Disjunction is in a privative opposition to conjunction, in which it is the marked member. Disjunction is a syntagmatic relation between propositions which are also in a paradigmatic relation, viz. in opposition.1 These propositions are presented as paradigmatic alternatives, none of them is asserted, it is left open which one of them is real. Disjunction therefore presupposes the notion of non-reality of propositions (s. Mauri 2008).
The primary subdivision for disjunction is between
- an alternative that matters; choice relevant and required: E1
- and an alternative that does not matter; choice irrelevant and not required: E2.
| . | You will give me your money or you will loose your life. |
| .b. | In the afternoons, we used to play tennis or go to the beach. |
Diagnostic paraphrases in English are:
- for a relevant choice: either
porq, - for an irrelevant choice: be it
p, be itq.
The disjunctive relation of relevant choice between p and q may be coded by a conditional construction ‘if not p, q’. Thus, E1' is a way of coding the thought of E1.
| '. | If you do not give me your money, you will loose your life. |
While there is, in , a causal relation between p and q that may seem to justify its conditional formulation, this is not a prerequisite for the paradigmatic relation between disjunction and conditional. It also obtains in .
| . | This is either an apple or a pear. |
| '. | If this is not an apple, (then) it is a pear. |
Other subdivisions of disjunction are analogous to those of conjunction.
1 In propositional calculus, the oppositive relation is irrelevant for the logical junctors of disjunction (∨) and exclusion (/).