Many of our sources of knowledge only afford us knowledge that is inexact. When trying to see how tall something is, or to hear how far away something is, or to remember how long something lasted, we may come to know some facts about the approximate size, distance or duration of the thing in question but we don’t come to know exactly what its size, distance or duration is. In some such situations we also have some pointed knowledge of (...) how inexact our knowledge is. That is, we can knowledgeably pinpoint some exact claims that we do not know. We show that standard models of inexact knowledge leave little or no room for such pointed knowledge. We devise alternative models that are not afflicted by this shortcoming. (shrink)

An inexact generalization like ‘ravens are black’ will be symbolized as a prepositional function with free variables thus: ‘Rx ⇒ Bx.’ The antecedent ‘Rx’ and consequent ‘Bx’ will themselves be called absolute formulas, while the result of writing the non-boolean connective ‘⇒’ between them is conditional. Absolute formulas are arbitrary first-order formulas and include the exact generalization ‘(x)(Rx → Bx)’ and sentences with individual constants like ‘Rc & Bc.’ On the other hand the non-boolean conditional ‘⇒’ can only occur (...) as the main connective in a formula. We shall also need to consider formulas with more than one free variable such as ‘xHy ⇒ xTy,’ which might express ‘if x is the husband of y then x is taller than y.’ Though it is inessential, it will simplify things to work in ‘n-languages’ with a finite number of individual constants c1,…, cn, which are interpreted as denoting the elements of the domains of the ‘n-models’ to be described below. (shrink)

In a series of recent papers, Timothy Williamson has argued for the surprising conclusion that there are cases in which you know a proposition in spite of its being overwhelmingly improbable given what you know that you know it. His argument relies on certain formal models of our imprecise knowledge of the values of perceptible and measurable magnitudes. This paper suggests an alternative class of models that do not predict this sort of improbable knowing. I show that such (...) models are motivated by independently plausible principles in the epistemology of perception, the epistemology of estimation, and concerning the connection between knowledge and justified belief. (shrink)

Exact sciences are described as sciences whose theories are formalized. These are contrasted to inexact sciences, whose theories are not formalized. Formalization is described as a broader category than mathematization, involving any form/content distinction allowing forms, e.g., as represented in theoretical models, to be studied independently of the empirical content of a subject-matter domain. Exactness is a practice depending on the use of theories to control subject-matter domains and to align theoretical with empirical models and not merely (...) a state of a science. Inexact biological sciences tolerate a degree of “mismatch” between theoretical and empirical models and concepts. Three illustrations from biological sciences are discussed in which formalization is achieved by various means: Mendelism, Weismannism, and Darwinism. Frege’s idea of a “conceptual notation” is used to further characterize the notion of a form/content distinction. (shrink)

Contents: PART 1. MODELS IN SCIENTIFIC PROCESSES. Joseph AGASSI: Why there is no theory of models. Ma??l??gorzata CZARNOCKA: Models and symbolic nature of knowledge. Adam GROBLER: The representational and the non-representational in models of scientific theories. Stephan HARTMANN: Models as a tool for the theory construction; some strategies of preliminary physics. William HERFEL: Nonlinear dynamical models as concrete construction. Elzbieta KA??L??USZY??N??SKA: Styles of thinking. Stathis PSILLOS: The cognitive interplay between theories and models: the (...) case of 19th century optics. PART 2. TOOLS OF SCIENCE. Nancy D. CARTWRIGHT, Towfic SHOMAR, Maricio SUAREZ: The tool-box of science. Javier ECHEVERRIA: The four contexts of scientific activity. Katline HAVAS: Continuity and change; kinds of negation in scientific progress. Matthias KAISER: The independence of scientific phenomena. W??l??adys??l??aw KRAJEWSKI: Scientific meta-philosophy. Ilkka NIINILUOTO: The emergence if scientific specialities: six models. Leszek NOWAK: Antirealism, realism and idealization. Rinat M. NUGAYEV: Classic, modern and postmodern scientific unification. Veikko RANTALA: Translation and scientific change. Gerhard SCHURZ: Theories and their applications - a case of nonmonotonic reasoning. Witold STRAWI??N??SKI: The unity of science today. Vardan TOROSIAN: Are the ethic and logic of science compatible. PART 3. UNSHARP APPROACHES IN SCIENCE. Ernest W. ADAMS: Problems and prospects in a theory of inexact first-order theories. Wolfgang BALZER and Gerhard ZOUBEK: On the comparison of approximative empirical claims. Gianpierro CATTANEO, Maria Luisa DALLA CHIARA, Roberto GIUNTINI: The unsharp approaches to quantum theory. Theo A.F. KUIPERS: Falsification versus efficient truth approximation. Bernhard LAUTH: Limiting decidability and probability. Jaros??l??aw PYKACZ: Many-valued logics in foundations of quantum mechanics. Roman R. ZAPATRIN: Logico-algebraic approach to spacetime quantization. (shrink)

