In this paper I discuss Newton's first optical paper. My aim is to examine the type of argument which Newton uses in order to convince his readers of the truth of his theory of colors. My claim is that this argument is an induction by elimination, and that the Newtonian method of justification is a kind of “generative justification”, a term due to T. Nickles. To achieve my aim I analyze in some detail the arguments in Newton's first optical paper, (...) relating the paper with Newton's other writings in optics, and especially his early correspondence in defence of his theory of colors. (shrink)

Newton claims that his theorems in the Opticks are derived from experiments alone. The paper explains this dictum by relating Newton’s proof method to an iconic conception of proof as opposed to a symbolic one. Theorems are not derived from hypotheses; instead properties of light are identified by experimental properties based on rules of inductive reasoning.

In studies of scientific methodology, surprisingly little attention has been given to tests of hypotheses. Such testing constitutes a methodology common to various scientific disciplines and is an essential factor in the development of science since it determines which theories are retained. The classical theory of tests is a major accomplishment but requires modification in order to produce a theory that accounts for the success of science. The revised theory is an analysis of the nondeductive aspect of scientific reasoning. It (...) results in a new definition of probability and a nonclassical point of view with regard to the foundations of probability. (shrink)

In studies of scientific methodology, surprisingly little attention has been given to tests of hypotheses. Such testing constitutes a methodology common to various scientific disciplines and is an essential factor in the development of science since it determines which theories are retained. The classical theory of tests is a major accomplishment but requires modification in order to produce a theory that accounts for the success of science. The revised theory is an analysis of the nondeductive aspect of scientific reasoning. It (...) results in a new definition of probability and a nonclassical point of view with regard to the foundations of probability. (shrink)

In studies of scientific methodology, surprisingly little attention has been given to tests of hypotheses. Such testing constitutes a methodology common to various scientific disciplines and is an essential factor in the development of science since it determines which theories are retained. The classical theory of tests is a major accomplishment but requires modification in order to produce a theory that accounts for the success of science. The revised theory is an analysis of the nondeductive aspect of scientific reasoning. It (...) results in a new definition of probability and a nonclassical point of view with regard to the foundations of probability. (shrink)

Gianantonio Tadini is the little known protagonist in an important experiment carried out in Bergamo between 1794 and 1795. Based on the measurement of the deviation of a falling body, the experiment owes much to the one that was conducted by Giambattista Guglielmini in Bologna in 1791, which aimed at demonstrating Earth’s rotation. Tadini’s experimental work represents the most successful attempt carried out before the 19th century, and it led to the first correct formulation of deviation’s measurement. In spite (...) of this, it is not well represented in the general literature on the history of experiments intended to show diurnal Earth’s motion.1 The discovery of Tadini’s diary of experiments as well as some notes and a part of his correspondence – preserved as manuscripts in the Angelo Mai municipal library in Bergamo – allows us now to reconstruct the history of Tadini’s experiment and of his reasoning about Guglielmini’s work. In this paper, I describe the genesis and the development of Tadini’s experiment, clarify the role played by the different personalities involved and set these trials against the background of the widest history of proofs on diurnal Earth’s rotation carried out in Europe in those years. (shrink)

This paper suggests a method to calculate a degree of validity for the proof of a statement which is derived from empirical statements by means of logic conclusions. The empirical statements are assumed not to be completely valid or their validity to be doubtful. The suggested rules are consistent with two-valued logic, yield decreasing validities with increasing number of applications of modus ponens and obey the law of the excluded middle. The actual calculation of validity values, the relation of (...) the suggested method to some truth tables of multi-valued logic and to fuzzy logic are discussed. (shrink)

