Goldman (1967) proposed that a subject s knows p if and only if p is appropriately causally connected to s’s believing p. He later on abandoned this theory (Goldman, 1976). The main objection to the theory is that the causal connection required by Goldman is compatible with certain problematic forms of luck. In this paper we argue that Goldman’s causal theory of knowledge can overcome the luck problem if causation is understood along interventionist lines. (...) We also show that the modified theory leads to the correct results in contexts involving other prominent forms of epistemic luck and compare it with other accounts on the market. (shrink)

This book seeks to offer original answers to all the major open questions in epistemology—as indicated by the book’s title. These questions and answers arise organically in the course of a validation of the entire corpus of human knowledge. The book explains how we know what we know, and how well we know it. The author presents a positive theory, motivated and directed at every step not by a need to reply to skeptics or subjectivists, but by the (...) need of a rational individual to know the world. -/- The author draws heavily from Ayn Rand’s theory of concepts as presented in her book, Introduction to Objectivist Epistemology, but departs from her epistemology—especially as explicated by leading exponents of her philosophy—in important ways. Areas of departure include the perception of entities and the role of probability theory in epistemology. -/- A main idea in the book is to begin the validation of the law of causality by identifying that existence causes our consciousness of it. Another key idea is this: The very fact that we perceive entities is the most basic and most extensive evidence that causal forces and causal interactions are regular. -/- Applying Ayn Rand’s principle that characteristics are ranges of measurement, the book offers a philosophical validation of “nonparametric predictive inference,” in turn providing an objective basis for prior probabilities in Bayesian analysis. -/- This book is primarily for a specialized readership—familiar with epistemological ideas and with Ayn Rand’s theory of concepts in particular. The last third of the book uses probability theory and mathematics somewhat beyond basic calculus, but less mathematical explanations are also included to make the general ideas accessible to lay readers. (shrink)

The poster boy for my paper is the King's Messenger in Lewis Carroll's Through the Looking Glass. Recall that since the White Queen lives backwards, her memory works forwards. She pities Alice who can only remember things after they happen. Alice asks which things the Queen remembers best: `Oh, things that happened the week after next,' the Queen replied in a careless tone. `For instance, . . . there's the King's Messenger. He's in prison now, being punished: and the trial (...) doesn't even begin till next Wednesday: and of course the crime comes last of all.' (Chapter V) Is the King's Messenger being treated unjustly? Why not prepunish people for their future crimes? True, it is generally easier to have knowledge about past crimes than future crimes. But is unpredictability the only problem with prepunishment? (shrink)

1 Cf. D. M. Armstrong, A Materialist Theory of Mind (London, 1968), Chapter 9; 'A Causal Theory of Knowledge' by Alvin I. Goldman, The Journal of Philosophy , Vol. LXIV, No. 12, June 22, 1967. A striking parallelism would appear to exist between 'the causal theory of knowledge' and the orthodox Stoic doctrine regarding the kataleptike phantasia . See, for example, Sextus Empiricus, Adversus Mathematicos 7.248 (reprinted in Stoicorum Veterum Fragmenta , edited by (...) H. F. A. von Arnim, Leipzig, 1921, Volume I, page 18, 59C): 'An apprehensive appearance is one which has been stamped and sealed by the actual, and in accordance with the actual thing itself, in such a way that it would not be produced by what is not (the) actual' (I am indebted for the wording of this somewhat controversial translation to my colleague Mr. M. B. Wallace). See the discussion and additional ref. (shrink)

Many mathematicians are platonists: they believe that the axioms of mathematics are true because they express the structure of a nonspatiotemporal, mind independent, realm. But platonism is plagued by a philosophical worry: it is unclear how we could have knowledge of an abstract, realm, unclear how nonspatiotemporal objects could causally affect our spatiotemporal cognitive faculties. Here I aim to make room in our metaphysical picture of the world for the causal relevance of abstracta.

