Grazer Philosophische Studien 91 (2015), 423–442.
AN ANALYSIS OF LOGICAL DETERMINISM1
Jan WOLEŃSKI Jagiellonian University, Kraków
Summary Logical determinism is the view that some logical principles entail ontological determinism, that is, the view that the past uniquely forces the shaping of the future. Th e principle of bivalence and the law of excluded middle are usually considered crucial for logical determinism. On another interpretation, logical determinism is the view that the truth-value of a future contingent sentence is decided sempiternally. Jan Łukasiewicz’s main motivation in inventing three-val- ued logic was to avoid logical determinism. Th e argument advanced in this paper intends to show that logical determinism is not derivable from classical logic.
1. Introduction
Th e problem addressed in this paper goes back to Aristotle and his con- siderations about tomorrow’s sea battle. In a famous passage in (De Inter- pretatione 19a 25–30; in Th e Works of Aristotle, vol. 1: Categoriae and De Intepretatione, tr. By E. M. Edghill, Oxford University Press, Oxford 1928), the Stagirite says: Everything must either be or not be, whether in the present or in the future, but it is not always possible to distinguish and state determinately which of these alternatives must necessarily come about. Let me illustrate. A sea-fi ght must take place to-morrow or not, but it is not necessary that it either should not take place to-morrow, neither it is necessary that it should not take place, yet it is necessary that it either should or should not take place to-morrow. Since propositions correspond with facts, it is evident that when in future events there is a real alternative, and a
1. Th is paper is based on my talk delivered at the conference Łukasiewicz in Dublin, held at University College Dublin, July 1996. Peter Simons also participated in this meeting. Some ideas related to determinism and logic employed in this paper appears in (Woleński 2003; Woleński 2004; Woleński 2006). potentiality in contrary directions, the corresponding affi rmation and denial have the same character. Th ese words initiated a considerable and lengthy discussion (for historical information and substantial assessments, see Bernstein 1992; Cahn 1967; Gaskin 1995; Hintikka 1977; Jordan 1963; Karpenko 1990; Lucas 1989; Vuillemin 1996; Zagzebski 1991, Rice 2013). Basically, two problems were discussed. Th e fi rst question was historical and concerned the way in which Aristotle should be interpreted. Did he revise logic or not? Literally under- stood, his text defends the principle of excluded middle but also tells us something about the logical value of future contingents, that is, sentences about accidental events which may or may not happen. Th e Stoics noted this problem as well. Th eir celebrated “Master argument” tried to prove that everything that is possible would happen in a more or less distant future. Th e second problem is systematic and concerns the question of how radical determinism or fatalism is related to some fundamental prin- ciples of logic, in particular, to the principle of bivalence. Roughly speak- ing, radical determinism (fatalism) is the view that the future is uniquely determined by the past or all future events are necessitated by the past. Th e view that classical logic deductively implies radical determinism (RD) is called logical determinism. Jan Łukasiewicz himself did not use this label. More precisely, his view was (see Łukasiewicz 1922; Łukasiewicz 1970; see also Simons 1989 for a discussion of Meinong’s treatment of the excluded middle) that the law of the excluded middle (EM) or the principle of bivalence (PB), both interpreted metalogically, entail radical determinism when we add the principle of causality (PC).2 Against (RD), Łukasiewicz constructed three-valued logic as a logical basis for indeter- minism and free-will.3 His reasoning goes like this: Take PB + PC. We have (the sign + replaces ‘and’ below)
(1) PB PC RD.
On this account, rejecting PB or limiting PC amounts to canceling a suf- fi cient condition for RD. But Łukasiewicz did more: He attacked both PB and PC as the suffi cient condition because he introduced objective
2. See (Urchs 1992) for further analysis of this question. 3. Some qualifi cations are in order here: see (Jordan 1963). In particular, the early Łukasiewicz maintained that formal logic and ontology are very closely related. However, he abandoned this position later and denied that logic has any metaphysical consequences.
424