The article sets out to clarify a number of confusions that exist in connection with the Born–Oppenheimer approximation (BOA) (Born-Oppenheimer, 1927). It is generally claimed that chemistry cannot be reduced to quantum mechanics because of the nature of this commonly used approximation in quantum chemistry, that is popularly believed to require a ‘clamping’ of the nuclei. It is also claimed that the notion of molecular structure, which is so central to chemistry, cannot be recovered from the quantum mechanical (...) description of molecules and that it must be imposed by hand through the BOA. Such an alleged failure of reduction is then taken to open the door to concepts such as emergence and downward causation. Another mistaken view is that chemists have no choice but to use the BOA whereas there is an entire sub-discipline which involves non-Born Oppenheimer calculations, and which regularly and successfully calculates many chemical and biochemical properties of molecules. Yet another misconception, according to the present author, is the view that the application of the BOA represents a violation of the Heisenberg Uncertainty Principle. Many of the claims made in the philosophy of chemistry community are based on the highly technical papers of authors such as Sutcliffe and Wooley, many of which date from about 50 years ago. While these authors remained skeptical of the possibility of recovering molecular structure from quantum mechanics, others maintained that it would eventually possible to do so. Significant progress has now been made in this direction. For example, whereas it is claimed that the full, or Coulombic Hamiltonian, for a molecule precludes the existence of molecular dipoles, some recent calculations have succeeded in obtaining the exact value of dipole moment of the LiH molecule. Even more significantly, a group in Norway has now succeeded in recovering the structure of the D3 + molecule in a completely ab initio manner without applying the BOA, but through the use of a Monte Carlo approach. (shrink)

Many philosophers appeal to the “fallacy of approximation”, or “problem of second best”. However, despite the pervasiveness of such appeals, there has been only a single attempt to provide a systematic account of what the fallacy is. We identify the shortcomings of this account and propose a better one in its place. Our account not only captures all the contexts in which approximation-based reasoning occurs but also systematically explains the several different ways in which it can be in (...) error. (shrink)

Straightforward theory revision, taking into account as effectively as possible the established nomic possibilities and, on their basis induced empirical laws, is conducive for (unstratified) nomic truth approximation. The question this paper asks is: is it possible to reconstruct the relevant theory revision steps, on the basis of incoming evidence, in AGM-terms? A positive answer will be given in two rounds, first for the case in which the initial theory is compatible with the established empirical laws, then for the (...) case in which it is incompatible with at least one such a law. (shrink)

What is the relation between what is good for you and how well you are doing? It is common and natural to think that the latter asymmetrically depends upon the former. I call this the molecular model of well-being, which holds that how well you are doing depends directly upon the presence of independently specifiable welfare goods in your life. Just about every contemporary theory of well-being embodies the form specified by the molecular model. Here I articulate and defend an (...) alternative way to think about well-being, a way based upon the notion of approximation. According to the approximation model of well-being, how well you are doing directly instead depends upon how closely you resemble an ideal way to live. One person is doing better than another just in case the life of the first more closely approximates the ideal life. To make this case I briefly sketch a substantive theory of well-being that employs it: what I take to be Aristotle’s view of well-being, which works as a proof of concept. We see that the approximation model of well-being can explain some patterns of value better than the molecular model can. (shrink)

This paper primarily deals with theconceptual prospects for generalizing the aim ofabduction from the standard one of explainingsurprising or anomalous observations to that ofempirical progress or even truth approximation. Itturns out that the main abduction task then becomesthe instrumentalist task of theory revision aiming atan empirically more successful theory, relative to theavailable data, but not necessarily compatible withthem. The rest, that is, genuine empirical progress aswell as observational, referential and theoreticaltruth approximation, is a matter of evaluation andselection, and (...) possibly new generation tasks forfurther improvement. The paper concludes with a surveyof possible points of departure, in AI and logic, forcomputational treatment of the instrumentalist taskguided by the `comparative evaluation matrix''. (shrink)

Critics frequently target Ernest Nagel’s model of reduction for its purported inadequacy in addressing the issue of approximation. In response, proponents of Nagel’s model have integrated approximations into the more comprehensive Generalized Nagel-Schaffner model, or the GNS model. However, this article contends that the pertinent criticisms and responses are both misplaced: There are no barriers to Nagel’s model incorporating approximations, and it assimilates them in a manner distinctly dissimilar to the approach of the GNS model. Indeed, Nagel’s model is (...) fundamentally _static_, providing invariant formal and informal conditions for reduction; and it is the _dynamic_ history of science that fulfills relevant conditions for reduction, thereby achieving different _degrees of reductive success_. Consequently, approximations are essentially extraneous to Nagel’s model, since they pertain chiefly to temporally based scientific knowledge and concern merely the _means_ (e.g., approximate or exact deductions) of fulfilling the conditions for reduction within specific problem contexts. This article also develops a Nagelian treatment of approximation, demonstrating how distinctive types of approximations aid in fulfilling various conditions for reduction and contribute to different degrees of reductive success. Two case studies are presented to illustrate the Nagelian treatment: The first examines the specific heat ratio anomaly within the traditional endeavor of reducing thermodynamics to statistical mechanics, and the second addresses the consumption puzzle in the context of reducing macroeconomics to microeconomics. (shrink)

