Our computational metaphysics group describes its use of automated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these components of Leibniz’s theory can be represented for investigation by means of (...) automated theorem provers and finite model builders. The fundamental theorem of Leibniz’s theory is derived using these tools. (shrink)

The paper critically discusses an empirical study by Mizrahi & Dickinson 2020, which analyzes in a huge data base (JSTORE) the incidence of three types of philosophical arguments. Their results are: 1. Deductive arguments were the most commeon type of argument in philosophy until the end of the 20th century. 2. Around 2008 a shift in methodology occurred, such that the indcutive arguments outweigh other types of argument. The paper, first, criticizes the empirical study as grossly false and considers the (...) - very limited - possibilities of recognition of argument types by present computer programs. (shrink)

This is the 3rd edition. Although a number of new technological applications require classical deductive computation with non-classical logics, many key technologies still do well—or exclusively, for that matter—with classical logic. In this first volume, we elaborate on classical deductive computing with classical logic. The objective of the main text is to provide the reader with a thorough elaboration on both classical computing – a.k.a. formal languages and automata theory – and classical deduction with the classical first-order predicate calculus (...) with a view to computational implementations, namely in automated theorem proving and logic programming. The present third edition improves on the previous ones by providing an altogether more algorithmic approach: There is now a wholly new section on algorithms and there are in total fourteen clearly isolated algorithms designed in pseudo-code. Other improvements are, for instance, an emphasis on functions in Chapter 1 and more exercises with Turing machines. (shrink)

2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and (...) they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics. (shrink)

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of (...) being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic. (shrink)

Science and engineering rely on the accumulation and dissemination of knowledge to make discoveries and create new designs. Discovery-driven genome research rests on knowledge passed on via gene annotations. In response to the deluge of sequencing big data, standard annotation practice employs automated procedures that rely on majority rules. We argue this hinders progress through the generation and propagation of errors, leading investigators into blind alleys. More subtly, this inductive process discourages the discovery of novelty, which remains essential in (...) biological research and reflects the nature of biology itself. Annotation systems, rather than being repositories of facts, should be tools that support multiple modes of inference. By combining deduction, induction and abduction, investigators can generate hypotheses when accurate knowledge is extracted from model databases. A key stance is to depart from ‘the sequence tells the structure tells the function’ fallacy, placing function first. We illustrate our approach with examples of critical or unexpected pathways, using MicroScope to demonstrate how tools can be implemented following the principles we advocate. We end with a challenge to the reader. (shrink)

Formal ontologies are nowadays widely considered a standard tool for knowledge representation and reasoning in the Semantic Web. In this context, they are expected to play an important role in helping automated processes to access information. Namely: they are expected to provide a formal structure able to explicate the relationships between different concepts/terms, thus allowing intelligent agents to interpret, correctly, the semantics of the web resources improving the performances of the search technologies. Here we take into account a problem (...) regarding Knowledge Representation in general, and ontology based representations in particular; namely: the fact that knowledge modeling seems to be constrained between conflicting requirements, such as compositionality, on the one hand and the need to represent prototypical information on the other. In particular, most common sense concepts seem not to be captured by the stringent semantics expressed by such formalisms as, for example, Description Logics (which are the formalisms on which the ontology languages have been built). The aim of this work is to analyse this problem, suggesting a possible solution suitable for formal ontologies and semantic web representations. The questions guiding this research, in fact, have been: is it possible to provide a formal representational framework which, for the same concept, combines both the classical modelling view (accounting for compositional information) and defeasible, prototypical knowledge ? Is it possible to propose a modelling architecture able to provide different type of reasoning (e.g. classical deductive reasoning for the compositional component and a non monotonic reasoning for the prototypical one)? We suggest a possible answer to these questions proposing a modelling framework able to represent, within the semantic web languages, a multilevel representation of conceptual information, integrating both classical and non classical (typicality based) information. Within this framework we hypothesise, at least in principle, the coexistence of multiple reasoning processes involving the different levels of representation. (shrink)

