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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.

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.

A sound and effective data ethics requires an independent and mature epistemology of data science. We cannot address the ethical risks associated with data science if we cannot effectively diagnose its epistemological failures, and this is not possible if the outcomes, methods, and foundations of data science are themselves immune to criticism. An epistemology of data science that guards against the unreflective reliance on data science blocks this immunity. Critical evaluations of the epistemic significance of data and of the impact of design-decisions in software engineering already contribute to this enterprise but leave the role of mathematics within data science largely unexamined. In this chapter we take a first step to fill this gap. In a first part, we emphasise how data, code, and maths jointly enable data science, and how they contribute to the epistemic and scientific respectability of data science. This analysis reveals that if we leave out the role of mathematics, we cannot adequately explain how epistemic success in data science is possible. In a second part, we consider the more contentious dual issue: Do explanations of epistemic failures in data science also force us to critically assess the role of maths in data science? Here, we argue that mathematics not only contributes mathematical truths to data science, but also substantive epistemic values. If we evaluate these values against a sufficiently broad understanding of what counts as epistemic success and failure, our question should receive a positive answer.

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.

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.

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.

The starting point of this paper is a version of intra-theoretical (logical) 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 (adapted to the 3-sided sequent-calculus used by Hjortland) 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. The latter leads to the general methodological recommendation that the conceptual resources used to think and talk about logic should be kept in line with the formal resources that are used to define and describe a logical theory.

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.

Modal logics have in the past been used as a unifying framework for the mini- mality 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.

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.

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.

To a first approximation, the sorites paradox, or paradox of the heap, proceeds thus.Consider n ? 1 grains of sand, and let n be large enough so that n ? 1 grains ofsand clearly and unambiguously make a heap. Consider, then, the followingprinciple: if n ? 1 grains of sand make a heap, then surely n grains also make aheap. Putting both seemingly acceptable assumptions together, we may concludethat n grains make a heap. Yet, if we can once reason along these lines, we canequally well apply this reasoning n times, and thus conclude that even a single grainof sand makes a heap. This last conclusion surely can’t be true, yet we arrived at itby (seemingly) correct reasoning from (apparently) true premises. An obviouslyfalse or at least clearly unacceptable conclusion that follows from otherwiseintuitively true premises is all we need to have a genuine paradox.One of the things van Deemter does is to defend a specific solution to the soritesparadox. However, this book does much more than that, and differs in that respectfrom the literature on vagueness philosophical logicians are accustomed to. In fact,apart from a brief description of the sorites paradox in the introduction, we have towait until Chapters 7 and 8 for a discussion of paradox as we know it.Already in the introduction van Deemter makes clear what his real target is;namely, the concept of False Clarity. The underlying theme of this book is the clashbetween vague expressions and concepts, and our tendency to talk and think aboutthese concepts as if they were crisp. By these lights, the sorites paradox is nothingmore than one particularly telling symptom of a broader phenomenon (though, inview of the more mundane examples van Deemter reviews, perhaps also amisleadingly artificial one).While most treatments of the phenomenon of vagueness traditionally focus on thesemantics of vague predicates, the present book sets out to answer at least two more

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.

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.

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.

