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It is not the case that Frege demonstrated that logical constants like 'and' and 'not' cannot be implicitly defined by their structural roles without presupposing their meanings.
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Reasons For
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Reason for
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1.
Structural roles can fully determine meaning without prior semantic content, as Wittgenstein argued for language games.
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2.
Frege conflates psychological understanding with logical definition; meanings can be structural without circularity.
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3.
Modern formal semantics successfully defines logical constants through truth conditions derived from structural roles alone.
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Reasons Against
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Reason against
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1.
Logical constants have determinate meanings independent of any formal system, which cannot be derived from structural roles alone.
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2.
Implicit definition through role-play leads to circularity: understanding 'and' requires already knowing what 'and' means.
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3.
The inference rules governing logical constants presuppose their semantic content to avoid equivocation.
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