This is our journal for developing Deduction Theory and studying Deep Learning and Artificial intelligence. Deduction Theory is a Theory of Deducing World’s Relativity by Information Coupling and Asymmetry. We focus on information processing, see intelligence as an information structure that relatively close object-oriented, probability-oriented, unsupervised learning, relativity information processing and massive automated information processing. We see deep learning and machine learning as an attempt to make all types of information processing relatively close to probability information processing. (...) We will discuss about how to understand Deep Learning and Artificial intelligence and why Deep Learning is shown better performance than the other methods by metaphysical logic. (shrink)

Automated influence is one of the most pervasive applications of artificial intelligence in our day-to-day lives, yet a thoroughgoing account of its associated individual and societal harms is lacking. By far the most widespread, compelling, and intuitive account of the harms associated with automated influence follows what I call the control argument. This argument suggests that users are persuaded, manipulated, and influenced by automated influence in a way that they have little or no control over. Based on (...) evidence about the effectiveness of targeted advertising as well as empirical results about the nature of attentional control, I provide reasons to reject this argument. In turn, I use C. Thi Nguyen’s theory of value collapse to develop a new account of the harmfulness of automated influence. (shrink)

Rapid advances in AI-based automation have led to a number of existential and economic concerns. In particular, as automating technologies develop enhanced competency they seem to threaten the values associated with meaningful work. In this article, we focus on one such value: the value of achievement. We argue that achievement is a key part of what makes work meaningful and that advances in AI and automation give rise to a number achievement gaps in the workplace. This could limit people’s ability (...) to participate in meaningful forms of work. Achievement gaps are interesting, in part, because they are the inverse of the (negative) responsibility gaps already widely discussed in the literature on AI ethics. Having described and explained the problem of achievement gaps, the article concludes by identifying four possible policy responses to the problem. (shrink)

This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent case, (...) we show that the refined calculi Ldm^m_nL derive theorems within a restricted class of (forestlike) sequents, allowing us to provide proof-search algorithms that decide single-agent STIT logics. We prove that the proof-search algorithms are correct and terminate. (shrink)

The article explores the problem of preferable technological changes in the context of work. To this end, it addresses the ‘why’ (motives and values) and the ‘how’ (organizational forms) of automation from a normative perspective. Concerning the ‘why,’ automation processes are currently mostly driven by values of economic efficiency. Yet, since automation processes are part of the basic structure of society, as is the division of labor, considerations of justice apply to them. As for the ‘how,’ the article suggests ‘fair (...) hybrid cooperation’ as an alternative ideal to guide automation priorities. It is achieved when the division of labor between humans and machines does not hinder, and preferably enables, workers’ experience of certain primary qualities in their work activity. By analogy with Rawls’ primary goods, these are qualities that it is necessary for every worker to experience in order to pursue their life plans: security, self-direction, self-development, dignity, and recognition. According to this criterion, the tasks to automate first are those hindering these contributive primary qualities. This provides us with a normative vocabulary and a standard to orient automation decisions but also to assess existing organizational forms and envisage alternative cooperative imaginaries. To illustrate how the ideal may play out in the real world, the article concludes with a ‘fair hybrid cooperation test’ and a nurse bots case for meaningful work. (shrink)

Automated influence, delivered by digital targeting technologies such as targeted advertising, digital nudges, and recommender systems, has attracted significant interest from both empirical researchers, on one hand, and critical scholars and policymakers on the other. In this paper, we argue for closer integration of these efforts. Critical scholars and policymakers, who focus primarily on the social, ethical, and political effects of these technologies, need empirical evidence to substantiate and motivate their concerns. However, existing empirical research investigating the effectiveness of (...) these technologies (or lack thereof), neglects other morally relevant effects—which can be felt regardless of whether or not the technologies "work" in the sense of fulfilling the promises of their designers. Drawing from the ethics and policy literature, we enumerate a range of questions begging for empirical analysis—the outline of a research agenda bridging these fields—and issue a call to action for more empirical research that takes these urgent ethics and policy questions as their starting point. (shrink)

Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. belief. However, this thought is undermined by the well-known preface paradox, leading a (...) number of philosophers to conclude that Deductive Cogency has at best a very limited role to play in our epistemic lives. I argue here that Deductive Cogency is still an important epistemic requirement, albeit not as a requirement on belief. Instead, building on a distinction between belief and acceptance introduced by Jonathan Cohen and recent developments in the epistemology of understanding, I propose that Deductive Cogency applies to the attitude of treating propositions as given in the context of attempting to understand a given phenomenon. I then argue that this simultaneously accounts for the plausibility of the considerations in favor of Deductive Cogency and avoids the problematic consequences of the preface paradox. (shrink)

Knowledge representation (KR) is actually more than representation: It involves also inference, namely inference of “new” knowledge, i.e. new facts. Logic programming is a suitable KR medium, but more often than not discussions on this programming paradigm focus on aspects other than KR. In this paper, I elaborate on the general theory of logic programming and give the essentials of two of its main implementations, to wit, Prolog and Datalog, from the viewpoint of deductive computing over knowledge bases, which includes (...) deductive programming. (shrink)

Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than forcing their unification. In this paper, we introduce nested sequent calculi for propositional standpoint logics---proof systems that manipulate trees whose nodes are multisets of formulae---and show how to automate standpoint reasoning by means of non-deterministic proof-search algorithms. To obtain worst-case complexity-optimal proof-search, we introduce a novel technique in the context (...) of nested sequents, referred to as "coloring," which consists of taking a formula as input, guessing a certain coloring of its subformulae, and then running proof-search in a nested sequent calculus on the colored input. Our technique lets us decide the validity of standpoint formulae in CoNP since proof-search only produces a partial proof relative to each permitted coloring of the input. We show how all partial proofs can be fused together to construct a complete proof when the input is valid, and how certain partial proofs can be transformed into a counter-model when the input is invalid. These "certificates" (i.e. proofs and counter-models) serve as explanations of the (in)validity of the input. (shrink)

Important decisions that impact humans lives, livelihoods, and the natural environment are increasingly being automated. Delegating tasks to so-called automated decision-making systems can improve efficiency and enable new solutions. However, these benefits are coupled with ethical challenges. For example, ADMS may produce discriminatory outcomes, violate individual privacy, and undermine human self-determination. New governance mechanisms are thus needed that help organisations design and deploy ADMS in ways that are ethical, while enabling society to reap the full economic and social (...) benefits of automation. In this article, we consider the feasibility and efficacy of ethics-based auditing as a governance mechanism that allows organisations to validate claims made about their ADMS. Building on previous work, we define EBA as a structured process whereby an entity’s present or past behaviour is assessed for consistency with relevant principles or norms. We then offer three contributions to the existing literature. First, we provide a theoretical explanation of how EBA can contribute to good governance by promoting procedural regularity and transparency. Second, we propose seven criteria for how to design and implement EBA procedures successfully. Third, we identify and discuss the conceptual, technical, social, economic, organisational, and institutional constraints associated with EBA. We conclude that EBA should be considered an integral component of multifaced approaches to managing the ethical risks posed by ADMS. (shrink)

The present article illustrates a conflict between the claim that rational belief sets are closed under deductive consequences, and a very inclusive claim about the factors that are sufficient to determine whether it is rational to believe respective propositions. Inasmuch as it is implausible to hold that the factors listed here are insufficient to determine whether it is rational to believe respective propositions, we have good reason to deny that rational belief sets are closed under deductive consequences.

This book offers a systematic and thorough philosophical analysis of the ways in which driving automation crosses path with ethical values. Upon introducing the different forms of driving automation and examining their relation to human autonomy, it provides readers with in-depth reflections on safety, privacy, moral judgment, control, responsibility, sustainability, and other ethical issues. Driving is undoubtedly a moral activity as a human act. Transferring it to artificial agents such as connected and automated vehicles necessarily raises many philosophical questions. (...) When driving is automated, what happens to its ethical dimensions? Could artificial agents accomplish ethical objectives on our behalf, take moral decisions in our place, and drive us into a more ethical transportation future? In doing so, would they be “moral” as we are or in a way that is similar to, but also remarkably different from, our own? And what role is yet to be played by human responsibility and commitment? The book addresses these questions with the aim of stimulating an interdisciplinary dialogue between different stakeholders. They include automotive engineers, computer scientists, and moral philosophers, as well as industry representatives, policymakers, regulators, transportation experts, and the general public. Indeed, connected and automated vehicles will not take the high road for us . We must drive them there. (shrink)

