Simulation modeling, the core thesis of Calculated Surprises, is transforming the established conception of mathematical modeling in fundamental ways. These transformations feed back into philosophy of science, opening up new perspectives on longstanding oppositions. The book integrates historical features with both practical case studies and broad reflections on science and technology.

A high profile context in which physics and biology meet today is in the new field of systems biology. Systems biology is a fascinating subject for sociological investigation because the demands of interdisciplinary collaboration have brought epistemological issues and debates front and centre in discussions amongst systems biologists in conference settings, in publications, and in laboratory coffee rooms. One could argue that systems biologists are conducting their own philosophy of science. This paper explores the epistemic aspirations of the field by (...) drawing on interviews with scientists working in systems biology, attendance at systems biology conferences and workshops, and visits to systems biology laboratories. It examines the discourses of systems biologists, looking at how they position their work in relation to previous types of biological inquiry, particularly molecular biology. For example, they raise the issue of reductionism to distinguish systems biology from molecular biology. This comparison with molecular biology leads to discussions about the goals and aspirations of systems biology, including epistemic commitments to quantification, rigor and predictability. Some systems biologists aspire to make biology more similar to physics and engineering by making living systems calculable, modelable and ultimately predictable—a research programme that is perhaps taken to its most extreme form in systems biology’s sister discipline: synthetic biology. Other systems biologists, however, do not think that the standards of the physical sciences are the standards by which we should measure the achievements of systems biology, and doubt whether such standards will ever be applicable to ‘dirty, unruly living systems’. This paper explores these epistemic tensions and reflects on their sociological dimensions and their consequences for future work in the life sciences. (shrink)

Looking at Hobbes ' theory of thinking as calculation and truth by convention shows that a certain type of scientism of the mind leads to fundamental problems. If truth is the artefact of social conventions about signs, and if thinking is nothing but the syntactical transformations of sign, a theory of thinking must have both: a strong concept of natural computation and a social theory of establishing sign-conventions. Hobbes does not, like modern physicalist theories of the mind, have both.

Un calcul logique, au sens large, est une méthode de résolution appliquée au traitement d'une structure propositionnelle. Les propositions constituant cette structure peuvent aussi bien être des expressions d'une langue naturelle (comme le français) que des expressions d'un langage formalisé (comme l'arithmétique), liées entre elles par une dépendance de nature fonctionnelle. Cet ouvrage constitue une introduction à deux outils de calcul en logique du premier ordre, soit le calcul en arbres de consistance et le calcul en déduction naturelle. La première (...) partie, centrée sur la notion de structure propositionnelle, expose les concepts, les objets et les méthodes propres à la logique propositionnelle. Dans la deuxième partie, la logique propositionnelle est étendue à la logique prédicative au moyen de la quantification et de concepts caractéristiques d'un langage du premier ordre. Les deux outils de calcul sont ensuite enrichis de manière à pouvoir traiter des fonctions propositionnelles, soit des prédicats du premier ordre.De nombreux exemples et exercices, accompagnés de leurs solutions, aideront l'étudiant à progresser vers des calculs toujours plus complexes et à raffiner ses méthodes de calcul logique. (shrink)

Wilfried Sieg. Calculations by Man and Machine: Mathematical Presentation.

These essays develop a Marxist response to and approach to aspects of the recent economic past in the United Kingdom. They reflect issues and controversies that have arisen within economic policy debate and the economic theory associated with the debate, highlighting the problematic nature of economic policy in the period since the mid-1970s. The book, first published in 1986, develops a line of argument organized around issues of ‘calculation’, thus challenging the orthodox Marxist framework and presenting a neo-Marxist analysis.