We obtain a relatively simple criterion for when a forcing has the $${<}\,\delta $$ -approximation property, generalizing a result of Unger. Afterwards we apply this criterion to construct variants of Mitchell Forcing in order to answer questions posed by Mohammadpour.

In my From Instrumentalism to Constructive Realism (2000) I have shown how an instrumentalist account of empirical progress can be related to nomic truth approximation. However, it was assumed that a strong notion of nomic theories was needed for that analysis. In this chapter it is shown, in terms of truth- and falsity-content, that the analysis already applies when, in line with scientific common sense, nomic theories are merely assumed to exclude certain conceptual possibilities as nomic possibilities. The resulting (...) generalized and thereby simplified approach to nomic truth approximation was strongly stimulated by the related work on conjunctive theories of Gustavo Cevolani, Vincenzo Crupi and Roberto Festa (Erkenntnis, 2011), in particular their systematic way of defining the truth- and falsity-content of a theory. It will be shown that explicating ‘(nomic) truth approximation’ and ‘empirical progress’ in these terms does justice to some basic instrumentalist/empiricist and realist conditions of adequacy. (shrink)

I provide an explicit formulation of empirical adequacy, the central concept of constructive empiricism, and point out a number of problems. Based on one of the inspirations for empirical adequacy, I generalize the notion of a theory to avoid implausible presumptions about the relation of theoretical concepts and observations, and generalize empirical adequacy with the help of approximation sets to allow for lack of knowledge, approximations, and successive gain of knowledge and precision. As a test case, I provide an (...) application of these generalizations to a simple interference phenomenon. (shrink)

In this chapter I will draw a very general picture of an overall pragmatic theory of justification from the viewpoint of truth approximation. Crucial is the comparative definition of success according to which a theory P* is more successful than a theory P if and only if (1) P* shares all general successes of P, that is all empirically confirmed general implications, and has some extra ones, and (2) P shares all empirical counter-examples of P*. The rule of success (...) says that if so far P* has been more successful than P, then – for the time being – accept P* as the better one and eliminate P. It is further argued that according to the pragmatic-instrumentalist view of scientific theories, theory elimination should exclusively be guided by the rule of success rather than by Popper’s rule of falsification – for it is pragmatically reasonable to accept the most successful theory available, even if this theory is known to be false. In the last part of the chapter, it is argued that the connection between pragmatic theory-success and truth approximation is otherwise rather close to Popper: at least ‘almost’ always, a theory which is closer to the truth will also turn out to be the pragmatically more successful theory. However, in the upshot, ‘being false’ and hence ‘being falsified’ are not very important for truth approximation. (shrink)

Assuming that the target of theory oriented empirical science in general and of nomic truth approximation in particular is to characterize the boundary or demarcation between nomic possibilities and nomic impossibilities, I have presented in Chap. 4 (“Models, postulates, and generalized nomic truth approximation”) the ‘basic’ version of generalized nomic truth approximation, starting from ‘two-sided’ theories. Its main claim is that nomic truth approximation can perfectly be achieved by combining two prima facie opposing views on theories: (...) (1) the traditional (Popperian) view: theories are (sets of models of) postulates that exclude certain possibilities from being realizable, enabling explanation and prediction and (2) the model view: theories are sets of models that claim to (approximately) represent certain realizable possibilities. Nomic truth approximation, i.e., increasing truth-content and decreasing falsity-content, becomes in this way revising theories by revising their models and/or their postulates in the face of increasing evidence.The basic version of generalized nomic truth approximation is in many respects as simple as possible. Among other things, it does not take into account that one conceptual possibility may be more similar (or closer) to another than a third one (is to that other). However, for example, one theory may include a possibility that is more similar to a wrongly not included possibility than another theory can offer. Similarly, for wrongly not excluded possibilities. In this chapter it will be shown that such ‘refined’ considerations can be taken into account by adapted clauses based on a ternary similarity relation between possibilities (structures). This allows again abductive conclusions about refined truth approximation if a theory is persistently more successful in the refined sense than another.It will also be indicated and illustrated that this refined approach enables a specification to the effect that refined truth approximation can be obtained by the method of idealization and subsequent concretization. Finally, the basic and the refined approach will be evaluated with regard to some general principles and objections that have been discussed in the literature. (shrink)