Human obsolescence is imminent. We are living through an era in which our activity is becoming less and less relevant to our well-being and to the fate of our planet. This trend toward increased obsolescence is likely to continue in the future, and we must do our best to prepare ourselves and our societies for this reality. Far from being a cause for despair, this is in fact an opportunity for optimism. Harnessed in the right way, the technology that hastens (...) our obsolescence can open us up to new utopian possibilities and enable heightened forms of human flourishing. (shrink)

A recent wave of academic and popular publications say that utopia is within reach: Automation will progress to such an extent and include so many high-skill tasks that much human work will soon become superfluous. The gains from this highly automated economy, authors suggest, could be used to fund a universal basic income (UBI). Today's employees would live off the robots' products and spend their days on intrinsically valuable pursuits. I argue that this prediction is unlikely to come true. (...) Historical precedent speaks against it, but the main problem is that the prediction fundamentally misunderstands how capitalism works—its incentives to increase or decrease production, its principles of income allocation, and the underlying conception of merit. (shrink)

Automated Influence is the use of Artificial Intelligence to collect, integrate, and analyse people’s data in order to deliver targeted interventions that shape their behaviour. We consider three central objections against Automated Influence, focusing on privacy, exploitation, and manipulation, showing in each case how a structural version of that objection has more purchase than its interactional counterpart. By rejecting the interactional focus of “AI Ethics” in favour of a more structural, political philosophy of AI, we show that the (...) real problem with Automated Influence is the crisis of legitimacy that it precipitates. (shrink)

Methods available for the axiomatization of arbitrary finite-valued logics can be applied to obtain sound and complete intelim rules for all truth-functional connectives of classical logic including the Sheffer stroke and Peirce’s arrow. The restriction to a single conclusion in standard systems of natural deduction requires the introduction of additional rules to make the resulting systems complete; these rules are nevertheless still simple and correspond straightforwardly to the classical absurdity rule. Omitting these rules results in systems for intuitionistic versions (...) of the connectives in question. (shrink)

The deductive validity of arguments from analogy is formally demonstrable. After a brief survey of the historical development of doctrines relevant to this claim the present article analyzes the “analogy of proper proportionality”, which meets two requirements of valid deduction. First, the referents of analogues by proportionality must belong to a common genus. Here it must be cautioned, however, that the common genus does not constitute the basis of the deductive inference. Rather, it is a prerequisite for the second (...) and decisive requirement, that the different logical content to which an analogous middle term corresponds must exhibit the same proportional relation to this common genus. In Section II I translate a natural language argument with such an analogous middle term into the language of classical first-order predicate calculus, and show that its conclusion follows from its premises with the force of deductive necessity. The rule of inference justifying the analogical entailment of the conclusion from the premises functions much like the familiar modus ponens rule, and could be called “modus ponens analogice”. The validity of this rule ought to be judged on the same basis as that of the traditional modus ponens rule – immediate logical intuition. The present article endeavors to facilitate this logical intuition by making the logical structure of inference by analogy formally explicit. (shrink)

The definitions of ‘deduction’ found in virtually every introductory logic textbook would encourage us to believe that the inductive/deductive distinction is a distinction among kinds of arguments and that the extension of ‘deduction’ is a determinate class of arguments. In this paper, we argue that that this approach is mistaken. Specifically, we defend the claim that typical definitions of ‘deduction’ operative in attempts to get at the induction/deduction distinction are either too narrow or insufficiently precise. We (...) conclude by presenting a deflationary understanding of the inductive/deductive distinction; in our view, its content is nothing over and above the answers to two fundamental sorts of questions central to critical thinking. (shrink)