Few philosophers that have been studied as much as Ibn Sīnā have been as much misunderstood. His extraordinary ability to reflect upon and write in a variety of styles about seemingly every topic in every domain has steered his thought from philosophy and theology to mysticism and esoterism. Instead of helping us to learn and understand better Ibn Sīnā than he has previously been understood, the recent surge of Avicennan studies only adds more confusion to the already complex social context (...) which he was living in. (shrink)

This paper evaluates Putnam’s argument in the first chapter of Reason, Truth and History, for the claim that we can know that we are not brains in a vat (of a certain sort). A widespread response to Putnam’s argument has been that if it were successful not only the world but the meanings of our words (and consequently our thoughts) would be beyond the pale of knowledge, because a causal theory of reference is not compatible with our (...) having knowledge of the meanings of our words. I argue that this is not so. I argue also, however, that given how Putnam argues (here) for the causal theory of reference, he cannot after all escape this consequence. (shrink)

The question discussed is whether the conditions for knowledge laid down by externalist or causal theories of knowledge render knowledge claims secure from scepticism of the cartesian kind. a simple account of such conditions encourages an affirmative answer. but such an account proves inadequate and some of the conditions of an adequate account are sketched. once these conditions are introduced, it is argued, knowledge claims appear as open as ever to sceptical challenge. however it is (...) also seen how modest knowledge claims may be upheld, and the conclusion reached is that the type of theory discussed allows us to compromise with scepticism rather than to capitulate. (shrink)

INTRODUCTION SECTION I In the last 20 years or so philosophers in the analytic tradition have taken an increasing interest in causal theories of a wide ...

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. (...) Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

Knowing is something that we do not have much of a theory about., p. 365.)Interest has recently been shown in causal theories of perception, memory, inference, reference, truth, justification and belief, as well as in a more general “causal theory of knowledge” which would embrace and connect all of these concepts within a broad epistemological framework. The burden of this paper is that prospects are poor for an interesting and general enough causal theory (...) of knowledge. A threat to generality arises from the causal theory's difficulties with knowledge of general truths. A threat to interest arises when attempts to accommodate general truths lead to a weakening of the notion of “causal connection” appealed to, making dubious the explanatory force of such an appeal. (shrink)

In his 1967 paper 'A Causal Theory of Knowing', Alvin Goldman sketched an account of empirical knowledge in terms of appropriate causal connections between the fact known and the knower's belief in that fact. This early causal account has been much criticized, even by Goldman himself in later years. We argue that the theory is much more defensible than either he or its other critics have recognized, that there are plausible internal and external resources (...) available to it which save it from many objections in the literature (in particular, objections raised by Harman, Pappas and Swain, Klein, Dretske, Goldman, Shope, Ackermann, Morawetz, and Collier). (shrink)

In his 1967 paper 'A Causal Theory of Knowing', Alvin Goldman sketched an account of empirical knowledge in terms of appropriate causal connections between the fact known and the knower's belief in that fact. This early causal account has been much criticized, even by Goldman himself in later years. We argue that the theory is much more defensible than either he or its other critics have recognized, that there are plausible internal and external resources (...) available to it which save it from many objections in the literature (in particular, objections raised by Harman, Pappas and Swain, Klein, Dretske, Goldman, Shope, Ackermann, Morawetz, and Collier). (shrink)

Fred Dretske's "Knowledge and the Flow of Information" is an extended attempt to develop a philosophically useful theory of information. Dretske adapts central ideas from Shannon and Weaver's mathematical theory of communication, and applies them to some traditional problems in epistemology. In doing so, he succeeds in building for philosophers a much-needed bridge to important work in cognitive science. The pay-off for epistemologists is that Dretske promises a way out of a long-standing impasse -- the Gettier problem. (...) He offers an alternative model of knowledge as information-based belief, which purports to avoid the problems justificatory accounts face. This essay looks closely at Dretske's theory. I argue that while the information-theoretic framework is attractive, it does not provide an adequate account of knowledge. And there seems to be no way of tightening the theory without introducing some version of a theory of justification -- the very notion Dretske's theory was designed to avoid. (shrink)

I have argued that the most recent versions of the causal theory are subject to serious limitations. The causal analysis of spatiotemporal coincidence considered in Section IV does not apply to space-times in which (1) fails. And current versions of the theory collapse altogether for typical cases of relativistic space-times which are closed in their temporal aspects. Second, I have pointed out that the program of recent causal theorists is based on a false dichotomy — (...) open vs. closed times; for only a small subclass of relativisitic space-times can be said to be either open or closed in their temporal aspects, and the causal theory seems incapable of handling the cases which fall in between. Third, I have argued that the general theory of relativity does not provide motivation for the causal theory; on the contrary, general relativity promotes the view of spacetime as a substantial entity.As a result, I do not see that the causal theorist has a convincing argument against the position which holds that in order to understand the subtle and complex temporal structures encompassed by relativity theory, one must accept space-time as an entity which cannot be analyzed away as an abstract mathematical construct used for representing the ‘physical’, i.e., causal, relations between events. And I cannot agree with van Fraassen (1970, p. 140) that Philosophers were not long in appreciating this development [i.e., relativity theory], and the consequent construction of the causal theory of time and space-time must be considered one of the major contributions of twentieth-century philosophy of science. For it seems to me that causal theorists have failed to appreciate this development and that the construction of the causal theory has served to obscure important and interesting facts about the temporal aspect of space-time. (shrink)

Extended Abstract This book introduces and develops a new, universal method of the scientific comprehension of reality providing the objective, ...