Assuming that the target of theory oriented empirical science in general and of nomic truth approximation in particular is to characterize the boundary or demarcation between nomic possibilities and nomic impossibilities, I have presented in Chap. 4 (“Models, postulates, and generalized nomic truth approximation”) the ‘basic’ version of generalized nomic truth approximation, starting from ‘two-sided’ theories. Its main claim is that nomic truth approximation can perfectly be achieved by combining two prima facie opposing views on theories: (...) (1) the traditional (Popperian) view: theories are (sets of models of) postulates that exclude certain possibilities from being realizable, enabling explanation and prediction and (2) the model view: theories are sets of models that claim to (approximately) represent certain realizable possibilities. Nomic truth approximation, i.e., increasing truth-content and decreasing falsity-content, becomes in this way revising theories by revising their models and/or their postulates in the face of increasing evidence.The basic version of generalized nomic truth approximation is in many respects as simple as possible. Among other things, it is qualitative in the sense that it is purely based on set-theoretic relations. The present chapter presents the straightforward quantitative concretization of it. According to the ‘expected success theorem’, based on some probabilistic experimental conditions, greater truthlikeness, or verisimilitude, leads to greater expected empirical success. This enables tentative nomic truth approximation conclusions by abductive reasoning. (shrink)

The present volume contains 14 contributions presented at a colloquium on "Structure and Approximation in Physical Theories" held at Osnabruck in June 1980. The articles are presented in the revised form written after the colloquium and hence also take account of the results of the discussion at the colloquium. It is a striking feature that the problem of approximation in physical theories has only recently found some attention in the philosophy of science, although the working physicist is con (...) stantly confronted with those questions. No interesting theory of exact science exactly fits its experimental data; almost every relation between different theories is an approximate one. There fore an adequate reconstruction of physical theories must take into account and conceptualize the moment of approximation. The majority of the articles in this book is centered around this subject. There are at least two elaborate, 'structuralistic' approaches to the formalization of physical theories in which the aspect of approximation has been incorporated: the approach due to P. Suppes, J. Sneed, W. Stegmuller ("S-approach") and the approach of G. Lud wig and his co-workers ("L-approach"). The articles in this book correspondingly fall into three classes: presentation, elaboration and critique of the L-approach [Hartkamper/Schmidt, Ludwig, Neumann, Werner, Schmidt, Mayr, Kamiah, Majer, Grafe] or of the S-approach [Moulines, Balzer, Cooke], and articles referring to both approaches or concerned with related matters [Scheibe, Pfarr, Castrigiano]. Of course, this is only a rough classification and each article must be appraised in its own right. (shrink)

Assuming that the target of theory oriented empirical science in general and of nomic truth approximation in particular is to characterize the boundary or demarcation between nomic possibilities and nomic impossibilities, I have presented in Chap. 4 (“Models, postulates, and generalized nomic truth approximation”) the ‘basic’ version of generalized nomic truth approximation, starting from ‘two-sided’ theories. Its main claim is that nomic truth approximation can perfectly be achieved by combining two prima facie opposing views on theories: (...) (1) the traditional (Popperian) view: theories are (sets of models of) postulates that exclude certain possibilities from being realizable, enabling explanation and prediction and (2) the model view: theories are sets of models that claim to (approximately) represent certain realizable possibilities. Nomic truth approximation, i.e., increasing truth-content and decreasing falsity-content, becomes in this way revising theories by revising their models and/or their postulates in the face of increasing evidence.The basic version of generalized nomic truth approximation is in many respects as simple as possible. Among other things, the basic version does not make a (theory-relative) distinction between an observational and a theoretical level. This raises the question to what extent in a stratified set-up (nomic) truth approximation on a theoretical level entails truth approximation on the observational level. In other words, the question whether ‘closer to the truth’ can be projected from the theoretical to the observational level. Of course, ‘empirical success’ is now explicated in observational terms, and ‘closer to the observational truth’ and ‘more successfulness’ are now related in the same way as in the unstratified case.The chapter closes with quantitative and refined versions of stratified nomic truth approximation in line with Chaps. 5 and 6, respectively. (Referential truth approximation is dealt with in Chap. 11 ). (shrink)

