Unlike the philosophers Toulmin is in conversation with, Toulmin thinks a theory of argumentation should be built from the ground up. The ground for Toulmin is just the way argumentation is actually practices in various fields. In other words, Toulmin is going to provide a descriptivist account of reason and justification based on a careful analysis of arguments.
From this analysis he develops his theory of the meaning of modal terms. So argues that modals have both (1)force and (2) criteria. By "force" he means "the practical implications of a terms use," and by "criteria" he means "the standards, grounds and reasons, by reference to which we decide in any context that the use of a modal term is appropriate" (28). A large part of his first chapter is taken up with establishing this framework via explanation of "impossibility and impropriety" (criteria), phases of arguments, etc.
The second chapter is a sort of ground clearing. He is attempting to show the limitations of formal-logic-as-the-only-logic [FLOL] arguments.
Much of this seems esoteric, but if I understand Toulmin correctly he is arguing that FLOL arguments are unjustified and motivated by a fear of subjectivism. After reviewing and rejecting FLOL arguments made by Kneale and Carnap, Toulmin states, "Our probablity-terms....show in practice, therefore, many of the the features which we discovered in the first essay to be characteristic of modal terms. In this respect, the mathematical treatment of 'probability' represents a natural extension of the term's more elementary uses" (85). This is important because it validates Toulmin's method, but it also shows that the type of logic defended by FLOL derives from more "elementary" reasoning. For Toulmin this means that where things are meaningfully quantifiable then let mathematics enter--but where they are not--we can still accept the usage of terms that appear to Carnapian FLOL's as illegitimate. We can do so because mathematical probability is an extension of everyday uses.
That's where I'm at as I work through Toulmin's arguments. It seems to me that the first chapters are ground clearing.
I'm looking forward to discussing this work tonight.
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