David Miller

The doctrine that the content of the conclusion of a deductively valid argument is included in the content of its premises, taken jointly, is a familiar one. It has important consequences for the question of what value valid arguments possess, since it indicates the poverty of three traditional answers: that arguments may and should be used as instruments of persuasion, that they may and should be used as instruments of justification; and that they may and should be used to advance knowledge. The truth is, however, that in each of these cases the argument has only a managerial role and, if there is any work done, it is the premises that do it. It will be maintained that this point has little force against the critical rationalist answer, which I shall defend, that the principal purpose of deductive reasoning from an assemblage of premises is the exploration of their content, facilitating their criticism and rejection. That said, the main aim of the present paper is not to promote critical rationalism but to consider some published objections to the doctrine that a statement asserts every statement that is validly deducible from it. The alleged counterexamples to be considered fall roughly into two groups: statements that emerge with time from a rich mathematical or empirical theory, but were originally unformulated and are deducible from the theory only in a non-trivial way (Frederick 2011, 2014; Williamson 2012); and statements, notably disjunctions, that are easily formulated and are deducible from a theory in a trivial way (Schurz & Weingartner 1987; Mura 1990, 2008; Gemes 1994; Yablo 2014). Each of these counterexamples will be evaluated and dismissed.