Complex arguments
Chrysippus listed five basic argument forms, called indemonstrables,[43][c] which all other arguments are reducible to:[44]
More information Indemonstrable arguments, Name[d] ...
| Indemonstrable arguments | Indemonstrable arguments | Indemonstrable arguments |
|---|---|---|
| Name[d] | Description | Example |
| Modus ponens | If p, then q. p. Therefore, q. | If it is day, it is light. It is day. Therefore, it is light. |
| Modus tollens | If p, then q. Not q. Therefore, not p. | If it is day, it is light. It is not light. Therefore, it is not day. |
| Modus ponendo tollens | Not both p and q. p. Therefore, not q. | It is not both day and night. It is day. Therefore, it is not night. |
| Strong modus tollendo ponens | Either p or q. Not p. Therefore, q. | It is either day or night. It is not day. Therefore, it is night. |
| Strong modus ponendo tollens | Either p or q. p. Therefore, not q. | It is either day or night. It is day. Therefore, it is not night. |
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There can be many variations of these five indemonstrable arguments.[45] For example the assertibles in the premises can be more complex, and the following syllogism is a valid example of the second indemonstrable (modus tollens):[32] "if both p and q, then r; not r; therefore not: both p and q" Similarly one can incorporate negation into these arguments.[32] A valid example of the fourth indemonstrable (strong modus tollendo ponens or exclusive disjunctive syllogism) is:[46] "either [not p] or q; not [not p]; therefore q" which, incorporating the principle of double negation, is equivalent to:[46] "either [not p] or q; p; therefore q."