There is growing concern that decision-making informed by machine learning (ML) algorithms may unfairly discriminate based on personal demographic attributes, such as race and gender. Scholars have responded by introducing numerous mathematical definitions of fairness to test the algorithm, many of which are in conflict with one another. However, these reductionist representations of fairness often bear little resemblance to real-life fairness considerations, which in practice are highly contextual. Moreover, fairness metrics tend to be implemented in narrow and targeted toolkits that (...) are difficult to integrate into an algorithm’s broader ethical assessment. In this paper, we derive lessons from ethical philosophy and welfare economics as they relate to the contextual factors relevant for fairness. In particular we highlight the debate around acceptability of particular inequalities and the inextricable links between fairness, welfare and autonomy. We propose Key Ethics Indicators (KEIs) as a way towards providing a more holistic understanding of whether or not an algorithm is aligned to the decision-maker’s ethical values. (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)

This paper discusses knowledge of opposites. In particular, attention is given to the linguistic notion of antonymy and how it represents oppositional relations that are commonly found in perception. The paper draws upon the long history of work on the formalisation of antonymy in linguistics and formal semantics, and also upon work on the perception of opposites in psychology, and an assessment is made of the main approaches. Treatments of these phenomena in linguistics and psychology posit that the principles (...) of minimal difference and invariance are centrally important. It will be suggested that the standard approach employing meaning postulates fails to capture the relevant notion of antonymy, in part because it is not informed by these principles, and in part due to a number of other problems with this kind of approach, many of which may be overcome by building in the central principles from the beginning. The paper also discusses the issue of whether we can know that opposites necessarily exclude each other and, if so, how. This issue is intertwined with what is known as the colour incompatibility problem that Wittgenstein wrangled with at various times during his life. The paper assesses various solutions to these problems including an approach that was first put forward by Jerrold J. Katz. The relation between this approach and the theory of determinables and determinates is also examined. A further development upon this approach is proposed and then applied to the case of the formalisation of antonymy. It is argued that this approach avoids the problems suffered by the main approaches discussed earlier in the paper. (shrink)

1. Une dispute épistémologique 1.1 Quatre itinéraires à proximité puis à distance des structuralismes 1.2 Un différend sur les « usages réglés du rationalisme » en sciences de l’homme 2. Les mots et les descriptions en sciences de l’homme 2.1 Une commune limitation du déterminisme linguistique 2.2 Un problème philosophique implicite : descriptions définies et noms propres 2.3 L’usage des descriptions définies en sciences de l’homme 2.4 Les (semi-)noms propres des sciences historiques 2.5 Le degré de généralité des concepts employés (...) et ses conséquences sur les raisonnements 3. La spécificité des raisonnements en sciences de l’homme 3.1 Quelle logique pour raisonner sur les phénomènes humains ? 3.2 Les usages d’une référence commune : la logique naturelle 3.3 Propositions et énoncés : divergences sur l’analyse des raisonnements 4. Le juste degré de formalisation du langage et des raisonnements 4.1 La formalisation des descriptions 4.2 Les modèles et la formalisation des raisonnements 4.3 Des formalisations qui s’ignorent 5. Le caractère historique des sciences de l’homme 5.1 Formaliser implique-t-il de dé-historiciser ? 5.2 Les mécanismes du changement scientifique 5.3 Pragmatique de l’intervention théorique. (shrink)

In order to decide whether a discursive product of human reason corresponds or not to the logical order, one must analyze it in terms of syntactic correctness, consistency, and validity. The first step in logical analysis is formalization, that is, the process by which logical forms of thoughts are represented in different formal languages or logical systems. Although each thought can be properly formalized in different ways, the formalization variants are not equally adequate. The adequacy of formalization seems to depend (...) on several essential features: parsimony, accuracy, transparency, fertility and reliability. Because there is a partial antinomy between these traits, it is impossible to find a perfectly adequate variant of formalization. However, it is possible and preferable to reach a reasonable compromise by choosing the variant of formalization which satisfies all of these fundamental characteristics. (shrink)

The Aristotelian origins of formal systems are outlined, together with Aristotle's use of causal terms in describing syllogisms. The precision and exactness of a formalism, based on the projection of logical forms into perceptive signs, is contrasted with foundational, abstract concepts, independent of any formalism, which are presupposed for the understanding of a formal language. The definition of a formal system by means of a Turing machine is put in the context of Wittgenstein's general considerations of a machine understood as (...) a sign. A modification of Łukasiewicz's logic Ł3 with the inclusion of justification terms is proposed in order to formally analyse some features of formalistic reasoning as a mechanical, causal affair within a wider context of "indeterminacy". (shrink)

