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It is not the case that Confusing the rule that any sign can generate an interpretant with the claim that infinitely many interpretants must exist commits a modal fallacy.
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Reasons For
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1.
The modal distinction may be artificial here: if signs inherently generate interpretants iteratively, the practical outcome approaches infinity regardless of modality.
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2.
Peirce's actual texts suggest interpretants propagate without natural stopping points, making 'possible infinity' functionally equivalent to required infinity.
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3.
Naming this a 'modal fallacy' assumes modal logic applies to semiosis, but Peirce's framework may operate outside standard logical categories.
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Reasons Against
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Reason against
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1.
Possibility (can generate) differs logically from actuality (must generate infinitely many). Conflating modal operators is a standard logical fallacy.
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2.
Peirce's semiotic theory allows finite interpretant chains in practice. The rule permits infinity without requiring it, avoiding modal confusion.
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3.
Distinguishing 'can' from 'must' preserves the theory's consistency with observable communication, which terminates in finite contexts.
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