H. P. Grice on 'satisfactory' as dummy for either 'buletically satisfactory' or 'doxastically satisfactory' -- after Hofstadter and McKinsey (1939)

Since the sentential forms will indicate which kind of value is involved, we can use the generic term 'satisfactory'. We import into the object language the phrases 'It is true that' and 'It is good that'; 'It is true that ⊢p' is to be satisfactory qua true just in case '⊢ p' is satisfactory qua true; and 'it is good that ! p' is to be satisfactory qua true just in case '! p' is satisfactory qua having practical value. At we introduce 'it is acceptable that' (with the syntactical provisions which I have been using); on the practical side, 'It is acceptable that ! p' will be true just in case 'it is good that ! p' is true.

We could now, if we wished, introduce generalized versions of some standard binary connectives; using 'φ' and 'ψ' to represent sentences (in either mode), we could stipulate that ⌈φ & ψ⌉ is satisfactory just in case ⌈φ⌉ is satisfactory and ⌈ψ⌉ is satisfactory, ⌈φ or ψ⌉ is satisfactory just in case one of the pair, ⌈φ and ψ⌉, is satisfactory, and ⌈φ → ψ⌉ is satisfactory just in case either ⌈φ⌉ is unsatisfactory or ⌈ψ⌉ is satisfactory. There are, however, a number of points to be made. (1) It is not fully clear to me just how strong the motivation would be for introducing such connectives, nor whether, if they are introduced, restrictions should not be imposed. The problematic examples will be, of course, the mixed ones (those in which one clause is judicative and the other volitive). It seems natural to look end p.88 for guidance from ordinary speech. "The beast is filthy and don't (I shan't) touch it" seems all right, but "Don't touch the beast and it is filthy" seems dubious, and "Touch the beast and it will bite you", while idiomatic, is not a conjunction, nor a genuine invitation to touch the beast. And "Either he is taking a bath or leave the bathroom door open" is perhaps intelligible, but "Leave the bathroom door open or he is taking a bath" seems considerably less so. (2) It is perhaps worth noting that, in unmixed cases, satisfactoriness would be specifiable either as satisfactoriness qua truth or as satisfactoriness qua practical value; but for mixed cases no such specification would be available unless we make a special stipulation (for example, that the volitive mode is to be dominant). (3) The real crunch comes, however, with negation (which I have been carefully ignoring). 'Not ⊢p' might perhaps be treated as equivalent to '⊢ not-p', but what about 'Not ! p'? What do we say in cases like, perhaps, "Let it be that I now put my hand on my head" or "Let it be that my bicycle faces north", in which (at least on occasion) it seems to be that neither '! A' nor '! ~A' is either satisfactory or unsatisfactory? What value do we assign to '~ ! A' and to '~ ! ~A'? Do we proscribe the forms altogether (for all cases)? But that would seem to be a pity, since '~ ! ~A' seems to be quite promising as a representation for 'you may (permissive) do A'; that is, I signify my refusal to prohibit your doing A. Do we disallow embedding of these forms? But that (again if we use them to represent 'may') seems too restrictive. Again, if '! A' is neither satisfactory nor unsatisfactory, do we assign a third 'value' to '! A' ('practically neuter'), or do we say that we have a 'practical value gap'? These and other such problems would require careful consideration; but I cannot see that they would prove insoluble, any more than analogous problems connected with presupposition are insoluble; in the latter case the difficulty is not so much to find a solution as to select the best solution from those which present themselves.