The anti-tuberculosis BCG vaccine was conceived and developed between 1905 and 1921 at Pasteur Institutes in France. Between 1921 and A. Calmette’s death in 1933, the vaccine went through a first period of national and international production and distribution for its use in humans. In France these activities were exclusively carried out by Calmette and his collaborators at the Pasteur Institute in Paris. Initially improvised production in a small room in the cellar gave way in 1931 to the construction of (...) the spacious and magnificent ‘New laboratories for research on tuberculosis and the preparation of the BCG’ within the premises of the Pasteur Institute. Presentation and image-building of the vaccine in France insisted on the fact that the BCG was not a commercial specialty but distributed free of charge. The technical monopoly of its production nevertheless lay with the Paris Pasteur Institute and standardization of scientific proof of safety, efficacy and stability was dominated by that Institute in France. In contrast, the international production and distribution of the vaccine was entrusted and transferred, free of charge, to trustworthy laboratories outside France. Multiplication of producers and users led to an increased need for standardization. For this process the analysis distinguishes between the standardization of scientific proof concerning safety, efficacy and stability of the vaccine and standardization of its medical uses. Whereas standardization was rather successful in the inter-war period in France, the international efforts remained rather unsuccessful. Only after world war II under Scandinavian leadership and in the context of mass vaccination programs supported by the WHO and UNICEF was the international standardization effectively implemented and succeeded at least to some extend. (shrink)

: "In this paper we compare computerized environments in which students complete proof construction exercises in formal logic. Afterbeing given a pretest for logical aptitude, three matched groups were presented identical course material on logic for approximately five weeks by a computer. During the treatment, all students were required to complete several hundred proof construction exercises. The three groups did the exercises and the midterm in different environments. The group with a more sophisticated interface performed better on the (...) midterm. Nearly all the difference in performance showed up in the harder problems. In a follow up experiment in which flexible strategic problem solving help was added to the environment, performance improved slightly, but the data are inconclusive.". (shrink)

In recent decades, experimental mathematics has emerged as a new branch of mathematics. This new branch is defined less by its subject matter, and more by its use of computer assisted reasoning. Experimental mathematics uses a variety of computer assisted approaches to verify or prove mathematical hypotheses. For example, there is “number crunching” such as searching for very large Mersenne primes, and showing that the Goldbach conjecture holds for all even numbers less than 2 × 1018. There are (...) “verifications” of hypotheses which, while not definitive proofs, provide strong support for those hypotheses, and there are proofs involving an enormous amount of computer hours, which cannot be surveyed by any one mathematician in a lifetime. There have been several attempts to argue that one or another aspect of experimental mathematics shows that mathematics now accepts empirical or inductive methods, and hence shows mathematical apriorism to be false. Assessing this argument is complicated by the fact that there is no agreed definition of what precisely experimental mathematics is. However, I argue that on any plausible account of ’experiment’ these arguments do not succeed. (shrink)

In this paper, we first briefly survey the main responses to the challenge that experimental philosophy poses to the method of cases, given the common assumption that the latter is crucially based on intuitive judgments about cases. Second, we discuss two of the most popular responses in more detail: the expertise defense and the mischaracterization objection. Our take on the expertise defense is that the available empirical data do not support the claim that professional philosophers enjoy relevant expertise in (...) their intuitive judgments about cases. In contrast, the mischaracterization objection seems considerably more promising than its largely negative reception has suggested. We argue that the burden of proof is thus on philosophers who still hold that the method of cases crucially relies on intuitive judgments about cases. Finally, we discuss whether conceptual engineering provides an alternative to the method of cases in light of the challenge from experimental philosophy. We argue that this is not clearly the case, because conceptual engineering also requires descriptive information about the concepts it aims to improve. However, its primarily normative perspective on our concepts makes it largely orthogonal to the challenge from experimental philosophy, and it can also benefit from the empirical methods of the latter. (shrink)

During the past decade, M.W. Evans and his coworkers have been developing so-called “Evans” or “ECE theory” that intends to serve as an unified field theory. One of its predictions is an existence of a radiation magnetic field called a “B(3)-field” which should accompany a circularly polarized electromagnetic radiation. This field should affect free electrons in two ways: (1) the electrons should behave in the B(3)-field in the same way as in a classical magnetic field (i.e., Larmor precession) and moreover, (...) (2) the electrons should undergo quantum interaction with the B(3)-field with the formation of a spin connection resonance. This paper presents an experimental test of the B(3)-field existence by observing the changes in trajectories of free electrons in special detector, when strong (up to 200 W/m2) continuous circularly polarized microwave radiation of a frequency of 2.45 GHz is applied. We have not detected any sign of B(3)-field in presented experiment. It follows that if the B(3)-field really exists, it should be at least 4 orders of magnitude smaller than the Evans’ theory predicts. (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)

