can obscure the very simple causality that we seek to discover through science: the systematic attempt to remove error, bias, wishful thinking, suggestion, obscurantism, fictionalism, and deceit from our language of testimony about the world we perceive, cognate, remember, hypothesize within, act, advocate, negotiate, and cooperate within.
Numbers are positional names of context independent, scale independent, informationally parsimonious, constant relations and mathematics consists of the grammar of that language.
In other words, Math is an extension of ordinary language, ordinary reason, and ordinary science: the attempt by which we attempt to obtain information about our world within, above, and below human scale, by the use of rational and physical instrumentation, to eliminate ignorance, error, bias, and deceit from our descriptions, and as a consequence our language, and as a consequence our collective knowledge.
The Philosophy of Aristocracy
The Propertarian Institute