We demonstrate via several examples how the backward error viewpoint can be used in the analysis of solutions obtained by perturbation methods. We show that this viewpoint is quite general and offers several important advantages. Perhaps the most important is that backward error analysis can be used to demonstrate the validity of the solution, however obtained and by whichever method. This includes a nontrivial safeguard against slips, blunders, or bugs in the original computation. We (...) also demonstrate its utility in deciding when to truncate an asymptotic series, improving on the well-known rule of thumb indicating truncation just prior to the smallest term. We also give an example of elimination of spurious secular terms even when genuine secularity is present in the equation. We give short expositions of several well-known perturbation methods together with computer implementations. We also give a generic backward error based method that is equivalent to iteration for regular perturbation. (shrink)

Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe a (...) general model that allows us to assess the quality of numerical solutions in terms of measures of computational errors that are completely interpretable in terms of modeling error. Finally, we emphasize that this type of error analysis involves forms of perturbation analysis that go beyond the basic model-theoretical and statistical/probabilistic tools typically used to characterize the scientific method; this demands that we revise and complement our reconstructive toolbox in a way that can affect our normative image of science. (shrink)

In this paper, criticisms are made of the main tenets of Professor Mellor's argument against ‘backwards’ causation. He requires a closed causal chain of events if there is to be ‘backwards’ causation, but this condition is a metaphysical assumption which he cannot totally substantiate. Other objections to Mellor's argument concern his probabilistic analysis of causation, and the use to which he puts this analysis. In particular, his use of conditional probability inequality to establish the ‘direction’ of causation is (...) shown to be in error. 1I am indebted to Drs H. Krips, L. O'Neill and to the anonymous referee for their suggestions and critical comments on earlier drafts. (shrink)

We argue that two powerful error-theoretic concepts provide a general framework that satisfactorily accounts for key aspects of the explanation of physical patterns. This method gives an objective criterion to determine which mathematical models in a class of neighboring models are just as good as the exact one. The method also emphasizes that abstraction is essential for explanation and provides a precise conceptual framework that determines whether a given abstraction is explanatorily relevant and justified. Hence, it increases our epistemological (...) understanding of how one should go about reconstructing scientific practices by making clear that, at a fundamental level, a key aspect of mathematical modeling consists in exactly solving nearby problems. (shrink)

One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates and implements (...) a strategy to show that the applicability of mathematics is very reasonable indeed. I distinguish three forms of the problem of the applicability of mathematics, and focus on one I call the problem of uncanny accuracy: Given that the construction and manipulation of mathematical representations is pervaded by uncertainty, error, approximation, and idealization, how can their apparently uncanny accuracy be explained? I argue that this question has found no satisfactory answer because our rational reconstruction of scientific practice has not involved tools rich enough to capture the logic of mathematical modelling. Thus, I characterize a general schema of mathematical analysis of real systems, focusing on the selection of modelling assumptions, on the construction of model equations, and on the extraction of information, in order to address contextually determinate questions on some behaviour of interest. A concept of selective accuracy is developed to explain the way in which qualitative and quantitative solutions should be utilized to understand systems. The qualitative methods rely on asymptotic methods and on sensitivity analysis, whereas the quantitative methods are best understood using backward error analysis. The basic underpinning of this perspective is readily understandable across scientific fields, and it thereby provides a view of mathematical tractability readily interpretable in the broader context of mathematical modelling. In addition, this perspective is used to discuss the nature of theories, the role of scaling, and the epistemological and semantic aspects of experimentation. In conclusion, we argue for a method of local and global conceptual analysis that goes beyond the reach of the tools standardly used to capture the logic of science; on their basis, the applicability of mathematics finds itself demystified. (shrink)

Summary The conical sundial from the museum Thyrrheion is found to be designed with cardinal parametersgeographical latitude ϕ = arc tan(3/5) = 30°57′50″half cone angle α = arc tan(4/9) = 23°57′45″radius at equinox r0 = 4 unciae = 98.7mm (pes monetalis)position of the cone tip h = 18 unciae = 444.3 mmThe half cone angle is equal to the angle of the ecliptic which leads to the special case of a conical sundial with the associated sphere being tangent at the (...) day line of the winter solstice. The ratio of sides in the generating triangle 4:9 may thus be interpreted as an approximation for the angle of ecliptic.The place of finding (operation) is 10° North of the intended latitude (design). The error of the sundial's indications due to the displacement are analyzed. (shrink)

The rapid expansion of computational tools and of data science methods in healthcare has, undoubtedly, raised a whole new set of bioethical challenges. As Laacke and colleagues rightly note,...

