Five-year-old children categorized as skilled versus unskilled counters were given verbal estimation and number word comprehension tasks with numerosities 20 – 120. Skilled counters showed a linear relation between number words and nonsymbolic numerosities. Unskilled counters showed the same linear relation for smaller numbers to which they could count, but not for larger number words. Further tasks indicated that unskilled counters failed even to correctly order large number words differing by a 2 : 1 ratio, whereas they performed well on (...) this task with smaller numbers, and performed well on a nonsymbolic ordering task with the same numerosities. These findings provide evidence that large, approximate numerosity representations become linked to number words around the time that children learn to count to those words reliably. (shrink)
Although children take over a year to learn the meanings of the first three number words, they eventually master the logic of counting and the meanings of all the words in their count list. Here, we ask whether children’s knowledge applies to number words beyond those they have mastered: Does a child who can only count to 20 infer that number words above ‘twenty’ refer to exact cardinal values? Three experiments provide evidence for this understanding in preschool children. Before beginning (...) formal education or gaining counting skill, children possess a productive symbolic system for representing number. q 2005 Published by Elsevier B.V. (shrink)
We are discovering more and more about the human genotypes and about the connections between genotype and behaviour. Do these advances in genetic information threaten our free will? This paper offers a philosopher’s perspective on the question.
Alan Garfinkel (1981) and Bas van Fraassen (1980), among others, have proposed a contrastive theory of explanation, according to which the proper form of an explanatory why-question is not simply "Why P?" but "Why P rather than Q?". Dennis Temple (1988) has argued in this journal that the contrastive explanandum "P rather than Q" is equivalent to the conjunction, "P and not-Q". I show that the contrast is not equivalent to the conjunction, nor to other plausible noncontrastive candidates. I then (...) consider David Lewis's (1986) proposal for the way contrasts determine an explanatory cause, which does not require recasting the contrastive explanandum. Lewis's proposal is found to be unacceptable, but it suggests an improvement that shows contrastive explanations to employ a mechanism of "causal triangulation", similar to Mill's method of difference. (shrink)
Earlier in this volume, Wesley Salmon has given a characteristically clear and trenchant critique of the account of non-demonstrative reasoning known by the slogan `Inference to the Best Explanation'. As a long-time fan of the idea that explanatory considerations are a guide to inference, I was delighted by the suggestion that Wes and I might work together on a discussion of the issues. In the event, this project has exceeded my high expectations, for in addition to the intellectual gain that (...) comes from the careful study of his essay, I have benefited enormously from the stream of illuminating emails and faxes that Wes has sent me during our collaboration. Doing philosophy together has been an education and a pleasure. Salmon's essay would place Inference to the Best Explanation beyond the pale of acceptable philosophical accounts of inference. According to Salmon, Inference to the Best Explanation has serious internal difficulties and compares very unfavourably with Bayesian approaches to these matters. My aim in the following remarks is irenic. I hope to show that a number of the claimed difficulties either are not really difficulties or are avoidable. In some cases, the avoidance will require a mild reinterpretation of the account that lies behind the slogan `Inference to the Best Explanation'; in others, it will require admitting limits to the scope of the account. For I accept at the outset that Inference to the Best Explanation cannot possibly be the whole story about the assessment of scientific hypotheses. For me, the interesting idea is simply that we sometimes decide how likely a hypothesis is to be correct in part by considering how good an explanation it would provide, if it were correct. This is the idea of explanatory considerations providing a guide to inference, and this is the idea that I will here promote. (shrink)
There is a natural objection to the epistemic coherence of Bas van Fraassen’s use of a distinction between the observable and unobservable in his constructive empiricism, an objection that has been raised with particular clarity by Alan Musgrave. We outline Musgrave’s objection, and then consider how one might interpret and evaluate van Fraassen’s response. According to the constructive empiricist, observability for us is measured with respect to the epistemic limits of human beings qua measuring devices, limitations ‘which will be described (...) in detail in the final physics and biology’ (van Fraassen 1980: 17). In order for the constructive empiricist to determine what counts as observable, he will have to appeal to our best scientific theories of light, human physiology, and so forth. To put the same point in a slightly more abstract way, in order to draw a distinction between observable and unobservable entities, the constructive empiricist needs to use his best scientific theory of observability – call it T* – to tell him the identity of the observable entities. This raises an interesting difficulty. Constructive empiricism is the view that ‘science aims to give us theories