In this paper I use the distinction between hard and soft information from the dynamic epistemic logic tradition to extend prior work on informational conceptions of logic to include non-monotonic consequence-relations. In particular, I defend the claim that at least some non-monotonic logics can be understood on the basis of soft or “belief-like” logical information, and thereby question the orthodox view that all logical information is hard, “knowledge-like”, information.

The Polymath Project is an online collaborative enterprise that was initiated in 2009, when Timothy Gowers asked whether and how groups could work together to solve mathematical problems that “do not naturally split up into a vast number of subtasks.” Gowers proposed to answer this question himself by actually trying to set up such a collaboration, based on interactions taking place in the comment-threads of a series of posts on a WordPress blog. Hence, the first project officially started in early (...) 2009, to be proclaimed successful only 6 weeks later (Gowers and Nielsen 2009). From its inception until April 2018, 15 more Polymath problems (and a handful of smaller or related ones) have been launched. These projects have attracted attention from different scholarly communities, including the philosophy of mathematical practices, from the perspective of which the Polymath Project can be seen as a vast repository of mathematics in action. This chapter continues previous work by its authors on the topic in question and topics related. More specifically, for the purposes of this volume, it is our aim to both summarize and expand upon these earlier contributions. The starting point is the above observation that in the past decade, the issue of “massively collaborative mathematics” (to be qualified below) has drawn quite some attention. However, does it also warrant intensive philosophical attention in particular? For, as exciting as these developments might be from mathematical and other points of view, the enhanced possibilities that have come with it do not per se give rise to any philosophical import. In Van Bendegem (2011), one of us has indeed tentatively argued for the philosophical relevance of these new dynamics of proof construction flowing from the wide availability and efficiency of Internet technology. We shall below briefly rehearse and update the argument given there. (shrink)

This paper develops and refines the suggestion that logical systems are conceptual artefacts that are the outcome of a design-process by exploring how a constructionist epistemology and meta-philosophy can be integrated within the philosophy of logic.

Up to now theories of semantic information have implicitly relied on logical monism, or the view that there is one true logic. The latter position has been explicitly challenged by logical pluralists. Adopting an unbiased attitude in the philosophy of information, we take a suggestion from Beall and Restall at heart and exploit logical pluralism to recognise another kind of pluralism. The latter is called informational pluralism, a thesis whose implications for a theory of semantic information we explore.

The distinction between distributive and non-distributive profiles figures prominently in current evaluations of the ethical and epistemological risks that are associated with automated profiling practices. The diagnosis that non-distributive profiles may coincidentally situate an individual in the wrong category is often perceived as the central shortcoming of such profiles. According to this diagnosis, most risks can be retraced to the use of non-universal generalisations and various other statistical associations. This article develops a top-down analysis of non-distributive profiles in which this (...) fallibility of non-distributive profiles is no longer central. Instead, it focuses on how profiling creates various asymmetries between an individual data-subject and a profiler. The emergence of informational, interest, and perspectival asymmetries between data-subject and profiler explains how non-distributive profiles weaken the epistemic position of a profiled individual. This alternative analysis provides a more balanced assessment of the epistemic risks associated with non-distributive profiles. (shrink)

Abstract: The core aim of this special issue is to present the philosophy of information as a way of doing philosophy, to focus on the contributions of Luciano Floridi to that area, and most important, to stimulate the debate on the most distinctive and controversial views he has defended in that context. This introduction contains a description of the philosophy of information, a discussion of two common misconceptions about the scope and the ambition of the philosophy of information, and a (...) brief overview of the essays in the issue. (shrink)

The logic of ‘being informed’ gives a formal analysis of a cognitive state that does not coincide with either belief, or knowledge. To Floridi, who first proposed the formal analysis, the latter is supported by the fact that unlike knowledge or belief, being informed is a factive, but not a reflective state. This paper takes a closer look at the formal analysis itself, provides a pure and an applied semantics for the logic of being informed, and tries to find out (...) to what extent the formal analysis can contribute to an information-based epistemology. (shrink)