The paper is a partly provocative essay edited as a humanitarian study in philosophy of science and social philosophy, reflecting on the practical, “anti-metaphysical” turn taken place since the 20th century and continuing until now. The article advocates that it is about time it to be overcome because it is the main obstacle for the further development of exact and natural sciences including mathematics therefore restoring the unity of philosophy and sciences in the dawn of modern science when the great (...) scientists were philosophers as a necessary condition for their revolutionary achievements, and the physicists were simultaneously mathematicians not less than philosophers and even theologians as Descartes, Newton, Leibnitz were just as their predecessors, Copernicus or Galileo Galilei. The revolution in science accomplished by them needed philosophy since any scientific revolution, then necessarily growing into social, needs philosophy; and if ones wish to prevent social revolutions originating from fundamental scientific discoveries, in turn relying on the close link of sciences and philosophy, they are to cut the link at issue, and just that happened in the 20th centuries therefore implicitly heralding a “brave new world” of eternal normal science without revolutions whether scientific or social. Fukuyama’s “end of history” requires an “end of scientific history” as it is an obligatory premise, and separating sciences from philosophy is sufficient for that, though proclaimed quite otherwise: as overcoming metaphysics preventing sciences and substituting them by quasi-sciences. Particularly, that “anti-metaphysical turn” has established for science to obey society absolutely and thoroughly, obviously a condition contradicting the scientific and social revolutions in Modernity featured by the domination of science over society by the mediation of philosophy able to translate all epochal scientific discoveries as social corollaries. A special attention is paid to quantum mechanics, being the frontier of physics in the 20th century, where that anti-metaphysical turn is discernibly concentrated and may be notated by the famous slogan “Shut up and calculate!” regardless of its authorship. Just the revolutionary discoveries in physics, for example those of “dark mass” and “dark energy” or entanglement force now its rejection therefore restoring the unity of philosophy, mathematics and physics, made ever possible the establishment of modern science by its emancipation from religion, and thus and ind final analysis, from society. (shrink)

We represent continuous functions on compact intervals by sequences of functions defined on finite sets of rational numbers. We call this an exact representation. This enables us to calculate the values of the function arbitrarily exactly, without roundoff errors. As an application we develop a procedure to transfer an exact representation of an increasing function into an exact representation of the corresponding inverse function.

As bibliographical classification of published journal items affects the denominator in this equation, we investigated how the numerator and denominator of the impact factor equation were generated for representative journals in two categories of the Journal Citation Reports. We performed a full text search of the 1st-ranked journal in 2004 JCR category “Medicine, General and Internal” and 61st-ranked journal, 1st-ranked journal in category “Multidisciplinary Sciences” and journal with a relative rank of CMJ. Large journals published more items categorized by Web (...) of Science as non-research items : 63% out of total 5,193 items in Nature and 81% out of 3,540 items in NEJM, compared with 31% out of 283 items in CMJ and only 2 out of 126 items in AABC. Some items classified by WoS as non-original contained original research data. These items received a significant number of citations: 6.9% of total citations in Nature, 14.7% in NEJM and 18.5% in CMJ. IF decreased for all journals when only items presenting original research and citations to them were used for IF calculation. Regardless of the journal’s size or discipline, publication of non-original research and its classification by the bibliographical database have an effect on both numerator and denominator of the IF equation. (shrink)

The proof of the Second Incompleteness Theorem consists essentially of proving the uniqueness and explicit definability of the sentence asserting its own unprovability. This turns out to be a rather general phenomenon: Every instance of self-reference describable in the modal logic of the standard proof predicate obeys a similar uniqueness and explicit definability law. The efficient determination of the explicit definitions of formulae satisfying a given instance of self-reference reduces to a simple algebraic problem-that of solving the corresponding fixed-point equation (...) in the modal logic. We survey techniques for the efficient calculation of such fixed-points. (shrink)

This paper contributes to the calculization of evocation and erotetic implication as defined by Inferential Erotetic Logic (IEL). There is a straightforward approach to calculizing (propositional) erotetic implication which cannot be applied to evocation. First-order evocation is proven to be uncalculizable, i.e. there is no proof system, say FOE, such that for all X, Q: X evokes Q iff there is an FOE-proof for the evocation of Q by X. These results suggest a critique of the represented approaches to calculizing (...) IEL. This critique is expanded into a programmatic reconsideration of the IEL-definitions of evocation and erotetic implication. From a different point of view these definitions should be seen as desiderata that may or may not play the role of a point of orientation when setting up "rules of asking". (shrink)

In his commentary on Lombardʼs Sentences, question 1, Robert Halifax OFM presents a remarkably original and inventive optical argument. It compares two pairs of luminous and opaque bodies with two shadow cones until the luminous bodies reach the zenith. In placing two moving human beings into the shadow cones whose moral evolution parallels the size of the shadows, Halifax creates an unprecedented shadow theater equipped with mathematics and theorems of motion from Thomas Bradwardineʼs Treatise on Proportions. This paper is a (...) first attempt at analyzing this imaginary experiment and the mathematics of the infinite it implies. It also shows that optics had new aims through its connexion with the theorems of motion of the Oxford Calculators. (shrink)