that are empirically adequate; and acceptance of a theory involves as belief only that it is empirically adequate’ (van Fraassen 1980:12). When he accepts a theory, the constructive empiricist only believes the statements of his scientific theories that are about observable entities. Thus, in order to know which statements of a scientific theory to believe, the constructive empiricist needs to know which statements of that theory are about observable entities. In particular then, the constructive empiricist only believes the statements of his theory of observability T* that are about observable entities. Therefore, in order to know which statements of T* he can believe, the constructive empiricist needs to know which statements of T* are about observable entities. However, it is T* that tells the constructive empiricist what counts as an observable entity: the constructive empiricist therefore needs to use T* to tell him which statements of T* he can believe. The fact that the distinction drawn by T* must also apply to itself is not an immediate cause for alarm.. (shrink)
It was David Hume’s great sceptical argument about non-demonstrative reasoning—the problem of induction—that hooked me on philosophy. I am still wriggling, but in the present essay I will not consider how the Humean challenge to justify our inductive practices might be met; rather, I ask why we had to wait until Hume for the challenge to be raised. The question is a natural one to ask, given the intense interest in scepticism before Hume for as far back as we can (...) see in the history of philosophy, and given that Hume’s sceptical argument is so simple and so fundamental. It is not so easy to answer. I am no historian of philosophy, and given the pull that the problem of induction exerts on my own philosophical thinking, I know there is a considerable risk that the historical speculations I consider here will turn out to be worthlessly anachronistic. But I hope not. (shrink)
In their important book, Causation in the Law, H. L. A. Hart and Tony Honore argue that causation in the law is based on causation outside the law, that the causal principles the courts rely on to determine legal responsibility are based on distinctions exercised in ordinary causal judgments. A distinction that particularly concerns them is one that divides factors that are necessary or sine qua non for an effect into those that count as causes for purposes of legal responsibility (...) and those that do not. Hart and Honore claim that this distinction is often one of fact rather than of legal policy, and that the factual basis is to be found in the ordinary distinction we draw between causes and 'mere conditions'. If this claim is correct, we may hope to illuminate the legal distinction by articulating the principles behind the ordinary one. This is a challenging task since, as in the case of most cognitive skills, we are far better at making particular judgments than we are at stating the general principles that underlie them. Hart and Honore devote the first part of their book to this difficult task. We have, then, two large projects. One is to articulate our ordinary notion of causation, especially the distinction between cause and mere condition. This is the project of constructing an 'ordinary model'. The other is to argue for what we may call the 'shared concept claim', the claim that the concept of legal cause is based on the ordinary notion of causation, that 'causal judgments, though the law may have to systematize them, are not specifically legal. They appeal to a notion which is part of everyday life' (1985, p. lv; all references to follow are from this edition). This essay will focus on Hart and Honore's ordinary model, rather than on their shared concept claim. In my judgment, Hart and Honore's case for some version of the shared concept claim is strong, so they are right to maintain that a better understanding of our ordinary notion of.. (shrink)
Karl Popper attempted to give an account of scientific research as the rational pursuit of the truth about nature without any appeal to what he took to be the fictitious notion of non-demonstrative or inductive support. Deductive inference can be seen to be inference enough for science, he claimed, once we appreciate the power of data to refute theory. Many of the standard objections to Popper's account purport to show that his deductivism actually entails a radical scepticism about the possibility (...) of scientific knowledge. Some of these objections appear unanswerable in the context of the traditional analysis of knowledge as justified true belief; but this is neither a conception of knowledge that Popper himself accepted nor one that is currently in fashion. Reliabilism, the view that knowledge is a true belief generated by a reliable method, is now a popular replacement for the traditional analysis and one that is closer to Popper's own conception of knowledge. My aim in this essay is to consider in brief compass the prospects of a reliabilist reading of Popper's account of science. Such a reading makes it possible to turn some of the standard objections helps to show which of Popper's views should be accepted and which rejected. (shrink)
