Much of what people do is embedded in their routine daily practices and is often not obvious--so why do we teach that the specification is formalizable
* Finally, many of the most important requirements of real programs are simply not formalizable
. I would hate to try to come up with a formal specification for the "playability" of a video game, or the probable hostility of a radar echo.
That a proof is formalizable
, that the formal proofs have the structural properties that they do, explains in part why proofs are convincing to mathematicians.
For example, in 1936 Gerhardt Gentzen gave a consistency proof for elementary arithmetic using extremely powerful nonelementary methods (as required by Godel's Incompleteness theorem), that is, methods not formalizable
in arithmetic itself involving transfinite induction.
?, 11 LAW, PROBABILITY & RISK 225, 235 (2012)
Writing of text-message-based public art installations as works that are "neither formalizable
as 'electronic literature' nor reducible to a singular medium," Rita Raley argues that these works imagine "expanded textual practices that are not-electronic literature, not-print, not-codex, not-mobile messaging, not-game, not-conversation, not-algorithmic instructions, not-data mining, not-collaborative content creation, but that which is situated in the interstitial field" (2013, 8).
In this scenario, the observer asks a sequence of questions of nature, formalizable
along the lines of "is the pointer between x and x+n?" Nature's reply is "yes" for the first 19 questions, occasioning a change in the density matrix corresponding to the wave function of the universe.