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise algorithmic (...) computation and to offer foundations for scientific computing. -/- The dissertation consists of three parts. In the first part, we examine what notion of 'algorithmic computation' underlies each approach and how it is respectively formalised. It is argued that the very existence of the two rival frameworks indicates that 'algorithm' is not one unique concept in mathematics, but it is used in more than one way. We test this hypothesis for consistency with mathematical practice as well as with key foundational works that aim to define the term. As a result, new connections between certain subfields of mathematics and computer science are drawn, and a distinction between 'algorithms' and 'effective procedures' is proposed. -/- In the second part, we focus on the second goal of the two rival approaches to real computation; namely, to provide foundations for scientific computing. We examine both frameworks in detail, what idealisations they employ, and how they relate to floating-point arithmetic systems used in real computers. We explore limitations and advantages of both frameworks, and answer questions about which one is preferable for computational modelling and which one for addressing general computability issues. -/- In the third part, analog computing and its relation to analogue (physical) modelling in science are investigated. Based on some paradigmatic cases of the former, a certain view about the nature of computation is defended, and the indispensable role of representation in it is emphasized and accounted for. We also propose a novel account of the distinction between analog and digital computation and, based on it, we compare analog computational modelling to physical modelling. It is concluded that the two practices, despite their apparent similarities, are orthogonal. (shrink)

This paper studies a formalisation of intuitionistic logic by Negri and von Plato which has general introduction and elimination rules. The philosophical importance of the system is expounded. Definitions of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system are formulated and corresponding reduction procedures for maximal formulas and permutative reduction procedures for maximal segments given. Alternatives to the main method used are also considered. It is shown that deductions in the system convert into normal form and that (...) deductions in normal form have the subformula property. (shrink)

This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of ‘maximal formula’, ‘segment’ and ‘maximal segment’ suitable to the system, and gives reduction procedures for them. It is then shown that deductions in the system convert into normal form, i.e. deductions that contain neither maximal formulas nor maximal segments, and that deductions in normal form satisfy the subformula property. Tarski’s Rule is treated as a general introduction rule for (...) implication. The general introduction rule for negation has a similar form. Maximal formulas with implication or negation as main operator require reduction procedures of a more intricate kind not present in normalisation for intuitionist logic. (shrink)

Ian Rumfitt has proposed systems of bilateral logic for primitive speech acts of assertion and denial, with the purpose of ‘exploring the possibility of specifying the classically intended senses for the connectives in terms of their deductive use’ : 810f). Rumfitt formalises two systems of bilateral logic and gives two arguments for their classical nature. I assess both arguments and conclude that only one system satisfies the meaning-theoretical requirements Rumfitt imposes in his arguments. I then formalise an intuitionist system of (...) bilateral logic which also meets those requirements. Thus Rumfitt cannot claim that only classical bilateral rules of inference succeed in imparting a coherent sense onto the connectives. My system can be extended to classical logic by adding the intuitionistically unacceptable half of a structural rule Rumfitt uses to codify the relation between assertion and denial. Thus there is a clear sense in which, in the bilateral framework, the difference between classicism and intuitionism is not one of the rules of inference governing negation, but rather one of the relation between assertion and denial. (shrink)

Ontologies represent principled, formalised descriptions of agents’ conceptualisations of a domain. For a community of agents, these descriptions may differ among agents. We propose an aggregative view of the integration of ontologies based on Judgement Aggregation (JA). Agents may vote on statements of the ontologies, and we aim at constructing a collective, integrated ontology, that reflects the individual conceptualisations as much as possible. As several results in JA show, many attractive and widely used aggregation procedures are prone to return inconsistent (...) collective ontologies. We propose to solve the possible inconsistencies in the collective ontology by applying suitable weakenings of axioms that cause inconsistencies. (shrink)

This chapter examines a common objection to sex robots: the symbolic-consequences argument. According to this argument sex robots are problematic because they symbolise something disturbing about our attitude to sex-related norms such as consent and the status of our sex partners, and because of the potential consequences of this symbolism. After formalising this objection and considering several real-world uses of it, the chapter subjects it to critical scrutiny. It argues that while there are grounds for thinking that sex robots could (...) symbolically represent a troubling attitude toward women (and maybe children) and the norms of interpersonal sexual relationships, the troubling symbolism is going to be removable in many instances and reformable in others. What will ultimately matter are the consequences of the symbolism but these consequences are likely to be difficult to ascertain. This may warrant an explicitly experimental approach to the development of this technology. (shrink)

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting to embeddings, (...) semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)

