Two complementary debates of the turn of the nineteenth and twentieth century are examined here: the debate on the legitimacy of hypotheses in the natural sciences and the debate on intentionality and ‘representations without object’ in philosophy. Both are shown to rest on two core issues: the attitude of the subject and the mode of presentation chosen to display a domain of phenomena. An orientation other than the one which contributed to shape twentieth-century philosophy of science is explored through the (...) analysis of the role given to assumptions in Boltzmann’s research strategy, where assumptions are contrasted to hypotheses, axioms, and principles, and in Meinong’s criticism of the privileged status attributed to representations in mental activities. Boltzmann’s computational style in mathematics and Meinong’s criticism of the confusion between representation and judgment give prominence to an indirect mode of presentation, adopted in a state of suspended belief which is characteristic of assumptions and which enables one to grasp objects that cannot be reached through direct representation or even analogies. The discussion shows how assumptions and the movement to fiction can be essential steps in the quest for objectivity. The conclusion restates the issues of the two debates in a contemporary perspective and shows how recent developments in philosophy of science and philosophy of language and mind can be brought together by arguing for a twofold conception of reference.Keywords: Assumption; Hypothesis; Description; Mode of presentation; Ludwig Boltzmann; Alexius Meinong. (shrink)

In this paper the use of mathematics in economics will be discussed, by comparing two approaches to mathematics, a Cartesian approach, and a Newtonian approach. I will argue that while mainstream economics is underpinned by a Cartesian approach which led to a divorce between mathematics and reality, the contributions of key authors of the Cambridge tradition, like Marshall, Keynes and Sraffa, are characterised by a Newtonian approach to mathematics, where mathematics is aimed at a study of reality. Marshall was influenced (...) by the Newtonian approach that still characterised many aspects of the Cambridge Mathematical Tripos, where the emphasis was on geometrical and mechanical examples rather than on symbolic (Cartesian) mathematics. Keynes, who criticised (Cartesian) symbolic mathematics, was indeed an admirer of Newton and of his method. Sraffa's mathematical constructions are also in line with the Newtonian approach where arithmetic and geometry were strictly separated, since Sraffa's mathematical constructions typically use arithmetic without engaging in the mixture between geometry and arithmetic that occurs in the Cartesian approach. View the Open Peer Discussion of this paper ». (shrink)

For many among the scientifically informed public, and even among physicists, Heisenberg's uncertainty principle epitomizes quantum mechanics. Nevertheless, more than 86 years after its inception, there is no consensus over the interpretation, scope, and validity of this principle. The aim of this chapter is to offer one such interpretation, the traces of which may be found already in Heisenberg's letters to Pauli from 1926, and in Dirac's anticipation of Heisenberg's uncertainty relations from 1927, that stems form the hypothesis of finite (...) nature. Instead of a mere mathematical theorem of quantum theory, or a manifestation of "wave-particle duality", the uncertainty relations turn out to be a result of a more fundamental premise, namely, the inherent limitation on spatial resolution that follows from the bound on physical resources. The implication of this view are far reaching: it depicts the Hilbert space formalism as a phenomenological, "effective", formalism that approximates an underlying discrete structure; it supports a novel interpretation of probability in statistical physics that sees probabilities as deterministic, dynamical transition probabilities which arise from objective and inherent measurement errors; and it helps to clarify several puzzles in the foundations of statistical physics, such as the status of the "disturbance" view of measurement in quantum theory, or the tension between ontology and epistemology in the attempts to describe nature with physical theories whose formalisms include subjective probabilities. Finally, this view also renders obsolete the entire class of interpretations of quantum theory that adhere to "the reality of the wave function". (shrink)

