Necessarily co-extensive concepts like 'triangular' and 'trilateral' are materially equivalent across all possible worlds yet are paradigmatically treated as distinct concepts in intensional semantics.

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Reasons For

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Reason for

1.Cognitive significance differs between 'triangular' and 'trilateral' despite identical extensions, demonstrating concepts are not reducible to their referents.
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2.Intensional contexts like belief ascriptions require distinction: one can understand 'trilateral' without immediately grasping 'triangular', proving conceptual distinctness.
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3.Conceptual identity requires sameness of cognitive content and inferential role, which 'triangular' and 'trilateral' lack despite co-extensionality.
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Reasons Against

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Reason against

1.If concepts are abstract meanings, metaphysical identity obtains when extensions coincide necessarily—differences are merely psychological or linguistic, not semantic.
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2.Intensional semantics treating co-extensive concepts as distinct conflates concepts with modes of presentation or cognitive routes to the same reference.
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3.The distinction collapses under scrutiny: any competent reasoner can move instantly from one concept to the other via basic geometry, suggesting no real conceptual gap.
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Key Terms

Distinct concepts(the claim that 'triangular' and 'trilateral' are treated as different in intensional semantics): Ideas that are meaningfully different from each other, even if they describe the same things.
Intensional semantics(the philosophical framework that treats 'triangular' and 'trilateral' as genuinely different concepts): A way of studying meaning that focuses on what concepts mean internally (their sense or definition) rather than just what they refer to in the real world.
Necessarily co-extensive(describing the relationship between 'triangular' and 'trilateral'): Two concepts that must always apply to exactly the same things—wherever one is true, the other is always true too.
Paradigmatically(as used to describe which dialogues best represent a pattern): In a way that serves as a perfect or typical example of something; acting as a model or standard case.
Triangular(example of a concept that always applies to the same objects as 'trilateral'): Having three angles or sides; the shape of a triangle.
Trilateral(example of a concept that always applies to the same objects as 'triangular'): Having three sides; another way of describing a triangle.
materially equivalent(Russell's usage in his 1893 paper for Sidgwick): mean the same as
possible worlds(Leibniz's modal semantics, anticipating contemporary possible-worlds semantics): Worlds that have existence in a tenuous sense; fictional worlds used to characterize the nature of possibles that are never actualized

Connections

2 topics

Modality & Possibility1 linked Philosophy of Language1 linked

Cognitive significance differs between 'triangular' and 'trilateral' despite ide...Conceptual identity requires sameness of cognitive content and inferential role,...

Details

Type: claim
Perspectives: 2 (1 for, 1 against)
Edits: 1 edit