The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation (...) schemes, in particular, as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning. (shrink)

Explores how to identify future-proof science. Peter Vickers takes a transdisciplinary approach in his analysis of 'scientific fact' in order to defend science against potentially dangerous scepticism.

Peirce stresses that the pragmatist qua pragmatist must embrace realism as opposed to nominalism. He offers as well “proofs” of realism which are open to various criticisms. Within the framework of his pragmatic vision, the experiential sense of realism is inseparable from the functioning of habit in the flow of time. What is being verified by experimental testing is, ultimately, not a particular scientific law, nor scientific laws in general, but rather the common sense expectation of predictive reliability rooted in (...) the primitive epistemic “feel” of real potentiality, a belief which is dubitable in principle, and which is, in fact, often doubted at the abstract, reflective levels of science, logic, and philosophy, but which, at the level of rudimentary perceptual experience is fundamental to our very sense of our world, and is well verified by the continual availability of our perceptual world. The concrete functioning of habit provides, epistemically, the conceptual counterpart of the real lawfulness held to exist in the world, and provides, ontologically, an example of this real lawfulness. Peirce’s dispositional theory of meaning leads to a metaphysics of realism as opposed to a nominalism, a realism not of eternal essences but a “process realism” in which there are real modes of behavior which govern what occurs. (shrink)

“Proof of concept” is a phrase frequently used in descriptions of research sought in program announcements, in experimental studies, and in the marketing of new technologies. It is often coupled with either a short definition or none at all, its meaning assumed to be fully understood. This is problematic. As a phrase with potential implications for research and technology, its assumed meaning requires some analysis to avoid it becoming a descriptive category that refers to all things scientifically exciting. (...) I provide a short analysis of proof of concept research and offer an example of it within synthetic biology. I suggest that not only are there activities that circumscribe new epistemological categories but there are also associated normative ethical categories or principles linked to the research. I examine these and provide an outline for an alternative ethical account to describe these activities that I refer to as “extended agency ethics”. This view is used to explain how the type of research described as proof of concept also provides an attendant proof of principle that is the result of decision-making that extends across practitioners, their tools, techniques, and the problem solving activities of other research groups. (shrink)

Mathematical investigation, when done well, can confer understanding. This bare observation shouldn’t be controversial; where obstacles appear is rather in the effort to engage this observation with epistemology. The complexity of the issue of course precludes addressing it tout court in one paper, and I’ll just be laying some early foundations here. To this end I’ll narrow the field in two ways. First, I’ll address a specific account of explanation and understanding that applies naturally to mathematical reasoning: the view proposed (...) by Philip Kitcher and Michael Friedman of explanation or understanding as involving the unification of theories that had antecedently appeared heterogeneous. For the second narrowing, I’ll take up one specific feature (among many) of theories and their basic concepts that is sometimes taken to make the theories and concepts preferred: in some fields, for some problems, what is counted as understanding a problem may involve finding a way to represent the problem so that it (or some aspect of it) can be visualized. The final section develops a case study which exemplifies the way that this consideration – the potential for visualizability – can rationally inform decisions as to what the proper framework and axioms should be. The discussion of unification (in sections 3 and 4) leads to a mathematical analogue of Goodman’s problem of identifying a principled basis for distinguishing grue and green. Just as there is a philosophical issue about how we arrive at the predicates we should use when making empirical predictions, so too there is an issue about what properties best support many kinds of mathematical reasoning that are especially valuable to us. The issue becomes pressing via an examination of some physical and mathematical cases that make it seem unlikely that treatments of unification can be as straightforward as the philosophical literature has hoped. Though unification accounts have a grain of truth (since a phenomenon (or cluster of phenomena) called “unification” is in fact important in many cases) we are far from an analysis of what “unification” is.. (shrink)

I explore, from a proof-theoretic perspective, the hierarchy of classical and paraconsistent logics introduced by Barrio, Pailos and Szmuc in (Journal o f Philosophical Logic,49, 93-120, 2021). First, I provide sequent rules and axioms for all the logics in the hierarchy, for all inferential levels, and establish soundness and completeness results. Second, I show how to extend those systems with a corresponding hierarchy of validity predicates, each one of which is meant to capture “validity” at a different inferential level. (...) Then, I point out two potential philosophical implications of these results. (i) Since the logics in the hierarchy differ from one another on the rules, I argue that each such logic maintains its own distinct identity (contrary to arguments like the one given by Dicher and Paoli in 2019). (ii) Each validity predicate need not capture “validity” at more than one metainferential level. Hence, there are reasons to deny the thesis (put forward in Barrio, E., Rosenblatt, L. & Tajer, D. (Synthese, 2016)) that the validity predicate introduced in by Beall and Murzi in (Journal o f Philosophy,110(3), 143–165, 2013) has to express facts not only about what follows from what, but also about the metarules, etc. (shrink)

An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice (...) of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape. (shrink)

A proof is given for the theorem that at least one bound state exists in a one-dimensional attractive potential however weak it may be. The proof is constructive in that it provides a method to explicitly solve the eigenvalue problem for the eigenvalues as well as the eigenfunctions. The method is well suited to precise numerical calculations.

