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    The supporting argument's step from 'sometimes not-Q' to ... — Carmelics
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    Challenges→The proposition 'Always, if every A is B, then every C is D' implies 'Never, if every A is B, then not every C is D'

    The supporting argument's step from 'sometimes not-Q' to 'not always Q' relies on the classical duality of quantified modals, which Ibn Sina's own modal square does not straightforwardly vindicate for conditional propositions.

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    Key Terms

    Classical duality(in logic)
    A symmetrical relationship between opposing concepts where if one thing is true, its opposite must be false—like how 'always' is the opposite of 'not always.'
    Conditional propositions(in logic)
    Statements with an 'if-then' structure, where one part depends on another—like 'if it rains, then the ground gets wet.'
    Ibn Sina
    Ibn Sina was a Persian philosopher and physician who lived about 1,000 years ago and is considered one of the most influential thinkers in history. He wrote major works on logic, medicine, and metaphysics that were studied in European universities for centuries and shaped how people understood everything from how the body works to how we think about existence itself. His medical encyclopedia was so authoritative that it remained a standard textbook in Europe well into the 1600s.
    Modal square(in logic)
    A logical diagram that shows how four related statements about necessity, possibility, and their opposites connect to each other; Ibn Sina created his own version of this traditional tool.

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    Quantified modals(in formal logic)
    Statements that combine 'sometimes/always' (quantifiers) with 'must/could/possibly' (modals)—like 'it's always necessary that Q' versus 'sometimes Q is possible.'
    Vindicate(as used in philosophical arguments)
    To prove or justify that something is correct or valid.
    modal(in logic and metaphysics)
    Dealing with possibility and necessity—questions about what could be true, what must be true, and what's merely contingent (could go either way).

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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

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    The proposition 'Always, if every A is B, then every C is D' implies 'Never, if ...

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