Frege, Bertrand Russell, and their colleagues confined logic to the study of formally valid arguments, as discussed in Aristotle's Analytics, and, by the same decision, expelled from logic all consideration of substantively sound arguments, as discussed, for example, in the Topics. ["The Construal of Reality," p. 109]And Toulmin, like Aristotle, would like to leave room for both, formal logic and "substantive" or "dialectical" reasoning when it comes to knowledge. However, Aristotle is clear about how formal logic should work in this context.
It is a 'demonstration', when the premisses from which the reasoning starts are true and primary, or are such that our knowledge of them has originally come through premisses which are primary and true …. Things are 'true' and 'primary' which are believed on the strength not of anything else but of themselves: for in regard to the first principles of science it is improper to ask any further for the why and wherefore of them; each of the first principles should command belief in and by itself. [Topics, Book 1, §1 translated by W. A. Pickard]If we begin with a first principle, something true in and of itself, then the rigorous consistency of formal logic insures what follows is true. But if we reject the very idea of first principles, that there can be anything in and of itself known to be true, formal logic can only claim consistency. The first rule of lying is to keep it consistent, and formal logic, without first principles, is an unquestioning accomplice in such efforts.