The set of 60 real rays in four dimensions derived from the vertices of a 600-cell is shown to possess numerous subsets of rays and bases that provide basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a basis-critical proof is one that fails if even a single basis is deleted from it). The proofs vary considerably in size, with the smallest having 26 rays and 13 bases and the largest 60 rays and 41 bases. There are at least 90 (...) basic types of proofs, with each coming in a number of geometrically distinct varieties. The replicas of all the proofs under the symmetries of the 600-cell yield a total of almost a hundred million parity proofs of the BKS theorem. The proofs are all very transparent and take no more than simple counting to verify. A few of the proofs are exhibited, both in tabular form as well as in the form of MMP hypergraphs that assist in their visualization. A survey of the proofs is given, simple procedures for generating some of them are described and their applications are discussed. It is shown that all four-dimensional parity proofs of the BKS theorem can be turned into experimental disproofs of noncontextuality. (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)

'Numbers and Proofs' presents a gentle introduction to the notion of proof to give the reader an understanding of how to decipher others' proofs as well as construct their own. Useful methods of proof are illustrated in the context of studying problems concerning mainly numbers (real, rational, complex and integers). An indispensable guide to all students of mathematics. Each proof is preceded by a discussion which is intended to show the reader the kind of thoughts they might (...) have before any attempt proof is made. Established proofs which the student is in a better position to follow then follow. Presented in the author's entertaining and informal style, and written to reflect the changing profile of students entering universities, this book will prove essential reading for all seeking an introduction to the notion of proof as well as giving a definitive guide to the more common forms. Stressing the importance of backing up "truths" found through experimentation, with logically sound and watertight arguments, it provides an ideal bridge to more complex undergraduate maths. (shrink)

Debiasing procedures are experimental methods aimed at correcting errors arising from the cognitive biases of the experimenter. We discuss two of these methods, the predesignation rule and randomization, showing to what extent they are open to the experimenter’s regress: there is no metarule to prove that, after implementing the procedure, the experimental data are actually free from biases. We claim that, from a contractarian perspective, these procedures are nonetheless defensible since they provide a warrant of the impartiality of (...) the experiment: we only need proof that the result has not been intentionally manipulated for prima facie acceptance. (shrink)

This paper examines Timothy Williamson's recent 'expertise defense' of armchair philosophy mounted by skeptical experimental philosophers. The skeptical experimental philosophers argue that the methodology of traditional 'armchair' philosophers rests up trusting their own intuitions about particular problem cases. Empirical studies suggest that these intuitions are not generally shared and that such intuitions are strongly influenced factors that are not truth conducive such as cultural background or whether or not the question is asked in a messy or tidy office. (...) Williamson's response is that the skeptical armchair philosophers trust the expertise of the social scientists, as they trust and use the methods of the social sciences to undermine trust in the judgment of armchair philosophers. Given this, the burden of proof is on the skeptical experimental philosopher to give us a reason to doubt the expertise of the armchair philosopher. I examine how our understanding of the history of philosophy is significant in this context. And suggest that prevalent false beliefs about the history of philosophy can lead to mistrust of the expertise of philosophers. (shrink)

An increasing number of learning goals refer to the acquisition of cognitive skills that can be described as ‘resource-based,’ as they require the availability, coordination, and integration of multiple underlying resources such as skills and knowledge facets. However, research on the support of cognitive skills rarely takes this resource-based nature explicitly into account. This is mirrored in prior research on mathematical argumentation and proof skills: Although repeatedly highlighted as resource-based, for example relying on mathematical topic knowledge, methodological knowledge, mathematical (...) strategic knowledge, and problem-solving skills, little evidence exists on how to support mathematical argumentation and proof skills based on its resources. To address this gap, a quasi-experimental intervention study with undergraduate mathematics students examined the effectiveness of different approaches to support both mathematical argumentation and proof skills and four of its resources. Based on the part-/whole-task debate from instructional design, two approaches were implemented during students’ work on proof construction tasks: (i) asequential approachfocusing and supporting each resource of mathematical argumentation and proof skills sequentially after each other and (ii) aconcurrent approachfocusing and supporting multiple resources concurrently. Empirical analyses show pronounced effects of both approaches regarding the resources underlying mathematical argumentation and proof skills. However, the effects of both approaches are mostly comparable, and only mathematical strategic knowledge benefits significantly more from the concurrent approach. Regarding mathematical argumentation and proof skills, short-term effects of both approaches are at best mixed and show differing effects based on prior attainment, possibly indicating an expertise reversal effect of the relatively short intervention. Data suggests that students with low prior attainment benefited most from the intervention, specifically from the concurrent approach. A supplementary qualitative analysis showcases how supporting multiple resources concurrently alongside mathematical argumentation and proof skills can lead to a synergistic integration of these during proof construction and can be beneficial yet demanding for students. Although results require further empirical underpinning, both approaches appear promising to support the resources underlying mathematical argumentation and proof skills and likely also show positive long-term effects on mathematical argumentation and proof skills, especially for initially weaker students. (shrink)