The ArgumentHistorians of science naturally tend to express interest in other forms of intellectual activity only when these intersect with science. This tendncy has produced a number of enlightening studies of what happens when science and (for instance) law or theology come into contact, but little by way of how science enters into the calculations and social status of such forms of knowledge after the conjuction has passed. Recent work in the sociology of professions, in contrast, has focused attention precisely (...) on those moments when the expert knowledge produced by different group doesnotoverlap. This has been the contribution of Andrew Abbortt's theory of “jurisdictional boundaries” between competing professions. The case of Victorian actuaries who worked hard to maintain unique intellectual claims in the competitive life insurance industry while maintainiing strong social connections and overlaps in knowledge with organized science, challenges the way both historians of science and sociologists of professions view contending knowledge claims. By observing what motivated actuaries to forge an alliance with men of science in the 1820s, then tracing their gradual recognition of a need to distance themselves from certain of the “scientific” values that had earlier informed their collective identity, it is possible to make sense of connections as well as disconnections between science and other forms of knowledge. A history of quantification from the actuaries' perspective, in other words, allows us to view science bothasandincontext. (shrink)

The importance of the Treatise on equations by Sharaf al-Dīn al-Ṭūsī has been brought to our attention by R. Rashed, who underlined the analytical aspects of this essentially algebraic work. Following Rashed, this article concentrates on one of these analytical concepts, namely the maximum of a polynomial expression f of degree 3. The purpose is to clarify the techniques that led al-Ṭūsī, when computing the maximum of f, to systematically display algebraic equations equivalent to f = 0. By demonstrating that (...) al-Ṭūsī's essentially algebraic proofs were also based on analytical procedures, we show that the presence of these equations was not fortuitous, but resulted from a correct understanding of the maximum of f. The accompanying geometrical representations were primarily for illustration. L'importance du Traité des équations de Sharaf al-Dīn al-Ṭūsī, a été mise en évidence par les travaux de R. Rashed, qui ont souligné les aspects analytiques de cette œuvre essentiellement algébrique. Parmi les notions analytiques qui figurent dans le Traité d'al-Ṭūsī, nous évoquerons uniquement celle du maximum d'une expression polynomiale du 3 e degré, f. La présente étude pourrait apporter une contribution à une problématique posée par R. Rashed: élucider les moyens et les techniques qui, lors du calcul du maximum, auraient conduit al-Ṭūsī à mettre systématiquement en valeur des équations équivalentes à fʹ = 0. Notre étude confirme que la présence de telles expressions n'est pas fortuite; elle découle d'une conception correcte du maximum de f. À cet effet, nous montrons que si les démonstrations utilisées par al-Ṭūsī sont essentiellement algébriques, elles s'appuient sur des procédés analytiques; les représentations géométriques qui les accompagnent constituent surtout des moyens de visualisation. (shrink)

This note is about the “calculational style” of presenting proofs introduced by Dijkstra and Scholten and adopted in some books on theoretical computer science. We define the concept of a calculation, which is a formal counterpart of the idea of a calculational proof. The definition is in terms of a new formalization DS of predicate logic. Any proof tree in the system DS can be represented as a sequence of calculations. This fact shows that any logically valid predicate formula (...) has a calculational proof. (shrink)

In this article, two separate aspects of Mises’ famous economic calculation argument are identified. The first concerns the fact that the profit-and-loss calculations that drive economic decisions regarding factors of production under capitalism cannot, by definition, take place under socialism since there cannot be any prices on which to base such calculations. The second concerns that idea that, owing to the nature of value, there is no alternative means of allocation, such as a calculus in terms of value. Although (...) both of these points are well-known and frequently invoked to pass a decisive judgment against socialism, they are in fact separate arguments which have thus far been inadequately distinguished in the Austrian literature. The objective of this paper is to highlight this distinction. I further illustrate the point by emphasizing the role of monetary calculation, which nonetheless plays a real role in capitalist economies. (shrink)