In discussions of standards of proof, a familiar perspective often emerges. According to what we call specificationism, standards of proof are legal rules that specify the quantum of evidence required to determine that a litigant’s claim has been proven. In so doing, they allocate the risk of error among litigants (and potential litigants), minimizing the risk of certain types of error. Specificationism is meant as a description of the way the rules actually function. We argue, however, that (...) its claims are either mistaken or at a minimum deeply misleading, especially when it comes to standard of proof rules (SPRs) that contain indeterminate formulas, as is typical. As against specificationism, we argue that SPRs are best understood as rules that confer competence to decide whether a given standard has been met—according to whatever vague or inchoate interpretation (if any) of the rule in question triers of fact implicitly or explicitly employ. We call this the competence-norm approach. (shrink)

In Prawitz’s semantics, the validity of an argument may be defined, either relatively to an atomic base which determines the meaning of the non-logical terminology, or relatively to the whole class of atomic bases, namely as logical validity. In the first case, which may be qualified as local, one has to choose whether validity of arguments is or not monotonic over expansions of bases, while in the second case, which may be qualified as global, one has to choose whether the (...) reduction functions which justify non-primitive inferences are or not base-depending. I claim that these oppositions enjoy some conceptual symmetries, and that these symmetries may be understood as putting restrictions on one’s choice both at the local and at the global level. This produces two different proof-theoretic semantics in line with Prawitz’s tenets. However, I also argue that the symmetries stem from a deeper interaction within Prawitz’s semantics, i.e. non-logical meanings vs interpretation of rules. This interaction is in turn based on some primitive ingredients which, when suitably combined, produce other two Prawitz-compatible readings. The four readings form a diagram where some order relations hold. I finally claim that this diagram is complete, namely that, if we combine the ingredients in ways other than those giving rise to the four readings above, we obtain nothing new, or nothing compatible with general semantic requirements. Thus, symmetries between the local and the global level, and interaction between non-logical meaning and interpretation of rules, produce a complete classification of potential Prawitzian semantics. (shrink)

Since Plato's time, philosophers have concentrated on developing moral theories to guide our actions. They have said we ought to act to maximize happiness; we ought to act to fulfill human potential; etc. But all of them have largely ignored a key question: Regardless of which acts are morally obligatory, can moral obligation as such be proven? Early in his book, Allen clarifies what sort of demonstration or justification can suffice as a proof that we are subject to (...) moral obligation. He analyzes some twentieth-century ethical theories which initially appear to serve as such a demonstration. Next, he examines at length the theory of contemporary English philosopher R.M. Hare. And finally, he reworks Hare's ideas into a complete proof that we are bound by moral obligation. Philosophers should value this book because it brings to light and defines a neglected but critical problem, and develops an innovative, thought-provoking solution. Serious students, too, will find it helpful because it provides a clearly written historical study of a central theme in twentieth-century ethics. (shrink)

The argument from potential has been hard to assess because the versions presented by friends and those presented by enemies have born very little resemblance to each other. I here try to improve this situation by attempting to bring both versions into enforced contact. To this end, I sketch a more detailed analysis of the modern concept of potential than any hitherto attempted. As one would expect, arguments from potential couched in terms of that notion are evident (...) non-starters. I then ask how the modern notion of potential needs to be supplemented in order to produce a more convincing argument. I then enquire whether the supplementations utilised in the most distinguished recent presentations of the argument have anything better than an ad hoc role to play in contemporary metaphysics. I conclude that the rehabilitation of the argument is unlikely; in any event, the onus of proof seems to be on the friend of that argument to show that it is uncontrived. Finally, I argue that the (modern) notion of potential has an important role to play in any plausible account of foetal value. (shrink)

This paper uses some modest claims about knowledge to identify a significant problem for contemporary American trial procedure. First, suppose that legal proof requires knowledge. In particular, suppose that the defendant in a jury trial is proven guilty only if the jury knows that the defendant is guilty. Second, suppose that knowledge is subject to pragmatic encroachment. In particular, whether the jury knows the defendant is guilty depends on what’s at stake in their decision to convict, including the consequences (...) that the defendant may face if convicted. Then in order to know whether a defendant has been proven guilty, jurors may need to know something about the potential consequences of conviction. But in nearly every American criminal trial, this information is withheld from jurors. -/- In §1, I lay out the philosophical premises of my argument. In §2, I say more about why these premises present a problem for American trial procedure, and I identify social and political structures that exacerbate the problem. I describe the reasoning that has led courts to withhold sentencing information from jurors, and I diagnose the flaw in this reasoning. In §3, I expand my initial argument, strengthening its conclusions and offering alternative sets of premises that still entail them. I argue that the legal ramifications of pragmatic encroachment depend on highly controversial questions in epistemology, questions about the precise nature of practical stakes. In §4, I propose strategies for legal reform. (shrink)