Scientific Models. On the most primitive level of scientific popularization, common sense analogies are omnipresent, and are indispensable to layman and popularizer alike. Reichenbach's discussion of Heisenberg's uncertainty principle--in terms of a police car's inevitable effect on the speed of traffic--is a nice example. "In our intercourse with electrons we cannot don civilian clothes; when we watch them we always disturb their traffic." In this or any other such use of metaphor, however, the purpose is merely illustrative, and in (...) an extremely naive or vague sense at that. The structural form A:B::C:D is clearly present, but the repeated ratios are of such a superficial, inexact and limited nature that no further inferences can be drawn from the one side of the proportion to the other. Only a familiarizing picture, helpful to the layman but fairly useless to the scientist, has been introduced. Still, it is also important to realize that the difference between the metaphorical popularization of science and the creative use of metaphor by scientists themselves is a difference in degree only, not of kind. (shrink)

I modify and generalize Carnap’s notion of frameworks as a way of unpacking Goodman’s metaphor of “making worlds with symbols”. My frameworks provide, metaphorically, a way of making worlds out of symbols in as much as all our framework-bound access to the world is through frameworks that always stand to be improved in accuracy, precision, and usually both. Such improvement is characterized in pragmatist terms.

In this paper we compare different models of vagueness viewed as a specific form of subjective uncertainty in situations of imperfect discrimination. Our focus is on the logic of the operator “clearly” and on the problem of higher-order vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare several accounts of vagueness as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s two-dimensional semantics, and the system we call (...) Centered semantics. We then propose a semantics of degrees of clarity, inspired from the signal detection theory model, and outline a view of higher-order vagueness in which the notions of subjective clarity and unclarity are handled asymmetrically at higher orders, namely such that the clarity of clarity is compatible with the unclarity of unclarity. (shrink)

The logic of inexactness, presented in this paper, is a version of the Łukasiewicz logic with predicates valued in [0, ∞). We axiomatize multi-valued models of equality and ordering in this logic guaranteeing their imbeddibility in the real line. Our axioms of equality and ordering, when interpreted as axioms of proximity and dominance, can be applied to the foundations of measurement (especially in the social sciences). In two-valued logic they provide theories of ratio scale measurement. In multivalued logic they (...) enable us to treat formally errors arising in nominal and ordinal measurements. (shrink)

Fuzzy logic is finding increased application in the control of real-world processes and in the work with and the manipulation of inexact knowledge. Two of the major attractions of fuzzy logic are: it permits one to express problems in (familiar) linguistic terms and it can be applied where the numerical mathematical model of a system may be too complex or impossible to build using conventional techniques. This book, written in an easily accessible style, assumes that students have a solid (...) background in embedded systems including basic logic design and C/C programming. (shrink)

Probability theory is the arithmetic of the real line constrained by special aleatory axioms. Fuzzy logic is also a kind of probability theory, but of considerably more mathematical and axiomatic complexity than the standard account. Fuzzy logic purp orts to model the human capacity for reasoning with inexact concepts. It does this by exploring the assumption that when we argue in inexact terms and draw inferences in imprecise vocabularies, we actually make computations about the embedded imprecision s. I (...) argue that this is in fact the last thing that we do, and indeed that we do the opposite. (shrink)