In A. Kumar, & M. Banerjee [(2012). Definable and rough sets in covering-based approximation spaces. In T. Li. (eds.), Rough sets and knowledge technology (pp. 488–495). Springer-Verlag], A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], authors proposed a pair of lower and upper approximation operators based on granules generated by quasiorders. This work is an extension of algebraic results presented therein. A characterisation has been (...) presented for those quasiorder-generated covering-based approximation spaces whose corresponding collections of definable and rough sets form Stone algebras. The notion of rough lattice was proposed in A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], A. Kumar [(2020). A Study of Algebras and Logics of Rough Sets Based on Classical and Generalized Approximation Spaces. In Transactions on Rough Sets XXII, LNCS (Vol. 12485, pp. 123–251). Springer]. Some special rough lattices are introduced in this work, viz. rough Stone algebra, ∼1-complemented and ∼2-complemented rough lattices. Representations of these algebras in terms of rough sets are obtained. Moreover, logics for these algebras are shown to be sound and complete with respect to rough set semantics. (shrink)

Within the context of the time-reversed S-matrix approach to photoionization, and employing a recently proposed strong-field solution to the Schrödinger equation, analytic expressions for the atomic photoionization rates are obtained here without using the dipole approximation. We show that the absorbed photon momentum shows up as a forward-directed momentum component for the photoelectron. All the expressions reported in this work have the correct limits when the dipole approximation is used.

The qualitative theory of nomic truth approximation, presented in Kuipers in his (from instrumentalism to constructive realism, 2000), in which ‘the truth’ concerns the distinction between nomic, e.g. physical, possibilities and impossibilities, rests on a very restrictive assumption, viz. that theories always claim to characterize the boundary between nomic possibilities and impossibilities. Fully recognizing two different functions of theories, viz. excluding and representing, this paper drops this assumption by conceiving theories in development as tuples of postulates and models, where (...) the postulates claim to exclude nomic impossibilities and the (not-excluded) models claim to represent nomic possibilities. Revising theories becomes then a matter of adding or revising models and/or postulates in the light of increasing evidence, captured by a special kind of theories, viz. ‘data-theories’. Under the assumption that the data-theory is true, achieving empirical progress in this way provides good reasons for the abductive conclusion that truth approximation has been achieved as well. Here, the notions of truth approximation and empirical progress are formally direct generalizations of the earlier ones. However, truth approximation is now explicitly defined in terms of increasing truth-content and decreasing falsity-content of theories, whereas empirical progress is defined in terms of lasting increased accepted and decreased rejected content in the light of increasing evidence. These definitions are strongly inspired by a paper of Gustavo Cevolani, Vincenzo Crupi and Roberto Festa, viz., “Verisimilitude and belief change for conjunctive theories” (Cevolani et al. in Erkenntnis 75(2):183–222, 2011). (shrink)

The de Broglie–Bohm pilot-wave theory provides an illuminating candidate solution to the philosophical problems that plague orthodox quantum theory. But the pilot-wave theory also has the potential to be of practical use to, for example, quantum chemists and condensed matter physicists who study many-body problems. In particular, the proprietary pilot-wave concept of the “conditional wave function” provides a novel perspective on and justification for a standard approach to many-body quantum systems in which the N-particle wave function is replaced by N (...) single-particle wave functions. Moreover, this uniquely Bohmian “small entanglement approximation” (SEA) can be understood as the most basic level in a hierarchy of well-defined approximation schemes. Here we explain all of this theoretical background and then explore several of these approximation schemes (the SEA and beyond) numerically in the context of a simple toy model system. (shrink)

In this paper, Taylor series is used to solve neutrosophic multi-objective programming problem (NMOPP). In the proposed approach, the truth membership, Indeterminacy membership, falsity membership functions associated with each objective of multi-objective programming problems are transformed into a single objective linear programming problem by using a first order Taylor polynomial series. Finally, to illustrate the efficiency of the proposed method, a numerical experiment for supplier selection is given as an application of Taylor series method for solving neutrosophic multi-objective programming problem (...) at end of this paper. (shrink)

Suppose that scientific realists believe that a successful theory is approximately true, and that constructive empiricists believe that it is empirically adequate. Whose belief is more likely to be false? The problem of underdetermination does not yield an answer to this question one way or the other, but the pessimistic induction does. The pessimistic induction, if correct, indicates that successful theories, both past and current, are empirically inadequate. It is arguable, however, that they are approximately true. Therefore, scientific realists overall (...) take less epistemic risk than constructive empiricists. (shrink)

