Equality, Identity, and Definition

We often use the phrase “is identified as” to mean “is defined as.”

In trigonometry, we study trigonometric identities, which are true for every value of the variables on both sides of the equation.  Thus, the trigonometric identities, following the simple definitions, also constitute lengthier trigonometric definitions.

Let’s look at three equations:

P’Q’ = p’a’Q’Basic outlays becoming basic incomes + p”a”Q””Costs” of Basic R&M in the surplus circuit[1]                       (1)

Π”K” = π”α”Κ”Pure surplus outlays  + π”α”Κ”surplus outlays for surplus R&M                        (2)

kn[f’n(t-a)-Bn] = f”n-1(t) – An-1[2]         (3)

In equations (1) and (2) we may replace the equals sign with the phrase is defined as or is identified as. 

There is a sense in which one may speak of the fraction of basic outlay that moves to basic income as the “costs” of basic production. … the greater the fraction that basic income is of total income (or total outlay), the less the remainder which constitutes the aggregate possibility of profit.  But what limits profit may be termed costs.  Hence we propose ….to speak of c’O’ and c”O” as costs of production, having warned the reader that the costs in question are aggregate and functional costs…. [CWL 15 156-57]

The equations relate certain functional flows such that the relations define the functionings and the functionings define the relations.  The whole structure is purely relational.  The equations constitute the definitions of certain functional flows called macroeconomic costs.  The formulations constitute definitions in mathematical forms representing faithfully the scientific macroeconomic relations.

Equation (3) defines or identifies a) a lag, and b) the accelerator and accelerated relations of constituent functional flows.

Scientific macroeconomics is the verification of that understanding which explainsthe concrete economic process by terms in their relations to one another.  The whole structure is purely relational.

 

 

 

[1]CWL 3, 156-58

[2]CWL 15, 37