My goal in this talk is to further develop the informational conception of logic proposed in [1] by motivating and exploring a methodology for logical practices (using, developing and thinking about logic) that is inspired by the methodology from the philosophy of information, with particular emphasis on its constructionist metaphilosophy [2]. Against this background, I’m interested in the following phenomenon: If a formalisation-process leads to the refinement of one or more concepts we are interested in (either because we are explicitly formalising them, or because we use them to talk about the concepts we are actually formalising), this often leads to a “splitting of notions”. In that case, the uncareful use of the original notions in combination with their refinements often leads to fallacies of equivocation. As suggested in [3], the development of a design-perspective on logic is meant to show that this phenomenon is a reason to abandon the original concepts, and not a reason to cast doubt on the proposed refinement. As a corollary, constructionism is logic contributes to the motivation of a pluralist perspective on logical practices. The proposed view has affinities with several contemporary and historical perspectives on logic. The emphasis on design is akin to Carnap’s own “logic first” approach, which he contrasted with a “philosophy first” approach to logical theorising, as well as to his views about explic­ation and conceptual engineering [4]. The proposed view also resembles the suggestion that our logical practice of formulating a logic should be seen as an entirely standard form of theory-building about a given subject- matter (Logic), rather than as the manipulation of Logic itself [5]. The application of insights from the method of abstraction (the methodological recommendation and formal tool to make explicit the interface we use to access the system we study) to the use and development of logic is entirely in line with the logic-as-model view proposed by Shapiro and Cook, and especially with its emphasis on the need to negotiate tradeoffs [6]. Even though the main lines of my proposal can be described in terms of the above views, I will develop it from first principles and focus explicitly on poietic aspects of actual logical practices. The basic tenet of constructionism as an epistemological thesis is that we can only know what we make. Our only knowledge is a maker’s knowledge; a knowledge of the artefacts we built and thus can examine from within (white box) rather than a user’s knowledge we acquire by observing what is given from without (black box). As Floridi puts it: “Knowledge is not about getting the message from the world; it is first and foremost about negotiating the right sort of communication with it. (…) [C]onstructionism is neither realism nor constructivism, because knowledge neither describes nor prescribes how the world is but inscribes it with semantic artefacts.” [2]. As a methodological recommendation, constructionism is less radical, and only calls for the complementation of conceptual analysis with conceptual engineering. This is the sense in which I’ll employ the term. When treated as a core ingredient of the philosophy of information, constructionism works hand in hand with the method of abstraction [7]. Whereas constructionism emphasises the need to engineer our access to the world, the method of abstraction provides the concepts that allow us to think about different ways of accessing the world, but also draws attention to the fact that since we can only know our models of the world, we cannot directly compare a model with the world (our only knowledge is by proxy), but only compare different models. This does not only imply that we can only compare levels of abstraction, but also that there is no most general, maximally precise or otherwise epistemically or ontologically fundamental level of abstraction that could play the role of final arbiter (for all means and purposes a direct access). As I shall argue, we can think about logics as semantic artefacts that allow us to access the world for descriptive as well as for deductive or inferential purposes. This is already a pluralist assumption, for if a logic acts as an interface or a communication-channel, we have no reason to assume that there is a single best all-purpose logic. Indeed, pluralism about levels of abstraction can naturally be associated with two important theoretical virtues of logical pluralism, namely: The freedom to make certain distinctions and/or fudge some other distinctions, and The freedom to outlaw certain expressions. One of the most visible tasks of the development of a formal logic is the design of a formal language. Since such formal languages are almost by definition artificial languages, the description of the rules that govern that language (formation-rules, truth-conditions, formal inference-patters) is much closer to conceptual engineering than it is to conceptual analysis. Narrowly conceived, language design is an uncontroversial example of process that has to result in an artefact that has to meet certain specifications (a perspicuous notation system or well-behaved language), but what would it mean to consider logical theorising as a whole as a design task? Highly simplified, such a view on logic would mark clear departure from traditional logical analysis, for where successful logical analysis results in a formal account that agrees with the data (something that is given), successful logical construction results in a formal account that meets a set of self-imposed specifications, which includes but is not limited to agreement with the data. An understanding of logical theorising as a whole in terms of meeting certain specifications gives a more radical pragmatic slant to the question of logic choice. It’s the pragmatics behind what Shapiro calls the negotiation of tradeoffs within his logic-as-model perspective, or what I call the balancing the logical virtues of deductive strength and discriminatory power (the ability to tell formulae apart). Putting this on the table raises the further question of what a specification for a problem in logical theorising might look like. If we understand a specification as a criterion for correctness and malfunction relative to a given level of abstraction [8], it is clear that in such a context success does not merely depend on general theoretical virtues, but also on context and/or application specific norms. By further developing this suggestion, we should arrive at an account of “logic-specification” that guides our design decisions in the sense that it tells us how to deal with tradeoffs between different desirable formal features. As a corollary, it also further embeds a logical pluralism within the methodology of the philosophy of information, since it is consistent with the view that some logics are more general than others, but also recognises that wider applicability always comes at a cost. References and Notes Allo and E. Mares, "Informational Semantics as a Third Alternative?", Erkenntnis, 77, no. 2, p. . 167-185, 2012. Floridi, "A defence of constructionism: philosophy as conceptual engineering", Metaphilosophy, 42, no. 3, p. . 282-304, 2011. Allo, "Synonymy and intra-theoretical pluralism", Australasian Journal of Philosophy, 93, no. 1, p. . 77-91, 2015. Carus, Carnap and Twentieth-Century Thought, no. Cambridge: Cambridge University Press, 2008. Priest, Doubt Truth to be a Liar, no. Oxford: Oxford University Press, 2006. Shapiro, Varieties of logic, no. Corby: Oxford University Press, 2014. Floridi, "The Method of Levels of Abstraction", Minds and Machines, 18, no. 3, p. 303-329, 2008. Turner, "Specification", Minds and Machines, 21, no. 2, p. 135-152, 2011.

