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fig.66—the hourglass is half half­-empty and half half-full

 Insofar as four­-billion-year retrospectives make life and choice strictly indiscernible, our (would­-be) scientific method takes a knee to ethics—but who’s? To defer indiscriminately to Laws of State and Church devalues both. For if we cannot tell customary grounds from theological, nor “inalienable rights” from the overthrown Divine Right of Kings, can “We” claim to enjoy any rights at all? In order to take our terms ‘on faith’ in copula (is, are, am), or to predicate anything of anything, we deem existential quantifiers (see below). But our drift from saying things about things to shunting formal symbols has done little to address the semantics consequent to primordial dichotomies such as All/None, Universal/Particular, and Affirmative/Negative.

 Aristotle, c.400BCE  —  “Some. . .men are not Mortal.”

 Boethius, c.500  —  “A certain. . .man is not Mortal.”

 Frege, c.1879  —  “At least one. . .man is not Mortal.”

 Russell, c.1910  —  “∃x. . .¬ (Mm)”      

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fig.67—pars sub toto: absolute relativity ≠ relative absolution

 To “be mortal” or “have mortality” is to not­-be, to have­-not; but to rephrase, say, “Socrates is not immortal” is merely a rhetorical tautology, to state that “Socrates is either mortal or not mortal” is a logical tautology, and to state that “Socrates is both mortal and not mortal” is a logical contradiction. So what? So—common parlance calls on the axes by analogy: as Universal is to particular, Absolute is to relative; as affirmative is to negative, additive is to subtractive. What—by way of folksy aphorism, figs.66­-67 show that the strange disjoint between the PA and PN follows from speaking of particular things and concepts in Universal terms. If we state “the glass is empty” of a water glass, “the glass is not full” follows per contravalence (non­-contradiction), “the glass contains at least some emptiness” per subalternation, etc.—but if we quip “the glass is either half­-empty or half-full” in the face of “that limit that is”, we press logical tautology into service as non­-logical truism: as particular creatures, we pose relative figures upon Absolute Grounds.

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