Chapter 1 constitutes an introduction to Gentzen calculi from two perspectives, logical and philosophical. It introduces the notion of generalisations of Gentzen sequent calculus and the discussion on properties that characterize good inferential systems. Among the variety of Gentzen-style sequent calculi, I divide them in two groups: syntactic and semantic generalisations. In the context of such a discussion, the inferentialist philosophy of the meaning of logical constants is introduced, and some potential objections – mainly concerning the choice of working (...) with semantic generalizations – are addressed. Finally, I’ll introduce the case studies that I’ll be dealing with in part II. Chapter 2 is concerned with the origins and development of Jaśkowski’s discussive logic. The main idea of this chapter is to systematize the various stages of the development of discussive logic related researches from two different angles, i.e., its connections to modal logics and its proof theory, by highlighting virtues and vices. Chapter 3 focuses on the Gentzen-style proof theory of discussive logic, by providing a characterization of it in terms of labelled sequent calculi. Chapter 4 deals with the Gentzen-style proof theory of relevant logics, again by employing the methodology of labelled sequent calculi. This time, instead of working with a single logic, I’ll deal with a whole family of them. More precisely, I’ll study in terms of proof systems those relevant logics that can be characterised, at the semantic level, by reduced Routley-Meyer models, i.e., relational structures with a ternary relation between states and a unique base element. Chapter 5 investigates the proof theory of a modal expansion of intuitionistic propositional logic obtained by adding an ‘actuality’ operator to the connectives. This logic was introduced also using Gentzen sequents. Unfortunately, the original proof system is not cut-free. This chapter shows how to solve this problem by moving to hypersequents. Chapter 6 concludes the investigations and discusses the future of the research presented throughout the dissertation. (shrink)

I present a novel interpretation of Frege’s attempt at Grundgesetze I §§29-31 to prove that every expression of his language has a unique reference. I argue that Frege’s proof is based on a contextual account of reference, similar to but more sophisticated than that enshrined in his famous Context Principle. Although Frege’s proof is incorrect, I argue that the account of reference on which it is based is of potential philosophical value, and I analyze the class of (...) cases to which it may successfully be applied. (shrink)

The Knowability Paradox purports to show that the controversial but not patently absurd hypothesis that all truths are knowable entails the implausible conclusion that all truths are known. The notoriety of this argument owes to the negative light it appears to cast on the view that there can be no verification-transcendent truths. We argue that it is overly simplistic to formalize the views of contemporary verificationists like Dummett, Prawitz or Martin-Löf using the sort of propositional modal operators which are employed (...) in the original derivation of the Paradox. Instead we propose that the central tenet of verificationism is most accurately formulated as follows: if φ is true, then there exists a proof of φ Building on the work of Artemov (Bull Symb Log 7(1): 1-36, 2001), a system of explicit modal logic with proof quantifiers is introduced to reason about such statements. When the original reasoning of the Paradox is developed in this setting, we reach not a contradiction, but rather the conclusion that there must exist non-constructed proofs. This outcome is evaluated relative to the controversy between Dummett and Prawitz about proof existence and bivalence. (shrink)

Is science getting at the truth? The sceptics – those who spread doubt about science – often employ a simple argument: scientists were sure in the past, and then they ended up being wrong. Such sceptics draw on dramatic quotes from eminent scientists such as Lord Kelvin, who reportedly stated at the turn of the 20th century “There is nothing new to be discovered in physics now,” shortly before physics was dramatically transformed. They ask: given the history of science, wouldn’t (...) it be naïve to think that current scientific theories reveal ‘the truth’, and will never be discarded in favour of other theories? Through a combination of historical investigation and philosophical-sociological analysis, Identifying Future-Proof Science defends science against such potentially dangerous scepticism. It is argued that we can confidently identify many scientific claims that are future-proof: they will last forever, so long as science continues. How do we identify future-proof claims? This appears to be a new question for science scholars, and not an unimportant one. It is argued that the best way to identify future-proof science is to avoid any attempt to analyse the relevant first-order scientific evidence, instead focusing purely on second-order evidence. Specifically, a scientific claim is future-proof when the relevant scientific community is large, international, and diverse, and at least 95% of that community would describe the claim as a ‘scientific fact’. In the entire history of science, no claim meeting these criteria has ever been overturned, despite enormous opportunity. (shrink)

