Anderson and Belnap's relevance logic, which enforces VSP, requires rejection of the disjunctive syllogism (A ∨ B, ¬A ⊢ B), a inference form Lewis and others argue is indispensable to ordinary reasoning.

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Reasons For

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Reason for

1.Disjunctive syllogism permits irrelevant premises: from 'Either unrelated-fact or B' and 'not unrelated-fact,' we derive B without logical connection.
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2.Relevance logic avoids paradoxes of material implication where A→B holds whenever A is false, regardless of any meaningful relation between A and B.
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3.Rejecting DS incentivizes explicit reasoning about actual connections between premises and conclusions rather than mechanical rule-following.
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Reasons Against

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Reason against

1.Ordinary reasoning demonstrably uses disjunctive syllogism constantly: 'Either it's raining or not; it's not raining; therefore it's not raining' succeeds.
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2.A logic that forbids DS must either reject classical tautologies like (A ∨ ¬A) or accept true conclusions from true premises, undermining its coherence.
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3.VSP's enforced restrictions create artificial inference barriers without empirically demonstrating people actually reason differently or better under such constraints.
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Key Terms

A ∨ B, ¬A ⊢ B(as symbolic notation for the disjunctive syllogism): Logical symbols representing the disjunctive syllogism: the ∨ means 'or,' ¬ means 'not,' and ⊢ means 'therefore/we can conclude.'
Anderson and Belnap(as the creators of relevance logic): Two 20th-century logicians (Alan Ross Anderson and Nuel Belnap) who developed a new system of logic to fix problems they saw in traditional logic.
Lewis(philosopher who created the similarity metric being discussed): David Lewis was a famous American philosopher who developed influential theories about possible worlds—alternative ways reality could have been.
Relevance logic(as the main subject of the statement): A system of logic that adds extra rules to make sure that when you use a statement to prove something, that statement actually has to be connected to what you're proving—unlike traditional logic, which allows unrelated statements.
VSP(as a technical acronym in logic): An abbreviation for a specific logical principle or property (the exact name varies, but it's a formal rule that logicians debate).
disjunctive syllogism(Cited as an argument form that becomes invalid under dialetheist semantics): The argument form in which from P ∨ Q and ¬P one infers Q
inference form(The statement describes specific inference forms as tools for determining whether arguments are valid.): A pattern of logical reasoning that shows how to reach a conclusion from certain starting statements or premises.

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2 topics

Modality & Possibility1 linked Philosophy of Language1 linked

A conditional is logically valid only if the antecedent and consequent share at ...A logic that forbids DS must either reject classical tautologies like (A ∨ ¬A) o...

Details

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