 One important philosophical aspect of logic, at least in the senses that deal with logical consequence and the forms of judgements, is its normativity. Logic seems to give us a guide how we ought to reason, and how we ought to draw inferences from one representation to another. But it is not at all clear what guide it gives us, and how we should understand more precisely what norms logic puts on our reasoning. For example, logic does not put us under the norm “If you believe \(A\) and you believe if \(A\) then \(B\) then you ought to believe \(B\).” After all, it might be that I should not believe \(A\) and if \(A\) then \(B\) in the first place. So, in particular I shouldn’t believe \(B\). A reductio ad absurdum is a form of argument that illustrates this. If I believe A and if A then \(0=1\), then this should lead me to abandon my belief in A, not lead to a belief that \(0=1\). The consequences of my beliefs can lead me to abandon them. Still, if I have some reasons for my beliefs then I have at least some prima facie, but not necessarily conclusive, reason to hold the consequences of those beliefs. Logic might thus tell us at least this much, though: whenever I have some reason to believe \(A\) and if \(A\) then \(B\), then I have a prima facie reason to believe \(B\). See (Harman 1986) for the view that logic has no distinctive normative role, and (Field 2009) for a nice critical discussion of Harman’s view and an argument why logic should be tied to norms of rationality.