We study some aspects of the emergence of _lógos_ from _xáos_ on a basal model of the universe using methods and techniques from algorithmic information and Ramsey theories. Thereby an intrinsic and unusual mixture of meaningful and spurious, emerging laws surfaces. The spurious, emergent laws abound, they can be found almost everywhere. In accord with the ancient Greek theogony one could say that _lógos_, the Gods and the laws of the universe, originate from “the void,„ or from _xáos_, a picture (...) which supports the unresolvable/irreducible lawless hypothesis. The analysis presented in this paper suggests that the “laws„ discovered in science correspond merely to syntactical correlations, are local and not universal. (shrink)

The beauty of electricity, or of any other force, is not that the power is mysterious and unexpected, touching every sense at unawares in turn, but that it is under law... Michael Faraday, Wheatstone's Electric Telegraph's Relation to Science (being an argument in favour of the full recognition of Science as a branch of Education), 1854.

Natural language provides a mechanism for cultural evolution by ensuring the persistent heredity of variations in both cultural information and information about its own construction. In the process, it not only facilitates but also limits our thinking to the ways its vocabulary and structures make possible. But the human capacity for metarepresentation frees cultural information from the restrictions of any one medium or language, and has also propelled the evolution of artefactual languages, which provide evolutionary mechanisms for specialist areas of (...) culture. And cooperation between diverse cultural specialists can stimulate further, innovative competition between the cultural information that they share. (shrink)

The aim of this paper is to propose an alternative behavioural definition of computation based simply on whether a system is capable of reacting to the environment—the input—as reflected in a measure of programmability. This definition is intended to have relevance beyond the realm of digital computers, particularly vis-à-vis natural systems. This will be done by using an extension of a phase transition coefficient previously defined in an attempt to characterise the dynamical behaviour of cellular automata and other systems. The (...) transition coefficient measures the sensitivity of a system to external stimuli and will be used to define the susceptibility of a system to be programmed. (shrink)

In his recent book, Time and Chance, David Albert claims that by positing that there is a uniform probability distribution defined, on the standard measure, over the space of microscopic states that are compatible with both the current macrocondition of the world, and with what he calls the “past hypothesis”, we can explain the time asymmetry of all of the thermodynamic behavior in the world. The principal purpose of this paper is to dispute this claim. I argue that Albert's proposal (...) fails in his stated goal—to show how to use the time‐reversible dynamics of Newtonian physics to “underwrite the actual content of our thermodynamic experience” (Albert 2000, 159). Albert's proposal can satisfactorily explain why the overall entropy of the universe as a whole is increasing, but it does not and cannot explain the increasing entropy of relatively small, relatively short‐lived systems in energetic isolation without making use of a principle that leads to reversibility objections. (shrink)

Newtonian forces are pushes and pulls, possessing magnitude and direction, that are exerted (in the first instance) by objects, and which cause (in particular) motions. I defend Newtonian forces against the four best reasons for denying or doubting their existence. A running theme in my defense of forces will be the suggestion that Newtonian Mechanics is a special science, and as such has certain prima facie ontological rights and privileges, that may be maintained against various challenges.

According to Interventionism, explanations cite invariant relations which hold among multiple variables. Interventionism incorrectly implies, however, that many common scientific explanations—which cite single‐variable boundary constraints—are not actually explanatory. So I propose a different account of explanation, similar in spirit to Interventionism, which gets those cases of scientific explanation right.

It has been argued that the fundamental laws of physics do not face a ‘problem of provisos’ equivalent to that found in other scientific disciplines (Earman, Roberts and Smith 2002) and there is only the appearance of exceptions to physical laws if they are confused with differential equations of evolution type (Smith 2002). In this paper I argue that even if this is true, fundamental laws in physics still pose a major challenge to standard Humean approaches to lawhood, as they (...) are not in any obvious sense about regularities in behaviour. A Humean approach to physical laws with exceptions is possible, however, if we adopt a view of laws that takes them to be the algorithms in the algorithmic compressions of empirical data. When this is supplemented with a distinction between lossy and lossless compression, we can explain exceptions in terms of compression artefacts present in the application of the lossy laws. (shrink)