Human–robot interactions are often affected by error situations that are caused by either the robot or the human. Therefore, robots would profit from the ability to recognize when error situations occur. We investigated the verbal and non-verbal social signals that humans show when error situations occur in human–robot interaction experiments. For that, we analyzed 201 videos of five human–robot interaction user studies with varying tasks from four independent projects. The analysis shows that there are two types (...) of error situations: social norm violations and technical failures. Social norm violations are situations in which the robot does not adhere to the underlying social script of the interaction. Technical failures are caused by technical shortcomings of the robot. The results of the video analysis show that the study participants use many head movements and very few gestures, but they often smile, when in an error situation with the robot. The results suggest that participants do not see the robot as a social interaction partner with comparable communication skills. Our findings have implications for builders and evaluators of human–robot interaction systems. The builders need to consider including modules for recognition and classification of head movements to the robot input channels. The evaluators need to make sure that the presence of an experimenter does not skew the results of their user studies. (shrink)

The anti-utopian technology critique of Ellul, Postman, and other important social analysts has been the primary mode of critical response to technological developments since the 1950s. However, this mode of technology critique has had a disappointingly small effect on the way we, as a society, receive technology. Rather than attribute this failure to the negativity of the anti-utopian perspective, this article suggests that there are other important and largely overlooked factors at work—in particular, the critics' inability to speak about technology (...) in a way that relates to us as social individuals coping with the contingencies and realities of the day-to-day use of technological devices. The purpose of this analysis is not to suggest that we abandon as irrelevant the work and ideas of technology critics such as Ellul and Postman but, on the contrary, to find a way to reframe their important ideas for wider acceptance. (shrink)

The issue of death due to medical errors is not new. We have all heard horror stories about patients dying in the hospital because of a drug mix-up or a surgery patient having the wrong limb amputated. Most people believed these stories were the exception to the rule until November 1999, when the Institute of Medicine issued a report entitled To Err Is Human: Building A Safer Health System. This report focused on medical errors and patient safety in U.S. hospitals. (...) The report indicated that as many as 44,000 to 98,000 people die each year in hospitals as a result of medical errors. These numbers suggest that more Americans are killed in U.S.hospitals every 6 months than died in the entire Vietnam War, and some have compared the alleged rate to fully loaded jumbo jets crashing every other day. This report was not without its critics. (shrink)

The issue of death due to medical errors is not new. We have all heard horror stories about patients dying in the hospital because of a drug mix-up or a surgery patient having the wrong limb amputated. Most people believed these stories were the exception to the rule until November 1999, when the Institute of Medicine issued a report entitled To Err Is Human: Building A Safer Health System. This report focused on medical errors and patient safety in U.S. hospitals. (...) The report indicated that as many as 44,000 to 98,000 people die each year in hospitals as a result of medical errors. These numbers suggest that more Americans are killed in U.S.hospitals every 6 months than died in the entire Vietnam War, and some have compared the alleged rate to fully loaded jumbo jets crashing every other day. This report was not without its critics. (shrink)

Probabilistic reasoning is heavily investigated in decision research. Violations of probability theory have been demonstrated numerously, for instance, the tendency to overestimate the joint probab...

Compared to other health care professions such as medicine, nursing and pharmacy, few studies have been conducted to examine the nature of practice errors in occupational and physical therapy. In an ongoing study to determine root causes, typographies and impact of occupational and physical therapy error on patients, focus group interviews have been conducted across the United States. A substantial number of harmful practice errors and/or other patient safety events (deviations or accidents) have been identified. Often these events have (...) had moral dimensions that troubled the therapist involved. In this article, six of these transcribed cases are analyzed, using predominant bioethical theories, ethical principles and professional codes of ethics. The cases and their analyses are intended to be exemplary, improving the readers’ ability to discern and critically address similar such events. Several patient safety strategies are suggested that might have prevented the events described in these cases. (shrink)

Dealing with errors in psychotherapy is challenging, both ethically and practically. There is almost no empirical research on this topic. We aimed (1) to explore psychotherapists’ self-reported ways of dealing with an error made by themselves or by colleagues, and (2) to reconstruct their reasoning according to the two principle-based ethical approaches that are dominant in the ethics discourse of psychotherapy, Beauchamp & Childress (B&C) and Lindsay et al. (L).

Generalized structured component analysis (GSCA) is a component-based approach to structural equation modeling (SEM), where latent variables are approximated by weighted composites of indicators. It has no formal mechanism to incorporate errors in indicators, which in turn renders components prone to the errors as well. We propose to extend GSCA to account for errors in indicators explicitly. This extension, called GSCA_M, considers both common and unique parts of indicators, as postulated in common factor analysis, and estimates a weighted (...) composite of indicators with their unique parts removed. Adding such unique parts or uniqueness terms serves to account for measurement errors in indicators in a manner similar to common factor analysis. Simulation studies are conducted to compare parameter recovery of GSCA_M and existing methods. These methods are also applied to fit a substantively well-established model to real data. (shrink)

Libertarians are mistaken to seek foundations, to take sides over moral approaches, and to have no proper theory of liberty.

Thelen et al. criticize “spatial coding” approaches to the A-not-B error. However, newer thinking about spatial coding provides more precise analytic categories and recognizes that different spatial coding systems normally coexist. Theorizing about spatial coding is largely compatible with dynamic-systems theory, augmenting it with an analysis of what one means when discussing “location at A” (or B).

