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

Inference to the best explanation—or, IBE—tells us to infer from the available evidence to the hypothesis which would, if correct, best explain that evidence. As Peter Lipton puts it, the core idea driving IBE is that explanatory considerations are a guide to inference. But what is the epistemic status of IBE, itself? One issue of contemporary interest is whether it is possible to provide a justification for IBE itself which is non- objectionably circular. We aim to carve out some (...) new space in this debate. In particular, we suggest that the matter of whether a given rule-circular argument is objectionably circular itself depends crucially on some subtle distinctions which have been made in the recent literature on perceptual warrant. By bringing these debates together, a principled reason emerges for why some kinds of rule-circular justifications for IBE are considerably less objectionable than others. (shrink)

The idea that a serious threat to scientific realism comes from unconceived alternatives has been proposed by van Fraassen, Sklar, Stanford and Wray among others. Peter Lipton's critique of this threat from underconsideration is examined briefly in terms of its logic and its applicability to the case of space-time and particle physics. The example of space-time and particle physics indicates a generic heuristic for quantitative sciences for constructing potentially serious cases of underdetermination, involving one-parameter family of rivals T_m that (...) work as a team rather than as a single rival against default theory T_0. In important examples this new parameter has a physical meaning and makes a crucial _conceptual_ difference, shrinking the symmetry group and in some case putting gauge freedom, formal indeterminism vs. determinism, the presence of the hole argument, etc., at risk. Methodologies akin to eliminative induction or tempered subjective Bayesianism are more demonstrably reliable than the custom of attending only to "our best theory": they can lead either to a serious rivalry or to improved arguments for the favorite theory. The example of General Relativity vs. massive spin 2 gravity, a recent topic in the physics literature, is discussed. Arguably the General Relativity and philosophy literatures have ignored the most serious rival to General Relativity. (shrink)

How do we go about weighing evidence, testing hypotheses, and making inferences? According to the model of _Inference to the Best Explanation_, we work out what to infer from the evidence by thinking about what would actually explain that evidence, and we take the ability of a hypothesis to explain the evidence as a sign that the hypothesis is correct. In _Inference to the Best Explanation_, Peter Lipton gives this important and influential idea the development and assessment it deserves. (...) The second edition has been substantially enlarged and reworked, with a new chapter on the relationship between explanation and Bayesianism, and an extension and defence of the account of contrastive explanation. It also includes an expanded defence of the claims that our inferences really are guided by diverse explanatory considerations, and that this pattern of inference can take us towards the truth. This edition of _Inference to the Best Explanation_ has also been updated throughout and includes a new bibliography. (shrink)

"How do we go about weighing evidence, testing hypotheses and making inferences? According to the model of 'inference to the Best explanation', we work out what to inter from the evidence by thinking about what would actually explain that evidence, and we take the ability of a hypothesis to explain the evidence as a sign that the hypothesis is correct. In inference to the Best Explanation, Peter Lipton gives this important and influential idea the development and assessment it deserves." (...) "The second edition has been substantially enlarged and reworked, with a new chapter on the relationship between explanation and Bayesianism, and an extension and defence of the account of contractive explanation. It also includes an expanded defence of the claims that our inferences really are guided by diverse explanatory considerations, and that this pattern of inference can take us towards the truth. This edition of Inference to the Best Explanation has also been updated throughout and incudes a new bibliography."--BOOK JACKET. (shrink)

How do we go about weighing evidence, testing hypotheses, and making inferences? The model of " inference to the best explanation " -- that we infer the hypothesis that would, if correct, provide the best explanation of the available evidence--offers a compelling account of inferences both in science and in ordinary life. Widely cited by epistemologists and philosophers of science, IBE has nonetheless remained little more than a slogan. Now this influential work has been thoroughly revised and updated, and features (...) a new introduction and two new chapters. Inference to the Best Explanation is an unrivaled exposition of a theory of particular interest in the fields both of epistemology and the philosophy of science. (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)

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)

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)

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 wellknown 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. (shrink)

Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgments can be made on deductive grounds. If an experimental result strictly contradicts a hypothesis, then the truth of (...) the data deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is non-demonstrative, or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. (shrink)