The results herein form part of a larger project to characterize the classification properties of the class of submodels of a homogeneous stable diagram in terms of the solvability (in the sense of [1]) of the potential isomorphism problem for this class of submodels. We restrict ourselves to locally saturated submodels of the monster model m of some power π. We assume that in Gödel's constructible universe ������, π is a regular cardinal at least the successor of the first (...) cardinal in which ������ is stable. We show that the collection of pairs of submodels in ������ as above which are potentially isomorphic with respect to certain cardinal-preserving extensions of ������ is equiconstructible with 0 # . As 0 # is highly "transcendental" over ������, this provides a very strong statement to the effect that potential isomorphism for this class of models not only fails to be set-theoretically absolute, but is of high (indeed of the highest possible) complexity. The proof uses a novel method that does away with the need for a linear order on the skeleton. (shrink)

A proof of pragmatism is proposed in Peirce's 1903 lecture series on Pragmatism as a Principle and Method of Right Thinking. It is necessary first to define what pragmatism is, a task for which a practitioner of the pragmatic maxim would be fitted, but which, however, must be highly problematic to a potential practitioner who does not yet know its full meaning. In order to clarify its meaning, Peirce uses a method he recommends for such conundrums in his (...) 1891 article, “The Architecture of Theories,” that is, “to make a systematic study of the conceptions out of which a philosophical theory may be built, in order to ascertain what place each conception may fitly occupy in such a theory and to what uses it is adapted”. Peirce's systematic study of the basis of logic and pragmatism in relation to it begins to appear around 1898 and peaks in 1903 when pragmatism's definition and role within the sciences is established in these lectures. (shrink)

In “The Gettier Problem and Legal Proof,” I argue that epistemic conditions that undermine knowledge in Gettier-type cases also potentially undermine legal verdicts. For this reason, I argue, there is a deeper connection between knowledge and legal proof than is typically presupposed or argued for in the scholarly legal literature. To support these claims, I present several examples illustrating how conditions that render epistemically justified beliefs merely accidentally true (and thus disqualify them as cases of genuine knowledge) may (...) also render evidentially well-supported verdicts merely accidentally true for similar reasons. Such “Gettierized” verdicts, I contend, fail to realize the epistemic goal or aim of legal proof. Thus I conclude there, legal proof includes something like a knowledge requirement—in the sense that legal verdicts aim not only at truth and sufficient evidential support but also, as with knowledge, at an appropriate connection between their truth and justifying evidential support. (shrink)

The European Union is making increased efforts to find simpler and more effective ways to function adequately in the eyes of its citizens by using ‘soft law’ instruments such as recommendations. Although they have no legally binding force, recommendations have practical and legal effects occurring partly due to their normative content in which a course of action is prescribed and further supported by arguments intended to persuade the addressees of a political position. Although recommendations function as persuasive instruments due to (...) their argumentation, the characteristics of argumentation and how it is employed to convince the addressee to comply with certain measures have not been investigated at all. The main goal of the paper is to explain how arguments are used by the European Commission when recommending Member States to follow a new course of action. First, we will unravel the justificatory reasons employed by the Commission in order to make Member States comply with new measures and we will show how these reasons are combined into an argumentative pattern : 1–23, 2016; J Argum Context 6: 3–26, 2017). This pattern basically prescribes a course of action to Member States, which is further supported by arguments in which the necessity and advantages of following the proposed course of action are justified. Second, we will explain how and why the way in which the arguments are combined in this complex pattern could be potentially persuasive for the Member States despite the legally non-binding character of recommendations. We will show that the European Commission tries to persuade the Member States to take new measures by evading the burden of proof imposed by the legislative framework. At a more specific level of analysis, we will delve into the implicit premises in the argumentation, which enable us to identify cases of evasion of the burden of proof due to the Commission’s use of implicit starting points which might not be accepted by the Member States. (shrink)

The guise of the good doctrine is the view that whatever we desire, we desire it under the guise of the good, i.e. it appears good to us in some way. In this paper I first clarify the role that the doctrine of the guise of the good plays in the first step of J. S. Mill’s proof of the principle of utility (in which he shows that one’s happiness is desirable as an end). Then I provide textual evidence (...) in favour of ascribing the doctrine to Mill, arguing that he commits to it to the extent that he equates finding something pleasant and thinking it desirable. Finally I counter two potential sources of evidence against ascribing the guise of the good to Mill: apparent desires based on ‘fixed ideas’, and those habitual desires which are no longer associated with finding their objects pleasant. I argue that ‘fixed ideas’ do not feed actual desires, and that the habitual desires which seem to escape the guise of the good, even if not uncommon, have a secondary status as desires. (shrink)