From the second half of the last century, there has been a widespread view in the Anglophone world that Kant’s transcendental deduction (aka TD) aims to vindicate our common-sense view of the world as composed of public and objective particulars against some unqualified forms of skepticism. This widespread assumption has raised serious doubt not only about the success of TD but also about the very nature of its argument in both editions of the Critique. Yet, if there is a (...) connection between TD and global skepticism, the intriguing question is: Who is this skeptic? According to Strawson, “the skeptic” is a hypothesis of a purely sense-datum experience. In contrast, the fact that TD turns on the key notion of self-consciousness has induced several other scholars to assume that the skeptic is no none but a Cartesian external-world skeptic. None of those readings find textual support or are compatible with the very structure of the first Critique. The question is: Does this mean that TD aims only to undermine empiricism, as Guyer suggests? I do not believe so. I am pretty convinced that TD addresses a peculiar form of global skepticism, namely “Hume’s challenge to reason.” Assuming that we cognize (erkennen) and experience (erfahren) appearances as objects as a requirement of Newtonian physics, TD aims to provide a justification of the principle that nature is uniform that is superior to Hume’s justification. (shrink)

This paper delves into the use of machine learning-based systems in decision-making processes and its implications for moral responsibility as traditionally defined. It focuses on the emergence of responsibility gaps and examines proposed strategies to address them. The paper aims to provide an introductory and comprehensive overview of the ongoing debate surrounding moral responsibility in automated decision-making. By thoroughly examining these issues, we seek to contribute to a deeper understanding of the implications of AI integration in society.

We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility quantifies over some (...) point on the diagonal. Thus, they are just like the epistemic operators for apriority and its dual. We take this extension of Fitch’s familiar derivation system to be a very natural one, since the new rules and labeled lines hereby introduced preserve the structure of Fitch’s own rules for the modal case. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

Cette étude montre comment le météorologue Edward Lorenz, dans deux articles de 1963 et 1964, explore les propriétés des systèmes chaotiques par des allers-retours entre une déduction mathématique (basée sur la théorie des systèmes dynamiques) et une étude des solutions numériques du système dit « de Lorenz » dans un régime d’instabilité. This study aims at showing how the metereologist Edward Lorenz, in two papers of 1963 and 1964, explores the properties of chaotic systems thanks to the interplay between a (...) mathematical deduction (based on dynamical systems theory) and a study of the mathematical solutions of the Lorenz system in an instability regime. (shrink)

In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermedi- ate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction sys- tems are built only for strong Kleene’s logic both with (...) one (A. Urquhart, G. Priest, A. Tamminga) and two designated values (G. Priest, B. Kooi, A. Tamminga). The purpose of this paper is to provide natural deduction systems for weak and intermediate regular logics both with one and two designated values. (shrink)

REVIEW OF: Automated Development of Fundamental Mathematical Theories by Art Quaife. (1992: Kluwer Academic Publishers) 271pp. Using the theorem prover OTTER Art Quaife has proved four hundred theorems of von Neumann-Bernays-Gödel set theory; twelve hundred theorems and definitions of elementary number theory; dozens of Euclidean geometry theorems; and Gödel's incompleteness theorems. It is an impressive achievement. To gauge its significance and to see what prospects it offers this review looks closely at the book and the proofs it presents.

In mathematics, the deductive method reigns. Without proof, a claim remains unsolved, a mere conjecture, not something that can be simply assumed; when a proof is found, the problem is solved, it turns into a “result,” something that can be relied on. So mathematicians think. But is there more to mathematical justification than proof? -/- The answer is an emphatic yes, as I explain in this article. I argue that non-deductive justification is in fact pervasive in mathematics, and that it (...) is in good epistemic standing. (shrink)

Harold Hodes in [1] introduces an extension of first-order modal logic featuring a backtracking operator, and provides a possible worlds semantics, according to which the operator is a kind of device for ‘world travel’; he does not provide a proof theory. In this paper, I provide a natural deduction system for modal logic featuring this operator, and argue that the system can be motivated in terms of a reading of the backtracking operator whereby it serves to indicate modal scope. (...) I prove soundness and completeness theorems with respect to Hodes’ semantics, as well as semantics with fewer restrictions on the accessibility relation. (shrink)