Informational semantics were first developed as an interpretation of the model-theory of substructural (and especially relevant) logics. In this paper we argue that such a semantics is of independent value and that it should be considered as a genuine alternative explication of the notion of logical consequence alongside the traditional model-theoretical and the proof-theoretical accounts. Our starting point is the content-nonexpansion platitude which stipulates that an argument is valid iff the content of the conclusion does not exceed the combined content (...) of the premises. We show that this basic platitude can be used to characterise the extension of classical as well as non-classical consequence relations. The distinctive trait of an informational semantics is that truth-conditions are replaced by information-conditions. The latter leads to an inversion of the usual order of explanation: Considerations about logical discrimination (how finely propositions are individuated) are conceptually prior to considerations about deductive strength. Because this allows us to bypass considerations about truth, an informational semantics provides an attractive and metaphysically unencumbered account of logical consequence, non-classical logics, logical rivalry and pluralism about logical consequence. (shrink)

Cognitive states as well as cognitive commodities play central though distinct roles in our epistemological theories. By being attentive to how a difference in their roles affects our way of referring to them, we can undoubtedly accrue our understanding of the structure and functioning of our main epistemological theories. In this paper we propose an analysis of the dichotomy between states and commodities in terms of the method of abstraction, and more specifically by means of infomorphisms between different ways to (...) classify states of information, information-bases, and evidential situations. (shrink)

The starting point of this paper is a version of intra-theoretical pluralism that was recently proposed by Hjortland [2013]. In a first move, I use synonymy-relations to formulate an intuitively compelling objection against Hjortland's claim that, if one uses a single calculus to characterise the consequence relations of the paraconsistent logic LP and the paracomplete logic K3, one immediately obtains multiple consequence relations for a single language and hence a reply to the Quinean charge of meaning variance. In a second (...) move, I explain how a natural generalisation of the notion of synonymy can be used to counter this objection, but I also show how the solution can be turned into an equally devastating ‘one logic after all’ type of objection. Finally, I propose the general diagnosis that these problems could only arise in the presence of conceptual distinctions that are too coarse to accommodate coherent pluralist theses. T.. (shrink)

In this paper I present a more refined analysis of the principles of deductive closure and positive introspection. This analysis uses the expressive resources of logics for different types of group knowledge, and discriminates between aspects of closure and computation that are often conflated. The resulting model also yields a more fine-grained distinction between implicit and explicit knowledge, and places Hintikka’s original argument for positive introspection in a new perspective.

The traditional connection between logic and reasoning has been under pressure ever since Gilbert Harman attacked the received view that logic yields norms for what we should believe. In this article I first place Harman's challenge in the broader context of the dialectic between logical revisionists like Bob Meyer and sceptics about the role of logic in reasoning like Harman. I then develop a formal model based on contemporary epistemic and doxastic logic in which the relation between logic and norms (...) for belief can be captured. (shrink)

This chapter contains sections titled: First Misconception Second Misconception The Chapters Conclusion Acknowledgments References.

In information societies, operations, decisions and choices previously left to humans are increasingly delegated to algorithms, which may advise, if not decide, about how data should be interpreted and what actions should be taken as a result. More and more often, algorithms mediate social processes, business transactions, governmental decisions, and how we perceive, understand, and interact among ourselves and with the environment. Gaps between the design and operation of algorithms and our understanding of their ethical implications can have severe consequences (...) affecting individuals as well as groups and whole societies. This paper makes three contributions to clarify the ethical importance of algorithmic mediation. It provides a prescriptive map to organise the debate. It reviews the current discussion of ethical aspects of algorithms. And it assesses the available literature in order to identify areas requiring further work to develop the ethics of algorithms. (shrink)

Modal logics have in the past been used as a unifying framework for the minimality semantics used in defeasible inference, conditional logic, and belief revision. The main aim of the present paper is to add adaptive logics, a general framework for a wide range of defeasible reasoning forms developed by Diderik Batens and his co-workers, to the growing list of formalisms that can be studied with the tools and methods of contemporary modal logic. By characterising the class of abnormality models, (...) this aim is achieved at the level of the model-theory. By proposing formulae that express the consequence relation of adaptive logic in the object-language, the same aim is also partially achieved at the syntactical level. (shrink)

This commentary is a reflection on a collaboration with the artist Rossella Biscotti and comments on how artistic research and logico-mathematical methods can be used to contribute to the development of critical perspectives on contemporary data practices.

