At least since Aristotle’s famous 'sea-battle' passages in On Interpretation 9, some substantial minority of philosophers has been attracted to the doctrine of the open future--the doctrine that future contingent statements are not true. But, prima facie, such views seem inconsistent with the following intuition: if something has happened, then (looking back) 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. 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. In short, such theorists seek to maintain both of the following two theses: (i) the open future: Future contingents are not true, and (ii) retro-closure: From the fact that something is true, it follows that it was the case that it would be true. It is well-known that reflection on the problem of future contingents has in many ways been inspired by importantly parallel issues regarding divine foreknowledge and indeterminism. In this paper, we take up this perspective, and ask what accepting both the open future and retro-closure predicts about omniscience. When we theorize about a perfect knower, we are theorizing about what an ideal agent ought to believe. Our contention is that there isn’t an acceptable view of ideally rational belief given the assumptions of the open future and retro-closure, and thus this casts doubt on the conjunction of those assumptions. (shrink)

In this paper we discuss the recent developments of logic and explain what can be done to promote a bright future for logic. After comments on the contest The Future of Logic that took place during the 5th UNILOG in Istanbul in 2015, we give a general idea of how logic can be practiced and understood, emphasizing in particular the distinction between logic as reasoning and logic as the science of reasoning. And (...) we discuss some projects we have launched: the book series Logic PhDs, series of events such as UNILOG, SQUARE and LIQ, the Logic Prizes Contest and the World Logic Day. (shrink)

This first volume of the Logic of the Future edition collects Peirce's writings on the historical development, theory and application of his graphical method and diagrammatic reasoning. Its 28 selections of texts and extensive general and volume int.

According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be identified with the probability that the event it describes will occur. After reviewing the history of related ideas in logic, I argue that it gives an understanding of probability which is particularly satisfactory for use in quantum mechanics. I (...) construct a lattice of future-tense propositions, with truth values in the interval [0, 1], and derive logical properties of these truth values given by the usual quantum-mechanical formula for the probability of a history. (shrink)

meaning of a proper name is simply its referent.[1] This thesis, however, brings with it a whole host of problems. One particularly thorny difficulty is that of negative existentials, sentences of the form ‘N does not exist’ (where ‘N’ is a proper name). Intuitively, some such sentences are true, but the direct reference theory seems to imply that they must be either false or meaningless. After all, if the meaning of a name is just its referent, then a sentence such (...) as ‘Mary does not exist’ is meaningless unless there exists a person Mary who is the referent of the name ‘Mary’. But if such a person exists, then the sentence denying her existence must be false.            Now it might be suggested that negative existentials involve a rather rare and specialized use of names, for which an alternate analysis might well be appropriate. One might, for example, have independent reasons for thinking that existence is not a predicate. Even if this is right, however, the analysis of fictional discourse poses difficulties for the direct reference theory that cannot be so easily avoided. The trouble is that fictional names—‘Sherlock Holmes’ and ‘Bilbo Baggins’, for example—lack referents; fictional characters do not exist. As a result, a simple application of the direct reference view to fictional discourse is entirely untenable—this would entail that claims regarding fictional characters are not only never true, but always meaningless.            The tendency in the philosophy of language has been to treat fictional discourse as a peripheral case, posing little threat to the direct reference view. And, as such, the fact that the analysis of fiction seems to run into intractable difficulties has been downplayed, and the fact the analyses on offer tend to be ad hoc has been tolerated. Typical strategies include treating fictional names as abbreviations for definite descriptions, supposing that fictional names occur within the scope of tacit fictive operators of various sorts, or taking them to directly refer to non-existent objects.. (shrink)

A famous puzzle called “Grandmother Paradox” is used to argue against the feasibility of traveling backward in time because of the logical and nomological problems such travel involves, and not only because we don’t have the technology to make it reality. The same kind of problems would be encountered in leaping forward in time and then returning to the time of departure. We argue that a similar family of problems also arise in our having foreknowledge of the future without (...) making any time travel. We point to the mysterious consequences of having access to a being, say a machine or a psychic, that can have infallible knowledge of the future and conveys this foreknowledge to human beings truthfully, without any lies or distortions. The cause of these mysterious consequences is the fact that such machines or psychics will raise logical and nomological complications reminiscent of the ones we encounter in time travel scenarios, and that is a strong reason why infallible foretellers cannot exist. We conclude that we can have foreknowledge of the future, in principle, only within certain narrow limits, if at all. (shrink)