I argue against the tendency in the philosophy of science literature to link abduction to the inference to the best explanation (IBE), and in particular, to claim that Peircean abduction is a conceptual predecessor to IBE. This is not to discount either abduction or IBE. Rather the purpose of this paper is to clarify the relation between Peircean abduction and IBE in accounting for ampliative inference in science. This paper aims at a proper classification—not justification—of types of scientific reasoning. In (...) particular, I claim that Peircean abduction is an in-depth account of the process of generating explanatory hypotheses, while IBE, at least in Peter Lipton’s thorough treatment, is a more encompassing account of the processes both of generating and of evaluating scientific hypotheses. There is then a two-fold problem with the claim that abduction is IBE. On the one hand, it conflates abduction and induction, which are two distinct forms of logical inference, with two distinct aims, as shown by Charles S. Peirce; on the other hand it lacks a clear sense of the full scope of IBE as an account of scientific inference. (shrink)
Peter Lipton has attempted to flesh out a model of Inference to the Best Explanation (IBE) by clarifying explanation in terms of a causal model. But Lipton's account of explanation makes an adequate explanation depend on a principle which is virtually identical to Mill's Method of Difference. This has the result of collapsing IBE on Lipton's account of it into causal inference as conceived by the Causal-Inference model of induction. According to this model, many of our inductions (...) are inferences from effects to their probable causes, and Mill's Methods are canons to guide such inferences. Thus, Lipton's account of IBE fails to represent an advance over the already familiar Causal-Inference Model of induction. (shrink)
Peter Lipton has argued that understanding can exist in the absence of explanation. We argue that this does not denigrate explanation's importance to understanding. Specifically, we show that all of Lipton's examples are consistent with the idea that explanation is the ideal of understanding, i.e. other modes of understanding ought to be assessed by how well they replicate the understanding provided by a good and correct explanation. We defend this idea by showing that for all of Lipton's (...) examples of non-explanatory understanding of why p , there exists a correct and reasonably good explanation that would provide greater understanding of p. (shrink)
The anti-realist argument from underconsideration focuses on the fact that, when scientists evaluate theories, they only ever consider a subset of the theories that can account for the available data. As a result, when scientists judge one theory to be superior to competitor theories, they are not warranted in drawing the conclusion that the superior theory is likely true with respect to what it says about unobservable entities and processes. I defend the argument from underconsideration from the objections of Peter (...)Lipton. I argue that the inconsistency that Lipton claims to find in the argument vanishes once we understand what the anti-realist means when she claims that scientists are reliable. I also argue that collapsing the distinction between relative and absolute evaluations, as Lipton recommends, has its costs. Finally, I briefly examine Richard Boyd's influential defence of realism. (shrink)
In this article, I compare two varieties of abduction as reconstructive models for analysing discovery. The first is 'Hansonian abduction', which is based on N. R. Hanson's formulations of abduction. The other is 'Harmanian abduction', the Inference to the Best Explanation (IBE) model, formulated especially by Gilbert Harman. Peter Lipton has analysed processes of discovery on the basis of his developed form of Harmanian abduction. I argue that Hansonian abduction would, however, be a more apt model for this purpose. (...) As an example, I reconstruct, in a Hansonian manner, Ignaz Semmelweis's research on childbed fever and compare it to the IBE reconstruction of Lipton. I argue that Hansonian abduction is in accordance with Lipton's aim of taking into account the distinction between actual and potential explanations on the one hand, and between likely and lovely explanations on the other. I maintain that a developed version of Hansonian abduction combined with loveliness gives an important, new conceptual means for analysing processes of discovery. (shrink)
I propose that in some cases we may infer the truth of an hypothesis, since it is the only hypothesis left unrefuted by the evidence (a la Sherlock Holmes). Peter Lipton's description of the Semmelweis case seems to provide an example of this. But he takes it to be a case of interence to the best (loveliest) explanation. I locate this source of difference of opinion in Lipton's equation of evidence with (non-factive) observation. This equation gives us too (...) little evidence; and it makes observation insufficient to refute a hypothesis. I contrast this with refutation by a known proposition. (shrink)
According to the argument from underconsideration, since theory evaluation is comparative, and since scientists do not have good reasons to believe that they are epistemically privileged, it is unlikely that our best theories are true. In this paper, I examine two formulations of this argument, one based on van Fraassen’s “bad lot” premise and another based on what Lipton called the “no-privilege” premise. I consider several moves that scientific realists might make in response to these arguments. I then offer (...) a revised argument that is a middle ground between realism and anti-realism, or so I argue. (shrink)