In this paper, we consider three different search strategies for a cut-free sequent system formalizing orthologic, and estimate the respective search spaces. Applying backward search, there are classes of formulae for which both the minimal proof length and the search space are exponential. In a combined forward and backward approach, all proofs are polynomial, but the potential search space remains exponential. Using a forward strategy, the potential search space becomes polynomial yielding a polynomial decision procedure for orthologic (...) and the word problem for free ortholattices. (shrink)

In this paper, we consider three different search strategies for a cut-free sequent system formalizing orthologic, and estimate the respective search spaces. Applying backward search, there are classes of formulae for which both the minimal proof length and the search space are exponential. In a combined forward and backward approach, all proofs are polynomial, but the potential search space remains exponential. Using a forward strategy, the potential search space becomes polynomial yielding a polynomial decision procedure for orthologic (...) and the word problem for free ortholattices. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Nature of Proof in PsychiatryPaul Lieberman (bio)Keywordspsychotherapy process, knowledge and psychiatry, externalism, WittgensteinThis vivid clinical report illustrates recognizably, and provocatively, a number of routine, but often unexamined, clinical questions. In its few paragraphs, it depicts challenges that each practitioner confronts, and, in the flux of clinical work, addresses, however implicitly and imperfectly, every day: From what data, and by what processes, does a clinical formulation, or way (...) of understanding, come into being? How do we appraise its accuracy and adequacy? Of what value is even a well-substantiated understanding, in the mind of the therapist, to the patient? What is the power of empathy as a treatment tool? How do we assess someone's status as a “good candidate for therapy?” When, typically, only the outlines of a problem are visible, and its origins and implications are largely hidden, by what right do we recommend psychotherapy, and with what conception, at what level of detail, of what its outcome will be? These are among the questions that Dr. Bailey's story challenges us to address.They are clinical questions, of course, because they deal with empirical matters of fact—psychological processes, outcomes studies, and evidence. But they are also philosophical because, as Freud insisted and Dr. Bailey shows, information obtained in the clinical situation often has power and authority that lead us to believe we understand what is going on, understand the other person, even in the absence of scientifically tested hypotheses, or the clear application of research-based evidence. Interactions between people—including clinical interactions—have a life and ability to engage us. Their meanings can seem so transparent and convincing that no doubt or questioning may seem cogent. At their most powerful, such experiences can reawaken us to important realms of experience and feeling which we might, otherwise, forget, ignore, suppress, deny, or in other ways keep out of awareness; they have the potential to arouse us and reconnect us with truths that, once revived, can seem both valid and important—perhaps the kind of experience that we may derive from works of art or literature (in fact, Dr. Bailey's account could be seen as a clinical parable—meant to be neither true nor false, but instructive). But even less dramatic examples are commonplace: we do routinely claim to know and be able to interpret and understand the actions of other people from our everyday interactions with and observations of them.What is less clear is how to account for these convictions and how to appraise their value, because they do not derive from established scientific procedures. Clinical intuition has a role throughout medicine, but we usually expect it to be subjected later to more rigorous tests to establish the correct diagnosis. Yet, as Dr. Bailey's case illustrates, clinical intuition in the psychiatric encounter seems somehow different. When Colin [End Page 225] leads Dr. Bailey to the conclusion that a “painful lack of wounds” has made him depressed, we find this credible. It seems similarly credible that Dr. Bailey might be anxious about his own capacity to defend his young family, because he says he is, that he perceives Colin as testing his manhood or sincerity, because that seems to fit Colin's temperament, that being accurately understood is helpful, because most of us have had that experience and valued it, and that, most generally, an absence of challenge or of activity could be depressing. But suppose a patient believed that a painful lack of wounds produced diabetes instead of depression, or suppose he had developed epilepsy and attributed that to an absence of combat experience. We might see these as ‘pre-scientific’ or ‘hypothesis-generating’ (or worse). By contrast, it seems timid to consider psychiatric formulations to be always and only provisional or hypothetical.In what ways and to what extent should we expect psychiatry to be different, and why? Several considerations suggest that psychiatry's reasons are not, always and everywhere, the same as those of general medicine, nor are its objectives.In general medicine, we distinguish between signs and symptoms, on the one hand, and “underlying” disease processes, on the other. But in psychiatry, this distinction can be... (shrink)

