Part VI – [TOTAL SCORE 10]

Place the following propositions in Standard Categorical Form and match them with one of the five categorical forms provided.

VI.1

It’s not true that not being an alien suffices for not being a philosopher.

Question

Part VI – [TOTAL SCORE 10]

Place the following propositions in Standard Categorical Form and match them with one of the five categorical forms provided.

VI.1

It’s not true that not being an alien suffices for not being a philosopher.

BlackTom AI · Accepted Answer

Let's unpack the proposition and translate it into standard categorical form step by step.

The given statement: 'It’s not true that not being an alien suffices for not being a philosopher.'
- 'not being an alien' is equivalent to 'not P'.
- 'not being a philosopher' is equivalent to 'not S'.
- 'suffices for' in a conditional sense corresponds to the implication (~P) -> (~S).

A classic logical equivalence tells us that (~P) -> (~S) is logically the same as (S -> P) (taking the contrapositive of S -> P yields ~P -> ~S, and vice versa).

Interpreting S as the class of Philosophers and P as the class of Aliens, the form S -> P translates to 'All S are P.'

Now evaluate the answer choices by preserving the intended mapping: S = Philosophers, P = Aliens.

Option 1: 'All S are P' with S = Philosophers and P = Aliens.
- This matches the derived form S -> P, i.e., 'All Philosophers are Aliens.'
- This is the correct structural translation of the given statement.

Option 2: 'All S are P' with S = Aliens and P = Philosophers.
- This flips the roles of S and P, yielding 'All Aliens are Philosophers,' which does not correspond to the original implication.

Option 3: 'No S are P' with S = Philosophers and P = Aliens.
- This would state 'No Philosophers are Aliens,' a much stronger and different claim than S -> P.

Option 4: 'Some S are P' with S = Philosophers and P = Aliens.
- This asserts at least one philosopher is an alien, which is not entailed by S -> P and is therefore incorrect as a translation here.

Option 5: 'Some S are not P' with S = Philosophers and P = Aliens.
- This would imply that some philosophers are not aliens, contradicting the S -> P form derived.

Option 6: 'Some S are not P' with S = Aliens and P = Philosophers.
- This is a mislabeling of roles and also asserts existence of some aliens that are not philosophers, which does not capture the original implication.

In summary, the reasoning points toward option 1 as the structurally accurate standard-form translation for the given proposition when S is Philosophers and P is Aliens. The other options either invert the roles, assert incompatible existential claims, or state forms that do not derive from the given conditional equivalence.

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Part VI – [TOTAL SCORE 10] Place the following propositions in Standard Categorical Form and match them with one of the five categorical forms provided. VI.1 It’s not true that not being an alien suffices for not being a philosopher.

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