Abstract: Some proponents of “experimental philosophy” criticize philosophers' use of thought experiments on the basis of evidence that the verdicts vary with truth-independent factors. However, their data concern the verdicts of philosophically untrained subjects. According to the expertise defence, what matters are the verdicts of trained philosophers, who are more likely to pay careful attention to the details of the scenario and track their relevance. In a recent article, Jonathan M. Weinberg and others reply to the expertise defence that (...) there is no evidence for such expertise. They now receive a reply in this article, which argues that they have misconstrued the dialectical situation. Since they have produced no evidence that philosophical training is less efficacious for thought experimentation than for other cognitive tasks for which they acknowledge that it produces genuine expertise, such as informal argumentation, they have produced no evidence for treating the former more sceptically than the latter. (shrink)

Originally published in 1973 the editors of this book collected together those studies which had been considered at the time to yield the best evidence in support of Freudian theory, and found on close examination that they failed to provide any such proof. Each paper is printed in full and is followed by a critical discussion which raises questions of statistical treatment, sufficiency of controls and alternative interpretations. The particular usefulness of this format is that it allows readers to (...) form their own opinions while providing helpful suggestions and guidelines on how to approach experimental studies with a critical mind. (shrink)

This paper trials new experimental methods for the analysis of natural language reasoning and the development of critical ordinary language philosophy in the wake of J.L. Austin. Philosophical arguments and thought experiments are strongly shaped by default pragmatic inferences, including stereotypical inferences. Austin suggested that contextually inappropriate stereotypical inferences are at the root of some philosophical paradoxes and problems, and that these can be resolved by exposing those verbal fallacies. This paper builds on recent efforts to empirically document inappropriate (...) stereotypical inferences that may drive philosophical arguments. We demonstrate that previously employed questionnaire-based output measures do not suffice to exclude relevant confounds. We then report an experiment that combines reading time measurements with plausibility ratings. The study seeks to provide evidence of inappropriate stereotypical inferences from appearance verbs that have been suggested to lie at the root of the influential ‘argument from illusion’. Our findings support a diagnostic reconstruction of this argument. They provide the missing component for proof of concept for an experimental implementation of critical ordinary language philosophy that is in line with the ambitions of current ‘evidential’ experimental philosophy. (shrink)

Many argued (Accardi and Fedullo, Pitowsky) that Kolmogorov's axioms of classical probability theory are incompatible with quantum probabilities, and that this is the reason for the violation of Bell's inequalities. Szabó showed that, in fact, these inequalities are not violated by the experimentally observed frequencies if we consider the real, “effective” frequencies. We prove in this work a theorem which generalizes this results: “effective” frequencies associated to quantum events always admit a Kolmogorovian representation, when these events are collected through different (...) experimental setups, the choice of which obeys a classical distribution. (shrink)

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)

Lance Rips describes a unified theory of natural deductive reasoning and fashions a working model of deduction, with strong experimental support, that is capable of playing a central role in mental life.

An important strand of current experimental philosophy promotes a new kind of methodological naturalism. This chapter argues that this new ‘metaphilosophical naturalism’ is fundamentally consistent with key tenets of Wittgenstein’s metaphilosophy, and can provide empirical foundations for therapeutic conceptions of philosophy. Metaphilosophical naturalism invites us to contribute to the resolution of philosophical problems about X by turning to scientific findings about the way we think about X – in general or when doing philosophy. This new naturalism encourages us to (...) use resources from psychology that can empirically vindicate precisely some of the most controversial aspects of Wittgenstein’s conception of philosophy: They can establish the need, and provide key tools, for something worth calling ‘therapy’, in philosophy. As ‘pudding proof’ this chapter shows how methods and findings from psycholinguistics motivate and facilitate a therapeutic approach to a characteristically philosophical problem: ‘the problem of perception’. (shrink)