BackgroundInnovations in technology have contributed to rapid changes in the way that modern biomedical research is carried out. Researchers are increasingly required to endorse adaptive and flexible approaches to accommodate these innovations and comply with ethical, legal and regulatory requirements. This paper explores how Dynamic Consent may provide solutions to address challenges encountered when researchers invite individuals to participate in research and follow them up over time in a continuously changing environment.MethodsAn interdisciplinary workshop jointly organised by the University of Oxford (...) and the COST Action CHIP ME gathered clinicians, researchers, ethicists, lawyers, research participants and patient representatives to discuss experiences of using Dynamic Consent, and how such use may facilitate the conduct of specific research tasks. The data collected during the workshop were analysed using a content analysis approach.ResultsDynamic Consent can provide practical, sustainable and future-proof solutions to challenges related to participant recruitment, the attainment of informed consent, participant retention and consent management, and may bring economic efficiencies.ConclusionsDynamic Consent offers opportunities for ongoing communication between researchers and research participants that can positively impact research. Dynamic Consent supports inter-sector, cross-border approaches and large scale data-sharing. Whilst it is relatively easy to set up and maintain, its implementation will require that researchers re-consider their relationship with research participants and adopt new procedures. (shrink)

The validity of the confinement limit obtain by Unanyan et al. (Phys Rev A 79:044101, 2009) is extended by including non-symmetric vector and scalar potentials. It shows that the confinement limit of one-dimensional Dirac particles in vector and scalar potentials is \(\lambda _C/\sqrt{2}\) , with \(\lambda _C\) being the Compton wavelength.

What explains change? Edward Feser argues in his ‘Aristotelian proof’ that the only adequate answer to these questions is ultimately in terms of an unchangeable, purely actual being. In this paper, I target the cogency of Feser’s reasoning to such an answer. In particular, I present novel paths of criticism—both undercutting and rebutting—against one of Feser’s central premises. I then argue that Feser’s inference that the unactualized actualizer lacks any potentialities contains a number of non-sequiturs.

This article explores the relationships between legal proof and fundamental epistemic concepts such as knowledge and justification. A survey of the legal literature reveals a confusing array of seemingly inconsistent proposals and presuppositions regarding these relationships. This article makes two contributions. First, it reconciles a number of apparent inconsistencies and tensions in accounts of the epistemology of legal proof. Second, it argues that there is a deeper connection between knowledge and legal proof than is typically argued for (...) or presupposed in the legal literature. This connection is illustrated through a discussion of the Gettier problem in epistemology. It is argued that the gap or disconnect between truth and justification that undermines knowledge in Gettier cases also potentially undermines the success of legal verdicts. (shrink)

The interplay of philosophical ambitions and technical reality have given birth to rich and interesting approaches to explain the oft-claimed special character of mathematical and logical knowledge. Two projects stand out both for their audacity and their innovativeness. These are logicism and proof-theoretic semantics. This dissertation contains three chapters exploring the limits of these two projects. In both cases I find the formal results offer a mixed blessing to the philosophical projects. Chapter 1. Is a logicist bound to the (...) claim that as a matter of analytic truth there is an actual infinity of objects? If Hume’s Principle is analytic then in the standard setting the answer appears to be yes. Hodes’s work pointed to a way out by offering a modal picture in which only a potential infinity was posited. However, this project was abandoned due to apparent failures of cross-world predication. I re-explore this idea and discover that in the setting of the potential infinite one can interpret first-order Peano arithmetic, but not second-order Peano arithmetic. I conclude that in order for the logicist to weaken the metaphysically loaded claim of necessary actual infinities, they must also weaken the mathematics they recover. Chapter 2. There have been several recent results bringing into focus the super-intuitionistic nature of most notions of proof-theoretic validity. But there has been very little work evaluating the consequences of these results. In this chapter, I explore the question of whether these results undermine the claim that proof-theoretic validity shows us which inferences follow from the meaning of the connectives when defined by their introduction rules. It is argued that the super-intuitionistic inferences are valid due to the correspondence between the treatment of the atomic formulas and more complex formulas. And so the goals of proof-theoretic validity are not undermined. Chapter 3. Prawitz (1971) conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister (2019). This chapter resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The chapter further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to allow double negation elimination for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic.Abstract prepared by Will Stafford extracted partially from the dissertation. (shrink)

Nudges have gained popularity as a behavioral change tool that aims to facilitate the selection of the sensible choice option by altering the way choice options are presented. Although nudges are designed to facilitate these choices without interfering with people’s prior preferences, both the relation between individuals’ prior preferences and nudge effectiveness, as well as the notion that nudges ‘facilitate’ decision-making have received little empirical scrutiny. Two studies examine the hypothesis that a social proof nudge is particularly effective when (...) people have no clear prior preference, either because people are indifferent (in a colour-categorization task; Study 1, N = 255) or because people experience a choice conflict (making shopping decisions about meat products; Study 2, N = 97). Both studies employed a social proof nudge to steer participants’ choices. The potential facilitating effect of the nudge was tested using a mouse-tracker paradigm that implicitly assessed experienced uncertainty during decision-making. Results showed that the nudge was effective in steering participants’ decisions; the facilitation effect (i.e., reduced uncertainty regarding the decision) was only observed for conflicting preferences, but not under indifference. A better understanding of when and how nudges can influence individuals’ behavior may help in deciding whether nudges are an appropriate policy tool for changing particular undesirable behavior. (shrink)

This paper investigates the ontological presuppositions of quantifier logic. It is seen that the actual infinite, although present in the usual completeness proofs, is not needed for a proper semantic foundation. Additionally, quantifier logic can be given an adequate formulation in which neither the notion of individual nor that of a predicate appears.