Temporal justification logic is a new family of temporal logics of knowledge in which the knowledge of agents is modelled using a justification logic. In this paper, we present various temporal justification logics involving both past and future time modalities. We combine Artemov’s logic of proofs with linear temporal logic with past, and we also investigate several principles describing the interaction of justification and time. We present two kinds of semantics for our temporal justification logics, (...) one based on interpreted systems and Fitting models and the other based on Mkrtychev models, and further, we establish soundness and completeness. We show that the internalization property holds in some of the temporal justification logics. We further investigate the two well-known epistemic-temporal notions of no forgetting and no learning in the framework of justification logics. Finally, we present temporal justification logics that avoid the logical omniscience problem. (shrink)

Prior has conjectured that the tense-logical system Gli obtained by adding to a complete basis for the classical propositional calculus the primitive symbolG, the definitionsDf. F:Fα=NGNαDf. L:Lα=KαGα,and the postulatesis complete for the logic of linear, infinite, transitive, discrete future time. In this paper it is demonstrated that that conjecture is correct and it is shown that Gli has the finite model property: see [4]. The techniques used are in part suggested by those used in Bull [2] and [3]:Gli (...) can be shown to be complete for the logic of linear, infinite, transitive, discrete future time in the sense that every formula of Gli which is true of such time can be proved as a theorem of Gli. For this purpose the notion of truth needs to be formalized. This formalization is effected by the construction of a model for linear, infinite, transitive, discrete future time. (shrink)

Throughout the twentieth century, the automation of formal logics in computers has created unprecedented potential for practical applications of logic—most prominently the mechanical verification of mathematics and software. But the high cost of these applications makes them infeasible but for a few flagship projects, and even those are negligible compared to the ever-rising needs for verification. One of the biggest challenges in the future of logic will be to enable applications at much larger scales and simultaneously at (...) much lower costs. This will require a far more efficient allocation of resources. Wherever possible, theoretical and practical results must be formulated generically so that they can be instantiated to arbitrary logics; this will allow reusing results in the face of today’s multitude of application-oriented and therefore diverging logical systems. Moreover, the software engineering problems concerning automation support must be decoupled from the theoretical problems of designing logics and calculi; this will allow researchers outside or at the fringe of logic to contribute scalable logic-independent tools. Anticipating these needs, the author has developed the Mmt framework. It offers a modern approach towards defining, analyzing, implementing, and applying logics that focuses on modular design and logic-independent results. This paper summarizes the ideas behind and the results about Mmt. It focuses on showing how Mmt. provides a theoretical and practical framework for the future of logic. (shrink)

The limitations of mathematical logic either as a tool for the foundations of mathematics, or as a branch of mathematics, or as a tool for artificial intelligence, raise the need for a rethinking of logic. In particular, they raise the need for a reconsideration of the many doors the Founding Fathers of mathematical logic have closed historically. This paper examines three such doors, the view that logic should be a logic of discovery, the view that (...) logic arises from method, and the view that logic is not the whole of reason, and on this basis proposes an alternative approach to logic. (shrink)

Prior's three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic $Q_t $ and give its axiomatization and semantics. We also argue that $Q_t $ provides a smooth solution to the problem of (...) class='Hi'>future contingents. (shrink)

This work is for scholars, researchers and students in history and philosophy of science focusing on Logical Empiricism and analytic philosophy (of science). It provides historical and systematic research and deals with the influence and impact of the Vienna Circle/Logical Empiricism on today's philosophy of science. It also explores the intellectual context of this scientific philosophy and focuses on main figures and peripheral adherents.