In this article, we offer a detailed study of two important episodes in the early history of high-energy physics, namely the development of the Chew and the Nambu-Jona-Lasinio models. Our study reveals that both models resulted from the combination of an old Hamiltonian, which had been introduced by earlier researchers, and two new approximation methods developed by Chew and by Nambu and Jona-Lasinio. These new approximation methods, furthermore, were the key component behind the models’ success. We take this (...) historical investigation to support two philosophical theses about the manner in which scientific modelling operates in high-energy physics. Both of these theses run counter to a view that is commonly accepted among philosophers of science: the view that all approximations can be embedded within an equivalent idealized system, and that whatever role the former might play in scientific modelling is therefore parasitic on the much more substantial work performed by the latter. Our first thesis, which we call “Distinctness,” states that approximation methods constitute an independent category of theoretical output from idealized systems. We thus believe that approximations and idealized systems constitute two independent types of objects, both of which are essential to the practice of modelling. Our second, more radical thesis is called “Content Determination.” Our claim here is that approximation methods can in fact be essential to assigning determinate physical content to the idealized systems with which they jointly operate. As we show, this is due to the fact that quantum field theory allows for a very thin characterization of idealized systems only, making the use of approximations necessary to supply additional content. We conclude the paper with a few reflections about the manner in which our two theses can be used to articulate David Kaiser’s views on the “vanishing of scientific theory” in physics after WWII. (shrink)

The effect of the rotating-wave approximation (RWA) on the coupling between an atom and the electromagnetic field is studied in the dipole approximation. It is demonstrated that use of the RWA results in an explicitly nonlocal interaction.

It is well known that for a given continuous function f : [0, 1] → ℝ and a number n there exists a unique polynomial pn ∈ Pn which best L1-approximates f. We establish the first upper bound on the complexity of the sequence n∈ ℕ, assuming f is polynomial-time computable. Our complexity analysis makes essential use of the modulus of uniqueness for L1-approximation presented in [13].

This paper highlights some connections between work on truth approximation and work in social epistemology, in particular work on peer disagreement. In some of the literature on truth approximation, questions have been addressed concerning the efficiency of research strategies for approximating the truth. So far, social aspects of research strategies have not received any attention in this context. Recent findings in the field of opinion dynamics suggest that this is a mistake. How scientists exchange and take into account (...) information about each others’ beliefs may greatly influence the accuracy and speed with which the scientific community as a whole approximates the truth. On the other hand, social epistemologists concerned with peer disagreement have so far neglected the question of how practices of responding to disagreements with peers fare with respect to the goal of approximating the truth. Again, work on opinion dynamics shows that this may be a mistake, and that how we ought to respond to disagreements with our peers may depend on the specific purposes of our investigations. (shrink)

Contents: IDEALIZATION, APPROXIMATION AND COUNTERFACTUALS IN THE STRUCTURALIST FRAMEWORK. Theo A.F. KUIPERS: The Refined Structure of Theories. C. ULISES and Reinhold STRAUB: Approximation and Idealization from the Structuralist Point of View. Ilkka A. KIESEPPÄ: A Note on the Structuralist Account of Approximation. C. ULISES MOULINES and Reinhold STRAUB: A Reply to Kieseppä. Wolfgang BALZER and Gerhard ZOUBEK: Structuralist Aspects of Idealization. Andoni IBARRA and Thomas MORMANN: Counterfactual Deformation and Idealization in a Structuralist Framework. Ilkka A. KIESEPPÄ: Assessing (...) the Structuralist Theory of Verisimilitude. IDEALIZATION, APPROXIMATION AND THEORY FORMATION. Leszek NOWAK: Remarks on the Nature of Galileo's Methodological Revolution. Ilkka NIINILUOTO: Approximation in Applied Science. Elke HEISE, Peter GERJETS and Rainer WESTERMANN: Idealized Action Phases. A Concise Rubicon Theory. Klaus G. TROITZSCH: Modelling, Simulation, and Structuralism. Veikko RANTALA and Tere VADÉN: Idealization in Cognitive Science. A Study in Counterfactual Correspondence. Matti SINTONEN and Mika KIIKERI: Idealization in Evolutionary Biology. Timo TUOMIVAARA: On Idealization in Ecology. Martti KUOKKANEN and Matti HÄYRY: Early Utilitarianism and Its Idealizations from a Systematic Point of View. IDEALIZATION, APPROXIMATION AND MEASUREMENT. Rainer WESTERMANN: Measurement-Theoretical Idealizations and Empirical Research Practice. Uwe KONERDING: Probability as an Idealization of Relative Frequency. A Case Study by Means of BTL-Model. Reinhard SUCK and Joachim WIENÖBST: The Empirical Claim of Probability Statements, Idealized Bernoulli Experiments and their Approximate Version. Pekka J. LAHTI: Idealizations in Quantum Theory of Measurement. (shrink)