The dispute over the viability of various theories of relativistic, dissipative fluids is analyzed. The focus of the dispute is identified as the question of determining what it means for a theory to be applicable to a given type of physical system under given conditions. The idea of a physical theory's regime of propriety is introduced, in an attempt to clarify the issue, along with the construction of a formal model trying to make the idea precise. This construction involves a (...) novel generalization of the idea of a field on spacetime, as well as a novel method of approximating the solutions to partial-differential equations on relativistic spacetimes in a way that tries to account for the peculiar needs of the interface between the exact structures of mathematical physics and the inexact data of experimental physics in a relativistically invariant way. It is argued, on the basis of these constructions, that the idea of a regime of propriety plays a central role in attempts to understand the semantical relations between theoretical and experimental knowledge of the physical world in general, and in particular in attempts to explain what it may mean to claim that a physical theory models or represents a kind of physical system. This discussion necessitates an examination of the initial-value formulation of the partial-differential equations of mathematical physics, which suggests a natural set of conditions---by no means meant to be canonical or exhaustive---one may require a mathematical structure, in conjunction with a set of physical postulates, satisfy in order to count as a physical theory. Based on the novel approximating methods developed for solving partial-differential equations on a relativistic spacetime by finite-difference methods, a technical result concerning a peculiar form of theoretical under-determination is proved, along with a technical result purporting to demonstrate a necessary condition for the self-consistency of a physical theory. (shrink)

Minimalism concerning truth is the view that that all there is to be said concerning truth is exhausted by a set of basic platitudes. In the first part of this thesis, I apply this methodology to the concept of knowledge. In so doing, I develop a model of inexact knowledge grounded in what I call minimal margin for error principles. From these basic principles, I derive the controversial result that epistemological internalism and internalism with respect to self-knowledge are untenable (...) doctrines. In the second part of this thesis, I develop a minimal theory of vagueness in which a rigorous but neutral definition of vagueness is shown to be possible. Three dimensions of vagueness are distinguished and a proof is given showing how two of these dimensions are equivalent facets of the same phenomenon. From the axioms of this minimal theory one can also show that there must be higher-order vagueness, contrary to what some have argued. In the final part of this thesis, I return to issues concerning the credentials of truth-minimalism. Is truth-minimalism compatible with the possibility of truth-value gaps? Is it right to say that truth-minimalism is crippled by the liar paradox? With respect to the former question, I develop a novel three-valued logical system which is both proof-theoretically and truth-theoretic ally well-motivated and compatible with at least one form of minimalism. With respect to the second question, a new solution to the liar paradox is developed based on the claim that while the liar sentence is meaningful, it is improper to even suppose that this sentence has a truth-status. On that basis, one can block the paradox by restricting the Rule of Assumptions in Gentzen-style presentations of the sentential sequent calculus. The first lesson of the liar paradox is that not all assumptions are for free. The second lesson of the liar is that, contrary to what has been alleged by many, minimalism concerning truth is far better placed than its rival theories to solve the paradox. (shrink)

The Free Choice effect—whereby \\) seems to entail both \ and \—has traditionally been characterized as a phenomenon affecting the deontic modal ‘may’. This paper presents an extension of the semantic account of free choice defended by Fusco to the agentive modal ‘can’, the ‘can’ which, intuitively, describes an agent’s powers. On this account, free choice is a nonspecific de re phenomenon that—unlike typical cases—affects disjunction. I begin by sketching a model of inexact ability, which grounds a modal approach (...) to agency in a Williamson -style margin of error. A classical propositional semantics combined with this framework can reflect the intuitions highlighted by Kenny ’s dartboard cases, as well as the counterexamples to simple conditional views recently discussed by Mandelkern et al.. In Section 3, I turn to an independently motivated actual-world-sensitive account of disjunction, and show how it extends free choice inferences into an object language for propositional modal logic. (shrink)

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic (...) completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, Łukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates. (shrink)

Four real-life dilemma cases collected from Hong Kong managers were included, along with two other cases previously used by Weber (1991), in an instrument designed to assess ethical reasoning capacity. This was completed by 86 part-time post-graduate students, all of whom were managers with at least four years working experience. Respondents'' measured ethical reasoning capacity appeared to be at least as high as comparable samples in the U.S.A. The mean ethical reasoning stage varied between cases. Contrary to expectations, the unfamiliarityper (...) se of a case did not affect ethical reasoning which instead tended toward higher measured stages when issues of public hazard or environmental pollution were introduced, and toward lower measured stages where personal or family finances were at stake. Two methodological points were made signalling the need for caution in research of this kind. First, because of reservations about the adequacy of the standard Kohlbergian model of ethical reasoning development, a scoring guide based on a revised Kohlbergian model of ethical reasoning was used to analyze the replies, rendering comparisons with other samples inexact. Second, the possible phenomenon of quasi Stage Five reasoning renders problematic the identification of true Stage Five ethical reasoning. (shrink)

