Logic / Unit 3 Logic 091 worked example, 60 to 90 seconds
Translation Walkthrough
The idea
Translating into standard form means asking what the original sentence asserts about which class, then rewriting it with an explicit quantifier, subject term, copula, and predicate term.
In practice
Five sentences. First: only members may vote. The word only marks the term after it as the predicate of the standard form, so this becomes all voters are members. Second: Socrates is mortal. A singular statement treats the individual as a class of one — all persons identical to Socrates are mortal beings. Third: dogs bark. No quantifier appears and the claim is general, so all dogs are barkers. Fourth: he always complains. The sentence is about times, so the classes are times — all times he speaks are times he complains. Fifth: the only exit is the north door. The only reverses what only does, giving all exits are north doors.
Where people slip
Only and the only look like the same instruction and place the terms in opposite positions. Only S are P becomes all P are S, while the only S are P becomes all S are P. Translate one as the other and the claim inverts, after which mood, figure, and the Venn test all run faithfully on a statement nobody made.
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