Kohlenbach, U., Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation, Annals of Pure and Applied Logic 64 27–94.We consider uniqueness theorems in classical analysis having the form u ε U, v1, v2 ε Vu = 0 = G→v 1 = v2), where U, V are complete separable metric spaces, Vu is compact in V and G:U x V → is a constructive function.If is proved by arithmetical means from analytical assumptions (...) x εXy ε Yx z ε Z = 0) only , then we can extract from the proof of → an effective modulus of uniqueness, which depends on u, k but not on v1,v2, i.e., u ε U, v1, v2 ε Vu, k εG, G 2-φuk→dv2-itk). Such a modulus φ can e.g. be used to give a finite algorithm which computes the zero of G on Vu with prescribed precision if it exists classically.The extraction of φ uses a proof-theoretic combination of functional interpretation and pointwise majorization. If the proof of → uses only simple instances of induction, then φ is a simple mathematical operation. (shrink)

The Born–Oppenheimer approximation is one of the central tenets of chemical dynamics and reactivity. Despite its central importance in chemistry, the Born–Oppenheimer approximation is often severely misinterpreted or misrepresented. More specifically, widespread claims about the Born–Oppenheimer approximation within the chemistry community imply that this approximation enforces the nuclei of a molecule to be (1) frozen and (2) treated as classical particles. Both claims are wrong. This article aims to discuss the derivation of the Born–Oppenheimer approximation (...) in a pedagogical way, representing the main steps of this derivation pictorially via a model molecular system. The pictorial derivation is then connected to the formal mathematical derivation for the interested reader. We hope that this pictorial derivation can help chemists to better understand the main steps leading to this key approximation and why the two claims mentioned above are incorrect. We also believe that a detailed understanding of the Born–Oppenheimer approximation is necessary to tackle problem in chemistry where this approximation breaks down, like photochemistry for example. (shrink)

Approximations form an essential part of scientific activity and they come in different forms: conceptual approximations (simplifications in models), mathematical approximations of various types (e.g. linear equations instead of non-linear ones, computational approximations), experimental approximations due to limitations of the instruments and so on and so forth. In this paper, we will consider one type of approximation, namely numerical approximations involved in the comparison of two results, be they experimental or theoretical. Our goal is to lay down the conceptual (...) and formal foundations of a local theory of partial truth. This is done by introducing and exploring the concept of truth space. (shrink)

Machine learning (ML) models are increasingly discussed in the philosophy of science in terms of idealization and even by analogy with toy models. I argue that this framing conflates idealization with approximation. Once the relevant ML target is specified as relations among features represented in data---relative to a target system---the claim that ML models are dissimilar to their targets becomes too coarse. Scientific ML models can and often must be approximately similar to their targets in the relevant respects. (...) class='Hi'>Approximation failure therefore provides the more direct standard of assessment, and ML models do not function as toy models. (shrink)

The so-called Preface Paradox seems to show that one can rationally believe two logically incompatible propositions. We address this puzzle, relying on the notions of truthlikeness and approximate truth as studied within the post-Popperian research programme on verisimilitude. In particular, we show that adequately combining probability, approximate truth, and truthlikeness leads to an explanation of how rational belief is possible in the face of the Preface Paradox. We argue that our account is superior to other solutions of the paradox, including (...) a recent one advanced by Hannes Leitgeb (Analysis 74.1). (shrink)

If we take the state function of quantum mechanics to describe belief states, arguments by Stairs and Friedman-Putnam show that the projection postulate may be justified as a kind of minimal change. But if the state function takes on a physical interpretation, it provides no more than what I call a fortuitous approximation of physical measurement processes, that is, an unsystematic form of approximation which should not be taken to correspond to some one univocal "measurement process" in nature. (...) This fact suggests that the projection postulate does not provide a proper locus for interpretive investigation. Readers will also find section 3's analysis of fortuitous approximations of independent interest and presented without the perils of quantum mechanics. (shrink)

It is proposed that we use the term “approximation” for inexact description of a target system and “idealization” for another system whose properties also provide an inexact description of the target system. Since systems generated by a limiting process can often have quite unexpected, even inconsistent properties, familiar limit systems used in statistical physics can fail to provide idealizations, but are merely approximations. A dominance argument suggests that the limiting idealizations of statistical physics should be demoted to approximations.

Approximations have come to occupy a central role within Bayesian cognitive science. Many cognitive scientists view current approximation-based models as showing that the mind approximates Bayesian inference. In this paper I interrogate this idea, asking what it means to claim that the mind approximates one computation by executing another. I look at three possible interpretations of such claims, finding problems with each. I argue that this poses challenges to one central rationale for the Bayesian approach, and to its top-down (...) methodology. (shrink)