For reasons that have more to do with the historiographical traditions of modern Jewish history and the history of critical thought than history itself, Georg Simmel – of Jewish descent – is rarely discussed within the frame of modern Jewish history. Bringing the two together as a theoretical contribution to Simmel studies and modern Jewish history alike, this article explores Simmel’s logic of contingency in the context of modern Jewish history. Which forms and types could Jews realistically seek to (...) fulfill from the perspective of Simmel’s thought? Which could they hope to escape and what could they expect from the future? The author suggests that in answering these questions we disclose a peculiar notion of ‘bounded contingency’ embedded in Simmel’s positing of a non-binary, ‘gray area’ between the necessary and the impossible. This hypothesis is tested in several distinct contexts: a letter on Zionism from around 1900; an odd passage on love in the excursus on ‘The Stranger’ (1908); and a letter on individuals of Jewish background in German academia (1906). Simmel’s coherency lies in the ‘realist’ approach he adopts to reality as the domain of the contingently possible. When applied to Jewish history in general and Zionism in particular, this notion not only explains why Zionism is unfeasible but also demystifies its emergence as an attempt to escape the status of stranger in Europe. It also evinces why this Jewish national enterprise inevitably carried within it the seeds of the problem it sought to solve. (shrink)

We present the history of the conference Applications of Algebra in Logic and Computer Science, whose twenty-third edition will be held in March, 2019. At the end we outline some plans for the future.

Finally, the first book started Peirceana. Peirceana is expected as a new series that provides access to both Peirce’s mostly unpublished late works and secondary papers, in which ideas of this American philosopher are developed. This edition is opened with three volumes on Peirce’s manuscripts on “Logic of the Future.” The thinker gave this definition to his theory of existential graphs, i.e., a diagrammatical logical project that includes three sections. The sections can roughly correspond to propositional logic, (...) first-order logic and modal logic. The theory of existential graphs is a particular conception. It predicts ideas of proof theory, mathematics of continuity, and cognitive sciences. Besides, it has an impressive philosophical foundation and perfectly emphasizes the importance of diagrammatic notations. Since many writings are published here for the first time, the edition per se is a significant event for the history of logic. However, Peirceana can do more than this. It urges to think of how the logic of 20‒21st centuries would have looked like if Peirce’s intentions were discovered earlier. At the same time, it clarifies the ground for contemporary investigations. Today we have a bunch of papers about various non-classical modifications, extensions, restrictions, and applications of the original theory. Peirceana is projected as the publication that can gather specialists (logicians, philosophers, as well as IT and cognitive science scholars) who are interested in the development of Peirce’s approach. It lets the readers reconsider our ordinary logical conceptions (e.g., reasoning, logical and language analysis, and others) as well as the conventional understanding of the evolution of modern logic. The current paper has two objectives: firstly, it estimates this diplomatic partly critical edition with its several thoroughly elaborated introductions, and secondly, it briefly introduces the existential graphs theory. A set of examples demonstrates the basic principles of this system. (shrink)

The aim of this paper is to investigate the problem of existential import in Abelard's modal logic, and to ask whether the system of logical relationships that he proposes for modal propositions ma...

Recently, Bourne constructed a system of three-valued logic that he supposed to replace Łukasiewicz’s three-valued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to Łukasiewicz’s system. However, finding some good motivations and lessons in his attempt, next I will suggest a better way of achieving his original goal in some sense. The crucial part of my way lies in reconsidering the significance of the (...) intermediate truth-value so as to reconstruct Łukasiewicz’s three-valued logic as a kind of extensional modal logic based on partial logic. (shrink)

This collection of articles explores a wide range of subject, from Godel’s incompleteness theorem, to possible technocalypse and neutrofuturology. Articles on historical debates on irrational number to electroculture, on vortex particle, or on different Neutrosophic applications are included.