Many of the benefits and burdens we might experience in our lives — from bank loans to bail terms — are increasingly decided by institutions relying on algorithms. In a sense, this is nothing new: algorithms — instructions whose steps can, in principle, be mechanically executed to solve a decision problem — are at least as old as allocative social institutions themselves. Algorithms, after all, help decision-makers to navigate the complexity and variation of whatever domains they are designed for. In (...) another sense, however, this development is startlingly new: not only are algorithms being deployed in ever more social contexts, they are being mechanically executed not merely in principle, but pervasively in practice. Due to recent advances in computing technology, the benefits and burdens we experience in our lives are now increasingly decided by automata, rather than each other. How are we to morally assess these technologies? In this chapter, I propose a preliminary conceptual schema for identifying and locating the various injustices of automated, algorithmic social decision systems, from a broadly liberal perspective. (shrink)

James Van Cleve has argued that Kant’s Transcendental Deduction of the categories shows, at most, that we must apply the categories to experience. And this falls short of Kant’s aim, which is to show that they must so apply. In this discussion I argue that once we have noted the differences between the first and second editions of the Deduction, this objection is less telling. But Van Cleve’s objection can help illuminate the structure of the B Deduction, (...) and it suggests an interesting reason why the rewriting might have been thought necessary. (shrink)

For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I (...) then develop an account on which informational contents are indeterminate in their membership. This allows there to be cases in which it is indeterminate whether a given deduction is informative. Nevertheless, on the picture I present, there are determinate cases of informative (and determinate cases of uninformative) inferences. I argue that the model I offer is the best way for an account of content to respect the meaning of the logical constants and the inference rules associated with them without collapsing into a classical picture of content, unable to account for informative deductive inferences. (shrink)

Advances in AI are powering increasingly precise and widespread computational propaganda, posing serious threats to national security. The military and intelligence communities are starting to discuss ways to engage in this space, but the path forward is still unclear. These developments raise pressing ethical questions, about which existing ethics frameworks are silent. Understanding these challenges through the lens of “cognitive security,” we argue, offers a promising approach.

In attempt to provide an answer to the question of origin of deductive proofs, I argue that Aristotle’s philosophy of math is more accurate opposed to a Platonic philosophy of math, given the evidence of how mathematics began. Aristotle says that mathematical knowledge is a posteriori, known through induction; but once knowledge has become unqualified it can grow into deduction. Two pieces of recent scholarship on Greek mathematics propose new ways of thinking about how mathematics began in the Greek (...) culture. Both claimed there was a close relationship between the culture and mathematicians; mathematics was understood through imaginative processes, experiencing the proofs in tangible ways, and establishing a consistent unified form of argumentation. These pieces of evidence provide the context in which Aristotle worked and their contributions lend support to the argument that mathematical premises as inductively available is a better way of understanding the origins of deductive practices, opposed to the Platonic tradition. (shrink)

In section 1, I develop epistemic communism, my view of the function of epistemically evaluative terms such as ‘rational’. The function is to support the coordination of our belief-forming rules, which in turn supports the reliable acquisition of beliefs through testimony. This view is motivated by the existence of valid inferences that we hesitate to call rational. I defend the view against the worry that it fails to account for a function of evaluations within first-personal deliberation. In the rest of (...) the paper, I then argue, on the basis of epistemic communism, for a view about rationality itself. I set up the argument in section 2 by saying what a theory of rational deduction is supposed to do. I claim that such a theory would provide a necessary, sufficient, and explanatorily unifying condition for being a rational rule for inferring deductive consequences. I argue in section 3 that, given epistemic communism and the conventionality that it entails, there is no such theory. Nothing explains why certain rules for deductive reasoning are rational. (shrink)

This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".

