Three approaches

A recurrent issue in the philosophy of logic concerns the question, with what kind of item logic deals, or perhaps primarily deals. The alternatives offered are usually sentences, statements and propositions, or, more rarely these days, judgments or beliefs. I have put the question in a deliberately vague way, since more than one issue seems to be involved. Once again, as with the issue about the meanings of connectives, quantifiers, etc., the problem concerns the relation between formal and informal arguments: what in informal arguments corresponds to the well-formed formulae of formal languages? It may be useful to distinguish three approaches to the question:

1. (i) syntactic: what, in natural languages, is the analogue of the ‘p’, ‘q’ of formal logic?

In speaking thus far of ‘sentence calculus’, I did not mean to beg this question. Some prefer to speak of ‘propositional calculus’, ‘propositional variables’, ‘propositional connectives’; and so far I have said nothing to justify my preference for the former usage.

1. (ii) semantic: what kind of item is capable of truth and falsity?

Since formal languages aim to represent those informal arguments which are valid extra-systematically, that is, which are truthpreserving, this will relate closely to the first issue.

1. (iii) pragmatic: what kinds of item should one suppose to be the ‘objects’ of belief, knowledge, supposition, etc.?

(‘Know’, ‘believe’, ‘suppose’, etc. are sometimes called the verbs of ‘propositional attitude’.) Since one can know, believe or suppose either something true or something false, the third will relate quite closely to the second issue.