Philosophical conceptual analysis is an experimental method. Focusing on this helps to justify it from the skepticism of experimental philosophers who follow Weinberg, Nichols & Stich. To explore the experimental aspect of philosophical conceptual analysis, I consider a simpler instance of the same activity: everyday linguistic interpretation. I argue that this, too, is experimental in nature. And in both conceptual analysis and linguistic interpretation, the intuitions considered problematic by experimental philosophers are necessary but epistemically irrelevant. (...) They are like variables introduced into mathematical proofs which drop out before the solution. Or better, they are like the hypotheses that drive science, which do not themselves need to be true. In other words, it does not matter whether or not intuitions are accurate as descriptions of the natural kinds that undergird philosophical concepts; the aims of conceptual analysis can still be met. (shrink)

Traditional debates about scientific realism tend to focus on issues concerning scientific representation and de-emphasize issues concerning scientific intervention. Questions about the relation between theories and the world, the nature of scientific inference, and the structure of scientific explanations have occupied a central place in the realism debate, while questions about experimentation and technology have not. Ian Hacking's experimental realism attempts to reverse this trend by shifting the defense of realism away from representation to intervention. Experimental realism, according (...) to Hacking, does not require us to believe that our theories are true, nor does its defense depend on inference to the best explanation. For Hacking, the strongest proof for realism is that we can manipulate objects: 'So far as I'm concerned, if you can spray them, then they are real'. (shrink)

The aim of this work is twofold. First, we survey the techniques developed in Perthame and Zubelli (Inverse Probl 23(3):1037–1052, 2007 ), Doumic et al. (Inverse Probl 25, 2009 ) to reconstruct the division (birth) rate from the cell volume distribution data in certain structured population structured population models. Secondly, we implement such techniques on experimental cell volume distributions available in the literature so as to validate the theoretical and numerical results. As a proof of concept, we use (...) the experimental data experimental data reported in the classical work of Kubitschek (Biophys J 9(6):792–809, 1969 ) concerning Escherichia coli in vitro experiments measured by means of a Coulter transducer-multichannel analyzer system (Coulter Electronics, Inc., Hialeah, FL, USA). Despite the rather old measurement technology, the reconstructed division rates still display potentially useful biological features. (shrink)

This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. -/- Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes (...) emerge that reflect recent developments in the field, such as issues concerning the logic of conditionals and the role played by visual elements in some mathematical proofs. -/- Featuring leading figures from experimental philosophy and the fields of philosophy of logic and mathematics, this collection reveals that empirical work in these disciplines has been quietly thriving for some time and stresses the importance of collaboration between philosophers and researchers in mathematics education and mathematical cognition. (shrink)

D.T. a 35-year-old woman, was found to have breast cancer. At the time of mastectomy axillary lymph nodes were positive and the cancer was classified as adenocarcinoma, grade 4. The patient underwent conventional chemotherapy. When it became apparent the disease was metastatic, the patient's oncologist contacted a well-known cancer center regarding the possibility of treating the patient with high dose chemotherapy and autologous bone marrow transplantation. The patient's health insurance provider informed the patient, however, that the treatment—estimated to cost in (...) the range of $150,000–200,000—was “considered experimental or research in nature” and therefore was not included in coverage. D.T. did not pursue this further. Approximately 2 years later, cancer was detected in the patient's spine. This time she applied to another well-known cancer center for HDC/ABMT. The cancer center agreed to accept her on the condition of proof of ability to pay for the treatment. Again her insurer refused coverage on the same grounds as before. D.T. found another source for the money, underwent treatment, then sued the insurance carrier. She sought a declaratory judgment that the treatment was covered under the insurance policy. The court ruled in favor of D.T. finding the contract phrase “considered experimental” ambiguous. (shrink)

