Object Theory - Abbreviations

Abbreviations

The object ■n□ demonstrates the use of "abbreviation", a way to simplify the denoting of objects, and consequently discussions about them, once they have been created "officially". Done correctly the definition would proceed as follows:

■□ ≡ ■1□, ■■□ ≡ ■2□, ■■■□ ≡ ■3□, etc, where the notions of ≡ ("defined as") and "number" are presupposed to be understood intuitively in the metatheory.

Kurt Godel 1931 virtually constructed the entire proof of his incompleteness theorems (actually he proved Theorem IV and sketched a proof of Theorem XI) by use of this tactic, proceeding from his axioms using substitution, concatenation and deduction of modus ponens to produce a collection of 45 "definitions" (derivations or theorems more accurately) from the axioms.

A more familiar tactic is perhaps the design of subroutines that are given names, e.g. in Excel the subroutine " =INT(A1)" that returns to the cell where it is typed (e.g. cell B1) the integer it finds in cell A1.