Lewisian reference magnetism about linguistic content determination [Lewis 1983 has been defended in recent work by Weatherson [2003] and Sider [2009], among others. Two advantages claimed for the view are its capacity to make sense of systematic error in speakers' use of their words, and its capacity to distinguish between verbal and substantive disagreements. Our understanding of both error and disagreement is linked to the role of usage and first order intuitions in semantics and in linguistic theory more (...) generally. I argue, partially on the basis of these more general considerations, that reference magnetism delivers implausible results. Specifically, I argue that the proponent of reference magnetism maintains her analysis of genuinely systematic error at the cost of an empirically unjustifiable error theory regarding ordinary usage. In response, I describe an alternative view of content determination—MUMPS, or Meaning is Use Minus Pragmatics—which is not committed to such error theories. Despite this advantage, MUMPS has high prima facie costs. On such a view, there is a great deal of variation in linguistic meaning across speakers and times. As a result, a large number of seemingly mistaken claims are analysed as expressing true propositions. Correspondingly, a large number of seemingly substantive disagreements are analysed as terminological. However, I argue that these consequences are not as costly as they seem. Despite appearances, MUMPS is consistent with objective, metaphysically realist adjudication of disagreements, even in cases where meanings are not shared and where both parties to a dispute speak truly. MUMPS thus allows for a more nuanced understanding of linguistic usage, change, and variation, without imposing a commitment to any form of metaphysical anti-realism. (shrink)

The standard backward-induction reasoning in a game like the centipede assumes that the players maintain a common belief in rationality throughout the game. But that is a dubious assumption. Suppose the first player X didn't terminate the game in the first round; what would the second player Y think then? Since the backwards-induction argument says X should terminate the game, and it is supposed to be a sound argument, Y might be entitled to doubt X's rationality. Alternatively, Y might (...) doubt that X believes Y is rational, or that X believes Y believes X is rational, or Y might have some higher-order doubt. X’s deviant first move might cause a breakdown in common belief in rationality, therefore. Once that goes, the entire argument fails. The argument also assumes that the players act rationally at each stage of the game, even if this stage could not be reached by rational play. But it is also dubious to assume that past irrationality never exerts a corrupting influence on present play. However, the backwards-induction argument can be reconstructed for the centipede game on a more secure basis.1 It may be implausible to assume a common belief in rationality throughout the game, however the game might go, but the argument requires less than this. The standard idealisations in game theory certainly allow us to assume a common belief in rationality at the beginning of the game. They also allow us to assume this common belief persists so long as no one makes an irrational move. That is enough for the argument to go through. (shrink)

We present Backward Clock, an original counterexample to Robert Nozick’s truth-tracking analysis of propositional knowledge, which works differently from other putative counterexamples and avoids objections to which they are vulnerable. We then argue that four ways of analysing knowledge in terms of safety, including Duncan Pritchard’s, cannot withstand Backward Clock either.

This text provides a critique of the subjective Bayesian view of statistical inference, and proposes the author's own error-statistical approach as an alternative framework for the epistemology of experiment. It seeks to address the needs of researchers who work with statistical analysis.

We propose an analysis of backward causation in terms of interventionism that can avoid several problems typically associated with backward causation. Its main advantage over other accounts is that it allows for reducing the problematic task of supporting backward causal claims to the unproblematic task of finding evidence for several ordinary forward directed causal hypotheses.

This article scrutinizes in detail much of the extant historiography on the controversy between biometricians and Mendelians, considering in particular how this controversy is related to the evolutionary synthesis. While the historiographic critique concentrates on William Provine’s standard account, it also extends to the proposal by Donald MacKenzie and Barry Barnes. What Provine and these sociologists of scientific knowledge have in common is a set of unquestioned assumptions about the nature of Darwinism, about William Bateson’s anti-Darwinism, and about the very (...) idea of an evolutionary “synthesis.” While these assumptions make for a compelling history of the synthesis, they engender an endemically asymmetrical perspective and bias historiography toward the mere confirmation of antecedent expectations, which renders the years from 1859 to 1929 an age of ignorance and misunderstanding. In contrast, a return to what was probably the original meaning of evolutionary “synthesis” allows for a symmetrical account. It yields an appreciation of the positive contributions made both by Mendelians and biometricians to the gradual development of Darwinism. The article concludes with a synopsis of this alternative account. (shrink)

According to David Albert, there are certain situations where we can cause events that lie in our past. In response to a well-known objection that we never observe backward causation, he argues that there are good reasons why we can’t tell when it obtains. However, I identify another difficulty with Albert’s view: at face value, it has the unattractive consequence that backward causation is not just possible, but rife. In this article, I show how this implication can be (...) blocked. I then use my analysis to defend Albert’s account from a second well-known objection, namely, that it allows us to control the past. (shrink)