This paper initiates the reverse mathematics of social choice theory, studying Arrow's impossibility theorem and related results including Fishburn's possibility theorem and the Kirman–Sondermann theorem within the framework of reverse mathematics. We formalise fundamental notions of social choice theory in second-order arithmetic, yielding a definition of countable society which is tractable in RCA0. We then show that the Kirman–Sondermann analysis of social welfare functions can be carried out in RCA0. This approach yields a proof of Arrow's theorem in RCA0, and (...) thus in PRA, since Arrow's theorem can be formalised as a Π01 sentence. Finally we show that Fishburn's possibility theorem for countable societies is equivalent to ACA0 over RCA0. (shrink)

In this paper I formalise the falsificationist proposal omitting Popper’s requirement of consistency. This omission results in (i) trivial theories being falsifiable in an inappropriate sense of the term, but also in (ii) some inconsistent non-trivial theories being so in an appropriate one. This justifies a slight alteration of the definition of falsifiability that excludes (i) but allows (ii). Instead of requiring that a falsifiable theory be consistent, my proposal only requires that the intersection of its classes of potential corroborators (...) and falsifiers be empty. (shrink)

In this paper I present a precise version of Stalnaker's thesis and show that it is both consistent and predicts our intuitive judgments about the probabilities of conditionals. The thesis states that someone whose total evidence is E should have the same credence in the proposition expressed by 'if A then B' in a context where E is salient as they have conditional credence in the proposition B expresses given the proposition A expresses in that context. The thesis is formalised (...) rigorously and two models are provided that demonstrate that the new thesis is indeed tenable within a standard possible world semantics based on selection functions. Unlike the Stalnaker-Lewis semantics the selection functions cannot be understood in terms of similarity. A probabilistic account of selection is defended in its place. -/- I end the paper by suggesting that this approach overcomes some of the objections often leveled at accounts of indicatives based on the notion of similarity. (shrink)

This article articulates and assesses an imperatival approach to the foundations of mathematics. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. We apply this idea to provide a novel formalisation of arithmetic and set theory in terms of such procedures, and discuss the significance of this perspective for the philosophy of mathematics.

One of the open problems in the philosophy of information is whether there is an information logic (IL), different from epistemic (EL) and doxastic logic (DL), which formalises the relation “a is informed that p” (Iap) satisfactorily. In this paper, the problem is solved by arguing that the axiom schemata of the normal modal logic (NML) KTB (also known as B or Br or Brouwer’s system) are well suited to formalise the relation of “being informed”. After having shown that IL (...) can be constructed as an informational reading of KTB, four consequences of a KTB-based IL are explored: information overload; the veridicality thesis (Iap → p); the relation between IL and EL; and the Kp → Bp principle or entailment property, according to which knowledge implies belief. Although these issues are discussed later in the article, they are the motivations behind the development of IL. (shrink)

The History of Ideas is presently enjoying a certain renaissance after a long period of disrepute. Increasing quantities of digitally available historical texts and the availability of computational tools for the exploration of such masses of sources, it is suggested, can be of invaluable help to historians of ideas. The question is: how exactly? In this paper, we argue that a computational history of ideas is possible if the following two conditions are satisfied: (i) Sound Method . A computational history (...) of ideas must be built upon a sound theoretical foundation for its methodology, and the only such foundation is given by the use of models , i.e., fully explicit and revisable interpretive frameworks or networks of concepts developed by the historians of ideas themselves. (ii) Data Organisation. Interpretive models in our sense must be seen as topic-specific knowledge organisation systems (KOS) implementable (i.e. formalisable) as e.g. computer science ontologies. We thus require historians of ideas to provide explicitly structured semantic framing of domain knowledge before investigating texts computationally, and to constantly re-input findings from the interpretive point of view. In this way, a computational history of ideas maximally profits from computer methods while also keeping humanities experts in the loop. We elucidate our proposal with reference to a model of the notion of axiomatic science in 18th -19th century Europe. (shrink)

The aim of this paper is to develop a consistent reading of Deleuze and Guattari’s account of capitalism by taking seriously their use of Kant’s philosophy in formulating it. In Sect. 1, I will set out the two different roots of the term axiomatic in Deleuze and Guattari’s thought. The first of these is the axiomatic approach to formalising fields of mathematics, and the second the Kantian account of the indeterminate relationship between the transcendental unity of apperception and the transcendental (...) object. In Sect. 2, we will see how this transcendental aspect of Deleuze and Guattari’s account of axiomatics is expressed in the notion of binding, which Deleuze and Guattari take to be a process that forces us to understand a field of entities in a certain manner, namely as clearly delimited and deployed in a homogeneous space. I will argue that this process of binding operates as a transcendental condition for capitalism for Deleuze and Guattari. Section 3 addresses some of the details of the capitalist axiomatic itself, drawing out why a Kantian reading of Deleuze and Guattari’s account of the axiomatic provides a response to some of the criticisms of it. Section 4 then analyses Deleuze and Guattari’s account of the outside of capitalism, using the double signification of the noumenal to understand the complex relationship between what they call the war machine and its representation within the axiomatic. (shrink)