Substructural pluralism about the meaning of logical connectives is best understood as the view that natural language connectives have all (and only) the properties conferred by classical logic, but that particular occurrences of these connectives cannot simultaneously exhibit all these properties. This is just a more sophisticated way of saying that while natural language connectives are ambiguous, they are not so in the way classical logic intends them to be. Since this view is usually framed as a means to resolve (...) paradoxes, little attention is paid to the logical properties of the ambiguous connectives themselves. The present paper sets out to fill this gap. First, I argue that substructural logicians should care about these connectives; next, I describe a consequence relation between a set of ambiguous premises and an ambiguous conclusion, and review the logical properties of ambiguous connectives; and finally, I highlight how ambiguous connectives can explain our intuitions about logical rivalry. (shrink)

In this paper I reassess Floridi's solution to the Bar-Hillel-Carnap paradox (the information-yield of inconsistent propositions is maximal) by questioning the orthodox view that contradictions cannot be true. The main part of the paper is devoted to showing that the veridicality thesis (semantic information has to be true) is compatible with dialetheism (there are true contradictions), and that unless we accept the additional non-falsity thesis (information cannot be false) there is no reason to presuppose that there is no such thing (...) like contradictory information. (shrink)

We present a multi-conclusion natural deduction calculus characterizing the dynamic reasoning typical of Adaptive Logics. The resulting system AdaptiveND is sound and complete with respect to the propositional fragment of adaptive logics based on CLuN. This appears to be the first tree-format presentation of the standard linear dynamic proof system typical of Adaptive Logics. It offers the advantage of full transparency in the formulation of locally derivable rules, a connection between restricted inference-rules and their adaptive counterpart, and the formulation of (...) abnormalities as a subtype of well-formed formulas. These features of the proposed calculus allow us to clarify the relation between defeasible and multiple-conclusion approaches to classical recapture. (shrink)

One of the basic principles of the general definition of information is its rejection of dataless information, which is reflected in its endorsement of an ontological neutrality. In general, this principles states that “there can be no information without physical implementation” (Floridi (2005)). Though this is standardly considered a commonsensical assumption, many questions arise with regard to its generalised application. In this paper a combined logic for data and information is elaborated, and specifically used to investigate the consequences of restricted (...) and unrestricted data-implementation-principles. (shrink)

Informational conceptions of logic are barely novel. We find them in the work of John Corcoran, in several papers on substructural and constructive logics by Heinrich Wansing, and in the interpretation of the Routley-Meyer semantics for relevant logics in terms of Barwises and Perrys theory of situations. Allo & Mares [2] present an informational account of logical consequence that is based on the content-nonexpantion platitude, but that also relies on a double inversion of the standard direction of explanation (in- (...) formation doesnt depend on a prior notion of meaning, but is used to naturalize meaning, and informational content is not defined relative to a pre-existing logical space, but that space is constructed relative to the level of abstraction at which information is assessed). In this paper I focus directly on one of the main ideas introduced in that paper, namely the contrast between logical discrimination and deductive strength, and use this contrast to (1) illustrate a number of open problems for an informational conception of logical consequence, (2) review its connection with the dynamic turn in logic, and (3) situate it relative to the research agenda of the philosophy of information. (shrink)

In this paper we provide a formal description of what it means to be in a local or partial information-state. Starting from the notion of locality in a relational structure, we define so-called adaptive gen- erated submodels. The latter are then shown to yield an adaptive logic wherein the derivability of Pφ is naturally interpreted as a core property of being in a state in which one holds the information that φ.

Floridi’s chapter on relevant information bridges the analysis of “being informed” with the analysis of knowledge as “relevant information that is accounted for” by analysing subjective or epistemic relevance in terms of the questions that an agent might ask in certain circumstances. In this paper, I scrutinise this analysis, identify a number of problems with it, and finally propose an improvement. By way of epilogue, I offer some more general remarks on the relation between (bounded) rationality, the need to ask (...) the right questions, and the ability to ask the right questions. (shrink)

Herbert Simon was definitely 20th century’s most influential proponent of bounded rationality. His work was of a highly philosophical nature, but—as made clear time and again in this book—his ideas did not originate in philosophy at all. If the present collection of essays has any value to the philosophically oriented reader, it lies in the way it shows how a traditionally philosophical topic as human rationality and action cannot be claimed by philosophy alone. Even more, it shows that important contributions (...) to the issue were made in a highly applied context. Therefore, even if Models of a Man: Essays in Memory of Herbert Simon is all but a philosophy textbook, it is of interest to anyone taking Simon ’s influence in philosophy seriously. (shrink)

