Computational models: a modest role for content

The computational theory of mind construes the mind as an information-processor and cognitive capacities as essentially representational capacities. Proponents of the view (hereafter, ‘computationalists’) claim a central role for representational content in computational models of these capacities. In this paper I argue that the standard view of the role of representational content in computational models is mistaken; I argue that representational content is to be understood as a gloss on the computational characterization of a cognitive process.     

Embodied cognition and linguistic comprehension

Traditionally, the language faculty was supposed to be a device that maps linguistic inputs to semantic or conceptual representations. These representations themselves were supposed to be distinct from the representations manipulated by the hearer’s perceptual and motor systems. Recently this view of language has been challenged by advocates of embodied cognition. Drawing on empirical studies of linguistic comprehension, they have proposed that the language faculty reuses the very representations and processes deployed in perceiving and acting. I review some of the evidence and arguments in favor of the embodied view of language comprehension, and argue that none of it is conclusive. Moreover, the embodied view itself blurs two important distinctions: first, the distinction between linguistic comprehension and its typical consequences; and second, the distinction between representational content and vehicles. Given that these distinctions are well-motivated, we have good reason to reject the embodied view of linguistic understanding.     

Signs, toy models, and the a priori: from Helmholtz to Wittgenstein

The Marburg neo-Kantians argue that Hermann von Helmholtz’s empiricist account of the a priori does not account for certain knowledge, since it is based on a psychological phenomenon, trust in the regularities of nature. They argue that Helmholtz’s account raises the ‘problem of validity’ (Gültigkeitsproblem): how to establish a warranted claim that observed regularities are based on actual relations. I reconstruct Heinrich Hertz’s and Ludwig Wittgenstein’s Bild theoretic answer to the problem of validity: that scientists and philosophers can depict the necessary a priori constraints on states of affairs in a given system, and can establish whether these relations are actual relations in nature. The analysis of necessity within a system is a lasting contribution of the Bild theory. However, Hertz and Wittgenstein argue that the logical and mathematical sentences of a Bild are rules, tools for constructing relations, and the rules themselves are meaningless outside the theory. Carnap revises the argument for validity by attempting to give semantic rules for translation between frameworks. Russell and Quine object that pragmatics better accounts for the role of a priori reasoning in translating between frameworks. The conclusion of the tale, then, is a partial vindication of Helmholtz’s original account.     

The intelligibility of motion and construction: Descartes’ early mathematics and metaphysics, 1619-1637

I argue for an interpretation of the connection between Descartes’ early mathematics and metaphysics that centers on the standard of geometrical intelligibility that characterizes Descartes’ mathematical work during the period 1619 to 1637. This approach remains sensitive to the innovations of Descartes’ system of geometry and, I claim, sheds important light on the relationship between his landmark Geometry (1637) and his first metaphysics of nature, which is presented in Le monde (1633). In particular, I argue that the same standard of clear and distinct motions for construction that allows Descartes to distinguish ‘geometric’ from ‘imaginary’ curves in the domain of mathematics is adopted in Le monde as Descartes details God’s construction of nature. I also show how, on this interpretation, the metaphysics of Le monde can fruitfully be brought to bear on Descartes’ attempted solution to the Pappus problem, which he presents in Book I of the Geometry. My general goal is to show that attention to the standard of intelligibility Descartes invokes in these different areas of inquiry grants us a richer view of the connection between his early mathematics and philosophy than an approach that assumes a common method is what binds his work in these domains together.     

Kant and the scope of analogy in the life sciences

In the present paper I investigate the role that analogy plays in eighteenth-century biology and in Kant's philosophy of biology. I will argue that according to Kant, biology, as it was practiced in the eighteenth century, is fundamentally based on analogical reflection. However, precisely because biology is based on analogical reflection, biology cannot be a proper science. I provide two arguments for this interpretation. First, I argue that although analogical reflection is, according to Kant, necessary to comprehend the nature of organisms, it is also necessarily insufficient to fully comprehend the nature of organisms. The upshot of this argument is that for Kant our understanding of organisms is necessarily limited. Second, I argue that Kant did not take biology to be a proper science because biology was based on analogical arguments. I show that Kant stemmed from a philosophical tradition that did not assign analogical arguments an important justificatory role in natural science. Analogy, according to this conception, does not provide us with apodictically certain cognition. Hence, sciences based on analogical arguments cannot constitute proper sciences.     

Margaret Cavendish and Joseph Glanvill: science, religion, and witchcraft

Many scholars point to the close association between early modern science and the rise of rational arguments in favour of the existence of witches. For some commentators, it is a poor reflection on science that its methods so easily lent themselves to the unjust persecution of innocent men and women. In this paper, I examine a debate about witches between a woman philosopher, Margaret Cavendish (1623-1673), and a fellow of the Royal Society, Joseph Glanvill (1636-1680). I argue that Cavendish is the voice of reason in this exchange—not because she supports the modern-day view that witches do not exist, but because she shows that Glanvill’s arguments about witches betray his own scientific principles. Cavendish’s responses to Glanvill suggest that, when applied consistently, the principles of early modern science could in fact promote a healthy scepticism toward the existence of witches.     