En las actividades ordinarias de nuestra vida cotidiana encontramos nuestros actos de percepción confrontados por las cosas materiales. A ellos ─actos de percepción─ les atribuimos una existencia "real" asumiéndolos de tal manera que los sumergimos y transfundimos, de forma múltiple e indefinida, dentro del entorno de realidades análogas que se unen para formar un único mundo al que yo, con mi propio cuerpo, pertenezco. Ahora bien sí frente a la cotidianidad descrita anteriormente asumimos una actitud escéptica acerca de lo que (...) es “real” en el mundo,nos descubriremos haciendo una reflexión filosófica. Bajo esta deliberación encontramos que, por ejemplo, la cualidad "verde", tiene existencia por medio de la sensación "verde"asociada a un objeto dado por la percepción, lo que nos lleva a pensar que no tiene sentido vincularla sensación como cosa en sí misma a cosas materiales existentes en sí mismos, esto nos lleva a pensar que las cualidades de los sentidostienen carácter subjetivo.A pesar de esta reflexión es conveniente acotar que esta subjetividad no interesaa las ciencias exactas ya que éstas procuran lo objetivo. Desde este punto de vista,encontramos dentro de los estudios de Galileo Galilei el principio que subyace al método matemáticoconstructivo de nuestra física moderna ; de esta manera, y bajo este principio,los colores ─ por ejemplo “verde”─ son solo vibraciones en un medio repudiando de esta forma el carácter subjetivo a la vez que se mantiene la objetividad. Sin embargo, dentro del campo de la filosofía el idealismo transcendental de Kant marca un cambio de paradigma en relación a lo anterior. Kant sostiene que no solamente las cualidades de los sentidos tienen carácter subjetivo, sino que espacio y tiempo, conceptos fundacionales dentro de la física, no tienen significación absoluta; en otras palabras, espacio y tiempo son formas de nuestra percepción. Para Kant aquello que sustenta nuestra percepción y aquello que sustenta el conocimiento matemático aplicado a la experiencia son lo mismo: intuiciones puras a priori del espacio y el tiempo. De esta manera, y bajo esta perspectiva, sólo la teoría de la relatividad deja muyen claro que las dos esencias: espacio y tiempo, como formas de la intuición en términos kantianos, no tienen lugar en el mundo construido por la física matemática concebida por Galileo. Según esto, los colores no son siquiera vibraciones en un medio sino simplemente una serie de valores de funciones matemáticas en las que se producen cuatro parámetros independientes que corresponden a las tres dimensiones del espacio y la del tiempo, expresado como principio general esto significa que el mundo real y cada uno de sus constituyentes con sus características sólo pueden ser, en términos husserlianos, objetos intencionales de actos de conciencia. En otras palabras: los datos inmediatos que recibo son las experiencias de la conciencia. Esto nos permite afirmar que la sensación de un objeto está presente de una forma físicamente real para mí con quien esa sensación se relaciona. Esto es lo que Brentano llama objeto intencional ;es así como al percibir un objeto, por ejemplo: veo este “libro” mi atención está totalmente dirigida hacia él. Yo "tengo" la percepción, pero sólo cuando hago de esta percepción ─ acto libre de reflexión ─algo que "conozco" con respecto a ella ─y no sólo el “libro”─ llego precisamente a un segundo acto: objetos intencionales de actos de conciencia, que son a los que referíamos antes. El objeto intencional es inmanente y lo que es inmanente es absoluto ; es exactamente lo que es en la forma en que lo tengo, y puedo reducir esto, su esencia, por los actos de reflexión. En otras palabras, es un componente real de mis experiencias; contrario a lo que sucede con el acto primario de percepción, donde el objeto es trascendental, esto es, se da en una experiencia de conciencia pero no es un componente real de la misma. Por otra parte, los objetos trascendentales tienen sólo una existencia fenoménica; son apariencias que se presentan de múltiples maneras. Ninguno de estos modos de aparición puede pretender presentar aquello que percibimos – por ejemplo el libro- tal como es en sí, además en toda percepción está involucrada la tesis de la realidad del objeto que aparece en ella; este último es, de hecho, un elemento fijo y duradero de la tesis general de la realidad del mundo. En resumen, lo que interesa ver claramente es la importancia enel dato de la conciencia como punto de partida en el que debemos situarnos si queremos comprender el significado absoluto. (shrink)

The main question addressed in this paper is whether some false sentences can constitute evidence for the truth of other propositions. In this paper it is argued that there are good reasons to suspect that at least some false propositions can constitute evidence for the truth of certain other contingent propositions. The paper also introduces a novel condition concerning propositions that constitute evidence that explains a ubiquitous evidential practice and it contains a defense of a particular condition concerning the possession (...) of evidence. The core position adopted here then is that false propositions that are approximately true reports of measurements can constitute evidence for the truth of other propositions. So, it will be argued that evidence is only quasi-factive in this very specific sense. (shrink)