As automating technologies are increasingly integrated into workplaces, one concern is that many of the human workers who remain will be relegated to more dull and less positively impactful work. This paper considers two rival theories of meaningful work that might be used to evaluate particular implementations of automation. The first is achievementism, which says that work that culminates in achievements to workers’ credit is especially meaningful; the other is the practice view, which says that work that takes the form (...) of an open-ended practice is especially meaningful. Of the two, the practice view is the better tool for assessing the future of meaningful work, because achievementism is explanatorily inadequate in two ways. Moreover, the practice view can explain why the most meaningful forms of work cannot be automated. A procedure can only be automated as long as the steps are defined, whereas, in such work, which steps to take is indefinitely open to redefinition. This reveals the real threat to meaningful work to be a political-economic one. The relevant ethical questions there have to do with how much creative control workers retain in crafting their own jobs, when those jobs involve meaningful work in collaboration with machines; and how to liberate workers from jobs that do not involve meaningful work, which should be left to machines anyway. (shrink)

What is an inference and when is an inference deductive rather than inductive, abductive, etc. The goal of this paper is precisely to determine what is that we, humans, do when we engage in deduction, i.e., whether there is something that satisfies both our pre-theoretical intuitions and theoretical presuppositions about deduction, as a cognitive process. The paper is structured in two parts: the first one deals with the issue of what is an inference. There, I will defend the (...) hypothesis that an inference is a causal process where an initial cognitive state causes another in such a way that the causal translation depends essentially on the content of the involved states. In other words, in an inference, a mental state A causes another B, partially because they have the content they have. Based on the conclusion from the first part, I will develop an account of deductive inference in the second part of the article. In order to achieve this, I will start by setting the stage and developing four constraints that an adequate account of deductive inference ought to satisfy. Then, I will present six different hypotheses that one might propose to characterize inferences of this kind. I have divided the proposals in two groups, the first one – which I will call the “logical proposals” – assume that whether an inference is a deduction or not depends exclusively on the content of the mental states involved in the inference, while the second – which I will call the “cognitive proposals” – reject the aforementioned assumption and instead recognize that extra cognitive information is required to determine whether an inference is a deduction or not. I will evaluate each proposal in turn, according to whether they satisfy the constraints introduced at the beginning of this second part. As a result of such evaluation, I will conclude that only one of the cognitive proposals actually satisfies the four constraints and therefore should be considered to give an adequate characterization of deductive inference. (shrink)

The traditional No-Miracles Argument (TNMA) asserts that the novel predictive success of science would be a miracle, and thus too implausible to believe, if successful theories were not at least approximately true. The TNMA has come under fire in multiple ways, challenging each of its premises and its general argumentative structure. While the TNMA relies on explaining novel predictive success via the truth of the theories, we put forth a deductive version of the No-Miracles argument (DNMA) that avoids inference to (...) the best explanation entirely. Instead, a relatively simple empirical framework and a probabilistic analysis can accomplish the ambitious goals of the TNMA while entirely sidestepping its problems. This close-but-distinct argument has many independent strengths and comparatively few weaknesses. Indeed, objections tailored specifically to the DNMA reveal surprising insights into how exactly NMAs are neither circular nor question-begging, as has been widely speculated. (shrink)

Automated decision making for sentencing is the use of a software algorithm to analyse a convicted offender’s case and deliver a sentence. This chapter reviews the moral arguments for and against employing automated decision making for sentencing and finds that its use is in principle morally permissible. Specifically, it argues that well-designed automated decision making for sentencing will better approximate the just sentence than human sentencers. Moreover, it dismisses common concerns about transparency, privacy and bias as unpersuasive (...) or inapplicable. The chapter also notes that moral disagreement about theories of just sentencing are plausibly resolved by applying the principle of maximising expected moral choiceworthiness, and that automated decision making is better suited to the resulting ensemble model. Finally, the chapter considers the challenge posed by penal populism. The dispiriting conclusion is that although it is in theory morally desirable to use automated decision-making for criminal sentencing, it may well be the case that we ought not to try. (shrink)

How is moral knowledge possible? This paper defends the anti-Humean thesis that we can acquire moral knowledge by deduction from wholly non-moral premises. According to Hume’s Law, as it has become known, we cannot deduce an ‘ought’ from an ‘is’, since it is “altogether inconceivable how this new relation can be a deduction from others, which are entirely different from it” (Hume, 1739, 3.1.1). This paper explores the prospects for a deductive theory of moral knowledge that rejects Hume’s (...) Law. (shrink)