Many mathematicians, physicists, and philosophers have suggested that the fact that mathematics—an a priori discipline informed substantially by aesthetic considerations—can be applied to natural science is mysterious. This paper sharpens and responds to a challenge to this effect. I argue that the aesthetic considerations used to evaluate and motivate mathematics are much more closely connected with the physical world than one might presume, and (with reference to case-studies within Galois theory and probabilistic number theory) show that they are correlated with (...) generally recognized theoretical virtues, such as explanatory depth, unifying power, fruitfulness, and importance. (shrink)

I respond to the frequent objection that structural realism fails to sharply state an alternative to the standard predicate-logic, object / property / relation, way of doing metaphysics. The approach I propose is based on what I call a ‘math-first’ approach to physical theories (close to the so-called ‘semantic view of theories') where the content of a physical theory is to be understood primarily in terms of its mathematical structure and the representational relations it bears to physical systems, rather than (...) as a collection of sentences that attempt to make true claims about those systems (a ‘language-first’ approach). I argue that adopting the math-first approach already amounts to a form of structural realism, and that the choice between epistemic and ontic versions of structural realism is then a choice between a language-first and math-first view of metaphysics; I then explore the status of objects (and properties and relations) in fundamental and non-fundamental physics for both versions of math-first structural realism. (shrink)

Despite the importance of the variational principles of physics, there have been relatively few attempts to consider them for a realistic framework. In addition to the old teleological question, this paper continues the recent discussion regarding the modal involvement of the principle of least action and its relations with the Humean view of the laws of nature. The reality of possible paths in the principle of least action is examined from the perspectives of the contemporary metaphysics of modality and Leibniz's (...) concept of essences or possibles striving for existence. I elaborate a modal interpretation of the principle of least action that replaces a classical representation of a system's motion along a single history in the actual modality by simultaneous motions along an infinite set of all possible histories in the possible modality. This model is based on an intuition that deep ontological connections exist between the possible paths in the principle of least action and possible quantum histories in the Feynman path integral. I interpret the action as a physical measure of the essence of every possible history. Therefore only one actual history has the highest degree of the essence and minimal action. To address the issue of necessity, I assume that the principle of least action has a general physical necessity and lies between the laws of motion with a limited physical necessity and certain laws with a metaphysical necessity. (shrink)

On the basis of what I call physico-formalist philosophy of mathematics, I will develop an amended account of the Kantian–Reichenbachian conception of constitutive a priori. It will be shown that the features attributed to a real object are not possessed by the object as a “thing-in-itself”; they require a physical theory by means of which these features are constituted. It will be seen that the existence of such a physical theory implies that a physical object can possess a property only (...) if other contingently existing physical objects exist; therefore, the intrinsic–extrinsic distinction is flawed. (shrink)

Why do we have records of the past and not the future? Entropic explanations for this ‘record asymmetry’ have been popular ever since Boltzmann. Foremost amongst these is Albert and Loewer’s account, which explains the record asymmetry using a low-entropy initial macrostate plus an initial probability distribution. However, the details of how this initial state underpins the record asymmetry are not fully specified. In this paper I attempt to plug this explanatory gap in two steps. First, I suggest the record (...) asymmetry is more immediately explained by the ‘fork asymmetry’, which their picture omits. Second, by relating the fork asymmetry to an initial state that’s metaphysically similar to theirs, I clarify how this ultimately underpins the record asymmetry. (shrink)

Perspectival realists often appeal to the methodology of science to secure a realist account of the retention and continued success of scientific claims through the progress of science. However, in the context of modern physics, the retention and continued success of scientific claims are typically only definable within a mathematical framework. In this article, I argue that this concern leaves the perspectivist open to Cassirer’s neo-Kantian critique of the applicability of mathematics in the natural sciences. To support this criticism, I (...) present a case study on the conservation of energy in modern physics. (shrink)