According to a causal model of explanation, we explain phenomena by giving their causes or, where the phenomena are themselves causal regularities, we explain them by giving a mechanism linking cause and effect. If we explain why smoking causes cancer, we do not give the cause of this causal connection, but we do give the causal mechanism that makes it. The claim that to explain is to give a cause is not only natural and plausible, but it also avoids many (...) of the objections to other accounts of explanation, such as the views that to explain is to give a reason to believe the phenomenon occurred, to somehow make the phenomenon familiar, or to give a Deductive-Nomological argument. Unlike the reason for belief account, a causal model makes a clear distinction between understanding why a phenomenon occurs and merely knowing that it does, and the model does so in a way that makes understanding unmysterious and objective. Understanding is not some sort of super-knowledge, but simply more knowledge: knowledge of the phenomenon and knowledge of its causal history. A causal model makes it clear how something can explain without itself being explained, and so avoids the regress of whys, since we can know a phenomenon's cause without knowing the cause of the cause. It also accounts for legitimate self-evidencing explanations, explanations where the phenomenon is an essential part of the evidence that the explanation is correct, so the explanation can not supply a non-circular reason for believing the phenomenon occurred. There is no barrier to knowing a cause through its effects and also knowing that it is their cause. The speed of recession of a star explains its observed red-shift, even though the shift is an essential part of the evidence for its speed of recession. The model also avoids the most serious objection to the familiarity view, which is that some phenomena are familiar yet not understood, since a phenomenon can be perfectly familiar, such as the blueness of the sky or the fact that the same side of the moon always faces the earth, even if we do not know its cause. Finally, a causal model avoids many of the objections to the Deductive-Nomological model. Ordinary explanations do not have to meet the requirements of the Deductive-Nomological model, because one does not need to give a law to give a cause, and one does not need to know a law to have good reason to believe that a cause is a cause. As for the notorious over-permissiveness of the Deductive-Nomological model, the reason recession explains red-shift but not conversely, is simply that causes explain effects but not conversely, and the reason a conjunction of laws does not explain its conjuncts is that conjunctions do not cause their conjuncts. (shrink)

This paper considers a central objection to evolutionary epistemology. The objection is that biological and epistemic development are not analogous, since while biological variation is blind, epistemic variation is not. The generation of hypotheses, unlike the generation of genotypes, is not random. We argue that this objection is misguided and show how the central analogy of evolutionary epistemology can be preserved. The core of our reply is that much epistemic variation is indeed directed by heuristics, but these heuristics are analogous (...) to biological preadaptations which account for the evolution of complex organs. We also argue that many of these heuristics or epistemic preadaptations are not innate but were themselves generatedby a process of blind variation and selective retention. (shrink)

Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...) forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgments can be make on deductive grounds. If an experimental result strictly contradicts a hypothesis, then the truth of (...) the evidence deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is nondemonstrative or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. (shrink)

Inspired by recent breakthroughs in predictive modeling, practitioners in both industry and government have turned to machine learning with hopes of operationalizing predictions to drive automated decisions. Unfortunately, many social desiderata concerning consequential decisions, such as justice or fairness, have no natural formulation within a purely predictive framework. In efforts to mitigate these problems, researchers have proposed a variety of metrics for quantifying deviations from various statistical parities that we might expect to observe in a fair world and offered a (...) variety of algorithms in attempts to satisfy subsets of these parities or to trade o the degree to which they are satised against utility. In this paper, we connect this approach to fair machine learning to the literature on ideal and non-ideal methodological approaches in political philosophy. The ideal approach requires positing the principles according to which a just world would operate. In the most straightforward application of ideal theory, one supports a proposed policy by arguing that it closes a discrepancy between the real and the perfectly just world. However, by failing to account for the mechanisms by which our non-ideal world arose, the responsibilities of various decision-makers, and the impacts of proposed policies, naive applications of ideal thinking can lead to misguided interventions. In this paper, we demonstrate a connection between the fair machine learning literature and the ideal approach in political philosophy, and argue that the increasingly apparent shortcomings of proposed fair machine learning algorithms reflect broader troubles faced by the ideal approach. We conclude with a critical discussion of the harms of misguided solutions, a reinterpretation of impossibility results, and directions for future research. (shrink)

Most laws are ceteris paribus (cp) laws: they say not that all Fs are G but only that All Fs are G all else being equal. Most philosophical accounts of laws, however, have focused on strict laws. This paper considers how some of the standard philosophical problems about laws change when we switch attention from strict to cp laws and what special problems these laws raise. It is argued that some cp laws do not simply reflect the complexity of the (...) world and the limitations of our minds. Correctly interpreted, they reveal the simplicity that underlies the complexity, a simplicity that it is without our cognitive powers to grasp. (shrink)

Should we regard Jennifer Lackey’s ‘Creationist Teacher’ as understanding evolution, even though she does not, given her religious convictions, believe its central claims? We think this question raises a range of important and unexplored questions about the relationship between understanding, factivity and belief. Our aim will be to diagnose this case in a principled way, and in doing so, to make some progress toward appreciating what objectual understanding—i.e., understanding a subject matter or body of information—demands of us. Here is the (...) plan. After some ground clearing in §1, §2 outlines and motivates a plausible working model—moderate factivity—for characterising the sense in which objectual understanding should be regarded as factive. §3 shows how the datum that we can understand false theories can, despite initial suggestions to the contrary, be assimilated straightforwardly within the moderate factivity model. §4 highlights how the inverse kind of case to that explored in §3—viz., a variant of Lackey’s creationist teacher case—poses special problems for moderate factivity. With reference to recent work on moral understanding by Hills, §5 proposes a solution to the problem, and §6 attempts to diagnose why it is that we might originally have been led to draw the wrong conclusion. (shrink)