Fragmentalism allows incompatible facts to constitute reality in an absolute manner, provided that they fail to obtain together. In recent years, the view has been extensively discussed, with a focus on its formalisation in model-theoretic terms. This paper focuses on three formalisations: Lipman’s approach, the subvaluationist interpretation, and a novel view that has been so far overlooked. The aim of the paper is to explore the application of these formalisations to the alethic modal case. This logical exploration will allow (...) us to study (i) cases of metaphysical incompatibility between modal facts and (ii) cases of modal dialetheias. In turn, this will enrich our understanding of the role of impossibility in the fragmentalist framework. (shrink)

Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on in our field—a (...) book would be needed for that. Instead, we have tried to select material that is of interest in its own right or exemplifies noteworthy features in interesting ways. Here are some themes that have guided us throughout the writing: • The back-and-forth between philosophy and modal logic. There has been a good deal of give-and-take in the past. Carnap tried to use his modal logic to throw light on old philosophical questions, thereby inspiring others to continue his work and still others to criticise it. He certainly provoked Quine, who in his turn provided—and continues to provide—a healthy challenge to modal logicians. And Kripke’s and David Lewis’s philosophies are connected, in interesting ways, with their modal logic. Analytic philosophy would have been a lot different without modal logic! • The interpretation problem. The problem of providing a certain modal logic with an intuitive interpretation should not be conflated with the problem of providing a formal system with a model-theoretic semantics. An intuitively appealing model-theoretic semantics may be an important step towards solving the interpretation problem, but only a step. One may compare this situation with that in probability theory, where definitions of concepts like ‘outcome space’ and ‘random variable’ are orthogonal to questions about “interpretations” of the concept of probability. • The value of formalisation. Modal logic sets standards of precision, which are a challenge to—and sometimes a model for—philosophy. Classical philosophical questions can be sharpened and seen from a new perspective when formulated in a framework of modal logic. On the other hand, representing old questions in a formal garb has its dangers, such as simplification and distortion. • Why modal logic rather than classical (first or higher order) logic? The idioms of modal logic—today there are many!—seem better to correspond to human ways of thinking than ordinary extensional logic. (Cf. Chomsky’s conjecture that the NP + VP pattern is wired into the human brain.) In his An Essay in Modal Logic (1951) von Wright distinguished between four kinds of modalities: alethic (modes of truth: necessity, possibility and impossibility), epistemic (modes of being known: known to be true, known to be false, undecided), deontic (modes of obligation: obligatory, permitted, forbidden) and existential (modes of existence: universality, existence, emptiness). The existential modalities are not usually counted as modalities, but the other three categories are exemplified in three sections into which this chapter is divided. Section 1 is devoted to alethic modal logic and reviews some main themes at the heart of philosophical modal logic. Sections 2 and 3 deal with topics in epistemic logic and deontic logic, respectively, and are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory. (shrink)

This paper presents a way of formalising definite descriptions with a binary quantifier ι, where ιx[F, G] is read as ‘The F is G’. Introduction and elimination rules for ι in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ιx[F, G] are given, and it is shown that deductions in the system can be brought into normal form.

First, I offer a short overview on the classical occidental philosophy as propounded by the ancient Greeks and the natural philosophies of the last 2000 years until the dawn of the empiricist logic of science in the twentieth century, which wanted to delimitate classical metaphysics from empirical sciences. In contrast to metaphysical concepts which didn’t reflect on the language with which they tried to explain the whole realm of entities empiricist logic of science initiated the end of metaphysical theories by (...) reflecting on the preconditions for foundation and justification of sentences about objects of investigation, i.e. a coherent definition of language in general, which was not the aim of classical metaphysics. Unexpectedly empiricist logic of science in the linguistic turn failed in the physical and mathematical reductionism of language and its use in communication, as will be discussed below in further detail. Nevertheless, such reflection on language and communication also introduced this vocabulary into biology. Manfred Eigen and bioinformatics, later on biolinguistics, used ‘language’ applied linguistic turn thinking to biology coherent to the logic of science and its formalisable aims. This changed significantly with the birth of biosemiotics and biohermeneutics. At the end of this introduction it will be outlined why and how all these approaches reproduced the deficiencies of the logic of science and why the biocommunicative approach avoids their abstractive fallacies. (shrink)

