Compound assertibles
More information Logical connectives, Name ...
| Logical connectives | Logical connectives |
|---|---|
| Name | Example |
| Conditional | if it is day, it is light |
| Conjunction | it is day and light |
| Disjunction | either it is day or night |
| Pseudo-conditional | since it is day, it is light |
| Causal | because it is day, it is light |
| Comparative | more likely it is day than night |
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Compound assertibles can be built up from simple ones through the use of logical connectives, which examine choice and consequence such as "if ... then", "either ... or", and "not both".[15][26] Chrysippus seems to have been responsible for introducing the three main types of connectives: the conditional (if), conjunctive (and), and disjunctive (or).[27] A typical conditional takes the form of "if p then q";[28] whereas a conjunction takes the form of "both p and q";[28] and a disjunction takes the form of "either p or q".[29] The or they used is exclusive, unlike the inclusive or generally used in modern formal logic.[30] These connectives are combined with the use of not for negation.[31] Thus the conditional can take the following four forms:[32] 1) "If p, then q" 2) "If not p, then q" 3) "If p, then not q" 4) "If not p, then not q." Later Stoics added more connectives: the pseudo-conditional took the form of "since p then q"; and the causal assertible took the form of "because p then q".[a] There was also a comparative (or dissertive): "more/less (likely) p than q".[33]