Hypotheticals and Inference Precepts

In ‘General Propositions and Causality’, F. P. Ramsey argued that for a large class of general propositions of the form ‘All Fs are Gs’, any such proposition amounts to a sort of rule: ‘If I meet an F, I shall regard it as a G’. For Ramsey, to express a rule of this sort is the same as expressing or reporting a psychological ‘habit’. That wouldn’t rule out genuine disagreement between somebody who uttered the quoted rule and somebody who e.g. uttered the rule ‘If I meet an F, I shall regard it as a non-G’, on account of its being possible for one to be proved right in what he believes (e.g. ‘This F is a G’) and the other wrong. Still, it would arguably be an improvement on Ramsey to infuse proper objectivity into the rule corresponding to ‘All Fs are Gs’ by rephrasing it more impersonally as: ‘If one meets an F, one should regard it as a G.’

Ramsey adopted this account of such general propositions especially because of problems connected with the view of them which he and Wittgenstein (in the Tractatus) had earlier maintained: the view according to which any general proposition is equivalent to the conjunction of all its instantiating propositions, so that ‘Everything is green’ amounts to ‘a is green and b is green and …’ A proposition ‘All Fs are Gs’ turns out to be a conjunction of propositions of the form ‘If x is an F, then x is a G’. The main difficulty Ramsey saw for this view was that it implied the existence of infinite conjunctions when the relevant domain is infinite, which would be the case where the domain is that of the natural numbers, assuming one can ‘quantify over’ numbers – but also, apparently, where the domain is the universal domain, as it is alleged to be for many propositions of the form ‘All Fs are Gs’. The notion of an infinite conjunction seemed to Ramsey to be a fudge, and at odds with the principle enunciated in the Tractatus that whatever can be said at all can be said clearly.