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Difficulty: EasySyllogism and Categorical Propositions

Given the universal affirmative categorical proposition 'All roses are flowers', its logically valid converse is 'All flowers are roses'.

Answer: Answer

Answer

The statement is False because converting 'All S are P' into 'All P are S' is an invalid logical conversion.
The statement is false because in categorical logic, a Universal Affirmative proposition ('All S are P') cannot be converted directly into another Universal Affirmative proposition ('All P are S'). Attempting to do so commits the fallacy of invalid conversion. The only valid conversion of an A-type statement is by limitation to a Particular Affirmative proposition ('Some P are S').

Step-by-Step Solution

1
Identify the logical form of the proposition.
The statement 'All roses are flowers' is a Universal Affirmative (A-type) proposition of the form 'All S are P'.
It affirms a universal relationship between the subject term ('roses') and predicate term ('flowers').
2
Apply the rules of immediate inference (conversion).
In traditional logic, the predicate of an A-type proposition is undistributed. An undistributed term cannot become distributed in the converse.
The rule of conversion requires that no term be distributed in the converse which was not distributed in the original proposition.
3
Determine the valid converse.
The valid conversion of 'All roses are flowers' by limitation is 'Some flowers are roses' (an I-type proposition).
Interchanging S and P while keeping the universal quantity creates an invalid inference.

Key Concept

Conversion of Categorical Propositions
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Topics

Syllogism and Categorical Propositions

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