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"If an existing population contains both mortal and immortal beings, some members of that population are not subject to death."

Is this statement considered logically necessarily true?

I personally think it is, but I'm not sure.

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    A statement is logically necessary if it is a logical validity. Yours is one assuming the usual relation between the meanings of "death" and "mortal": ∃x∃y(M(x)∧¬M(y)) → ∃z¬M(z).
    – Conifold
    Commented Oct 12, 2019 at 11:34
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    This is an obvious example of begging the question.
    – Rob
    Commented Nov 11, 2019 at 20:54

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Logic means or is understood in a great variety of ways; often it is simply used as synonymous with reason in the sense that in daily life reason is distinguished from emotion. The most common technical sense of the word in the history of the West, from crica 300 BC until 1900 or so, was the syllogism. In syllogistic logic all the weight is on what happens prior to the premise entering the logical form. Determining if the premises are true is prior to the syllogism. Once supplied and taken to be true, drawing correct inferences from them is for the most part trivial work.

Something like the statement: There is a population. One can call a premise.

There is a population. Within it are both mortals and immortals. It follows mechanically that: some members of the population are immortal. (Assuming that we understand immortal to mean "not subject to death" your statement holds by the art or mechanical operation of deriving correct inferences.)

The latter development of logic, in our own time, slipped out of the grips of daily life, where Russell still had hopes of retaining it. And became sheer mathematical formality which excluded the difficulty of establishing the premise from its chief content. On the other hand it was overcome and set aside by the Germans in the turn to Phenomenology and Ontology.

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  • This doesn't answer the question. Commented Mar 10, 2020 at 20:23

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