This thesis focuses on expressively rich languages that can formalise talk about probability. These languages have sentences that say something about probabilities of probabilities, but also sentences that say something about the probability of themselves. For example: (π): “The probability of the sentence labelled π is not greater than 1/2.” Such sentences lead to philosophical and technical challenges; but can be useful. For example they bear a close connection to situations where ones confidence in something can affect whether it is (...) the case or not. The motivating interpretation of probability as an agent's degrees of belief will be focused on throughout the thesis. -/- This thesis aims to answer two questions relevant to such frameworks, which correspond to the two parts of the thesis: “How can one develop a formal semantics for this framework?” and “What rational constraints are there on an agent once such expressive frameworks are considered?”. (shrink)

As biological and biomedical research increasingly reference the environmental context of the biological entities under study, the need for formalisation and standardisation of environment descriptors is growing. The Environment Ontology (ENVO) is a community-led, open project which seeks to provide an ontology for specifying a wide range of environments relevant to multiple life science disciplines and, through an open participation model, to accommodate the terminological requirements of all those needing to annotate data using ontology classes. This paper summarises ENVO’s (...) motivation, content, structure, adoption, and governance approach. (shrink)

We introduce a family of operators to combine Description Logic concepts. They aim to characterise complex concepts that apply to instances that satisfy \enough" of the concept descriptions given. For instance, an individual might not have any tusks, but still be considered an elephant. To formalise the meaning of "enough", the operators take a list of weighted concepts as arguments, and a certain threshold to be met. We commence a study of the formal properties of these operators, and study some (...) variations. The intended applications concern the representation of cognitive aspects of classi cation tasks: the interdependencies among the attributes that de ne a concept, the prototype of a concept, and the typicality of the instances. (shrink)

The model of self-referential truth presented in this paper, named Revision-theoretic supervaluation, aims to incorporate the philosophical insights of Gupta and Belnap’s Revision Theory of Truth into the formal framework of Kripkean fixed-point semantics. In Kripke-style theories the final set of grounded true sentences can be reached from below along a strictly increasing sequence of sets of grounded true sentences: in this sense, each stage of the construction can be viewed as an improvement on the previous ones. I want to (...) do something similar replacing the Kripkean sets of grounded true sentences with revision-theoretic sets of stable true sentences. This can be done by defining a monotone operator through a variant of van Fraassen’s supervaluation scheme which is simply based on ω-length iterations of the Tarskian operator. Clearly, all virtues of Kripke-style theories are preserved, and we can also prove that the resulting set of “grounded” true sentences shares some nice features with the sets of stable true sentences which are provided by the usual ways of formalising revision. What is expected is that a clearer philosophical content could be associated to this way of doing revision; hopefully, a content directly linked with the insights underlying finite revision processes. (shrink)

This paper explores taste fragmentalism, a novel approach to matters of taste and faultless disagreement. The view is inspired by Kit Fine’s fragmentalism about time, according to which the temporal dimension can be constituted—in an absolute manner—by states that are pairwise incompatible, provided that they do not obtain together. In the present paper, we will apply this metaphysical framework to taste states. In our proposal, two incompatible taste states (such as the state of rhubarb’s being tasty and the state of (...) rhubarb’s being distasteful) can both constitute reality in an absolute manner, although no agent can have joint access to both states. We will then develop a formalised version of our view by means of an exact truthmaker semantics for taste assertions. Within this framework—we argue—our linguistic and inferential practices concerning cases of faultless disagreement are elegantly vindicated, thus suggesting that taste fragmentalism is worth of further consideration. (shrink)

Semantic externalism in the style of McDowell and Evans faces a puzzle formulated by Pryor: to explain that a sentence such as 'Jack exists' is only a posteriori knowable, despite being logically entailed by the seemingly logical truth 'Jack is self-identical', and hence being itself a logical truth and therefore a priori knowable. Free logics can dissolve the puzzle. Moreover, Pryor has argued that the existentially hedged 'If Jack exists, then Jack is self-identical', when properly formalised, is a logical truth (...) in a system of neutral free logic and therefore a priori knowable, while it does not entail that Jack exists. The latter holds also for negative free logic. In response, Yeakel has argued that on any system of neutral free logic existence hedges will either entail some unwanted existence claims or they will not entail some wanted existence claims. The dilemma also holds for any non-positive free logic. It will be shown that the extension of one of the systems of neutral free logic with a truth operator escapes Yeakel's dilemma, whereas no other non-positive free logic when extended with the truth operator does the same (or it breaks quantifier exchangeability). (shrink)

The view of nature we adopt in the natural attitude is determined by common sense, without which we could not survive. Classical physics is modelled on this common-sense view of nature, and uses mathematics to formalise our natural understanding of the causes and effects we observe in time and space when we select subsystems of nature for modelling. But in modern physics, we do not go beyond the realm of common sense by augmenting our knowledge of what is going on (...) in nature. Rather, we have measurements that we do not understand, so we know nothing about the ontology of what we measure. We help ourselves by using entities from mathematics, which we fully understand ontologically. But we have no ontology of the reality of modern physics; we have only what we can assert mathematically. In this paper, we describe the ontology of classical and modern physics against this background and show how it relates to the ontology of common sense and of mathematics. (shrink)