This paper presents a novel understanding of the notion of calculability. In Gricean frameworks, calculability is defined in terms of how speakers can infer an implicature. The relevant inferences must e.g. be based on maxims of conversation or cooperation principles. Meanwhile, I suggest to define calculability in terms of when, or under which conditions, speakers can infer an implicature. An implicature is calculable if hearers can infer its existence even supposing that the implicature is not semantically encoded. This approach avoids (...) familiar challenges, including recently prominent challenges from pragmatic particularism. (shrink)

We derive the first analytical formula for the density of "Dark Matter" (DM) at all length scales, thus also for the rotation curves of stars in galaxies, for the baryonic Tully–Fisher relation and for planetary systems, from Einstein's equations (EE) and classical approximations, in agreement with observations. DM is defined in Part I as the energy of the coherent gravitational field of the universe, represented by the additional equivalent ordinary matter (OM), needed at all length scales, to explain classically, with (...) inclusion of the OM, the _observed coherent_ gravitational field. Our derivation uses both EE and the Newtonian approximation of EE in Part I, to describe semi-classically in Part II the advection of DM, created at the level of the universe, into galaxies and clusters thereof. This advection happens proportional with their own classically generated gravitational field g, due to self-interaction of the gravitational field. It is based on the universal formula ρ D = λgg′ 2 for the density ρ D of DM advected into medium and lower scale structures of the observable universe, where λ is a universal constant fixed by the Tully–Fisher relations. Here g′ is the gravitational field of the universe; g′ is in main part its own source, as implied in Part I from EE. We start from a simple electromagnetic analogy that helps to make the paper generally accessible. This paper allows for the first time the exact calculation of DM in galactic halos and at all levels in the universe, based on EE and Newtonian approximations, in agreement with observations. (shrink)

The theory of rational choice is one of the most recent paradigms for the study of religion that strongly argues against previously dominant approaches such as the secularization thesis. The theory relies on more or less acceptable assumptions drawn from economic models of rational behavior, and offers interesting explanations or predictions supported by an impressive amount of data. The innovative approach introduced by the advocates or rational choice is a shift in focus from the demand side to the supply side (...) of religion, emphasizing religious entre- preneurs and competing churches that act rationally in a religious market. In spite of the criticism directed to their assumption, the ambiguousness of the utility concept, the male centered perspective, or the total disregard of the influence of emotions when making decisions, the theory of rational choice remains one of the most seri- ous challenges to alternative theories of religious behaviour. (shrink)

For the anti-realist, the truth about a subject's past thoughts and attitudes is determined by what he is subsequently disposed to judge about them. The argument for an anti-realist interpretation of Wittgenstein's view of past-tense statements seems plausible in three cases: dreams, calculating in the head, and thinking. Wittgenstein is indeed an anti-realist about dreaming. His account of calculating in the head suggests anti-realism about the past, but turns out to be essentially realistic. He does not endorse general anti-realism about (...) past thoughts; but his treatment does in some cases involve elements of anti-realism, unacceptable in some instances but possibly correct in others. (shrink)

Principles of communication allow the listener to infer (upon hearing (1) that unless the speaker believed that (1alt) were false, the speaker would have uttered (1alt).

Parmi d’autres, cet ouvrage témoigne que nous sommes dans une époque de collaboration active entre la communauté médicale, notamment hospitalière, et la communauté philosophique. Son auteur, J.-P. Cléro, s’appuie en effet sur un travail mené dans le cadre de divers espaces éthiques ou écoles de soin médical et sur des échanges nourris avec plusieurs médecins. Comme il l’indique lui-même, ce contexte l’a incité à revenir à la philosophie morale et à proposer en son sein un parcours orienté par..

Parmi d’autres, cet ouvrage témoigne que nous sommes dans une époque de collaboration active entre la communauté médicale, notamment hospitalière, et la communauté philosophique. Son auteur, J.-P. Cléro, s’appuie en effet sur un travail mené dans le cadre de divers espaces éthiques ou écoles de soin médical et sur des échanges nourris avec plusieurs médecins. Comme il l’indique lui-même, ce contexte l’a incité à revenir à la philosophie morale et à proposer en son sein un parcours orienté par..