§1. Introduction. The problem raised by the liar paradox has long been an intriguing challenge for all those interested in the concept of truth. Many “solutions” have been proposed to solve or avoid the paradox, either prescribing some linguistical restriction, or giving up the classical true-false bivalence or assuming some kind of contextual dependence of truth, among other possibilities. We shall not discuss these different approaches to the subject in this paper, but we shall concentrate on a kind of formal (...) construction which was originated by Kripke's paper “Outline of a theory of truth” [11] and which, in different forms, reappears in later papers by various authors.The main idea can be presented as follows: assume a first order language ℒ containing, among other unspecified symbols, a predicate symbolTintended to represent the truth predicate for ℒ. Assume, also, a fixed modelM= 〈D, I〉 whereDcontains all sentences of ℒ andIinterprets all non-logical symbols of ℒ exceptTin the usual way. In general,Dmight contain many objects other than sentences of ℒ but as that would raise the problem of the meaning of sentences in whichTis applied to one of these objects, we shall assume that this is not the case. (shrink)

Theo AF Kuipers THE THREEFOLD EVALUATION OF THEORIES A SYNOPSIS OF FROM INSTRUMENTALISM TO CONSTRUCTIVE REALISM. ON SOME RELATIONS BETWEEN CONFIRMATION, EMPIRICAL PROGRESS, AND TRUTH APPROXIMATION (2000) ABSTRACT.

Our aim here is to show that an enigmatic text of Avicenna's Glosses, devoted to the problem of evil, takes on its full meaning in the light of the last chapter of the Šifā ' on De generatione et corruptione. We will see how Avicenna, deepening and developing a cosmological argument already present in the commentary of Alexander of Aphrodisias on the De generatione, ends up building most of his theodicy on the relative incommensurability of the different celestial periods. All (...) the problem of divine Justice is thus reinterpreted in terms of opposition between discrete and continuous. Finally we will show the importance that this development of Avicenna had in Western Christendom in the 14th century, and the complex relationship which Leibniz has with it in his recently edited reflections on the Great Year. (shrink)

The paper introduces a new non-factive theory of knowledge, employing the recent theory of verisimilitude developed by Jakob Süskind to model the relative adequacy of representations as their approximation to truth. It makes the relation of representation one of the necessary conditions of knowledge without requiring the truth condition to be satisfied. However, the relation of knowledge to truth is built at the meta-level into the notion of the adequacy of representations, which enables the proposed theory to cover any (...) thinkable case of research yielding real knowledge, although of a non-factive kind. Despite its universality, the theory relativizes knowledge to a set of research questions, while rejecting alethic relativism, which — it is argued — does not provide a satisfactory explanation of truth in reasoning about the growth and extinction of scientific knowledge. (shrink)

In this paper, we investigate the problem of truth approximation via belief merging, i.e., we ask whether, and under what conditions, a group of inquirers merging together their beliefs makes progress toward the truth about the underlying domain. We answer this question by proving some formal results on how belief merging operators perform with respect to the task of truth approximation, construed as increasing verisimilitude or truthlikeness. Our results shed new light on the issue of how rational (dis)agreement (...) affects the inquirers’ quest for truth. In particular, they vindicate the intuition that scientific inquiry, and rational discussion in general, benefits from some heterogeneity in opinion and interaction among different viewpoints. The links between our approach and related analyses of truth tracking, judgment aggregation, and opinion dynamics, are also highlighted. (shrink)

Resumen: Este artículo se propone ahondar en la función política del relato distópico, entendido como un tipo de imagen política. Siguiendo la intuición de Gordin, Tilley y Prakash (2010) de que las distopías son utopías que han errado su curso, se plantea que el relato distópico busca construir una imagen política indeseable que permita romper la captura del deseo que ha producido la persecución de una determinada ilusión-utopía. Se propone, como criterio de lectura de las narrativas distópicas, que su emergencia (...) y proliferación se produce a partir de las experiencias históricas que dan cuenta del fracaso del ímpetu emancipador de la modernidad y su deriva en sistemas sociales y políticos que perfeccionan la dominación. En particular, en los términos de Wallerstein (1995), el proceso con el que la modernidad de la tecnología se impone históricamente a la modernidad de la liberación. Abstract: This article aims to delve into the political function of the dystopian narrative, understood as a type of political image. Following of Gordin, Tilley & Prakash´s (2010) intuition, that dystopias are utopias that have gone wrong, it suggests that the dystopian narrative seeks to build an undesirable political image that permits the breaking away from the capture of desire produced by the pursuit of a certain utopia-illusion. We propose, as a key to the reading of dystopian narratives, that their emergence and proliferation stems from the historical experiences that account for the failure of the emancipatory impetus of modernity and its drift into social and political systems that perfect domination. Specifically, in the terms of Wallerstein (1995), the process by which the modernity of technology is historically imposed on the modernity of liberation. (shrink)