Source: Facebook

—“I have been wanting to ask more about mathematical platonism, is this an example of such? If so could make an example of him so I can learn?”—

Yes. Although when we talk about mathematics, precisely because mathematics is so trivially simple, the use of “pseudoscientific prose” does not necessarily impact one’s ability to use it. So it’s a lot like ancient metallurgy, astrology or aristotelian physics.

And so just as metalsmiths talked about spirits, astrologers talked about gods and demigods, theologians talked about god and heaven, mathematicians still make use of archaic ‘fictionalist’ (platonic) prose as did astrologers and theologians.

But that does not mean that while the categories relations and values that they discuss in mathematics cannot be restated in scientific “true” operational prose. It’s just that when you do so the triviality of mathematics and the pseudoscientific content of the prose is obvious.

Lets start with defining a number. A number consists of a positional name. The name of a position in an order. Positional Naming using positional numbers assisted us in creating positional names beyond our ability to remember names, and beyond our ability to conceive or compare.

All mathematical operations consist of addition or subtraction of positions. But because the only property positional names possess is position, then the positional names (numbers) all constitute ratios to (scales of) the reference.

But since anything we refer to that is “countable’ (and some references are not directly countable – water and air, must be divided in to volumetric units for example before we can count them), can be measured using the ratios provided by positional names …

… we gain scale and reference independence, or rather ‘the ability to construct general rules of arbitrary precision” using nothing but these positional names. Positional names are not like words, open to conflation or misinterpretation.They have only one property: position…

… And because they have only one property of position, they have one unavoidable deductive property: ratio to the referent. … Now, some operations yield another positional name (a ratio), some yield a partial name (a fraction), and some yield an indivisible ratio ….

… the position of which cannot be named by positional naming. This means that while some operations (changes by addition or subtraction) have no positional name, and as such can only be represented by a function. Ergo, there exists no square root of two, only the function.

So mathematicians have spent a very long time inventing very creative means by which to conflate number (positional name produced by the operation of positional naming) with the categories of results of the operations of addition and subtraction: …

… divisible(positional name/number) = entities, divisible to divisible ratio (fraction) = measurements, and divisible to indivisible ratio (function) = general rules requiring context to provide limits, and directional spatial (and all that results from directions), and …

… finally to physics representing forces of n-dimensions, and lastly to semantic relations, expressing only relative weights of relations. Which is where math breaks down and we must turn to operations (semantics, economics, computing.) where categories are inconstant.

There exist only positional names (zero dimensions). We can add a dimension and imagine a line (measurement). We can add direction and add -measurement. We can ad another dimension and create areas. We can add another dimension and create spaces. We can add another dimension …

and create time. We can add another dimension and create competition (forces). We can add n-dimensions and create causalities (algebraic geometry). We can add obseve the consequences of the externalities produced by algebraic patterns (lie groups), and then repeat the cycle…

with lie groups as the next primitive category (referent), and repeat the entire process all over again. Which is how we categorize subatomic(wave), particle(object), chemistry, biology, sentience. or physics engineering, programming, language. The same hierarchical process.

So mathematics is very simple. It’s consists of the use of positional names to create general rules of arbitrary precision using some number of dimensions of causality. In other words, it’s the discipline of measurement. It is highly successful in constant relations and less …

… so with inconstant relations. And mathematicians are very little different from medieval monks inventing nonsense language to justify a very simple moral code by which to extract rents from the population in return for training them to extend kinship trust to non-kin.

Math is, like law, one of those disciplines that is terribly simple and it’s access limited to a priesthood willing to make use of the priestly vocabulary as a signal of conformity. Unfortunately mathematical pseudoscience in economics has been possible because of platonism.

So in closing, think of mathematical terminology like a language of theology referencing a heaven that doesn’t exist. That does not however stop the monks from growing food, fermenting beer, performing clerical services, and generally pretending that they have sacred knowledge.

Why? Because measuring stuff is actually pretty simple. All you need to do is know the dimensions and create a means of measurement. Everything else is just a byproduct of the simplicity of a positional names as an infungible category by which all is somehow commensurable.