Two arguments for scientific realism unified

Inferences from scientific success to the approximate truth of successful theories remain central to the most influential arguments for scientific realism. Challenges to such inferences, however, based on radical discontinuities within the history of science, have motivated a distinctive style of revision to the original argument. Conceding the historical claim, selective realists argue that accompanying even the most revolutionary change is the retention of significant parts of replaced theories, and that a realist attitude towards the systematically retained constituents of our scientific theories can still be defended. Selective realists thereby hope to secure the argument from success against apparent historical counterexamples. Independently of that objective, historical considerations have inspired a further argument for selective realism, where evidence for the retention of parts of theories is itself offered as justification for adopting a realist attitude towards them. Given the nature of these arguments from success and from retention, a reasonable expectation is that they would complement and reinforce one another, but although several theses purport to provide such a synthesis the results are often unconvincing. In this paper I reconsider the realist’s favoured type of scientific success, novel success, offer a revised interpretation of the concept, and argue that a significant consequence of reconfiguring the realist’s argument from success accordingly is a greater potential for its unification with the argument from retention.     

Newton’s notion and practice of unification

In this paper I deal with a neglected topic with respect to unification in Newton’s Principia. I will clarify Newton’s notion (as can be found in Newton’s utterances on unification) and practice of unification (its actual occurrence in his scientific work). In order to do so, I will use the recent theories on unification as tools of analysis (Kitcher, Salmon and Schurz). I will argue, after showing that neither Kitcher’s nor Schurz’s account aptly capture Newton’s notion and practice of unification, that Salmon’s later work is a good starting point for analysing this notion and its practice in the Principia. Finally, I will supplement Salmon’s account in order to answer the question at stake.     

On geometric objects,the non-existence of a gravitational stress-energy tensor,and the uniqueness of the Einstein field equation

The question of the existence of gravitational stress-energy in general relativity has exercised investigators in the field since the inception of the theory. Folklore has it that no adequate definition of a localized gravitational stress-energetic quantity can be given. Most arguments to that effect invoke one version or another of the Principle of Equivalence. I argue that not only are such arguments of necessity vague and hand-waving but, worse, are beside the point and do not address the heart of the issue. Based on a novel analysis of what it may mean for one tensor to depend in the proper way on another, which, en passant, provides a precise characterization of the idea of a “geometric object”, I prove that, under certain natural conditions, there can be no tensor whose interpretation could be that it represents gravitational stress-energy in general relativity. It follows that gravitational energy, such as it is in general relativity, is necessarily non-local. Along the way, I prove a result of some interest in own right about the structure of the associated jet bundles of the bundle of Lorentz metrics over spacetime. I conclude by showing that my results also imply that, under a few natural conditions, the Einstein field equation is the unique equation relating gravitational phenomena to spatiotemporal structure, and discuss how this relates to the non-localizability of gravitational stress-energy. The main theorem proven underlying all the arguments is considerably stronger than the standard result in the literature used for the same purposes (Lovelock's theorem of 1972): it holds in all dimensions (not only in four); it does not require an assumption about the differential order of the desired concomitant of the metric; and it has a more natural physical interpretation.     

The material theory of induction and the epistemology of thought experiments

John D. Norton is responsible for a number of influential views in contemporary philosophy of science. This paper will discuss two of them. The material theory of induction claims that inductive arguments are ultimately justified by their material features, not their formal features. Thus, while a deductive argument can be valid irrespective of the content of the propositions that make up the argument, an inductive argument about, say, apples, will be justified (or not) depending on facts about apples. The argument view of thought experiments claims that thought experiments are arguments, and that they function epistemically however arguments do. These two views have generated a great deal of discussion, although there hasn't been much written about their combination. I argue that despite some interesting harmonies, there is a serious tension between them. I consider several options for easing this tension, before suggesting a set of changes to the argument view that I take to be consistent with Norton's fundamental philosophical commitments, and which retain what seems intuitively correct about the argument view. These changes require that we move away from a unitary epistemology of thought experiments and towards a more pluralist position.     

Explanation,understanding, and unrealistic models

How can false models be explanatory? And how can they help us to understand the way the world works? Sometimes scientists have little hope of building models that approximate the world they observe. Even in such cases, I argue, the models they build can have explanatory import. The basic idea is that scientists provide causal explanations of why the regularity entailed by an abstract and idealized model fails to obtain. They do so by relaxing some of its unrealistic assumptions. This method of ‘explanation by relaxation’ captures the explanatory import of some important models in economics. I contrast this method with the accounts that Daniel Hausman and Nancy Cartwright have provided of explanation in economics. Their accounts are unsatisfactory because they require that the economic model regularities obtain, which is rarely the case. I go on to argue that counterfactual regularities play a central role in achieving ‘understanding by relaxation.’ This has a surprising implication for the relation between explanation and understanding: Achieving scientific understanding does not require the ability to explain observed regularities.     