The increased use of information technology in every day health care creates vast amounts of stored health data that can be used for research. The secondary research use of routinely collected data raises questions about appropriate consent mechanisms for such use. One option is meta consent where individuals state their own consent preferences in relation to future use of their data, e.g. whether they want the data to be accessible to researchers under conditions of specific consent, broad consent, blanket consent (...) or not at all. This study investigates whether meta consent preferences can be successfully elicited by a smartphone application in the adult Danish population. A smartphone app was developed for the elicitation of meta consent preferences. An invitation to use the app was distributed to a stratified, representative sample of the Danish adult population. The meta consent choices, the use of the app, user experience data, and demographic data were logged and analysed statistically using IBM SPSS version 20. Of 1000 potential respondents 221 used the app. One hundred eighty-eight of the respondents were female and 103 male. The age range was 19 to 79 years with an average of 51 years. Most users indicate 1) that they find the choices they are asked to make easy to understand, 2) that the application is easy to use, and 3) that this kind of choice should be offered to people. It is possible to collect meta consent preferences in the general, adult population using a smartphone app. (shrink)

In this paper I demonstrate how certain contemporary atheists have problematically conflatedatheismwithagnosticism(knowingly or unknowingly). The first type of conflation issemantic fusion, where the lack of belief in God is combined with the outright denial of God, under the single label of ‘atheism’. The second ismorphological fissionwhich involves the separation of atheism into two subcategories where lack of belief in God is labelled asnegativeatheism and outright denial of God aspositiveatheism – and while here they are more explicitly demarcated, they are still (...) positioned under the broad notion of atheism. I argue in this paper that atheism should be better used as thepropositional denialof God and thatuncertaintyandunknowability about Godshould be reserved to characterise agnosticism. Conflating these positions under the single term ‘atheism’ mischaracterises agnostics and inflates the territory of atheists. In clarifying these terms, I review how the nuances in the prefixa-in atheism have potentially contributed towards these misnomers. I also suggest the use of the categories ‘local atheism’ and ‘global atheism’ to clarify on whom the burden of proof lies within the discourse. (shrink)

In Physical Theory Mr. Lenzen writes, “Thus the concept of thing is the concept of a class of aspects which are in the past, present, or future for several minds.” Again, in Mind and the World-Order, Mr. Lewis defines “thing” as “… a complex of properties or qualities, recognizable by some uniformity of appearance.” Without questioning the metaphysics implied in these two definitions of “thing” I shall accept them as quite compatible and as useful in defining the rôle of experience (...) in the construction of scientific objects. If in “Pragmatism and Metaphysics” Mr. Morris has not established proof of the existence of objects independent of any and all experience of them, he certainly has shown conclusively that the possibility of experiencing objects is independent of any and all observers. (shrink)

This article is a methodological discussion of formal approaches to the question of identity of proofs from a philosophical standpoint. First, an introduction to the question of identity of proofs itself is given, followed by a brief reconstruction of the so-called normalisation thesis, proposed by Dag Prawitz in 1971, in which some of its core mathematical and conceptual traits are presented. After that, a comparison between the normalisation thesis and the more well-known Church-Turing thesis on computability is carried out in (...) three main parts: the first dedicated to highlighting some of the analogies between them; the second, their most remarkable differences; and the third, to the possible relations of dependence between the two. Based on these considerations, some concluding remarks concerning the potential of the normalisation thesis and similar approaches to the question of identity of proofs are made in the last section. (shrink)

Specifically tailored industrial control systems attacks are becoming increasingly sophisticated, accentuating the need of ICS cyber security. The nature of these systems makes traditional IT security measures not suitable, requiring expressly developed security countermeasures. Within the past decades, research has been focused in network-based intrusion detection systems. With the appearance of software-defined networks, new opportunities and challenges have shown up in the research community. This paper describes the potential benefits of using SDNs in industrial networks with security purposes and (...) presents the set up and results of a pilot experiment carried out in a scaled physical implementation. The experimental set up consists in the detection of ICMP flood and packet payload alteration based on signature comparison. Results point to the potential viability of the technology for intrusion detection and the need of researching in architectural scalability. (shrink)

An ambitious ethical theory ---Alan Gewirth's "Principle of Generic Consistency"--- is encoded and analysed in Isabelle/HOL. Gewirth's theory has stirred much attention in philosophy and ethics and has been proposed as a potential means to bound the impact of artificial general intelligence.

