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Disjunctive Syllogisms
- either ... or ... statements are disjunctions
- The either really does not add anything most of the time
- Sometimes, however, either indicates the use of the exclusive sense of the word or.
- For example, in the following statement is there anything that prevents both from being the case?
| Either the sun is shining or the birds are singing |
- Compare that with the following statement.
| Either the sun is shining or the sun is not shining |
- The problem in logic is that you have to know whether one statement's truth interferes with another's. In order to avoid this, we will assume that they do not interfere. We will always use the inclusive sense of the word or.
- So, for a statement such as
| Either the sun is shining or the birds are singing |
We will simply say that
Where
| SS may be the case |
| BS may be the case |
| SS and BS may both be the case |
| But between SS and BS at least one must be the case |
- A syllogism that contains a disjunction is a disjunctive syllogism
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