This paper considers how we decide whether to believe what we are told. Inference to the Best Explanation, a popular general account of non-demonstrative reasoning, is applied to this task. The core idea of this application is that we believe what we are told when the truth of what we are told would figure in the best explanation of the fact that we were told it. We believe the fact uttered when it is part of the best explanation of the (...) fact of utterance. Having provided some articulation of this account of testimonial inference, the paper goes on to consider whether the account is informative and whether it is plausible. (shrink)

Machine learning algorithms are increasingly used to shape high-stake allocations, sparking research efforts to orient algorithm design towards ideals of justice and fairness. In this research on algorithmic fairness, normative theorizing has primarily focused on identification of “ideally fair” target states. In this paper, we argue that this preoccupation with target states in abstraction from the situated dynamics of deployment is misguided. We propose a framework that takes dynamic trajectories as direct objects of moral appraisal, highlighting three respects in which (...) such trajectories can be subject to evaluation in relation to their temporal dynamics, robustness, and representation. (shrink)

Several of the essays in this collection discuss the `binding problem', the problem of explaining in neurophysiological terms how it is that we see the various perceptual qualities of a physical object, such as its shape, colour, location and motion, as features of a single object. The perceived object seems to us a unitary thing, but its sensory properties are diverse and turn out to be processed in different areas of the brain. How then does the brain manage the integration? (...) Readers of the essays in this collection may find themselves suffering from an analogous binding problem about the study of consciousness, though this problem is conceptual rather than perceptual, and here the difficulty is to achieve the integration rather than to understand how an effortless integration is achieved. Consciousness is the ideal topic for inter-disciplinary investigation. It is a central concern of such diverse disciplines as neurophysiology, evolutionary biology, psychology, cognitive science, philosophy and theology, among others, yet none of these disciplines has come close to providing full answers to the central questions that consciousness raises. Inter-disciplinary investigation seems an obvious way forward, but it generates the conceptual binding problem that this collection displays. The standard of the essays is very high, but it is extraordinarily difficult to integrate their content into anything like a single picture. We are all apparently talking about the same phenomenon, the conscious awareness of the world that each of us enjoys first-hand, but it is quite unclear how to see the very different things we say about this phenomenon as part of a single picture, or even as parts of different but compatible pictures. Having raised the binding problem for the inter-disciplinary study of consciousness, I hasten to say that I will not attempt even a partial substantive solution here: that is left as an exercise for the readers of this book. (shrink)

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)

At a New York cocktail party shortly after the war, a young and insecure physics postgraduate was heard to blurt out to a woman he had met there: ‘I just want to know what Truth is!’ This was Thomas Kuhn and what he meant was that specific truths such as those of physics mattered less to him than acquiring metaphysical knowledge of the nature of truth. Soon afterwards, he gave up physics, but rather than take up philosophy directly, he approached (...) it by way of the history of science. The work that followed, especially The Structure of Scientific Revolutions , published in 1962 and now with sales of well over a million copies, makes his the most important contribution to the history and philosophy of science of the twentieth century. (shrink)

Bas van Fraassen wants to be an empiricist, but he is deeply dissatisfied with traditional versions of empiricism. So he is developing a new approach: epistemological voluntarism. Let me be blunt. Van Fraassen is an outstanding philosopher, and his new epistemology is important. But The Empirical Stance is a difficult book, because voluntarism is a difficult position to articulate. In what follows I attempt to clarify the situation a little, or at least to explain why it resists clarification.

Typically, fair machine learning research focuses on a single decision maker and assumes that the underlying population is stationary. However, many of the critical domains motivating this work are characterized by competitive marketplaces with many decision makers. Realistically, we might expect only a subset of them to adopt any non-compulsory fairness-conscious policy, a situation that political philosophers call partial compliance. This possibility raises important questions: how does partial compliance and the consequent strategic behavior of decision subjects affect the allocation outcomes? (...) If k% of employers were to voluntarily adopt a fairness-promoting intervention, should we expect k% progress (in aggregate) towards the benefits of universal adoption, or will the dynamics of partial compliance wash out the hoped-for benefits? How might adopting a global (versus local) perspective impact the conclusions of an auditor? In this paper, we propose a simple model of an employment market, leveraging simulation as a tool to explore the impact of both interaction effects and incentive effects on outcomes and auditing metrics. Our key findings are that at equilibrium: (1) partial compliance by k% of employers can result in far less than proportional (k%) progress towards the full compliance outcomes; (2) the gap is more severe when fair employers match global (vs local) statistics; (3) choices of local vs global statistics can paint dramatically different pictures of the performance vis-a-vis fairness desiderata of compliant versus non-compliant employers; (4) partial compliance based on local parity measures can induce extreme segregation. Finally, we discuss implications for auditors and insights concerning the design of regulatory frameworks. (shrink)