The problem of future contingents is regarded as an important philosophical problem in connection with determinism and it should be treated by tense logic. Prior’s early work focused on the problem, and later Prior studied branching-time tense logic which was invented by Kripke. However, Prior’s idea to use three-valued logic for the problem seems to be still alive. In this paper, we consider partial and paraconsistent approaches to the problem of future contingents. These approaches theoretically (...) meet Aristotle’s interpretation of future contingents. (shrink)

Aim: This aim of this study is to describe the development of a program logic model to guide arts-based psychosocial practice delivered in rural South African farming communities affected by transgenerational traumas.Background: The rationale for developing a program logic model for arts-based psychosocial practice in South Africa was based on the lack of evidence for effective community arts-based psychosocial interventions for collective trauma, unknown consensus about best practices and the need for developing cogent collective psychosocial practices. Further to (...) this, the aims and benefits of the practice required clarity given the psychosocial complexity of the environment within which the practices for this population are being offered. The logic model offers a valuable resource for practitioners, participants and funders to understand the problem being addressed, how practice is defined, as well as the impact of practice and on intermediate and longer term goals.Methods: The authors used a systematic iterative approach to describe the operationalization of arts-based psychosocial practice. This resulted in the design of the logic model being informed by data from focus groups, an overview of the literature regarding transgerenational trauma in this population, operational policies and organizational documents. The development of the logic model involved actively investigating with practitioners their work with remote farming communities. We thematised practitioners practice constructs to identify salient practice elements and their relationship to perceived benefits and lastly feedback from practitioners and participants following implementation to make adjustments to the logic model.Results: The results were clearly identified in the form of visual mapping using the design of a program logic model. The logic model was divided into 5 parts and was verified by practitioners following implementation. The parts of the program logic model are main presenting problem, operational processes, practice elements, benefits, and impact and review. (shrink)

" The best way to predict the future is to invent it. —Alan Kay _1_ It is obvious that there are patterns of cultural change—evolution in the neutral sense—and any theory of cultural change worth more than a moment's consideration will have to be Darwinian in the minimal sense of being consistent with the theory of evolution by natural selection of Homo sapiens. —Daniel Dennett _2_ The future is here. It's just not widely distributed yet. —William Gibson _3_ (...) It is the magician's wand, by means of which he may summon into life whatever form and mould he pleases. —Charles Darwin commenting on the power of artificial selection _4_ " This article introduces an applied Theory of Evolution of Artificial Systems, called Directed Evolution. The theory is grounded in fifty years of research on Inventive Engineering known as TRIZ, which started in the former Soviet Union by G. Altshuller and continues today. The theory has generated a set of Patterns and Lines of Evolution that represent a compilation of trends that document strong, historically recurring tendencies in the development of manmade systems in general and technological systems in particular. Directed Evolution is the systematic applied-oriented process for “predicting” future generations of a system by inventing them along these evolutionary patterns. The current article introduces the theory, reflects on its basic underlying logic, and provides a broad historical context and intellectual justification for such an effort. It shows that the quest of DE theory and practice falls well within the boundaries of past pursuits to identify evolutionary patterns of complex systems and to use these patterns to control and manipulate possible futures of artificial systems. (shrink)

The solution of the problem of the future random events truth is considered in Vasil’ev’s logic. N. A. Vasil’ev graded the logic according to two levels—the level of facts, i.e. time fixed events, and the level of notions or rules, governing these facts. The mathematical construction previously suggested for imaginary Vasil’ev’s logic, extends to the early variant of his logic—a logic of notions. In the paper, we investigate the meaning of problematic and uncertain assertions (...) introduced by Vasil’ev. As a result, we developed a model of Vasil’ev’s logic of facts that resolves also the truth problem of future random events. The imaginary logic has also been extended to the level of notions, and the law of the excluded eighth is gotten in it. The correspondence between Vasil’ev’s terms “some” and “all” and modern quantifiers is discussed. (shrink)

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 not only gives 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... (shrink)