Over the course of more than two millennia the philosophical school of Mīmāṃsā has thoroughly analyzed normative statements. In this paper we approach a formalization of the deontic system which is applied but never explicitly discussed in Mīmāṃsā to resolve conflicts between deontic statements by giving preference to the more specific ones. We first extend with prohibitions and recommendations the non-normal deontic logic extracted in Ciabattoni et al. from Mīmāṃsā texts, obtaining a multimodal dyadic version of the deontic logic \. (...) Sequent calculus is then used to close a set of prima-facie injunctions under a restricted form of monotonicity, using specificity to avoid conflicts. We establish decidability and complexity results, and investigate the potential use of the resulting system for Mīmāṃsā philosophy and, more generally, for the formal interpretation of normative statements. (shrink)

A macroscopic experiment capable of detecting a signature of spinorial sign changes is discussed. If realized, it would determine whether Bell inequalities are satisfied for a manifestly local, classical system. By providing an explicitly local-realistic derivation of the EPR-Bohm type spin correlations, it is demonstrated why Bell inequalities must be violated even in such a manifestly local, macroscopic domain, just as strongly as they are in the microscopic domain. The proposed experiment has the potential to transform our understanding of (...) the relationship between classical and quantum physics. (shrink)

Many experiments have been conducted over the past eight decades to explore whether the ostensible psychic ability of psychokinesis (PK, or "mind over matter") might be a genuine human potential, and the most extensive of these have involved attempts to mentally influence the output of electronic, binary-bit random number generators (RNGs). Research of this type can generally be divided into two lines: proof-oriented (concerned with the accumulation and statistical evaluation of data from controlled experiments designed specifically to test (...) for the presence of PK effects on the microscopic scale) and process-oriented (concerned with conducting exploratory experiments designed to systematically vary certain test conditions in order to search for and identify any physical, biological, and psychological factors which might have a role in improving or moderating PK effects). To help orient novice investigators and cross-disciplinary researchers who may be considering work along these lines (as well as offer some initial guiding insight on possible directions for future research), this paper provides a general review of some of the notable proof- and process-oriented findings that have been obtained to date in experimental microscopic PK research using RNGs. The review generally indicates that although a considerable amount of proof-oriented data for micro-PK has accumulated over the years, the relatively sparse amount of process-oriented data available at present leaves a lot of open questions regarding the underlying factors involved, providing ample opportunity for novice investigators and cross-disciplinary researchers to make valuable research contributions in the future. (shrink)

In recent years it has been demonstrated that the use of the traditional property registry models involves the risk of corruption along with long waiting times. This paper points out the main problems associated with conventional models and makes a survey of the new ones that are based on blockchain technology. This type of model is already being developed as a proof of concept by different countries. With the use of this technology in land registry systems, it is possible (...) to improve the transparency of the processes as well as optimize costs and execution time. To show the theoretical results of this study, the Spanish land registry has been taken as an example of a use case scenario. (shrink)

In current philosophical research, there is a rather one-sided focus on the foundations of proof. A full picture of mathematical practice should however additionally involve considerations about various methodological aspects. A number of these is identified, from large-scale to small-scale ones. After that, naturalism, a philosophical school concerned with scientific practice, is looked at, as far as the translations of its epistemic principles to mathematics is concerned. Finally, we call for intensifying the interaction between both dimensions of practice and (...) epistemology. (shrink)

In current philosophical research, there is a rather one-sided focus on the foundations of proof. A full picture of mathematical practice should however additionally involve considerations about various methodological aspects. A number of these is identified, from large-scale to small-scale ones. After that, naturalism, a philosophical school concerned with scientific practice, is looked at, as far as the translations of its epistemic principles to mathematics is concerned. Finally, we call for intensifying the interaction between both dimensions of practice and (...) epistemology. (shrink)

In current philosophical research, there is a rather one-sided focus on the foundations of proof. A full picture of mathematical practice should however additionally involve considerations about various methodological aspects. A number of these is identified, from large-scale to small-scale ones. After that, naturalism, a philosophical school concerned with scientific practice, is looked at, as far as the translations of its epistemic principles to mathematics is concerned. Finally, we call for intensifying the interaction between both dimensions of practice and (...) epistemology. (shrink)

In the 1870s, Carl Neumann proposed the so-called method of the arithmetic mean for solving the Dirichlet problem on convex domains. Neumann’s approach was considered at the time to be a reliable existence proof, following Weierstrass’s criticism of the Dirichlet principle. However, in 1937 H. Lebesgue pointed out a serious gap in Neumann’s proof. Curiously, the erroneous argument once again involved confusion between the notions of infimum and minimum. The objective of this paper is to show that Lebesgue’s (...) sharp criticism of Neumann’s proof was only partially justified. (shrink)