We are addicted to explanation, constantly asking and answering why-questions. But what does an explanation give us? I will consider some of the possible goods, intrinsic and instrumental, that explanations provide. The name for the intrinsic good of explanation is `understanding', but what is this? In the first part of this paper I will canvass various conceptions of understanding, according to which explanations provide reasons for belief, make familiar, unify, show to be necessary, or give causes. Three general features of (...) explanation will serve as tests of these varied conceptions. These features are: a) the distinction between knowing that a phenomena occurs and understanding why it does; b) the possibility of giving explanations that are not themselves explained; c) the possibility of explaining a phenomenon in cases where the phenomenon itself provides an essential part of the reason for believing that the explanation is correct. There are many other aspects of our explanatory practices that a good account of explanation and understanding should capture, but these simple tests provide surprisingly effective diagnostic tools for the evaluation of broad conceptions of the nature of understanding. It will turn out that the causal conception of understanding does particularly well on the tests, though of course it too faces various difficulties. The balance of this essay focuses on the causal conception. After addressing some of the difficulties it faces, I will ask.. (shrink)

Peter Lipton; VI*—Is the Best Good Enough?, Proceedings of the Aristotelian Society, Volume 93, Issue 1, 1 June 1993, Pages 89–104, https://doi.org/10.1093/aris.

Protagoras, of all the ancient philosophers, has perhaps attracted the most interest in modern times. His saying ‘Man is the measure of all things’ caused Schiller to adopt him as the patron of the Oxford pragmatists, and has generally earned him the title of the first humanist. Yet the exact delineation of his philosophcal position remains a baffling task. Neumann, writing on Die Problematik des ‘Homo-mensura’ Satzes in 1938,2 concludes that no certainty whatever can be reached on the meaning of (...) the dictum, since ‘man’, ‘measure’, and ‘things’ are all ambiguous, nor can we tell which of the three is the predicate. The time is past when it was believed that a man's philosophy could be understood apart from the events of his life and the circumstances of his age: yet in the case of Protagoras the historical method of approach has hardly been attempted, although the impact of environment was perhaps more decisive in the formation of philosophical concepts in the Greek world than anywhere else. The reality about which the Greek philosopher spoke had three aspects: it was either the one universe of physics, or the political unity, or God. For example, the book of Heracleitus Περ φσεως was divided into three chapters or logoi, About the Whole, a political, and a theological. Neither physics nor theology supplies from its own subject-matter the form in which this reality was described. (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)

An effect is typically explained by citing a cause, but not any cause will do. The oxygen and the spark were both causes of the fire, but normally only the spark explains it. What then distinguishes explanatory from unexplanatory causes? One might attempt to characterise this distinction in terms of intrinsic features of the causes. For example, some causes are changes while others are standing conditions, and one might claim that only the changes explain. Both the spark and the oxygen (...) are causes of the fire, but only the spark is a change, and perhaps this is the reason only the spark explains. On the other hand, one might attempt to characterise the distinction between explanatory and unexplanatory causes in terms of the relation between cause and effect. For example, only some causes are sufficient for their effects, and perhaps only sufficient causes explain. There is, however, an elementary feature of the distinction between explanatory and unexplanatory causes that neither an intrinsic nor a relational approach are well-suited to capture. This is the so-called `interest-relativity' of explanation: the very same cause may be explanatory for one person but not for another. When there is a famine in India, an Indian peasant may explain this by citing the drought, while a member of the World Health Organization may instead cite the failure of the Indian government to stock adequate reserves of food (Hart and Honore, 1985, pp. (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)

The achievements of the textile industry in Roman Britain are often underestimated as a result of the meagreness of our available evidence. The Edict on maximum prices issued by Diocletian in A.D. 301 shows that British capes commanded high prices on the markets of the Empire, and that in the late third century A.D. British rugs were the best in the world. In view of the competition from the traditional centres of rug manufacture in the East, this is an astonishing (...) achievement. (shrink)

The received translation and interpretation of many of the technical terms current in the textile industry of the Roman Empire are inaccurate, because lexicographers have either fought shy of being precise, or have thought that they recognized in the ancient world technical processes which originated at a much later date. The evidence is often equivocal or insufficient, but may still yield details that have been overlooked. The textile expression scutulatus, to take an example, deserves more attention than Blümner has devoted (...) to it. When it refers to the appearance of a garment, Lewis and Short, s.v. scutulatus, translate ‘diamond or lozenge-shaped, checkered’. It seems worth while to attempt a more precise translation, and, if possible, to estimate the significance in context of the goods so designated. (shrink)