Abstract: “Ockhamism” and “Molinism” are labels used to designate distinct, but closely related theories in the debate over future contingents. According to Ockhamism some future contingents are true: a true future contingent faithfully represents what will happen in the actual future. It turns out that a simple-minded representation of Ockhamism within the framework of Branching Time proves to be highly problematic, as it gives no interpretation of future tense in non-actual circumstances and, as a result, disables compositional semantics. As a response, many BT theorists turned to Molinism – a theory that assigns truth values not only to actual future contingents, but also to merely possible ones. Such a theory was naturally understood as a strengthening of Ockhamism according to which some of the so-called counterfactuals of freedom (i.e., counterfactuals with a contingent consequent) are true. According to Ockhamism the future contingent, “The coin will land heads,” uttered before the coin toss may be true. According to Molinism, even if I don’t toss the coin, the counterfactual future contingent “Had I tossed the coin, it would’ve landed heads,” may still be true. I will first explain that one can (and probably should) address the formal problems of Ockhamism without resorting to Molinism. Then, I outline the intuition that Molinism is indeed a strengthening of Ockhamism and that one could subscribe to the second without subscribing to the first. Finally, I present a formal theory that allows Ockhamism without Molinism. According to this theory, every future contingent is either true or false, while all the counterfactual future contingents are neither true nor false.
Abstract: The model of so-called Branching-Time was introduced by Saul Kripke and Arthur Prior to investigate indeterminism and temporal asymmetry between “settled” past and “open” future. The model was often adopted for various formal (primarily semantic) purposes, but the proper philosophical interpretation of the model was usually highly underdeveloped. The purpose of the paper is to fill in the interpretative gap and analyze the structure underlying the branching model. I first observe that it is highly misleading to assume that the structure represents the branching of time. Such an understanding is open to many common sense and scientific objections. I argue that it is much more reasonable to understand the elements of the structure as branching possibilities. I then propose an account of the structure in fashion of genuine (or extreme) modal realism of David Lewis – as consisting of non-modal and non-tensed events. Many claims of branching theorists suggest such non-modal account of reality. In particular, their insistence that no particular modal viewpoint is privileged – which I call modal neutrality – is readily understood within the non-modal picture of branching. I propose, however, an interpretation of the branching structure that weds modal neutrality with modal primitivism. The idea is inspired by non-standard tense realism (non-standard A-theory) proposed by Kit Fine. I also outline a potential trap inherent in such an account of branching reality: an unskilful attempt to combine modal neutrality with modal primitivism might lead to an indefensible amalgam of ideas which Nuel Belnap dubbed the Thin Red Line.
Abstract: Contemporary speech act theory was originally developed by Austin (1962) and further elaborated by Searle (1969, 1975, 1979) as an account of the illocutionary aspects of utterances in ordinary language. In particular, this theory searched for a foundational account of the linguistic dimension of human action. Later it found widespread application in the philosophy of mind, philosophy of law and, more recently, in the foundation of social sciences. However, in the philosophy of mathematics and of logic very little attention has been paid to pragmatic phenomena; indeed, pragmatic aspects of mathematical language are almost universally ignored. The purpose of this paper is to apply the machinery of contemporary speech act theory (especially Searle and Vanderveken (1985)) to the essential aspects of mathematics as a science. This hypothesis should not be understood as a defense of an anti-realist ontology of mathematical entities or propositions. Indeed, as I shall argue, this hypothesis is largely independent of any such ontology. Even if one adopts a strict realist view of mathematical entities, the discovery of these entities and of their structure depends largely on some illocutionary acts. It should also not be confounded with the trivial claim that communication among mathematicians is done in part using natural language and, as such, it is impregnated with illocutionary acts (questions, assertions, promises, praises, invitations, etc.).; the working hypothesis is that even at the level of highly abstract and formalized language there are some essential illocutionary acts as well as some illocutionary force indicators.
Abstract: My primary goal in this paper is to defend the plausibility of Kripke’s (1980) thesis that there are contingent a priori truths, and to fill out some gaps in Kripke’s own account of these truths. But the strategy here adopted is, to the best of my knowledge, still unexplored and different from the one adopted both by Kripke himself and by his critics. I first argue that Kripke’s examples of such truths can only be legitimate if seen as introduced by performative utterances (in Austin’s (1962) sense). And, if this is so, we can apply the machinery of illocutionary act theory (especially Searle and Vanderveken (1985)) to these utterances to explain how one can have a priori knowledge of some contingent facts generated by the utterances themselves. I shall argue that the overall strategy can fill out two gaps in Kripke’s original account: first, we can explain the nature of the truth-makers of contingent a priori truths (they are institutional facts in Searle’s (1969) sense, broadly conceived) and, second, we can explain how contingent a priori knowledge can be transmitted from one speaker to another (via the notion of illocutionary commitment).