Content-type: text/html Downes.ca ~ Stephen's Web ~ What is a relevant connective?

Stephen Downes

Knowledge, Learning, Community

This is a lovely paper that takes you deep deep deep into the depths of logic and semantics. It proposes a standard of 'relevance' for connectives (where a connective is a logical operator like (but not limited to) 'or', 'and', if-then' or 'not'). We can postulate the existence of many alternative connectives, or (like intuitionist logicians) reinterpret the semantics of existing connectives (denying, for example, double negation or excluded middle). Three criteria for relevance are offered, including most interestingly a principle of heredity (formally, "If a entailsA and a ≤ b, then b entails A", but you can think of it as (roughly) similar to inheritance in object oriented programming languages). Why is this even remotely important? It makes very clear, in a very plausible way, that in any logic, "the motivating ideology is often important for the development of formal and philosophical work on that logic."

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Stephen Downes Stephen Downes, Casselman, Canada
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