Yablo has argued for an alternative form of if-thenism that is more conducive with his figurative fictionalism. This commentary sets out to challenge whether the remainder, ρ, tends to be an inaccurate representation of the conditions that are supposed to complete the enthymeme from φ to Ψ. Whilst by some accounts the inaccuracies shouldn't set off any alarm bells, the truth of ρ is too inexact. The content of ρ, a partial truth, must display a sensitivity to the contextual (...) background conditions for subtraction to work properly in Yablo's view. Using a toy example, I argue that Yablo's subtraction model tends to yield partial truths as remainders that fail to rule out inaccurate expressions that may prove to be problematic for it. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Sigewiza’s CureJennifer H. Radden (bio)Keywordsbiopsychosocial model, Hildegard of Bingen, associationist presuppositions, causation, power of suggestionSuzanne Phillips and Monique Boivin provide us with a sympathetic and compelling account of how the various elements of Hildegard’s sophisticated amalgam of ritual, magic, religion, dietary and other medical remedies, caring, and community, formed a seamless cure for Sigewiza’s affliction. Whether Hildgard’s approach reflects an early instance of the biopsychosocial “model” is a separate (...) claim, and may be challenged. But that her ministrations somehow effected a cure in this case seems—if not without a doubt, then very likely.Descriptions of Sigewiza’s condition, with its “clumping together of blackness and steam” caused by a “constellation of humors,” echo those of other medieval writers speaking of the humoral disorder of melancholia—at that time an encompassing category for a range of symptoms and syndromes that would today be assigned as different mental disorders. In these descriptions a variety of explanations for mental illness are quite typically introduced, including biological, social, supernatural, dietary and astrological ones. Phillips and Boivin take care to point out that Hildegard was not offering her remedies as alternatives, but rather proposing them as at work jointly and in a range of causal directions, exhibiting mutual influence, and feedback loops. As these authors say, multiple explanations “were often held simultaneously... in reference to a specific case” (Phillips and Boivin 2007, XX). And the factors that might cause the system to move out of balance are many: food, emotions, the soul, the mind, actions, and spiritual forces. So although deeds may cause bodily changes and their psychological accompaniments, “problems in the diet might affect the humors which would then have psychological effects, which demons might... use as opportunities to cause further trouble in the spirit, mind, and body” (Phillips and Boivin 2007, 365).What first struck me about Hildegard’s description of these many distinct causes interacting in complex ways is its compatibility with the multi-causal accounts of depression (and other mental disorder) frequently proffered in our own time. Daily habits (e.g., diet, sleep and exercise regimes), genetic predispositions, including biological states of fragility, external events, experiences of loss, social roles, and cultural beliefs—not to mention spontaneous recovery, and placebo effects—are all regularly implicated in the onset and course of conditions such as depression.Still, the similarity to these modern causal accounts may be somewhat misleading and we must beware of overstating it. In favoring and pressing on Hildegard’s holistic understanding, moreover, Phillips and Boivin perhaps insufficiently emphasize significant dissimilarities between Hildegard’s and our contemporary accounts.It is the interaction between the various elements making up Sigewiza’s cure that is most noteworthy [End Page 373] in this account, as Phillips and Boivin recognize. Yet that relationship itself seems in some ways surprisingly problematic: difficult for us to make sense of, and profoundly unmodern. Granted, we think we see the way these approaches probably influenced how Sigewiza felt and responded; but it is not so clear how Hildegard saw things. Like a lot of thinking in medieval times, Hildegard’s account provides us with glimpses of an understanding of the world that today looks prescientific and in that respect, almost precausal. (So, to the extent that the biopsychosocial model is understood as a causal one, the case of Sigewiza may exemplify it only inexactly.)It is not merely the range and type of causes, including supernatural and astrological ones, in accounts such as Hildegard’s that distinguish it from today’s analyses. It is also the reliance of such accounts on what seems to be a different metaphysics, one of associations or qualities.Associationist presuppositions can be found in accounts of health and illness from before, during, and long after, Hildegard’s time. Three examples of this pervasive, but puzzling thinking serve to illustrate. The melancholiac’s perceived swarthiness and darkened skin color—regularly noted from the time of the Greek physicians and an established part of the medieval iconography in images of melancholy—were not, or not primarily, thought to be a causal result of the darkness of his bile, as one might suppose. Instead, this coloring seems... (shrink)