Standard refinements of epistemic and doxastic logics that avoid the problems of logical and deductive omniscience cannot easily be generalised to default reasoning. This is even more so when defeasible reasoning is understood as tentative reasoning; an understanding that is inspired by the dynamic proofs of adaptive logic. In the present paper we extend the abnormality (preference) models for adaptive consequence with a set of open worlds to account for this type of inferential dynamics. In doing so, we argue that unlike for mere deductive reasoning, tentative inference cannot be modelled without such open worlds.

In this paper we investigate the topic of ambiguous connectives, as it was recently explored by Paoli (J. Philos. Logic 32:531–548,2003), from an informational perspective. That is, starting from the framework of informational pluralism Allo (Computing, Philosophy, and Cognitive Science.Cambridge Scholars Press, Cambridge,41–52,2007a) Allo (J. Philos. Logic 36:659–694,2007b), we ask what it means for a message of the form ‘A or B’, to be informative. Using these disjunctive messages as an example, we answer three traditional objections to substructural logic and logical pluralism, and eventually show that the linear or relevant logician’s road to unambiguous connectives is consistent with informational pluralism.

Notes on Contributors. Introduction. 1 Putting Information First: Luciano Floridi and the Philosophy of Information (PATRICK ALLO). Knowledge. 2 The Value of Knowledge and the Pursuit of Survival (SHERRILYN ROUSH). 3 Knowledge Transmissibility and Pluralistic Ignorance: A First Stab (VINCENT F. HENDRICKS). Agency. 4 Meeting Floridi's Challenge to Artificial Intelligence from the Knowledge-Game Test for Self-Consciousness (SELMER BRINGSJORD). Semantic Information. 5 Information Without Truth (ANDREA SCARANTINO AND GUALTIERO PICCININI). 6 Information and Knowledge a la Floridi (FRED ADAMS). Methodology. 7 Abstraction, Law, and Freedom in Computer Science (TIMOTHY COLBURN AND GARY SHUTE). Metaphysics. 8 Structuralism and Information (OTA VIO BUENO). Ethics. 9 Why Information Ethics Must Begin with Virtue Ethics (RICHARD VOLKMAN). Replies. 10 The Philosophy of Information: Ten Years Later (LUCIANO FLORIDI). Epilogue. 11 Philosophy in the Information Age (TERRELL WARD BYNUM). Index.

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 generated submodels. The latter are then shown to yield an adaptive logic wherein the derivability of

Because the conclusion of a correct proof follows by necessity from its premises, and is thus independent of the mathematician's beliefs about that conclusion, understanding how different pieces of mathematical knowledge can be distributed within a larger community is rarely considered an issue in the epistemology of mathematical proofs. In the present chapter, we set out to question the received view expressed by the previous sentence. To that end, we study a prime example of collaborative mathematics, namely the Polymath Project, and propose a simple formal model based on epistemic logics to bring out some of the core features of this case-study.

In the contemporary society a massive amount of data is generated continuously by various means, and they are called Big-Data sets. Big Data has potential and limits which need to be understood by statisticians and statistics consumers, therefore it is a challenge to develop Big-Data Literacy to support the needs of constructive, concerned, and reflective citizens. However, the development of the concept of statistical literacy mirrors the current gap between purely technical and socio-political characterizations of Big Data. In this paper, we review the recent history of the concept of statistical literacy and highlight the need to integrate the new challenges and critical issues from data science associated with Big Data, including ethics, epistemology, mathematical justification, and math washing. First published February 2020 at Statistics Education Research Journal Archives

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.