I aim to show that one way of testing the mettle of a theory of scientific explanation is to inquire what that theory entails about the status of brute facts. Here I consider the nature of brute facts, and survey several contemporary accounts of explanation vis a vis this subject (the Friedman-Kitcher theory of explanatory unification, Humphreys' causal theory of explanation, and Lipton's notion of 'explanatory loveliness'). One problem with these accounts is that they seem to entail that (...) brute facts represent a gap in scientific understanding. I argue that brute facts are non-mysterious and indeed are even explainable by the lights of Salmon's ontic conception of explanation (which I endorse here). The plausibility of various models of explanation, I suggest, depends to some extent on the tendency of their proponents to focus on certain examples of explananda - I ponder brute facts qua explananda here as a way of helping us to recognize this dependency. (shrink)
The second edition of Peter Lipton’s classic text contains new and important material on the causal model of explanation, the relation of inference to the best explanation to the Bayesian account of scientific reasoning, how exactly explanation guides inference, and why we ought to think that explanatory virtues are truth-tropic. Lipton is a wonderfully clear writer and a thorough and subtle philosopher, and his book is both a student-friendly introduction to the issues addressed, and essential reading for expert (...) epistemologists and philosophers of science. Appeal to the notion of inference to the best explanation is ubiquitous in defences of scientific realism, but also elsewhere in philosophy where the explanatory virtues of theories are often the only purported grounds for accepting or rejecting them. Despite this, most authors are far from explicit about the details of inference to the best explanation, and Lipton’s book is the most sustained investigation of the relationship between explanation and inference currently available. Furthermore, Lipton is exemplary in his engagement with the problems his arguments face, and judiciously modest in his claims, though not so modest as to court triviality. Hence, the book is replete with interesting and careful arguments. Everyone interested in epistemology or philosophy of science ought to read this book. That said, in my discussion below I will concentrate on what I regard as problems with some of Lipton’s arguments. The model of explanation which he develops is contrastive and causal. Lipton is clear that he does not think all explanations are causal, but he does think that many are, especially in science, and. (shrink)
Marc Alspector-Kelly claims that Bas van Fraassen’s primary challenge to the scientific realist is for the realist to find a way to justify the use of some mode of inference that takes him from the world of observables to knowledge of the world of unobservables without thereby abandoning empiricism. It is argued that any effort to justify such an “inferential wand” must appeal either to synthetic a priori or synthetic a posteriori knowledge. This disjunction turns into a dilemma for the (...) empirically-minded realist as either disjunct leads to unwanted consequences. In this paper, I split the horns of this dilemma by arguing that the realist can justify one particular such mode of inference – abduction – without committing himself to rationalism. The realist may justify this mode of inference by appealing to the analytic a priori axioms of the probability calculus. I show that Peter Lipton’s tripartite defense of abduction constitutes such a method of justification. (shrink)
It is claimed that Kuipers' approach to explanation opens the possibility for a further refinement of his own refined HD method for the evaluation of theories. One severe problem for the HD method, refined or not, is theory-ladeness. Given that experimental results are theory-laden, the comparative evaluation of alternative hypotheses is always relative to background knowledge. This difficulty can be avoided by supplementing HD considerations with the principle of inference to the best explanation. The authors sketch a program for doing (...) this. The general idea plays on some similarities between Kuipers' account of explanation and Lipton's. The former, however, is considered more flexible than the latter, which makes it even more attractive for the purpose under consideration. (shrink)
Van Fraassen's argument from the "bad lot" challenges realist interpretations of inference to the best explanation (IBE). In this paper I begin by discussing the replies suggested by S. Psillos and P. Lipton. I do not find them convincing. However, I think that van Fraassen's argument is flawed. First of all, it is a non sequitur. Secondly, I think that the real target for the scientific realist is the underlying assumption that epistemic justification results from a comparative assessment among (...) rival explanations. I argue that justification for believing an explanation does not depend on comparison, but on the extent that criteria of explanatory goodness are fulfilled. Therefore, in addition to offering more or less intuitive IBE-tailored arguments, realists fond of IBE should have to analyze the implicit standards of explanatory goodness. In the last section I distinguish between contextual and transcontextual criteria concerning explanatory goodness. Concerning the latter, I focus on consilience, simplicity, analogy and conservatism. \\\ Un argumento empleado por van Fraassen contra las interpretaciones realistas de la inferencia a la mejor explicación es el argumento "del mal lote". El articulo comienza discutiendo las réplicas de S. Psillos y P. Lipton. Aunque ninguna me parece convincente, pienso que el argumento de van Fraassen no resiste un examen cuidadoso. En primer lugar, la conclusión antirrealista que él extrae es un non sequitur. Además, el argumento parte de un supuesto muy cuestionable, a saber, que la justificación de una explicacion es resultado de una comparacion con sus rivales. En mi opinion, la justificación no depende de esto, sino del grado en que la explicacion satisface ciertos criterios de bondad explicativa, independientemente de que haya o no comparación. En consecuencia, la socorrida estrategia de defender el realismo cientifico basándose en la IBE pasa necesariamente por un análisis de los criterios implicitos de bondad explicativa. Mi propuesta es distinguir entre criterios contextuales y transcontextuales. En los últimos incluyo: la diversidad de la evidencia explicada, la simplicidad, la analogia y el conservadurismo. (shrink)