It is well known that Bayes’ theorem (with likelihood ratios) can be used to calculate the impact of evidence, such as a ‘match’ of some feature of a person. Typically the feature of interest is the DNA profile, but the method applies in principle to any feature of a person or object, including not just DNA, fingerprints, or footprints, but also more basic features such as skin colour, height, hair colour or even name. Notwithstanding concerns about the extensiveness of databases (...) of such features, a serious challenge to the use of Bayes in such legal contexts is that its standard formulaic representations are not readily understandable to non-statisticians. Attempts to get round this problem usually involve representations based around some variation of an event tree. While this approach works well in explaining the most trivial instance of Bayes’ theorem (involving a single hypothesis and a single piece of evidence) it does not scale up to realistic situations. In particular, even with a single piece of match evidence, if we wish to incorporate the possibility that there are potential errors (both false positives and false negatives) introduced at any stage in the investigative process, matters become very complex. As a result we have observed expert witnesses (in different areas of speciality) routinely ignore the possibility of errors when presenting their evidence. To counter this, we produce what we believe is the first full probabilistic solution of the simple case of generic match evidence incorporating both classes of testing errors. Unfortunately, the resultant event tree solution is too complex for intuitive comprehension. And, crucially, the event tree also fails to represent the causal information that underpins the argument. In contrast, we also present a simple-to-construct graphical Bayesian Network (BN) solution that automatically performs the calculations and may also be intuitively simpler to understand. Although there have been multiple previous applications of BNs for analysing forensic evidence—including very detailed models for the DNA matching problem, these models have not widely penetrated the expert witness community. Nor have they addressed the basic generic match problem incorporating the two types of testing error. Hence we believe our basic BN solution provides an important mechanism for convincing experts—and eventually the legal community—that it is possible to rigorously analyse and communicate the full impact of match evidence on a case, in the presence of possible errors. (shrink)

Ludwig von Mises argued that (1) economic calculation under socialism is impossible, and that (2) the lack of calculation would entail chaos and starvation. In these pages, Bryan Caplan has accepted the first claim but rejected the second, and has argued further that in real‐world attempts to implement socialism, it was the lack of incentives, not the absence of economic calculation, that was responsible for economic chaos. I suggest, against Caplan's interpretation, that by “chaos” Mises meant the (...) lack of calculation, rather than some further state of affairs entailed by this lack. So interpreted, Mises's argument escapes the brunt of Caplan's criticisms. (shrink)

This paper explores how calculative cultures shape perceptions of models and practices of model use in the financial industry. A calculative culture comprises a specific set of practices and norms concerning data and model use in an organizational setting. Drawing on interviews with model users working in algorithmic securities trading, I argue that the introduction of complex machine-learning models changes the dynamics in calculative cultures, which leads to a displacement of human judgment in quantitative finance. In this paper, I distinguish (...) between three calculative cultures: an idealistic culture of undivided trust in models, a pragmatic culture of skepticism toward model accuracy, and a pragmatic idealist culture of early stage skepticism and implementation and production-phase idealism. Based on the empirical material, the analysis engages with examples of each of the three calculative cultures. The study contributes to the social studies of finance and science and technology studies more broadly by showing how perceptions of models shape and are shaped through model work in data-intensive, computerized finance. (shrink)

When physical structures resonate in proximity to each other they will under certain circumstances 'sync up' in a shared resonance frequency. This is the phenomenon of spontaneous selforganization. General resonance theory (GRT), a theory of consciousness developed by Hunt and Schooler, suggests that consciousness is a product of various shared resonance frequencies at different physical scales. I suggest a heuristic for calculating the boundaries and resulting capacity for phenomenal consciousness in such resonating structures. Shared resonance results in phase transitions in (...) the speed and bandwidth of information exchange and thus richer and more complex consciousness. This approach is a solution to the 'combination problem' and 'boundary problem' of consciousness. The proposed mathematical heuristic is a practical approach for identifying potential conscious structures and the spatial and temporal boundaries of such structures over time, and also for calculating the capacity for phenomenal consciousness of any putative conscious entity. The slowest-frequency shared resonance -- the 'slowest common denominator'-- is the limiting factor for the spatial extent of any macro-consciousness. Various synchrony indexes are discussed. I describe some limitations of the proposed framework, and how it compares to Tononi's integrated information theory. IIT's constellation- qualia characterization framework is compatible with GRT and may be a useful tool in conjunction with GRT's quantification framework. (shrink)

Peter Spirtes. Calculating TETRAD Constraints Implied by Directed Acyclic Graphs.