An important question in language evolution is whether segmentation as a linguistic process is able to yield compositionality. Segmentation is hypothesized to be a process to bridge the gap between holistic and compositional lexicons. However, to date no thorough analytical method has been provided to test the feasibility of segmentation. In this paper, an analytical model is presented that can predict the probability of encountering various kinds of overlaps by observing utterance pairs, and the probability of finding confirmation in the (...) language for newly extracted segments. Language users start by using a previously evolved holistic lexicon to communicate about simple environments. They segment these holistic utterances to smaller pieces, which can be used as elements of a compositional lexicon. The model reveals that the feasibility of segmentation depends on the definition of counterexamples, i.e. those associations (pairs), which either cause ambiguous extraction of segments, or do not allow segmentation at all. On one hand if inexact overlaps are considered to be contradictory (i.e. causing confusion) to a perfect exact overlap, then the probability is so minuscule that it renders the role of segmentation marginal during language evolution. On the other hand, if such inexact counterexamples are able to be segmented unambiguously due to extra cognitive capacities, segmentation may have a much higher feasibility. Keywords: segmentation; fractionation; analysis; holistic; protolanguage; compositionality. (shrink)

An important question in language evolution is whether segmentation as a linguistic process is able to yield compositionality. Segmentation is hypothesized to be a process to bridge the gap between holistic and compositional lexicons. However, to date no thorough analytical method has been provided to test the feasibility of segmentation. In this paper, an analytical model is presented that can predict the probability of encountering various kinds of overlaps by observing utterance pairs, and the probability of finding confirmation in the (...) language for newly extracted segments. Language users start by using a previously evolved holistic lexicon to communicate about simple environments. They segment these holistic utterances to smaller pieces, which can be used as elements of a compositional lexicon. The model reveals that the feasibility of segmentation depends on the definition of counterexamples, i.e. those associations, which either cause ambiguous extraction of segments, or do not allow segmentation at all. On one hand if inexact overlaps are considered to be contradictory to a perfect exact overlap, then the probability is so minuscule that it renders the role of segmentation marginal during language evolution. On the other hand, if such inexact counterexamples are able to be segmented unambiguously due to extra cognitive capacities, segmentation may have a much higher feasibility. Keywords: segmentation; fractionation; analysis; holistic; protolanguage; compositionality. (shrink)

Worldviews affect human behavior, and how we behave affects the world around us. Animism and so-called higher religions remain influential world-views; but the scientific worldview is comparably significant, and has under-gone drastic change during the twentieth century. The physical science ideal of mathematical precision and predictability, as elaborated by Galileo, Newton, and their heirs, underwent an amazing transformation in the twentieth century when Big Bang cosmology substituted an expanding, unstable universe for the Newtonian world machine. As a result, a grand (...) convergence of the sciences seems to be emerging around an evolutionary vision of how new aspects of reality emerge locally from new levels of complexity, like the heavier atoms, forged in stellar furnaces, the living molecules that arose in earth's primordial seas, and the symbolic systems invented by human societies perhaps as recently as forty thousand years ago. History, once a hopelessly inexact laggard among the sciences, might even become something of a model for other disciplines, since it deals with the most complex levels of reality we are aware of, that is, the world of agreed-upon meanings that guides our interaction with one another and with the biological, chemical, and physical worlds around us. (shrink)

Hájek (Erkenntnis 70(2):211–235, 2009) argues that probabilities cannot be the limits of relative frequencies in counterfactual infinite sequences. I argue for a different understanding of these limits, drawing on Norton’s (Philos Sci 79(2):207–232, 2012) distinction between approximations (inexact descriptions of a target) and idealizations (separate models that bear analogies to the target). Then, I adapt Hájek’s arguments to this new context. These arguments provide excellent reasons not to use hypothetical frequencies as idealizations, but no reason not to use (...) them as approximations. (shrink)