Cartwright attempts to argue from an analysis of the composition of forces, and more generally the composition of laws, to the conclusion that laws must be regarded as false. A response to Cartwright is developed which contends that properly understood composition poses no threat to the truth of laws, even though agreeing with Cartwright that laws do not satisfy the "facticity" requirement. My analysis draws especially on the work of Creary, Bhaskar, Mill, and points towards a general rejection of Cartwright's (...) view that laws, especially fundamental laws, should be seen as false. (shrink)

RESUMEN La sección 1 introduce lo que llamo la tesis del colapso de las estructuras matemáticas y las estructuras físicas. La sección 2 examina si acaso la indispensabilidad de las matemáticas para la física fundamental involucra la adopción del platonismo matemático, en este caso acerca de estructuras matemáticas, como argumenta el realismo estructural óntico. La sección 3 muestra que la adopción de la tesis del colapso arriesga introducir la hipótesis del universo matemático. Desde la perspectiva de la concepción inferencial en (...) filosofía de las matemáticas aplicadas, la sección 4 examina aspectos epistémicos del rol de las matemáticas en la teorización científica, derivando distinciones entre estructuras matemáticas y estructuras físicas. El argumento concluye en la sección 5 indicando algunos límites para la presente estrategia. ABSTRACT Section 1 introduces what I call the collapse thesis, which holds that the boundaries of mathematical and physical structures blur or even vanish in certain areas of fundamental physics. Section 2 examines the claim that the indispensability of mathematics to fundamental physics requires the adoption of mathematical Platonism, this time concerning the reality of mathematical structures, as ontic structural realism contends. Section 3 demonstrates that the collapse thesis introduces the threat of the mathematical universe hypothesis. Then, from the perspective of the inferential conception in the philosophy of applied mathematics, section 4 examines epistemic features of the role of mathematics in scientific theorizing, drawing distinctions between mathematical and physical structures. Lastly, the argument closes in section 5 pointing out some of the limits of the proposed strategy for a distinction. (shrink)

This article examines the nineteenth-century debate about scientific method between John Stuart Mill and William Whewell. Contrary to standard interpretations (given, for example, by Achinstein, Buchdahl, Butts, and Laudan), I argue that their debate was not over whether to endorse an inductive methodology but rather over the nature of inductive reasoning in science and the types of conclusions yielded by it. Whewell endorses, while Mill rejects, a type of inductive reasoning in which inference is employed to find a property or (...) cause shared by the observed members of a class, which is generalized to all its members, including the unobserved ones. Because of this, Whewell’s inductivism, unlike Mill’s, is able to yield theoretical hypotheses referring to unob-servables such as molecules and light waves. This is contrary to the claims of some critics of inductivism who argue that inductivism is unable to yield such hypotheses. Moreover, I suggest that Whewell’s view of induction conforms more closely than Mill’s view to the practice of scientists such as Kepler, Newton, and Fresnel, who do attempt to discover laws involving unobservables. (shrink)

In this paper I demonstrate that, contrary to the standard interpretations, William Whewell's view of scientific method is neither that of the hypothetico-deductivist nor that of the retroductivist. Rather, he offers a unique inductive methodology, which he calls "discoverers' induction." After explicating this methodology, I show that Kepler's discovery of his first law of planetary motion conforms to it, as Whewell claims it does. In explaining Whewell's famous phrase about "happy guesses" in science, I suggest that Whewell intended a distinction (...) between "inductions," which can be empirically verified, and "mere hypotheses"--or guesses--which cannot. Finally, I argue that Whewell's discoverers' induction is a view worthy of our attention today, because it avoids a number of problems faced by prominent alternative methodologies. (shrink)

The arrow of time is a familiar phenomenon we all know from our experience: we remember the past but not the future and control the future but not the past. However, it takes an effort to keep records of the past, and to affect the future. For example, it would take an immense effort to unmix coffee and milk, although we easily mix them. Such time directed phenomena are sub- sumed under the Second Law of Thermodynamics. This law characterizes our (...) experience of the arrow of time in terms of an increase of a theoretical magnitude called entropy. Statistical mechan- ics tries to explain the Second Law as an effect of the behavior of the microscopic particles that make up the universe. Since our senses are too coarse to see this microstructure, statistical mechanics describes our experience in terms of probability, or in terms of the partial information we have about the particles. In this paper we explain the workings of statistical mechanics; how it accounts for probability as an objective feature of the world based on the underlying dynamics; how it accounts for our memories of the past; how the statistical mechanical probability under- writes the Second Law; and how, at the same time, it leads to a violation of the Second Law by the so-called Maxwell’s Demon. (shrink)

