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Inverse View
It is not the case that The idea-variation method requires that the replacing idea belong to the same semantic category as the idea it replaces
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Reasons For
2 perspectives
Reason for 1 of 2
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1.
Frege's context principle shows that semantic category membership is determined by inferential role, not prior to substitution.
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2.
If category is fixed only through use in valid inferences, the variation method itself partly constitutes category boundaries, making the constraint circular.
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Reason for 2 of 2
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1.
Bolzano's own examples permit substitution of ideas with different extensions, suggesting category is defined functionally by position in the proposition-form.
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2.
A purely positional criterion of semantic category makes the same-category constraint trivially satisfied by any substitution, rendering it vacuous rather than restrictive.
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Reasons Against
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Reason against
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1.
A replacing idea that does not fit the semantic category of the replaced idea produces a result that is not a genuine (well-formed) proposition
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2.
Genuine propositions are the intended output of the variation operation
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