Individuals of many animal species are said to have a personality. It has been shown that some individuals are bolder than other individuals of the same species, or more sociable or more aggressive. In this paper, we analyse what it means to say that an animal has a personality. We clarify what an animal personality is, that is, its ontology, and how different personality concepts relate to each other, and we examine how personality traits are identified in biological practice. Our (...) analysis shows that biologists often study specific personality traits, such as boldness, sociability or aggressiveness, rather than personalities in general. We claim that personality traits are best understood as dispositions and that they are operationally defined in terms of certain sets of behaviours, which are studied in specific experimental set-ups. Furthermore, we develop an integrative philosophical account that specifies and formalises three criteria for identifying personality traits, which are used in biological practice. For an individual animal to have a personality trait it must, first, behave differently than others. Second, these behavioural differences must be stable over a certain time, and third, they must be consistent in different contexts. (shrink)

Measures and theories of information abound, but there are few formalised methods for treating the contextuality that can manifest in different information systems. Quantum theory provides one possible formalism for treating information in context. This paper introduces a quantum inspired model of the human mental lexicon. This model is currently being experimentally investigated and we present a preliminary set of pilot data suggesting that concept combinations can indeed behave non-separably.

Preference relations are intensively studied in Economics, but they are also approached in AI, Knowledge Representation, and Conceptual Modelling, as they provide a key concept in a variety of domains of application. In this paper, we propose an ontological foundation of preference relations to formalise their essential aspects across domains. Firstly, we shall discuss what is the ontological status of the relata of a preference relation. Secondly, we investigate the place of preference relations within a rich taxonomy of relations (e.g. (...) we ask whether they are internal or external, essential or contingent, descriptive or nondescriptive relations). Finally, we provide an ontological modelling of preference relation as a module of a foundational (or upper) ontology (viz. OntoUML). The aim of this paper is to provide a sharable foundational theory of preference relation that foster interoperability across the heterogeneous domains of application of preference relations. (shrink)

: According to Kant, the arguments of rational psychology are formal fallacies that he calls transcendental paralogisms. It remains heavily debated whether there actually is any formal error in the inferences Kant presents: according to Grier and Allison, they are deductively invalid syllogisms, whereas Bennett, Ameriks, and Van Cleve deny that they are formal fallacies. I advance an interpretation that reconciles these extremes: transcendental paralogisms are sound in general logic but constitute formal fallacies in transcendental logic. By formalising the paralogistic (...) inference, I will pinpoint the error as an illegitimate existential presupposition. Since - unlike transcendental logic - general logic abstracts from all objects, this error can only be detected in transcendental logic. (shrink)

Worrall argued that structural realism provides a ‘synthesis’ of the main pro-realist argument – the ‘No Miracles Argument’, and the main anti-realist argument – the ‘Pessimistic Induction’. More recently, however, it has been claimed that each of these arguments is an instance of the same probabilistic fallacy – sometimes called the ‘base-rate fallacy’. If correct, this clearly seems to undermine structural realism and Magnus and Callender have indeed claimed that both arguments are fallacious and ‘without [them] we lose the rationale (...) for … structural realism ’. I here argue that what have been shown to be fallacious are simply misguided formalisations of ‘the’ arguments and that when they are properly construed they continue to provide powerful motivation for favouring structural realism. (shrink)

Many philosophers argue that Keynes’s concept of the “weight of arguments” is an important aspect of argument appraisal. The weight of an argument is the quantity of relevant evidence cited in the premises. However, this dimension of argumentation does not have a received method for formalisation. Kyburg has suggested a measure of weight that uses the degree of imprecision in his system of “Evidential Probability” to quantify weight. I develop and defend this approach to measuring weight. I illustrate the (...) usefulness of this measure by employing it to develop an answer to Popper’s Paradox of Ideal Evidence. (shrink)

Both in formal and computational natural language semantics, the classical correspondence view of meaning – and, more specifically, the view that the meaning of a declarative sentence coincides with its truth conditions – is widely held. Truth (in the world or a situation) plays the role of the given, and meaning is analysed in terms of it. Both language and the world feature in this perspective on meaning, but language users are conspicuously absent. In contrast, the inferentialist semantics that Robert (...) Brandom proposes in his magisterial book ‘Making It Explicit’ puts the language user centre stage. According to his theory of meaning, the utterance of a sentence is meaningful in as far as it is a move by a language user in a game of giving and asking for reasons (with reasons underwritten by a notion of good inferences). In this paper, I propose a proof-theoretic formalisation of the game of giving and asking for reasons that lends itself to computer implementation. In the current proposal, I flesh out an account of defeasible inferences, a variety of inferences which play a pivotal role in ordinary (and scientific) language use. (shrink)