As Vincent Hendricks remarks early on in this book, the formal and mainstream traditions of epistemic theorising have mostly evolved independently of each other. This initial impression is confirmed by a comparison of the main problems and methods practitioners in each tradition are concerned with. Mainstream epistemol- ogy engages in a dialectical game of proposing and challenging definitions of knowledge. Formal epistemologists proceed differently, as they design a wide variety of axiomatic and model-theoretic methods whose consequences they investigate independently of (...) the need of giving counterexample-free definitions of knowledge. Or at least, this is a common way to explain where both disciplines stand in the larger landscape of epistemic theorising, and why interactions between them remain scarce. The main ambition of this book is to show that the distinction between formal and mainstream approaches should not preclude a fruitful interaction, and that it only takes the right outlook on their respective practices to disclose plenty of room for interaction. (shrink)

Coherent, well organized text familiarizes readers with complete theory of logical inference and its applications to math and the empirical sciences. Part I deals with formal principles of inference and definition; Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Last section introduces numerous examples of axiomatically formulated theories in both discussion and exercises. Ideal for undergraduates; no background in math or philosophy required.

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)

This book launches a sustained defense of a radical interpretation of the doctrine of the open future. Patrick Todd argues that all claims about undetermined aspects of the future are simply false.

It is widely accepted that there is what has been called a non-hypocrisy norm on the appropriateness of moral blame; roughly, one has standing to blame only if one is not guilty of the very offence one seeks to criticize. Our acceptance of this norm is embodied in the common retort to criticism, “Who are you to blame me?”. But there is a paradox lurking behind this commonplace norm. If it is always inappropriate for x to blame y for a (...) wrong that x has committed, then all cases in which x blames x (i.e. cases of self-blame) are rendered inappropriate. But it seems to be ethical common-sense that we are often, sadly, in position (indeed, excellent, privileged position) to blame ourselves for our own moral failings. And thus we have a paradox: a conflict between the inappropriateness of hypocritical blame, and the appropriateness of self-blame. We consider several ways of resolving the paradox, and contend none is as defensible as a position that simply accepts it: we should never blame ourselves. In defending this startling position, we defend a crucial distinction between self-blame and guilt. (shrink)

This paper offers a new approach to an old debate about superaddition in Locke. Did Locke claim that some objects have powers that are unrelated to their natures or real essences? The question has split commentators. Some (Wilson, Stuart, Langton) claim the answer is yes and others (Ayers, Downing, Ott) claim the answer is no. This paper argues that both of these positions may be mistaken. I show that Locke embraced a robust epistemic humility. This epistemic humility includes ignorance of (...) the real essences of bodies, of the causal processes underlying the production of natural phenomena, and of God’s method of creation. I show how this epistemic humility offers strong support for an agnostic response to the question of superaddition. Locke did not intend to claim that bodies either do or do not have properties unrelated to their real essences. Instead, his primary goal in discussing the topic was to emphasize the strict limits to human knowledge. (shrink)

Management and Morality provides a comprehensive and accessible overview of the moral and ethical dimension to organizational and individual behavior, while adding an original, developmental perceptive. Management and Morality combines organizational theory and behavior with approaches to organizational and individual development. The first two sections of the book, Ethical Thinking and Management Practice, and Moral Issues in Organizations, provide a clear and thorough coverage of these areas relevant to ethical behavior in and of organizations. On this basis, the third section, (...) A Developmental Perspective, develops a new approach to ethical development of organizations and individuals concerned with the improvement of organizational structures, processes, and practices so as to allow for individual morality and individual moral behavior. Rich in its coverage of the field and variety of ideas, Management and Morality will be essential reading to students and academics in management, business and organizational ethics, organizational behavior and development, and organizational sociology. (shrink)

Incompatibilism about responsibility and determinism is sometimes directly construed as the thesis that if we found out that determinism is true, we would have to give up the reactive attitudes. Call this "the consequence". I argue that this is a mistake: the strict modal thesis does not entail the consequence. First, some incompatibilists (who are also libertarians) may be what we might call *resolute responsibility theorists* (or "flip-floppers"). On this view, if we found out that determinism is true, this would (...) not be to find out that no one is responsible; instead, what this would suggest is that incompatibilism is after all false. Second, some incompatibilists may instead deny the claim that if we found out that no one deserves the reactiveattitudes, we would have to give up the reactive attitudes. Call this position *innocent incompatibilism*. I explore several different reasons why the fact that no one deserves the reactive attitudes likely does not translate into a requirement for us to give up the reactive attitudes. The upshot: incompatibilism may be practically irrelevant, even if true. (shrink)

