display all the ideas for this combination of texts
2 ideas
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. |
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. |