Given below are two premises ((a) and (b)). From those two premises four…
2017
Given below are two premises ((a) and (b)). From those two premises four conclusions (i), (ii), (iii) & (iv) are drawn. Select the code that states the conclusions validly drawn from the premises (taking singly or jointly.)
Premises :
(a) Untouchability is a curse.
(b) All hot pans are untouchable.
Conclusions :
(i) All hot pans are curse.
(ii) Some untouchable things are hot pans.
(iii) All curses are untouchability.
(iv) Some curses are untouchability.
Codes :
Answer: D. (ii) and (iv) — Concept A categorical syllogism is valid only when it runs on exactly three terms, each carrying one fixed sense throughout. If a word changes its meaning…
- A.
(i) and (ii)
- B.
(ii) and (iii)
- C.
(iii) and (iv)
- D.
(ii) and (iv)
Attempted by 1 students.
Show answer & explanation
Correct answer: D
Concept
A categorical syllogism is valid only when it runs on exactly three terms, each carrying one fixed sense throughout. If a word changes its meaning between the two premises, the argument really contains four terms, and nothing at all can be inferred by joining the premises.
Two separate rules govern what a single universal affirmative premise ("All S are P") yields on its own:
Conversion by limitation is legitimate: "All S are P" yields "Some P are S".
Simple conversion is not: "All S are P" does not yield "All P are S", because P is undistributed in the premise but distributed in that conclusion — an illicit conversion.
Applying it to these premises
Cast both premises in standard form. Premise (a) becomes "All untouchability is curse", and premise (b) becomes "All hot pans are untouchable things".
Inspect the middle term. Premise (a) is about untouchability, the social practice; premise (b) calls a hot pan untouchable in the physical sense of being too hot to touch. The word that looks shared carries two different senses, so the pair actually has four terms and no conclusion can be drawn by chaining them.
Test "All hot pans are curse". It is reachable only by chaining the two premises through that middle term, which the shift in sense blocks. It does not follow.
Test "Some untouchable things are hot pans". It is the conversion by limitation of premise (b) taken by itself. It follows.
Test "All curses are untouchability". It is the simple conversion of premise (a); "curse" is undistributed in the premise but distributed here, so it is an illicit conversion. It does not follow.
Test "Some curses are untouchability". It is the conversion by limitation of premise (a) taken by itself. It follows.
Cross-check
Conclusion | Route it needs | Does it follow? |
|---|---|---|
All hot pans are curse | Chain both premises through the middle term | No — four terms |
Some untouchable things are hot pans | Conversion by limitation of premise (b) | Yes |
All curses are untouchability | Simple conversion of premise (a) | No — illicit conversion |
Some curses are untouchability | Conversion by limitation of premise (a) | Yes |
Every conclusion that survives is drawn from one premise on its own, which the stem expressly permits when it says the conclusions may be taken singly or jointly. The equivocation is also what makes this item well posed: if "untouchable" and "untouchability" were a single term, "All hot pans are curse" would follow as well and two different codes would qualify.
Answer: the code listing (ii) and (iv) — "Some untouchable things are hot pans" together with "Some curses are untouchability".