Full Idea
Our deductive practices seem to presuppose the Cut Law.
Gist of Idea
Normal deduction presupposes the Cut Law
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 2.3)
Book Reference
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.43
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.