This experimental study provides further support for a theory of meaning first put forward by Bar-Hillel and Carnap in 1953 and foreshadowed by Asimov in 1951. The theory is the Popperian notion that the meaningfulness of a proposition is its a priori falsity. We tested this theory in the first part of this paper by translating to logical form a long, tightly written, published text and computed the meaningfulness of each proposition using the a priori falsity measure. We then (...) selected the top propositions—by a priori falsity—and strung them together to form ad hoc abstracts and compared these abstracts with the published summary. The results were startling: translation to logical form, followed by application of the Asimovian idea and Bar-Hillel/Carnap mathematics as elaborated into an AI/NLP proposal in Fulda (1986, 1988), produced excellent abstracts, thereby providing a proof-of-concept that merely by knowing the logical form of long text passages, one can produce reasonable abstracts of them—without actually understanding the text. We here report on a second experiment analyzing, in the exact same manner, the correspondence that followed the published text of the first experiment. While the results of this confirming experiment are less startling, they nevertheless provide additional confidence in the promise of the technique. In other words, were the results of these two experiments to generalize, that would show that logical form captures much more semantics than has heretofore been considered likely. Far from (as is commonly supposed) being merely the syntactical rewrite of text into formal notation, translation to logical form, even when undertaken with almost no knowledge about the particular predicates, individual constants, or other objects referred to in that form, might capture the core of the meaning in some important sense. -/- Note: There is a key difference in the /style/ of the texts analyzed in I and II in this long paper, divided into two only for practical reasons—space; the first text analyzed is written in a tight mathematical style, while the second is written in the discursive style of philosophy. -/- Finally, the unusual (for me) length of this two-part paper is justified by its being data-driven. (shrink)

We focus on the thesis that action understanding is a function of the mirror neuron system. According to our opinion, understanding is a process that runs through hermeneutic circles from the “Vorverständnis” (“previous understanding”) to steps of deeper understanding. Our critique relates to the narrow neuroscientific definition of action understanding as the capacity to recognize several movements as belonging to one action. After a reconstruction of the model's developments, we will challenge the claims of the model by Rizzolatti and Sinigaglia (...) (2010). By analyzing the relation between the experimental results and its interpretation, we will conclude that there is no proof that mirror neuron activity leads to action understanding. (shrink)

A common reaction among idealist philosophers to the classical syntactic characterization of proof so crisply articulated by Tarski is an urgent but inchoate Angst that something momentous is missing, an awesome intimation of bereftness. The simple fact is that in many pursuits proof involves an empirical appeal, an operation that Tarski excludes from the domain of proof and assigns to the company of confirmation. In Tarski’s terms, empirical statements never even admit of the predicate true, let alone (...) proved, unless perhaps they hanker after truth or proof in the limit in some dimly understood and always unsuccessful way. Some sources of queasiness about the syntactic account are not hard to pinpoint. On the syntactic account, the injunction “Prove it!” can never be fulfilled, or even well-formedly uttered, in regard to an empirical statement, ┏∅, therefore ∅┓ is valid for any well-formed ∅ in a given first-order language, for any theorem, t, ┏∅, therefore t┓ is an impeccable proof for any well-formed ∅ in the classical languages. It is easy to think, with Bradley, that there is an important and legitimate, if not formally well-articulated sense of proof, characteristic of much of philosophical reasoning and argumentation, which is badly misrepresented by the syntactic conception. The kind of proof often sought after in theology, and sought after and found in the law, and the experimental and social sciences, is not purely syntactic. Idealists, of course, have frequently expressed dissatisfaction with the Tarski conception of truth. We will here extend this skepticism to the Tarski notion of proof. (shrink)

An important appeal of strategy-proofness is the robustness that it implies. Under a strategy-proof voting rule, every individual has an optimal strategy independently of the behavior of all other voters, namely truth-telling. In particular, optimal play is robust with respect to the beliefs voters may have about the type and the behavior of the other voters. Following Blin and Satterthwaite (Economet J Economet Soc 45(4):881–888, 1977), we call this logically weaker property “belief-independence.” In this paper, we give a number (...) of examples of voting rules that are belief-independent but not strategy-proof. However, we also show that belief-independence implies strategy-proofness under a few natural additional conditions. The notion of belief-independence naturally leads to a the strengthening of strategy-proofness to “robust” strategy-proofness which requires that no voter whose true preference may come from a restricted domain can benefit by submitting any unrestricted preference ordering given any unrestricted preference profile for all other voters. There are examples of strategy-proof voting rules (on a restricted domain) that are not robustly strategy-proof, but under natural additional conditions the two properties are shown to be equivalent. (shrink)

