Source: p 256, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley
Many propositions that involve the words “only,” “none but,” “none except,” and “no . . . except” are exclusive propositions. Efforts to translate them into categorical propositions often lead to confusing the subject term with the predicate term. To avoid such confusion keep in mind that language following “only,” “none but,” “none except,” and “no . . . except” goes in the predicate term of the categorical proposition. For example, the statement
- “Only executives can use the silver elevator” is translated
[✓] 2. “All people who can use the silver elevator are executives.” [✓]If it were translated
[✘] 3. “All executives are people who can use the silver elevator,”
the translation would be incorrect. [✘]
I accept that 2 is the correct, and 3 is the incorrect, translation of 1; but I wish to dig deeper: What are the steps and thought processes behind translating 3 (the generalisation of 1) into 4 (the generalisation of 2)? Can a Venn Diagram depict why only 4 is correct, and 5 is incorrect?
- Only A are B. ✓ 4. All B are A. ✓ ✘ 5. All A are B. ✘
I already read the textbook's caution on the ambiguity of 'only', about which I ask not:
Also note that many English statements containing “only” are ambiguous because “only” can be interpreted as modifying alternate words in the statement. [...]