Open Future and Logic

2020

I argue that the semantics of sentences expressing future contingent propositions is best viewed as being based on a clear distinction between a time at which a proposition is true and a time at which a state of affairs that makes it true gets actualized. That a prediction is true here and now means that its truth-maker gets actualized later. This is not to say that if a contingent proposition p concerning the future is true at t, it acquires the truth-value true at t only retrospectively, at a later moment. Nor must this be seen as suggesting that it is a settled, unpreventable fact at t that p is true at t. It just means that the reason for its present truth is something that happens later on: the future happens to evolve in such a way as to make a truth-maker of p obtain. In this case, then, it can be said that at t, p is truth-maker indeterminate, or that it has an indeterminate truth-maker. I develop a formal semantics based on this analysis in the follow-up article ‘A Formal F...

alanrhoda.net

Supervaluationism holds that the future is undetermined, and as a consequence of this, statements about the future may be neither true nor false. In the present paper, we explore the novel and quite different view that the future is abundant: statements about the future do not lack truth-value, but may instead be glutty, that is both true and false. We will show that (1) the logic resulting from this "abundance of the future" is a non-adjunctive paraconsistent formalism based on subvaluations, which has the virtue that all classical laws are valid in it, while no formula like φ ∧ ¬φ is satisfiable (though both φ and ¬φ may be true in a model); (2) The peculiar behaviour of abundant logical consequence has an illuminating analogy in probability logic; (3) abundance preserves some important features of classical logic (not preserved in supervaluationism) when it comes to express those important retrogradations of truth which are presupposed by the argument de praesenti ad praeteritum.

FUTURE LOGIC, 1990

FUTURE LOGIC is an original and wide-ranging treatise of formal logic. It deals with deduction and induction, of categorical and conditional propositions, involving the natural, temporal, extensional, and logical modalities. This is the first work ever to strictly formalize the inductive processes of generalization and particularization, through the novel methods of factorial analysis, factor selection and formula revision. This is the first work ever to develop a formal logic of the natural, temporal and extensional types of conditioning (as distinct from logical conditioning), including their production from modal categorical premises.

1981

A temporal logic is defined which contains both linear and branching operators. The underlying model is the tree of all possible computations. The following metatheoretical results are proven: 1) an exponential decision procedure for satisfiability; 2)a finite model property; 3)the completeness of an axiomatization.

Noûs, 2019

At least since Aristotle's famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to what we might call the doctrine of the open future. This doctrine maintains that future contingent statements-roughly, statements saying of causally undetermined events that they will happen-are not true. 1 But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking backwards) it was the case that it would happen. How can it be that, looking forwards, it isn't true that there will be a sea-battle, while also being true that, looking backwards, it was the case that there would be a sea-battle? This tension forms, in large part, what might be called the problem of future contingents. Some theorists respond to this tension by insisting that one of the intuitions here must simply be denied. For example, so-called Peircians give up the backward-looking intuition, while so-called Ockamists give up the forward-looking intuition (see Prior 1967: 113-135). But a dominant trend in temporal logic and semantic theorizing about future contingents seeks to validate both intuitions. Theorists in this tradition-including some interpretations of Aristotle, but paradigmatically, Thomason (1970), as well as more recent developments in Belnap, et.al (2001) and MacFarlane (2003, 2014)-have argued that the apparent tension between the intuitions is in fact merely apparent. 2 In short, such philosophers seek to maintain both of the following two theses:

Logical Investigations, 2013

We consider the logic QCTL, a first-order exten- sion of CTL defined as a logic of Kripke frames for CTL. We study the question about recursive enumerability of its fragments specified by a set of temporal modalities we use. Then we discuss some questions concerned axiomatizability and Kripke completeness.

Synthese

Explanations of the genuine openness of the future often appeal to objective indeterminacy. According to the received view, such indeterminacy is indeterminacy of certain future-tensed state of affairs that presently obtain. We shall call this view the weak indeterminate present, to distinguish it from the view we will defend in this paper, which we dub the strong indeterminate present. According to our view, unsettledness of the future is grounded on the present indeterminacy of some present-tensed state of affairs. In order for an indeterminate present-tensed state of affairs to explain the unsettledness of a future-tensed state of affairs, there has to be a connection between the two. We argue that this connection can only be provided if we look at the internal structure of the relevant state of affairs. Finally, we will suggest that the best background theory to explain the connection are the so-called spontaneous collapse models of quantum mechanics.

