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“We are induced to postulate that being, at least for us, sets limits because we live, in the horizon of the entities and [...] of that limit that is being­-for-death. Either we do not talk of being because its presence overwhelms us, or, as soon as we talk of it, among the first statements that we are accustomed to considering a model of all certain premises, we find ‘All men are mortal’.”—Eco 1997

 We follow the four elementary forms of assertion from the two oppositions (of Universal/Particular and Affirmative/Negative) through Aristotle’s LSO, both as a Square (above) and as a Plot (over). Thus, we find that all of our declarative statements as to things or people are still bound by this antiquated fourfold, for to refer to any (particular) thing is to indicate what it is by which (universal) qualities it does (affirmative) or does not (negative) present to the senses. We see the four types of statement stand in such relation to one another as to make all six entailments seem self­-evident; but if one statement is given as true, can we deduce truth values for the other three? Deduction from UA and UN statements is trivial: IF “All men are mortal” is true THEN “No men are mortal” is false, etc.

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—alas, the PA and PN are problematic: IF “Some men are mortal” is true THEN “Some men are not mortal” could be true or false; who knows? not even Bertrand Russell. In taking Aristotle’s syllogism as the elementary form for logical deduction, the textbook example imputes strength and weakness to all propositional logics:


 Major premise  —  “All men [subject] are Mortal [predicate].”

 Minor premise  —  “Socrates [subject] is a Man [predicate].”

 Conclusion  —  “Socrates [subject] is Mortal [predicate].”


How can we verify the Major premise? As Wittgenstein 1921 attests, “It is quite impossible for a proposition to state that it itself is true.”   The bind is doubled by the Particularity of every thing that ‘exists’—that is, both terms, subject (“men”) and Predicate (“Mortal”), being ‘Universal categories’ necessarily presuppose existential axioms: “Men exist” and “Mortality exists.” As a hypostasis of ‘Death,’ the category of ‘Mortality’ lacks ipso facto determinability; in contrariwise consequence, ‘Life’ is itself categorically non­-predicable.

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