Assertion, denial, content, and (logical) form

Abstract

I discuss Greg Restall's attempt to generate an account of logical consequence from the incoherence of certain packages of assertions and denials. I take up his justification of the cut rule and argue that, in order to avoid counterexamples to cut, he needs, at least, to introduce a notion of logical form. I then suggest a few problems that will arise for his account if a notion of logical form is assumed. I close by sketching what I take to be the most natural minimal way of distinguishing content and form and suggest further problems arising for this route.Explaining logical consequence in terms of necessary truth-preservation or some variant thereof is very common, but such explanations face difficulties. For one thing, logical consequence seems broader than truth-preservation. Imperatives, for example, can plausibly stand in relations of logical consequence, yet imperatives are neither true or false. Necessary truth preservation, by itself, will thus not explain how we can make logical mistakes in reasoning from imperatives. For another, necessary truthpreservation accounts, even when cashed out in terms of logical form, have difficulty directly satisfying our intuition that a relatively small set of constitutive rules govern the meaning of a logical constant. Why is failing to conform to, e.g. modus ponens, more indicative of a failure to grasp the meaning of the conditional than failing to conform to, e.g. Peirce's law. Third, note that some non-classical logicians, such as B Jack Woods