Combining Texts

Ideas for 'Causation', 'On Nature Itself (De Ipsa Natura)' and 'The Boundary Stones of Thought'

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2 ideas

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

18813	Logical consequence is a relation that can extended into further statements [Rumfitt]
	Full Idea: Logical consequence, I argue, is distinguished from other implication relations by the fact that logical laws may be applied in extending any implication relation so that it applies among some complex statements involving logical connectives.
	From: Ian Rumfitt (The Boundary Stones of Thought [2015], 3.3)
	A reaction: He offers implication in electronics as an example of a non-logical implication relation. This seems to indicate that logic must be monotonic, that consequence is transitive, and that the Cut Law always applies.

5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-

18808	Normal deduction presupposes the Cut Law [Rumfitt]
	Full Idea: Our deductive practices seem to presuppose the Cut Law.
	From: Ian Rumfitt (The Boundary Stones of Thought [2015], 2.3)
	A reaction: That is, if you don't believe that deductions can be transitive (and thus form a successful chain of implications), then you don't really believe in deduction. It remains a well known fact that you can live without the Cut Law.