We present a model of the distribution of labour in science. Such models tend to rely on the mechanism of the invisible hand . Our analysis starts from the necessity of standards in distributed processes and the possibility of multiple standards in science. Invisible hand models turn out to have only limited scope because they are restricted to describing the atypical single-standard case. Our model is a generalisation of these models to J standards; single-standard models such as Kitcher are a (...) limiting case. We introduce and formalise this model, demonstrate its dynamics and conclude that the conclusions commonly derived from invisible hand models about the distribution of labour in science are not robust against changes in the number of standards. (shrink)

David Lewis is widely regarded as the philosopher who introduced the concept of common knowledge. His account of common knowledge differs greatly from most later accounts in philosophy and economy, with the central notion of his theory being ‘having reason to believe’ rather than ‘knowledge’. Unfortunately, Lewis’s account is rather informal, and the argument has a few gaps. This paper assesses two major attempts to formalise Lewis’s account and argues that these formalisations are missing a crucial aspect of this account. (...) Therefore, a new reconstruction is proposed, which explicitly discusses ‘reasons’ and uses a logic inspired by justification logic. (shrink)

Sentences containing definite descriptions, expressions of the form ‘The F’, can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ιx[F, G] is read as ‘The F is G’. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INFι of intuitionist negative free logic extended by such a quantifier, which was presented (...) in (Kürbis 2019), INFι is first compared to a system of Tennant’s and an axiomatic treatment of a term forming ι operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INFι in which the G of ιx[F, G] is restricted to identity. INFι is then compared to an intuitionist version of a system of Lambert’s which in addition to the term forming operator has an operator for predicate abstraction for indicating scope distinctions. The two systems will be shown to be equivalent through a translation between their respective languages. Advantages of the present approach over the alternatives are indicated in the discussion. (shrink)

Julian Schlöder (2018) examines Timothy Williamson's proposal that knowledge is the norm of assertion within the context of deontic logic. He argues for two claims, one concerning the formalisation of the thesis that knowledge is a norm of assertion and another concerning the formalisation of the thesis that knowledge is the only norm of assertion. On the basis of these claims, Schlöder goes on to raise a series of problems for Williamson's proposal. In response, I argue that both (...) of Schlöder's claims can—and should—be rejected. (shrink)

If the allusive stratagems can claim to define a new type of systematicity, it is because they give access to a space where the singularity, the diagram and the metaphor may interlace, to penetrate further into the physico-mathematic intuition and the discipline of the gestures which precede and accompany ‘formalisation’. This interlacing is an operation where each component backs up the others: without the diagram, the metaphor would only be a short-lived fulguration because it would be unable to operate: (...) without the metaphor, the diagram would only be a frozen icon, unable to jump over its bold features which represent the images of an already acquired knowledge; without the subversion of the functional by the singular, nothing would come to oppose the force of habit. (shrink)

The existential insecurity of human beings has induced them to create protective spheres of symbols: myths, religions, values, belief systems, theories, etc. Rationality is one of the key factors contributing to the construction of civilisation in technical and symbolic terms. As Hankiss (2001) has emphasised, protective spheres of symbols may collapse – thus causing a profound social crisis. Social and political transformations had a tremendous impact at the end of the 20th century. As a result, management theories have been revised (...) in order to deal with transition and uncertainty. Francis Fukuyama's (2000) approach is supportive of hierarchical organisation as the best solution when facing a 'disruption'. The notion of Homo Hierarchicus has been based on, allegedly, rational presumptions. This paper contributes to the discussion on hierarchy within contemporary organisations. It criticises so-called 'natural' and 'rational' necessities justifying hierarchy. A key issue identified by the paper is the formalisation of language in claiming value-free knowledge and 'detached' observation as the basis for neutral rationality and aspired efficiency. This should be seriously reconsidered as hindering rather than aiding understanding of social complexity. All in all, Homo Hierarchicus appears to be misleading rather than helping symbolic sphere or construct. (shrink)