Wright holds that the following two theses are jointly incoherent: Rules determine correct language use. These rules are discoverable via internal reflection on language use. I argue that incoherence is derivable from alone and examine two types of probabilistic accounts that model a modification of, one in terms of inexact knowledge, the other in terms of viewing semantic rules as reasons for linguistic actions. Both accommodate tolerance by breaking the link between justified assertion and truth, but incoherence threatens their (...) conception of justified assertion. I argue that the rules-as-reasons approach can relocate sharp boundaries to a place where they are not only more tolerable, but to be expected. (shrink)

We argue that the epistemic theory of vagueness cannot adequately justify its key tenet-that vague predicates have precisely bounded extensions, of which we are necessarily ignorant. Nor can the theory adequately account for our ignorance of the truth values of borderline cases. Furthermore, we argue that Williamson’s promising attempt to explicate our understanding of vague language on the model of a certain sort of “inexact knowledge” is at best incomplete, since certain forms of vagueness do not fit Williamson’s model, (...) and in fact fit an alternative model. Finally, we point out that a certain kind of irremediable inexactitude postulated by physics need not be-and is not commonly-interpreted as epistemic. Thus, there are aspects of contemporary science that do not accord well with the epistemicist outlook. (shrink)

In Everett’s many-worlds interpretation, where quantum measurements are seen as decoherence events, inexact decoherence may let large worlds mangle the memories of observers in small worlds, creating a cutoff in observable world measure. I solve a growth–drift–diffusion–absorption model of such a mangled worlds scenario, and show that it reproduces the Born probability rule closely, though not exactly. Thus, inexact decoherence may allow the Born rule to be derived in a many-worlds approach via world counting, using a finite number (...) of worlds and no new fundamental physics. (shrink)

We use formal semantic analysis based on new constructions to study abstract realizability, introduced by Läuchli in 1970, and expose its algebraic content. We claim realizability so conceived generates semantics-based intuitive confidence that the Heyting Calculus is an appropriate system of deduction for constructive reasoning.Well-known semantic formalisms have been defined by Kripke and Beth, but these have no formal concepts corresponding to constructions, and shed little intuitive light on the meanings of formulae. In particular, the completeness proofs for these semantics (...) do not generate confidence in the sufficiency of the Heyting Calculus, since we have no reason to believe that every intuitively constructive truth is valid in the formal semantics.Läuchli has proved completeness for a realizability semantics with formal concepts analogous to constructions. We argue in some detail that, in spite of a certain inherent inexactness of the analogy, every intuitively constructive truth is valid in Läuchli semantics, and therefore the Heyting Calculus is powerful enough to prove all constructive truths. Our argument is based on the postulate that a uniformly constructible object must be communicable in spite of imprecision in our language, and that the permutations in Läuchli's semantics represent conceivable imprecision in a language, while allowing a certain amount of freedom in choosing the particular structure of the language.We give a detailed generalization of Läuchli's proof of completeness for the propositional part of the Heyting Calculus, in order to make explicit constructive and algebraic content.In our treatment, we establish several new results about Läuchli models. We show how to extend the sconing and gluing constructions familiar from Kripke and Frame semantics and Topos theory, to Läuchli models, and use them to give an algebraic approach to countermodel construction. In particular, the Läuchli arguments are given without the restriction to the integers, Z, as a group of permutations, which makes much of the coding scheme used in Läuchli's original paper transparent.We also make use of a new propositions-as-types syntax for the Heyting calculus, with limited nondeterminism, in which validity of formulae can be decided without loop-detection. (shrink)

