A logic for 'because'

TL;DR: A logic for ‘because’ is developed based on systematic connections between ‘ because’ and the truth-functional connectives.

Abstract: In spite of its significance for everyday and philosophical discourse, the explanatory connective 'because' has not received much treatment in the philosophy of logic. The present paper develops a logic for 'because' based on systematic connections between 'because' and the truth- functional connectives. §1. Introduction. 1.1. The project. In the philosophy of logic, the natural language connectives 'and', 'or', 'not', and 'if . . . then' are widely discussed and so are their formal counterparts, such as the truth-functional connectives of classical logic or counterfactual and strict con- ditionals in modal systems. Considerably less attention has been paid to the explanatory connective 'because'. One simple reason may be that 'because' is quite complicated to handle. 'Because' is obviously not an extensional operator: the truth of the two clauses in a 'because'-sentence is compatible both with the truth of the sentence (JFK died because he was shot) and with its falsity (JFK died because Chernobyl exploded). But not only is 'because' nonexten- sional, it is even hyperintensional: necessarily equivalent clauses are not substitutable salva veritate in its context. This immediately follows if (i) some true 'because'-sentences have a main clause expressing a necessary truth, and (ii) not all necessary truths are explained by exactly the same things. For, assume that S expresses a necessary truth (e.g., that {2} contains a prime number), and that there is at least one true instance of S because φ (e.g., '{2} contains a prime number because it contains 2 and 2 is prime'). If 'because' was at most an intensional operator, S could be substituted salva veritate with any neces- sarily equivalent clause, that is, with any sentence expressing a necessary truth. Hence, any 'because'-clause that would explain S would equally explain any other necessary truth. (An analogous reasoning applies to necessarily true 'because'-clauses of 'because'- sentences.) But necessary truths are not the only cases that illustrate the hyperintensionality of 'because'. To wit, the majority of philosophers in the debate about truth accept the Aris- totelian insight that the following schema is valid for true instances of 'p': 1 Truth That p is true because p (but not vice versa). Given this insight, 'because' must be hyperintensional. For, the two clauses 'p' and 'that p is true' agree in truth-value with respect to every possible world. Since the clauses are furthermore cognitively equivalent (a speaker who understands them normally has to adopt the same epistemic stance towards them), the example yields the yet stronger result that