Several high-profile mathematical problems have been solved in recent decades by computer-assisted proofs. Some philosophers have argued that such proofs are a posteriori on the grounds that some such proofs are unsurveyable; that our warrant for accepting these proofs involves empirical claims about the reliability of computers; that there might be errors in the computer or program executing the proof; and that appeal to computer introduces into a proof an experimental element. I argue that none of these (...) arguments withstands scrutiny, and so there is no reason to believe that computer-assisted proofs are not a priori. Thanks are due to Michael Levin, David Corfield, and an anonymous referee for Philosophia Mathematica for their helpful comments. Earlier versions of this paper were presented at the Hofstra University Department of Mathematics colloquium series, and at the 2005 New Jersey Regional Philosophical Association; I am grateful to both audiences for their comments. CiteULike Connotea Del.icio.us What's this? (shrink)

A common reaction among idealist philosophers to the classical syntactic characterization of proof so crisply articulated by Tarski is an urgent but inchoate Angst that something momentous is missing, an awesome intimation of bereftness. The simple fact is that in many pursuits proof involves an empirical appeal, an operation that Tarski excludes from the domain of proof and assigns to the company of confirmation. In Tarski’s terms, empirical statements never even admit of the predicate true, let alone (...) proved, unless perhaps they hanker after truth or proof in the limit in some dimly understood and always unsuccessful way. Some sources of queasiness about the syntactic account are not hard to pinpoint. On the syntactic account, the injunction “Prove it!” can never be fulfilled, or even well-formedly uttered, in regard to an empirical statement, ┏∅, therefore ∅┓ is valid for any well-formed ∅ in a given first-order language, for any theorem, t, ┏∅, therefore t┓ is an impeccable proof for any well-formed ∅ in the classical languages. It is easy to think, with Bradley, that there is an important and legitimate, if not formally well-articulated sense of proof, characteristic of much of philosophical reasoning and argumentation, which is badly misrepresented by the syntactic conception. The kind of proof often sought after in theology, and sought after and found in the law, and the experimental and social sciences, is not purely syntactic. Idealists, of course, have frequently expressed dissatisfaction with the Tarski conception of truth. We will here extend this skepticism to the Tarski notion of proof. (shrink)

We further develop a recent new proof (by Greenberger, Horne, and Zeilinger—GHZ) that local deterministic hidden-variable theories are inconsistent with certain strict correlations predicted by quantum mechanics. First, we generalize GHZ's proof so that it applies to factorable stochastic theories, theories in which apparatus hidden variables are causally relevant to measurement results, and theories in which the hidden variables evolve indeterministically prior to the particle-apparatus interactions. Then we adopt a more general measure-theoretic approach which requires that GHZ's argument (...) be modified in order to produce a valid proof. Finally, we motivate our more general proof's assumptions in a somewhat different way from previous authors in order to strengthen the implications of our proof as much as possible. After developing GHZ's proof along these lines, we then consider the analogue, for our proof, of Bohr's reply to the EPR argument, and conclude (pace GHZ) that in at least one respect (viz. that of most concern to Bohr) the proof is no more powerful than Bell's. Nevertheless, we point out some new advantages of our proof over Bell's, and over other algebraic proofs of nonlocality. And we conclude by giving a modified version of our proof that, like Bell's, does not rely on experimentally unrealizable strict correlations, but still leads to a testable “quasi-algebraic” locality inequality.“... to admit things not visible to the gross creatures that we are is, in my opinion, to show a decent humility, and not just a lamentable addiction to metaphysics.”J. S. Bell. (shrink)

The issue of what constitutes a valid logical inference is a difficult question. At a minimum, we believe a permissible step in a proof must provide the reader with rational grounds to believe that the new step is a logically necessary consequence of previous assertions. However, this begs the question of what constitutes these rational grounds. Formalist accounts typically describe valid rules of inferences as those that can be found by applying one of the explicit rules of inference in (...) the formal system in which the proof is couched. However, philosophers of mathematics find such a description unhelpful because many inferences in the proofs that mathematicians actually produce cannot be expressed in a formal language, at least not without seriously distorting the semantic content of the inference (e.g., Larvor, 2012). In this chapter, we investigate mathematicians’ perceptions of a particular kind of inference in a particular setting. Specifically, we shed light on what types of graphical inferences mathematicians find permissible in a real analysis proof. Following Larvor (in press), we examine mathematicians’ reactions to metrical graphical inferences (i.e., inferences whose validity depends on the accuracy of the graph that was drawn and whose validity can be changed by minor deformations) and nonmetrical graphical inferences (i.e., inferences whose validity does not depend on a the accuracy of the graph and whose validity is not vulnerable to local deformations). The goal of this chapter is threefold. First, we demonstrate that most mathematicians reject metrical graphical inferences as impermissible in a real analysis proof. Second, we show that many mathematicians regard nonmetrical graphical inferences as permissible in a real analysis proofs. Third, we illustrate how mathematicians collectively disagree on the permissibility of nonmetrical inferences. (shrink)