Locke famously claimed that morality was capable of demonstration. But he also refused to provide a system of demonstrative morality. This paper addresses the mismatch between Locke’s stated views and his actual philosophical practice. While Locke’s claims about demonstrative morality have received a lot of attention it is rare to see them discussed in the context of his general theory of demonstration and his specific discussions of particular demonstrations. This paper explores Locke’s general remarks about demonstration as well as his (...) claims about demonstration in natural philosophy, mathematics, and morality. Careful attention to these detailed discussions motivates a reevaluation of Locke’s views on demonstrative knowledge of morality. Specifically, while Locke did believe that some demonstrative moral knowledge might be in-principle available to us he also believed that facts about the difficulty of demonstration meant that this knowledge would in-practice be largely unattainable. (shrink)

The text includes fragments of his work that have never before been translated.

I want to suggest that it would be bad if compatibilism were true, and that this gives us good reason to think that it isn't. This is, you might think, an outlandish argument, and the considerable burden of this paper is to convince you otherwise. There are two key elements at stake in this argument. The first is that it would be ‐ in a distinctive sense to be explained ‐ bad if compatibilism were true. The thought here is that (...) compatibilism ultimately presents us with a picture on which, in principle, powerful manipulators can effectively guarantee that finite moral agents should become blameworthy. To my mind, this isn't just false ‐ though I think that it is ‐ it is also such that it would be bad (unfortunate, undesirable…) if it were true. The second is that the fact that it would be ‐ in this sense ‐ bad if true gives us reason to think that it isn't. It may be bad that there is no afterlife. But that, in itself, hardly gives us reason to think that there is an afterlife. That is true, but ‐ as others before me have suggested ‐ when the object of the relevant badness is morality itself, the inference seems secure. A more general aim of the paper is to investigate the nature of this very form of argument in itself, and I compare my argument (inter alia) to a recent argument from Sayre–McCord against the possibility of genuine moral dilemmas. (shrink)

In this paper back-and-forth structures are applied to the semantics of natural language. Back-and-forth structures consist of an event structure and an interval structure communicating via a relational link; transitions in the one structure correspond to transitions in the other. Such entities enable us to view temporal constructions (such as tense, aspect, and temporal connectives) as methods of moving systematically between information sources. We illustrate this with a treatment of the English present perfect, and progressive aspect, that draws on ideas (...) developed in Moens & Steedman (1988), and discuss the role of rich ontologies in formal semantics. (shrink)

This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.

In this paper, we clarify, unpack, and ultimately resist what is perhaps the most prominent argument for the compatibility of free will and determinism: the epistemic argument for compatibilism. We focus on one such argument as articulated by David Lewis: (i) we know we are free, (ii) for all we know everything is predetermined, (iii) if we know we are free but for all we know everything is predetermined, then for all we know we are free but everything is predetermined, (...) (iv) if for all we know we are free but predetermined, then it is really possible that we are, so (v) compatibilism. We uncover how the crucial epistemic modality underlying (iv) must be understood, and contend that, understood this way, the libertarian can resist (iv). Importantly, however, resisting the argument does commit the libertarian to what has been called “flip-flopping”—but we argue that this is perfectly coherent. We conclude by articulating two crucially ways the libertarian can resist the argument, by saying that we can know that determinism is false "from the armchair". (shrink)

A small consortium of philosophers has begun work on the implications of epistemic networks (Zollman 2008 and forthcoming; Grim 2006, 2007; Weisberg and Muldoon forthcoming), building on theoretical work in economics, computer science, and engineering (Bala and Goyal 1998, Kleinberg 2001; Amaral et. al., 2004) and on some experimental work in social psychology (Mason, Jones, and Goldstone, 2008). This paper outlines core philosophical results and extends those results to the specific question of thresholds. Epistemic maximization of certain types does show (...) clear threshold effects. Intriguingly, however, those effects appear to be importantly independent from more familiar threshold effects in networks. (shrink)