Write a short note on If ‘Some philosophers are poets’ is True, then what is the truth value of the following propositions ? No philosophers are poets.
Write a short note on If ‘Some philosophers are poets’ is True, then what is the truth value of the following propositions ? No philosophers are poets.
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If the proposition "Some philosophers are poets" is true, it establishes the existence of at least one philosopher who is also a poet. However, it does not preclude the possibility that there are other philosophers who are not poets. Therefore, the truth value of the proposition "No philosophers are poets" must be evaluated in light of this information.
The proposition "No philosophers are poets" is a universal negative statement, asserting that there are no philosophers who belong to the category of poets. For this proposition to be true, there should not be any philosopher who is also a poet. However, the truth of the original proposition "Some philosophers are poets" does not necessarily contradict the proposition "No philosophers are poets."
Even if there is at least one philosopher who is a poet, it does not invalidate the proposition "No philosophers are poets," as long as there are other philosophers who are not poets. The presence of a subset of philosophers who are poets does not negate the possibility of another subset of philosophers who are not poets.
Therefore, given that "Some philosophers are poets" is true, it does not determine the truth value of the proposition "No philosophers are poets." The truth value of the latter proposition remains undetermined without additional information about the entire population of philosophers.