The paper discusses the origin of dark matter and dark energy from the concepts of time and the totality in the final analysis. Though both seem to be rather philosophical, nonetheless they are postulated axiomatically and interpreted physically, and the corresponding philosophical transcendentalism serves heuristically. The exposition of the article means to outline the “forest for the trees”, however, in an absolutely rigorous mathematical way, which to be explicated in detail in a future paper. The “two deductions” are two successive (...) stage of a single conclusion mentioned above. The concept of “transcendental invariance” meaning ontologically and physically interpreting the mathematical equivalence of the axiom of choice and the well-ordering “theorem” is utilized again. Then, time arrow is a corollary from that transcendental invariance, and in turn, it implies quantum information conservation as the Noether correlate of the linear “increase of time” after time arrow. Quantum information conservation implies a few fundamental corollaries such as the “conservation of energy conservation” in quantum mechanics from reasons quite different from those in classical mechanics and physics as well as the “absence of hidden variables” (versus Einstein’s conjecture) in it. However, the paper is concentrated only into the inference of another corollary from quantum information conservation, namely, dark matter and dark energy being due to entanglement, and thus and in the final analysis, to the conservation of quantum information, however observed experimentally only on the “cognitive screen” of “Mach’s principle” in Einstein’s general relativity. therefore excluding any other source of gravitational field than mass and gravity. Then, if quantum information by itself would generate a certain nonzero gravitational field, it will be depicted on the same screen as certain masses and energies distributed in space-time, and most presumably, observable as those dark energy and dark matter predominating in the universe as about 96% of its energy and matter quite unexpectedly for physics and the scientific worldview nowadays. Besides on the cognitive screen of general relativity, entanglement is available necessarily on still one “cognitive screen” (namely, that of quantum mechanics), being furthermore “flat”. Most probably, that projection is confinement, a mysterious and ad hoc added interaction along with the fundamental tree ones of the Standard model being even inconsistent to them conceptually, as far as it need differ the local space from the global space being definable only as a relation between them (similar to entanglement). So, entanglement is able to link the gravity of general relativity to the confinement of the Standard model as its projections of the “cognitive screens” of those two fundamental physical theories. (shrink)

This book provides a critical reflection on automated science and addresses the question whether the computational tools we developed in last decades are changing the way we humans do science. More concretely: Can machines replace scientists in crucial aspects of scientific practice? The contributors to this book rethink and refine some of the main concepts by which science is understood, drawing a fascinating picture of the developments we expect over the next decades of human-machine co-evolution. The volume covers examples (...) from various fields and areas, such as molecular biology, climate modeling, clinical medicine, and artificial intelligence. The explosion of technological tools and drivers for scientific research calls for a renewed understanding of the human character of science. This book aims precisely to contribute to such a renewed understanding of science. (shrink)

In the transcendental deduction, the central argument of the Critique of Pure Reason, Kant seeks to secure the objective validity of our basic categories of thought. He distinguishes objective and subjective sides of this argument. The latter side, the subjective deduction, is normally understood as an investigation of our cognitive faculties. It is identified with Kant’s account of a threefold synthesis involved in our cognition of objects of experience, and it is said to precede and ground Kant’s proof (...) of the validity of the categories in the objective deduction. I challenge this standard reading of the subjective deduction, arguing, first, that there is little textual evidence for it, and, second, that it encourages a problematic conception of how the deduction works. In its place, I present a new reading of the subjective deduction. Rather than being a broad investigation of our cognitive faculties, it should be seen as addressing a specific worry that arises in the course of the objective deduction. The latter establishes the need for a necessary connection between our capacities for thinking and being given objects, but Kant acknowledges that his readers might struggle to comprehend how these seemingly independent capacities are coordinated. Even worse, they might well believe that in asserting this necessary connection, Kant’s position amounts to an implausible subjective idealism. The subjective deduction ismeant to allay these concerns by showing that they rest on a misunderstanding of the relation between these faculties. This new reading of the subjective deduction offers a better fit with Kant’s text. It also has broader implications, for it reveals the more philosophically plausible account of our relation to the world as thinkers that Kant is defending – an account that is largely obscured by the standard reading of the subjective deduction. (shrink)