I confront Feyerabend's position and critical rationalism in order to have a foundation or starting point for my (historical) investigation. The main difference of his position towards falsificationism is the belief that different theories cannot be discussed rationally. Feyerabend is convinced that Galilei's observations with the telescope in the historical context of the Copernican revolution supports his criticism. In particular, he argues that the Copernican theory was supported by deficient hypotheses, and falsifications were disposed by ad hoc hypotheses and propaganda. (...) Furthermore, he claims that his philosophy of science reconstructs Galilei's defence of the Copernican theory. He introduces a central principle of his position (the principle of tenacity) in order to justify a research strategy of not eliminating falsified theories. He tries to show that the tenacious defence of a theory corresponds to Galilei's defence of the Copernican theory. Remarkably, Feyerabend's approach to explain the development of science earns an important support from his interpretation of Galilei's observations. On this basis I give a falsificationist interpretation of Galilei's observations with the telescope, and oppose this interpretation to Feyerabend's. From a falsificationist perspective, auxiliary hypotheses compete during the Copernican revolution which can (with some effort) be critically discussed. Then I analyse the historical case in order to test Feyerabend's interpretation of the Copernican revolution. Inter alias I investigate thoroughly whether Galilei, as Feyerabend claims, immunised falsifications of the Copernican theory by the introduction of ad hoc hypotheses. The investigation considers Galilei's explanation of Venus' phases, his establishment of the irradiation hypothesis, the explanation of the telescope's functionality, and the role of the reproducibility of the observations with the telescope. Finally I provide a rational reconstruction of Galilei's falsification of the Ptolemaic theory. The formalisation shows that Galilei was not a cautious critical rationalist, but a very confident scientist using the method of falsification. (shrink)

A mesure qu'ils avancent dans leur œuvre de prospection, les sémioticiens s'aperçoivent que tout est communication, la langue bien sûr, mais aussi les images, les sons, les objets, les gestes, et que tous ces phénomènes constituent des systèmes de signes qui doivent être étudiés en ramenant chaque message aux codes qui en régissent l'émission et la compréhension. Comprendre les systèmes de signes impose toutefois d'envisager les codes comme des structures, puis de recouvrir à des structures toujours plus vastes, dans un (...) mouvement de régression vers la matrice originelle de toute communication possible, vers un prétendu Code des Codes qui devrait représenter la détermination " naturelle " précédant toute culture. Mais si la sémiotique s'engageait dans cette voie, elle ne pourrait qu'aboutir à la " source " de toute structure possible, forcément non structurée, à ce qu'Umberto Ecco appelle la structure absente. Son livre, tout en refusant ce Code des Codes, essaie de montrer que tout acte communicatif est dominé par la présence massive de codes socialement et historiquement déterminés. La sémiotique découvre ainsi dans la dialectique entre code et message les rapports entre l'univers de signes et l'univers des idéologies, qui se reflètent dans les modes communicatifs préconstitués, et elle relie le monde des choses au monde de la culture, qui formalise les choses non pas pour les reconnaître comme elles sont mais afin de les transformer. Après avoir étudié dans L'œuvre ouverte (1965) les structures des langages expérimentaux de l'art contemporain, Umberto Ecco traite ici l'ensemble des problèmes sémiotiques et ce livre constitue à la fois sa contribution à la recherche en cours et le panorama actuellement le plus vaste et le plus complet sur les préalables constitutifs à toute sémiotique et sur l'état présent du structuralisme. (shrink)

This paper presents rules of inference for a binary quantifier I for the formalisation of sentences containing definite descriptions within intuitionist positive free logic. I binds one variable and forms a formula from two formulas. Ix[F, G] means ‘The F is G’. The system is shown to have desirable proof-theoretic properties: it is proved that deductions in it can be brought into normal form. The discussion is rounded up by comparisons between the approach to the formalisation of definite (...) descriptions recommended here and the more usual approach that uses a term-forming operator ι, where ιxF means ‘the F’. (shrink)

An important lesson that philosophy can learn from the Turing Test and computer science more generally concerns the careful use of the method of Levels of Abstraction (LoA). In this paper, the method is first briefly summarised. The constituents of the method are “observables”, collected together and moderated by predicates restraining their “behaviour”. The resulting collection of sets of observables is called a “gradient of abstractions” and it formalises the minimum consistency conditions that the chosen abstractions must satisfy. Two useful (...) kinds of gradient of abstraction – disjoint and nested – are identified. It is then argued that in any discrete (as distinct from analogue) domain of discourse, a complex phenomenon may be explicated in terms of simple approximations organised together in a gradient of abstractions. Thus, the method replaces, for discrete disciplines, the differential and integral calculus, which form the basis for understanding the complex analogue phenomena of science and engineering. The result formalises an approach that is rather common in computer science but has hitherto found little application in philosophy. So the philosophical value of the method is demonstrated by showing how making the LoA of discourse explicit can be fruitful for phenomenological and conceptual analysis. To this end, the method is applied to the Turing Test, the concept of agenthood, the definition of emergence, the notion of artificial life, quantum observation and decidable observation. It is hoped that this treatment will promote the use of the method in certain areas of the humanities and especially in philosophy. (shrink)