Contesting Carceral Logic provides an innovative and cutting-edge analysis of how carceral logic is embedded within contemporary society, emphasizing international perspectives, the harms and critiques of using carceral logic to respond to human wrongdoing, and exploring penal abolition thought. With chapters from scholars across many disciplines, people in prison, as well as penal abolition activists, the book explores what a future without carceral logic would look like, as well as how such a future is (...) to be developed. The book is also an exploration of penal abolition thought as it is developing in the twenty-first century. Diverse geographical, cultural, identity and experiential frames inform the book's themes of analysing carceral logic as it harms disparate people in disparate places, creating anti-carceral knowledge, exploring case studies pointing to radical alternatives, and to contesting carceral logic from below. Ultimately, Contesting Carceral Logic provides the reader with an alternative and critical perspective from which to reflect on carceral logic, the punitive state and the criminalizing systems that almost exclusively dominate across the world. Finally, it raises the questions of how we are to build communities as well as transform our response to human wrongdoing in ways that are not defined by racism/ethnocentrism, class war and heteropatriarchy. Contesting Carceral Logic will be of great interest to not only scholars and activists, but also provides an introduction to key carceral issues and debates for students of penology, criminology, social policy, geography, politics, philosophy, social work and social history programmes in countries all around the world. (shrink)

With globalisation and neoliberalism as significant phenomena impacting the function and role of higher education institutions (Barnett, 2013), the discursive practices of such institutions as mani...

For the last thirty years or so, there has been a search underway for a theory that can accommodate our intuitions in regard to moral duties to future generations. The object of this search has proved surprisingly elusive. The classical moral theories in the literature all have perplexing implications in this area. Classical Utilitarianism, for instance, implies that it could be better to expand a population even if everyone in the resulting population would be much worse off than in (...) the original. The main problem has been to find an adequate population theory, that is, a theory about the moral value of states of affairs where the number of people, the quality of their lives, and their identities may vary. Since, arguably, any reasonable moral theory has to take these aspects of possible states of affairs into account when determining the normative status of actions, the study of population theory is of general import for moral theory. A number of theories have been proposed in the literature that purport to avoid counterintuitive implications such as the one mentioned above. The suggestions are diverse: introducing novel ways of aggregating welfare into a measure of value, revising the notion of a life worth living, questioning the way we can compare and measure welfare, counting people’s welfare differently depending on the temporal location or the modal features of their lives, and challenging the logic of axiological and normative concepts. We investigate the concepts and assumptions involved in these theories as well as their implications for population theory. In our discussion, we propose a number of intuitively appealing and logically weak adequacy conditions for an acceptable population theory. Finally, we consider whether it is possible to find a theory that satisfies all of these conditions. We prove that no such theory exists. (shrink)

A presente investigação questiona a essência teo-lógica dos futuros contingentes. Para o efeito, analisa-se, primeiramente, a argumentação segundo a qual, sob certas con­dições lógicas, teológicas, ontológicas e cosmológicas anti-necessitantes, detetadas por G. W. Leibniz (conciliando a posição de St. Agostinho com a de L. Molina e W. Ockham), a abertura contingente do futuro parece ser compatível com o regime das “verdades contingentes pré-determinadas”, regime enquadrado teologicamente pelo princípio do “futuro melhor” ou do “único futuro verdadeiro”. No entanto, os futuros contingentes (...) incitam, com e contra Aristóteles, ao desenvolvimento de uma lógica temporal e plurivalente, ao modo de J. Łukasiewicz ou A. Prior. Esta lógica garante a abertura do futuro sem o oneroso custo metafísico da adesão a uma teo-lógica omni-determinante. A crítica do determinismo lógico, daí resultante, afigura-se mais coadunável com as condições pós-metafísicas ine­rentes à episteme agnóstica contemporânea, mas, nesse caso, a abertura do futuro impli­caria uma profunda redefinição das próprias ideias e funções de “Deus”, “matéria”, “história” e “verdade”. (shrink)

Prior investigated a tense logic with an operator for ‘historical necessity’, where a proposition is necessary at a time iff it is true at that time in all worlds ‘accessible’ from that time. Axiomatisations of this logic all seem to require non-standard axioms or rules. The present paper presents an axiomatisation of a first-order version of Prior’s logic by using a predicate which enables any time to be picked out by an individual in the domain of interpretation.

Preliminaries: Terminology and Notation We may make a distinction between temporally definite and temporally indefinite sentences. ...