Statistical mechanics is the name of the ongoing attempt to explain and predict certain phenomena, above all those described by thermodynamics on the basis of the fundamental theories of physics, in particular mechanics, together with certain auxiliary assumptions. In another paper in this journal, Foundations of statistical mechanics: Mechanics by itself, I have shown that some of the thermodynamic regularities, including the probabilistic ones, can be described in terms of mechanics by itself. But in order to prove those regularities, in (...) particular the time asymmetric ones, it is necessary to add to mechanics assumptions of three kinds, all of which are under debate in contemporary literature. One kind of assumptions concerns measure and probability, and here, a major debate is around the notion of “typicality.” A second assumption concerns initial conditions, and here, the debate is about the nature and status of the so-called past hypothesis. The third kind of assumptions concerns the dynamics, and here, the possibility and significance of “Maxwell's Demon” is the main topic of discussions. This article describes these assumptions and examines the justification for introducing them, emphasizing the contemporary debates around them. (shrink)

This article compares treatments of the Stern–Gerlach experiment across different physical theories, building up to a novel analysis of electron spin measurement in the context of classical Dirac field theory. Modeling the electron as a classical rigid body or point particle, we can explain why the entire electron is always found at just one location on the detector but we cannot explain why there are only two locations where the electron is ever found. Using non-relativistic or relativistic quantum mechanics, we (...) can explain both uniqueness and discreteness. Moving to more fundamental physics, both features can be explained within a quantum theory of the Dirac field. In a classical theory of the Dirac field, the rotating charge of the electron can split into two pieces that each hit the detector at a different location. In this classical context, we can explain a feature of electron spin that is often described as distinctively quantum but we cannot explain another feature that could be explained within any of the other theories. (shrink)

The dynamics of neural populations capture the laws of the mindThis paper focuses on the level of neural networks. Examining the case of recurrent neural networks, the paper argues that the dynamics of neural populations form a privileged level of explanation in cognitive science. According to Schöner, this level is privileged, because it enables cognitive scientists to discover the laws governing organisms’ cognition and behaviour.

This paper develops a means–end analysis of an inductive problem that arises in particle physics: how to infer from observed reactions conservation principles that govern all reactions among elementary particles. I show that there is a reliable inference procedure that is guaranteed to arrive at an empirically adequate set of conservation principles as more and more evidence is obtained. An interesting feature of reliable procedures for finding conservation principles is that in certain precisely defined circumstances they must introduce hidden particles. (...) Among the reliable inductive methods there is a unique procedure that minimizes convergence time as well as the number of times that the method revises its conservation principles. Thus the aims of reliable, fast and steady convergence to an empirically adequate theory single out a unique optimal inference for a given set of observed reactions—including prescriptions for when exactly to introduce hidden particles. (shrink)

We give an overview of the practice of developing and using complex climate models, as seen from experiences in a major climate modelling center and through participation in the Coupled Model Intercomparison Project. We discuss the construction and calibration of models; their evaluation, especially through use of out-of-sample tests; and their exploitation in multi-model ensembles to identify biases and make predictions. We stress that adequacy or utility of climate models is best assessed via their skill against more naïve predictions. The (...) framework we use for making inferences about reality using simulations is naturally Bayesian, and has many points of contact with more familiar examples of scientific epistemology. While the use of complex simulations in science is a development that changes much in how science is done in practice, we argue that the concepts being applied fit very much into traditional practices of the scientific method, albeit those more often associated with laboratory work. (shrink)