[Peter Lipton] From a reliabilist point of view, our inferential practices make us into instruments for determining the truth value of hypotheses where, like all instruments, reliability is a central virtue. I apply this perspective to second-order inductions, the inductive assessments of inductive practices. Such assessments are extremely common, for example whenever we test the reliability of our instruments or our informants. Nevertheless, the inductive assessment of induction has had a bad name ever since David Hume maintained that any (...) attempt to justify induction by means of an inductive argument must beg the question. I will consider how the inductive justification of induction fares from the reliabilist point of view. I will also consider two other well-known arguments that can be construed as inductive assessments of induction. One is the miracle argument, according to which the truth of scientific theories should be inferred as the best explanation of their predictive success; the other is the disaster argument, according to which we should infer that all present and future theories are false on the grounds that all past theories have been found to be false. \\\ [John Worrall] Science seems in some ways to have been remarkably successful. What does this success tell us about the epistemological status of current scientific claims? Peter Lipton considers various meta-inductive arguments each of which start from premises about science's 'track record'. I show that his endorsements of the 'strongest' of these are, on analysis, remarkably weak. I argue that this is a reflection of difficulties within the general epistemological framework that he adopts-that of reliabilism. Finally, I briefly outline the quite different approach that I take to this issue, in the process responding to Lipton's criticisms of the 'pessimistic meta-induction'. (shrink)
[Peter Lipton] From a reliabilist point of view, our inferential practices make us into instruments for determining the truth value of hypotheses where, like all instruments, reliability is a central virtue. I apply this perspective to second-order inductions, the inductive assessments of inductive practices. Such assessments are extremely common, for example whenever we test the reliability of our instruments or our informants. Nevertheless, the inductive assessment of induction has had a bad name ever since David Hume maintained that any (...) attempt to justify induction by means of an inductive argument must beg the question. I will consider how the inductive justification of induction fares from the reliabilist point of view. I will also consider two other well-known arguments that can be construed as inductive assessments of induction. One is the miracle argument, according to which the truth of scientific theories should be inferred as the best explanation of their predictive success; the other is the disaster argument, according to which we should infer that all present and future theories are false on the grounds that all past theories have been found to be false. \\\ [John Worrall] Science seems in some ways to have been remarkably successful. What does this success tell us about the epistemological status of current scientific claims? Peter Lipton considers various meta-inductive arguments each of which start from premises about science's 'track record'. I show that his endorsements of the 'strongest' of these are, on analysis, remarkably weak. I argue that this is a reflection of difficulties within the general epistemological framework that he adopts-that of reliabilism. Finally, I briefly outline the quite different approach that I take to this issue, in the process responding to Lipton's criticisms of the 'pessimistic meta-induction'. (shrink)
This paper evaluates the claim that it is possible to use nature’s variation in conjunction with retention and selection on the one hand, and the absence of ultimate groundedness of hypotheses generated by the human mind as it knows on the other hand, to discard the ascription of ultimate certainty to the rationality of human conjectures in the cognitive realm. This leads to an evaluation of the further assumption that successful hypotheses with specific applications, in other words heuristics, seem to (...) have a firm footing because they were useful in another context. I argue that usefulness evaluated through adaptation misconstrues the search for truth, and that it is possible to generate talk of randomness by neglecting aspects of a system’s insertion into a larger situation. The framing of the problem in terms of the elimination of unfit hypotheses is found to be unsatisfying. It is suggested that theories exist in a dimension where they can be kept alive rather than dying as phenotypes do. The proposal that the subconscious could suggest random variations is found to be a category mistake. A final appeal to phenomenology shows that this proposal is orphan in the history of epistemology, not in virtue of its being a remarkable find, but rather because it is ill-conceived. (shrink)
