*Mathematics*

*Defined as**'*

__Ideo____metry__*'*--

*The**Deductive***,**.

*Formal**-**Logical**Moment**of**Its**Meaning*
Dear Readers,

In the definition, given below,
we do

**define**__not__**as ‘ideometry...’, only in some***mathematics*__non__*-*, that excludes the usual account of**standard sense****as “axioms” and “postulates” finding, as “rules of inference” and “primitives” deciding, and as “theorems proving”, from the***mathematics***as the***former***of that proving activity.***foundations*
The ‘ideometry’, the ‘measurement of the ideas’, that are
the “primitives”, the “rules of inference”, and the “axiom

__s__”**“postulate***/*__s__” of a [e.g., of a candidate, or in-development]*axiom*__s__*-*of**system****, e.g., of a***mathematics**newly**-***developing****, or***branch***, of***application***, is accomplished -- using the word “measured” in the expanded,***mathematics***F**.**.**__E__**. sense -- by drawing out their [conjoint]**__D__**,***deductive**formal**-***logical****, and by the**__consequences__**of those**__usefulness__**--**__consequences__**in the form of**__consequences__**,***theorems***, and***lemmas***;***corollaries***even if only in terms of the cognitive-esthetic pleasure of the mathematician**__usefulness__**author in the***/***that (s)he has***system***, but, hopefully,***created**also*,**in the less narcissistic sense of the**__usefulness__**and***scientific***,***technological*__h__*uman**-***societal self**-**reproductive self**-**force***contributions**/benefits**/utility***of that**__consequences__*axiom*__s__*-*, e.g., due to the**system***capability*of*its***to***equations**model**/predict**-*of**for****salient**aspects*nature**/*__h__*uman***.***experience*
In the

*real***of**__h__*uman praxis***, as opposed to its***mathematics***,***mystified myths and fables***and**

*axioms***do**

*postulates*

__not__**, or**

*descend**“*, as

**fall from the heavens**”*“*, from above, from some

**immaculate conceptions**”*“*.

**transcendental realm**”

__Candidate__**are tried-out, to see whether or not, and to what extent, their conjoint implications achieve the**

*axioms***and**

*goals***to**

*motives***which the**

*fulfill*

*axiom*__s__*-*is to be

**system****in the first place.**

*created***,**

*Axioms***,**

*postulates***, and**

*primitives***, are**

*rules of inference***themselves accessible by**

__not__**, as Plato pointed out, so long ago, but are the**

*deductive logic***«**

*logical***» --**

*arché***by**

*derived***, according to Plato -- from which**

__dialectical__means

*all***is to be**

__else__**.**

*deduced*
In the

**of the***process***of a***development**new**axiomatic***, the implications of the***system***«**__candidate__**», in effect,***arché***, and***feed back upon***-- refl***act back upon***ct**__e__**refl***/***x upon, and refl**__e__**x upon -- those**__u__**, via the**__candidates__**,***active***of the***living mediation*__h__*uman***(***agent***) of this***s***.***development*
This

**results in***process***to those***changes***«**__candidate__**» when their implications fall short of their desiderata, and, thus,***arché**also***the***change**deductive***, in an**__consequences__**, that***iterative process***as long as, e.g.,***continues**the***of**__h__*uman agents***see***mathematics***for, and***need***for, the***hope***of the***improvement**axiom*__s__*-*, relative to its desiderata.**system**
Thus, the very

**of a***development***,***mathematical***is a***axiomatic system**self**-*, and a**refl**__e__xive function*self**-*, conducted by**refl**__u__xive function__h__*uman***, and is, in that sense,***mathematicians**also*a*‘‘‘*-- a__non__linear**process**’’’**of ‘ideometry’, mediated by***process***.***formal deduction*
Regards,

Miguel

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