Many important regulatory decisions are taken by professionals employing limited and conflicting evidence. We conduct an experiment in a merger regulation setting, identifying the role of different standards of proof, volumes of evidence, cost of error and professional or lay decision making. The experiment was conducted on current practitioners from 11 different jurisdictions, in addition to student subjects. Legal standards of proof significantly affect decisions. There are specific differences because of professional judgment, including in how error costs and (...) volume of evidence are taken into account. We narrow the range of explanations for why professional decision making matters. (shrink)

The ArgumentThis essay describes the emergence and stabilization in French and English experimental accounts, in second half of the seventeenth century, of the narrative sequence: X did (some process in the laboratory) and X saw (something happen), where X stands for a pronoun, I or we in English,je, nousoronin French. Focussing on the French case, it shows how the use of the collective pronounonin the experimental accounts registered in the files of the Académie des Sciences is directly related (...) to the will of this newly created institution to assert a collective authority on the production and legitimization of experimental matters-of-fact produced in the laboratory. It is argued, through the case of the discovery of the blind spot in the eye by Mariotte, that this new narrative form imbeds a construal of the experiment as a public spectacle, and of the proof as a witnessing event, which eludes the Academy's attempts to monopolize the process of fact validation and favors the diffusion and display of experiments in front of larger audiences. The question of whether a privileged witness such as the King of France who patronized the Academy could not have constituted by himself a suitable audience to ensure a full legitimization of experimental matters-of-fact while remaning within the bounds of academic practices is addressed. It is answered in the negative by providing evidence for the lack of interest of the absolute monarch in experiments. On the other hand, the outdoor practices of observation and measurement are shown to interfere in a constructive manner with the absolutist power and to capture the attention of the absolutist monarch, where laboratory experiments had failed. It is proposed that natural philosophers in the early modern period bear the burden of proof in buying credibility for the phenomena they try, by paying a tribute to the standing of the patrician elites that witness their experiments. This makes sense in a straightforward manner of the lack of interest of the King of France in a practice which exalts the power of the very group he is trying hard to control through the absolutist structure of power. (shrink)

In order to claim that one has experimentally tested whether a noncontextual ontological model could underlie certain measurement statistics in quantum theory, it is necessary to have a notion of noncontextuality that applies to unsharp measurements, i.e., those that can only be represented by positive operator-valued measures rather than projection-valued measures. This is because any realistic measurement necessarily has some nonvanishing amount of noise and therefore never achieves the ideal of sharpness. Assuming a generalized notion of noncontextuality that applies to (...) arbitrary experimental procedures, it is shown that the outcome of a measurement depends deterministically on the ontic state of the system being measured if and only if the measurement is sharp. Hence for every unsharp measurement, its outcome necessarily has an indeterministic dependence on the ontic state. We defend this proposal against alternatives. In particular, we demonstrate why considerations parallel to Fine’s theorem do not challenge this conclusion. (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)

One of the most notorious — and dismissive — passages in Wittgenstein’s Philosophical Investigations is Part II section xiv, which begins like this: The confusion and barrenness of psychology is not to be explained by calling it a “young science”; its state is not comparable with that of physics, for instance, in its beginnings. (Rather with that of certain branches of mathematics. Set theory.) For in psychology there are experimental methods and conceptual confusion. (As in the other case conceptual (...) confusion and methods of proof.) The existence of the experimental method makes us think we have the means of solving the problems which trouble us; though problem and method pass one another by. Strong words. But we know that at one stage in his life Wittgenstein’s interest in psychology was sufficient for him to have done some experimental research, and that he was well acquainted with the work of at least some of the prominent psychologists active in his own lifetime. That is, his quoted remarks were not made from ignorance; and we should accordingly take them seriously enough to consider why he made them, what he had in mind, and to what extent — if any — they may have been (and, though this was all a long time ago, may still be) justified. (shrink)