Now, it is against this exclusive disjunction, of either a temporal or eternal-cyclic linearity, that I would posit the positive value of multiple and divergent or incompossible lines of time.
One way of thinking beyond this exclusive disjunction, where the future is merely our already existing catastrophic present or a nostalgically orientalist conception of a timeless indigenous other is by way of a time that is multilinear.
It is just this 'as if' strategy that I wish to contest by refusing the exclusive disjunction of nonlinear temporalities.
A B A [disjunction] B (1,0,0) (1,0,0) (1,0,0) (1,0,0) (0,0,1) (1,0,1) (0,0,1) (0,1,0) (0,1,1) (0,0,1) (1,0,0) (1,0,1) (0,1,0) (0,0,1) (0,1,1) (0,1,0) (0,1,0) (0,1,0) 2.6 Strong or exclusive disjunction:
Exclusive disjunction the fuzzy propositions (A) and (B) is the following:
Indeed, a rigorous interpretation of the exclusive disjunction does not allow assuming that, when it has, for example, three disjuncts, such a disjunction is true only if one, and only one, of their disjuncts is true.
Although at a certain moment the Stoics could accept an inclusive disjunction, the sources are very clear in this regard and show us that the basic disjunction in the Stoicism was the exclusive disjunction. As indicated by O'Toole and Jennings, (3) such sources include passages written by authors such as Cicero, (4) Gellius, (5) Galen, (6) Sextus Empiricus, (7) and Diogenes Laertius.
We mean by "o": conjunction, disjunction, exclusive disjunction
, Sheffer's stroke, and equivalence.
Disjunction permits the expression of a choice between two or more members of a set of possibilities (as in do you want the fish or the meat dinner?) or the expression of a set of options (as in I usually have coffee or tea in the mornings); there are some more specific distinctions which might be made, as in exclusive disjunction (one disjunct or the other, but not both) and inclusive disjunction (one or both disjuncts), etc.
Three types of distinctions are made, between 1) a structure in which the speaker asks for information, the listener is not being asked to make a choice between two items but rather to inform the speaker, and the effect is similar to exclusive disjunction; 2) a structure which requires a choice of the listener, which may be either choice-based or exclusive disjunction; and 3) a syntactically disjunctive structure which has non-disjunctive semantics, often similar to a polar question or an inclusive disjunction.
In short, we are in effect, in this intensional setting, taking for granted the combined principles of excluded middle and contradiction, which, with the help of a symbol for exclusive disjunction that is the inverse of the usual symbol for inclusive disjunction, we may express by the formula ~A [conjunction] A', in which A stands for any proposition.(7) The rela tion between~p LI> q' and ~A [conjunction] A' is worth some comment.
As these combinations are mutually exclusive conjunctions, let us join them by our symbol for exclusive disjunction, ~[conjunction]]'.