2019

This is the second volume of a collection of papers centered on the work of Arthur Prior. It draws on material presented at two conferences: one held in Copenhagen from 22nd-24th November 2017, and a shorter event held at Roskilde University on 2nd March 2018 as part of the Annual Meeting of the Danish Philosophical Society. 1 Like its predecessor, this collection is broad in sweep: it contains papers discussing the history of Arthur Prior's life and work, papers on philosophical themes introduced, elaborated, or alluded to by Prior, and papers that draw their inspiration from Arthur Prior's rich and varied contributions to logic. This subdivision is hardly sharp. Many contributions -much in the spirit of Prior's own work -move easily between history, philosophy, and logic. Moreover, like its predecessor, this volume concludes with a paper that views the Prior Internet Resources from the perspective of the digital humanities. In short, both volumes illustrate the breadth of the Prior Project, the topic to which we now turn. "Prior Project" is a usefully ambiguous term. It can be read as referring to aspects of Arthur Prior's own lifelong intellectual project, an exploration which wove his life and work tightly together. For example, Prior wrestled with theological issues (such as predestination) and these fed back into his writing (in the case of predestination, via his work on branching time).

Boston: Walter de Gruyter. The book is simultaneously the first volume of a new de Gruyter series "Peirceana", edited by Francesco Bellucci and Ahti Pietarinen. To Peirce scholars and other aficionados of logic, semiotics, and pragmatism, 2017 brought the great news of Bellucci's Speculative Grammar book, providing the eye-opening first detailed chronological overview over Peirce's career-length developing of his semiotics. Now, the first volume of Ahti Pietarinen's long-awaited three-volume publication of the totality of Peirce's writings on his mature logic representation system known as Existential Graphs (EGs) not only give us a plethora of hitherto unpublished Peirce papers but also a new and in many ways surprising view into the origin and development of this important fruit of Peirce's last, creative philosophical burst taking its beginning around 1896, famously to peak in his annus mirabilis of 1903. Ahti Pietarinen has spent an admirable effort not only to find, collect and transcribe the enormous amount of Peirce's EG writings, but also to frame and comment the results in a planned three-volume, 2000-pages critical edition named Logic of the Future. The title has been chosen from a 1909 letter to William James in which Peirce describes the EG system and exclaims: "This ought to be The Logic of the Future". Now, the first volume of this gargantuan work has appeared, subtitled "History and Applications". A brief general introduction presents the layout of the whole planned edition, while another brief intro takes the uninitiated reader into the central issues of Existential Graphs. The tentative principle of selection of texts is ambitious: to be "comprehensive", that is, publishing the majority of the some 5000 ms. pages in which Peirce address EGs, including a vast amount of alternate text versions presented as footnotes and appendices to texts presented. A second principle is the overall chronological structure of the three volumes. A third is that texts already published (in the CP, in the NEM, or elsewhere) are left out. The two latter criteria, however, are rules of thumbs not rigorously followed. This appears from the detailed 100-pages introduction to the present volume, which goes through each of the volume's 28 selected texts and text collections from Peirce's writings, spanning the period from 1895 to 1911. The selection is not strictly chronological, however, which is partially a result of the overall disposition of all of the three volumes. In a certain sense, the central volume of the whole project is that of volume two, still to appear, to cover Peirce's intense 1903 developments and presentations of the EGs in the "Logical Tracts" and the "Lowell Lectures", each of which are planned to fill one subvolume of Logic of the Future volume two. The third and final volume, "Pragmaticism and Correspondence" then, is planned to contain post-1903 EG writings related to Peirce's Pragmaticism paper series in the Monist, in which Peirce puts the EGs to use in his mature arguments for pragmatism if not decidedly a proof of pragmatism-as well as Peirce's presentation and discussion of the EGs in lengthy correspondence with colleagues. These selection choices leave for the first volume primarily a batch of central texts documenting the early development of the EGs from 1896-98, forming the epicenter of the present volume. A bit surprisingly, this is flanked by two other batches of texts. First, texts 1-4, a small selection of philosophy-of-logic papers, most of them late, around 1910; Pietarinen's argument is that these texts present Peirce's most clarified general view of logic, as a preparation