Question

All men are chairs. John Doe is a man. In logical language, therefore:

• A. John Doe is a chair
• B. John Doe is a human being and therefore he cannot be a chair
• C. A man cannot be a chair in any case
• D. Chairs can be men

Answer 1

The Correct Option is A

The correct option is (A): John Doe is a chair.

Answer 2

This question is a classic test of deductive reasoning: given the premises 'All men are chairs' and 'John Doe is a man,' we must determine what follows purely by logical structure, treating the premises as true for the sake of the argument, however absurd they may sound in reality. This follows the pattern of a categorical syllogism: All A are B; C is A; therefore C is B.

1. John Doe is a chair: Substituting into the syllogism form, A = 'men,' B = 'chairs,' C = 'John Doe.' Since John Doe belongs to 'men' and all 'men' belong to 'chairs,' John Doe must belong to 'chairs' by strict deduction. This directly matches the valid syllogistic conclusion.
2. John Doe is a human being and therefore he cannot be a chair: This brings in outside, real-world knowledge that is not part of the given premises. Deduction problems like this require us to accept the premises as given and reason strictly within them, not to reject the premises using outside facts.
3. A man cannot be a chair in any case: This directly contradicts the first premise, 'All men are chairs,' which we are instructed to treat as true for the purpose of the exercise. Rejecting a given premise is not a valid logical operation within this kind of question.
4. Chairs can be men: This reverses the direction of the original statement. 'All men are chairs' only tells us that every member of 'men' is inside 'chairs,' it says nothing about whether every chair is a man. Assuming the reverse is a classic converse error.

Applying strict deduction to the two given premises, without introducing outside real-world assumptions, the only conclusion that follows is that John Doe belongs to the category 'chairs.'

Therefore, the correct answer is John Doe is a chair.

Answer 3

This question can be settled with formal symbolic logic. Writing 'All men are chairs' as \( \forall x \, (\text{Man}(x) \rightarrow \text{Chair}(x)) \) and 'John Doe is a man' as \( \text{Man}(\text{John Doe}) \), universal instantiation lets us substitute John Doe for \( x \) to get \( \text{Man}(\text{John Doe}) \rightarrow \text{Chair}(\text{John Doe}) \). Combined with the second premise, modus ponens then delivers \( \text{Chair}(\text{John Doe}) \) directly, with no room for outside assumptions about what men or chairs actually are.

1. John Doe is a chair: This is exactly what modus ponens produces once we plug John Doe into the universal rule and combine it with the fact that he is a man. The symbols do not care whether the conclusion sounds strange, only whether the inference rule was applied correctly, and it was.
2. John Doe is a human being and therefore he cannot be a chair: This introduces a new predicate, 'human being', and a new rule, 'humans cannot be chairs', neither of which exists anywhere in \( \forall x \, (\text{Man}(x) \rightarrow \text{Chair}(x)) \) or \( \text{Man}(\text{John Doe}) \). Formal derivation only allows conclusions that follow from the given formulas, and this option smuggles in an outside axiom.
3. A man cannot be a chair in any case: This would require negating the very premise \( \forall x \, (\text{Man}(x) \rightarrow \text{Chair}(x)) \) that the derivation starts from. You cannot derive the negation of a premise you have accepted as true for the argument.
4. Chairs can be men: Symbolically, this claims \( \forall x \, (\text{Chair}(x) \rightarrow \text{Man}(x)) \), which is the converse of the given implication. An implication \( P \rightarrow Q \) does not entail its converse \( Q \rightarrow P \), so this cannot be derived from the premise given.

Applying universal instantiation and modus ponens strictly to the two given formulas leaves only one derivable conclusion.

Therefore, the correct answer is John Doe is a chair.