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It is not the case that Peirce's type-token distinction entails that linguistic types are abstract repeatable structures, not located at any single spatio-temporal coordinate.
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Reasons For
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Reason for
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1.
Types only exist when tokens are instantiated; without physical instances, there's nothing to make types real or meaningful.
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2.
Abstract repeatable structures require mental or conventional activity to exist; they depend on cognition, not independent reality.
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Reasons Against
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Reason against
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1.
The same word 'cat' appears in multiple locations simultaneously, suggesting types transcend individual physical instances.
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2.
Abstract mathematical objects like numbers are non-spatial yet meaningful; linguistic types may share this ontological status.
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3.
If types were located at specific coordinates, we'd need arbitrary rules to identify which token instance constitutes 'the' type.
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