Reflections on Kant’s concept (and intuition) of space

In this paper, I investigate an important aspect of Kant’s theory of pure sensible intuition. I argue that, according to Kant, a pure concept of space warrants and constrains intuitions of finite regions of space. That is, an a priori conceptual representation of space provides a governing principle for all spatial construction, which is necessary for mathematical demonstration as Kant understood it.     

On the epistemological foundations of the law of the lever

In this paper I challenge Paolo Palmieri’s reading of the Mach—Vailati debate on Archimedes’ proof of the law of the lever. I argue that the actual import of the debate concerns the possible epistemic (as opposed to merely pragmatic) role of mathematical arguments in empirical physics, and that construed in this light Vailati carries the upper hand. This claim is defended by showing that Archimedes’ proof of the law of the lever is not a way of appealing to a non-empirical source of information, but a way of explicating the mathematical structure that can represent the empirical information at our disposal in the most general way.     

Modelling and representing: An artefactual approach to model-based representation

The recent discussion on scientific representation has focused on models and their relationship to the real world. It has been assumed that models give us knowledge because they represent their supposed real target systems. However, here agreement among philosophers of science has tended to end as they have presented widely different views on how representation should be understood. I will argue that the traditional representational approach is too limiting as regards the epistemic value of modelling given the focus on the relationship between a single model and its supposed target system, and the neglect of the actual representational means with which scientists construct models. I therefore suggest an alternative account of models as epistemic tools. This amounts to regarding them as concrete artefacts that are built by specific representational means and are constrained by their design in such a way that they facilitate the study of certain scientific questions, and learning from them by means of construction and manipulation.     

Cartesian analysis and synthesis

This paper aims to provide an explication of the meaning of ‘analysis’ and ‘synthesis’ in Descartes’ writings. In the first part I claim that Descartes’ method is entirely captured by the term ‘analysis’, and that it is a method of theory elaboration that fuses the modern methods of discovery and confirmation in one enterprise. I discuss Descartes’ methodological writings, assess their continuity and coherence, and I address the major shortcoming of previous interpretations of Cartesian methodology. I also discuss the Cartesian method in the context of other conceptions of scientific method of that era and argue that Descartes’ method significantly transforms these conceptions. In the second part I argue that mathematical and natural-philosophical writings exhibit this kind of analysis. To that effect I examine in Descartes’ writings on the method as used in mathematics, and Descartes’ account of the discovery of the nature of the rainbow in the Meteors. Finally, I briefly assess Descartes’ claim regarding the universality of his method.     

Evidence and explanation in Cicero's On Divination

In this paper, I examine Cicero's oft-neglected De Divinatione, a dialogue investigating the legitimacy of the practice of divination. First, I offer a novel analysis of the main arguments for divination given by Quintus, highlighting the fact that he employs two logically distinct argument forms. Next, I turn to the first of the main arguments against divination given by Marcus. Here I show, with the help of modern probabilistic tools, that Marcus' skeptical response is far from the decisive, proto-naturalistic assault on superstition that it is sometimes portrayed to be. Then, I offer an extended analysis of the second of the main arguments against divination given by Marcus. Inspired by Marcus' second main argument, I formulate, explicate, and defend a substantive principle of scientific methodology that I call the “Ciceronian Causal-Nomological Requirement” (CCR). Roughly, this principle states that causal knowledge is essential for relying on correlations in predictive inference. Although I go on to argue that Marcus' application of the CCR in his debate with Quintus is dialectically inadequate, I conclude that De Divinatione deserves its place in Cicero's philosophical corpus, and that ultimately, its significance for the history and philosophy of science ought to be recognized.     

Harmony and simplicity: aesthetic virtues and the rise of testability

Copernicus claimed that his system was preferable in part on the grounds of its superior harmony and simplicity, but left very few hints as to what was meant by these terms. Copernicus’s pupil, Rheticus, was more forthcoming. Kepler, influenced by Rheticus, articulated further the nature of the virtues of harmony and simplicity. I argue that these terms are metaphors for the structural features of the Copernican system that make it more able to effectively exploit the available data. So it is a mistake to conclude that early Copernicans could only offer aesthetic or pragmatic arguments; they could and did offer evidential ones as well. Moreover, the evidential arguments they offered parallel current arguments in the philosophical literature.     

Structure,scale and emergence

In this paper I consider the structures that chemists and physicists attribute at the molecular scale to substances and materials of various kinds, and how they relate to structures and processes at other scales. I argue that the structure of a substance is the set of properties and relations which are preserved across all the conditions in which it can be said to exist. In short, structure is abstraction. On the basis of this view, and using concrete examples, I argue that structures, and therefore the chemical substances and other materials to which they are essential, are emergent. Firstly, structures themselves are scale-dependent because they can only exist within certain physical conditions, and a single substance may have different structures at different scales (of length, time and energy). Secondly, the distinctness of both substances and structures is a scale-dependent relationship: above a certain point, two distinct possibilities may become one. Thirdly, the necessary conditions for composition, for both substances and molecular species, are scale-dependent. To know whether a group of nuclei and electrons form a molecule it is not enough to consider energy alone: one also has to know about their environment and the lifetime over which the group robustly hangs together.