Philosophers since antiquity have argued the merits of mathematics as a normative aid in ethical decision-making and of the mathematization of ethics a theoretical discipline. Recently, Anagnostopoulos, Annas, Broadie and Hutchinson have probed such issues said to be of interest to Aristotle. Despite their studies, the sense in which Aristotle either opposed or proposed a mathematical ethics in subject-matter and method remains unclear. This paper attempts to clarify the matter. It shows Aristotle’s matrix of exactness and inexactness for ethical subject-matter (...) and ethical method in the Nicomachean Ethics. Then it probes a resultant puzzle from the matrix, namely, the HL model of the happy life without consideration of mathematical justice and the HJL model of the happy life with such consideration. Finally, it examines Aristotle’s twofold rationale for differentiating these two models in his overall moral feedback loop system: differences in the intellectual virtue of good deliberation; the priority of friendship over justice for the happy life. This suggests Aristotle saw no objection either to using mathematics as an aid to ethical decision-making for a happy life, or to mathematizing at least some parts of an ethical theory of eudaimonism. (shrink)

Dans cet essai, je tente de répondre à quelques-unes des objections habituellement adressées au cosmopolitisme, en prenant en considération la perspective de ceux que cette doctrine risque d’affecter, à savoir, les immigrants. J’argue que certaines de ces objections se fondent sur des conceptions simplifiées à l’excès et empiriquement inexactes de ce que sont la communauté et l’identité culturelle. J’examine aussi en détail la controverse entourant les possibles implications autoritaristes — ou impérialistes — des propositions visant à faire d’un système moral-légal (...) un modèle pour le monde. L’objectif général de cet article est d’explorer les conditions permettant l’établissement d’une règle de justice cosmopolitique, dans un contexte mondial marqué par des différences culturelles et une extrême inégalité dans l’accès aux ressources et au pouvoir décisionnel. Certaines questions relatives à la motivation morale sont aussi abordées. (shrink)

" In Imagination and the Meaningful Brain, psychoanalyst Arnold Modell claims that subjective human experience must be included in any scientific...

Models as Mediators discusses the ways in which models function in modern science, particularly in the fields of physics and economics. Models play a variety of roles in the sciences: they are used in the development, exploration and application of theories and in measurement methods. They also provide instruments for using scientific concepts and principles to intervene in the world. The editors provide a framework which covers the construction and function of scientific models, and explore the (...) ways in which they enable us to learn about both theories and the world. The contributors to the volume offer their own individual theoretical perspectives to cover a wide range of examples of modelling, from physics, economics and chemistry. These papers provide ideal case-study material for understanding both the concepts and typical elements of modelling, using analytical approaches from the philosophy and history of science. (shrink)

The use of fictional models is extensive and rewarding in modern science. This fact captured the attention of philosophers of science, who are focusing on questions such as the following: is it possible for a fictional model to be explanatory? And, if so, in virtue of what is such a fictional model explanatory? In this paper, I discuss these questions in relation to the realism vs. anti-realism debate in philosophy of science. I focus on work developed by Alisa Bokulich (...) who has argued for the explanatory role played by fictional models, claiming that it can be accommodated by realism in ‘a broad sense’. To this end, Bokulich introduced what she called ‘an eikonic conception’ of explanation, as opposed to the so-called ‘ontic’ conception. This move, Bokulich claims, allows non-causal explanations to be acceptable to a modified version, as opposed to a ‘naïve’ brand of realism. Roughly, a fictional model can capture aspects of reality if it manages to act as a proxy for a theory targeting a physical system. As Bokulich explains with the example of James Clerk Maxwell’s use of mechanical models, this is due to structural correspondences between a model and a theory at a certain level of abstraction. However, Bokulich does not explain how the model grasps reality. In this paper, I fill this missing piece of the puzzle. While I agree with Bokulich on the explanatory function of fictional models, I shall invoke her reading of Maxwell’s work to draw a different conclusion. Specifically, I argue that structural correspondences at various levels form what I call ‘a ladder of abstractions’ which connects aspects of a target system to the corresponding depths of descriptions. Modifying in these terms the scope of ‘representing a system’, I suggest that Bokulich’s proposed modification of realism is obviated. (shrink)

Scientific models invariably involve some degree of idealization, abstraction, or nationalization of their target system. Nonetheless, I argue that there are circumstances under which such false models can offer genuine scientific explanations. After reviewing three different proposals in the literature for how models can explain, I shall introduce a more general account of what I call model explanations, which specify the conditions under which models can be counted as explanatory. I shall illustrate this new framework by (...) applying it to the case of Bohr's model of the atom, and conclude by drawing some distinctions between phenomenological models, explanatory models, and fictional models. (shrink)