I have so far ignored Earman's Section IV in which spatiotemporal coincidence is discussed. The answer will be clear from the preceding: the exact definitions and principles of the exact theories we have displayed are to be discussed with reference to the special and not the general theory of relativity. But moreover, Earman's transition from (C) to (1) assumes what we do not grant: that events are causally connectible exactly if the points in the mathematical space-time at which they (...) are located are linked by a causal curve.This captures in a nutshell my own conclusions. The first is that the causal theory, after its success vis-à-vis the STR, must now provide a detailed analysis of spatiotemporal concepts in the GTR. The second is that the points raised by Earman do not provide substantive reasons for doubting the adequacy of the causal theory to this task, because Earman insists in his extrapolations on a much closer relation between the empirical structure of events and the mathematical structures that model it than ought to be assumed. (shrink)

In Memory: A Philosophical Study, Bernecker argues for an account of contiguity. This Contiguity View is meant to solve relearning and prompting, wayward causation problems plaguing the causal theory of memory. I argue that Bernecker’s Contiguity View fails in this task. Contiguity is too weak to prevent relearning and too strong to allow prompting. These failures illustrate a problem inherent in accounts of memory causation. Relearning and prompting are both causal relations, wayward only with respect to our (...) interest in specifying remembering’s requirements. Solving them requires saying more about remembering, not causation. I conclude by sketching such an account. (shrink)

First published in 1962. Kant’s philosophical works, and especially the _Critique of Pure Reason_, have had some influence on recent British philosophy. But the complexities of Kant’s arguments, and the unfamiliarity of his vocabulary, inhibit understanding of his point of view. In _Kant’s Theory of Knowledge _an attempt is made to relate Kant’s arguments in the _Critique of Pure Reason _to contemporary issues by expressing them in a more modern idiom. The selection of issues discussed is intended to (...) present a continuous argument, of an epistemological kind, which runs centrally through the _Critique_. The argument deals with essentially with the problems, raised in the Transcendental Analytic, about the status of categories. It deals with certain preliminary assumptions made in setting these problems, and discusses the way in which the various sections of the Analytic contribute to their solution. It also deals with Kant’s criticisms of traditional metaphysics, and ends with an account of his effort in the Third Antinomy to resolve the conflict between freedom and causality, and so to effect a transition of knowledge to moral philosophy. (shrink)

The deep crisis in modern fundamental science development is ever more evident and openly recognised now even by mainstream, official science professionals and leaders. By no coincidence, it occurs in parallel to the world civilisation crisis and related global change processes, where the true power of unreduced scientific knowledge is just badly missing as the indispensable and unique tool for the emerging greater problem solution and further progress at a superior level of complex world dynamics. Here we reveal the (...) mathematically exact reason for the crisis in conventional science, containing also the natural and unified problem solution in the form of well-specified extension of usual, artificially restricted paradigm. We show how that extended, now causally complete science content provides various "unsolvable" problem solutions and opens new development possibilities for both science and society, where the former plays the role of the main, direct driver for the latter. We outline the related qualitative changes in science organisation, practice and purposes, giving rise to the sustainability transition in the entire civilisation dynamics towards the well-specified superior level of its unreduced, now well understood and universally defined complexity. (shrink)

In the recent philosophy of explanation, a growing attention to and discussion of non-causal explanations has emerged, as there seem to be compelling examples of non-causal explanations in the sciences, in pure mathematics, and in metaphysics. I defend the claim that the counterfactual theory of explanation (CTE) captures the explanatory character of both non-causal scientific and metaphysical explanations. According to the CTE, scientific and metaphysical explanations are explanatory by virtue of revealing counterfactual dependencies between the (...) explanandum and the explanans. I support this claim by illustrating that CTE is applicable to Euler’s explanation (an example of a non-causal scientific explanation) and Loewer’s explanation (an example of a non-causal metaphysical explanation). (shrink)

This book explains exactly what human knowledge is. The key concepts in this book are structures and algorithms, i.e., what the readers “see” and how they make use of what they see. Thus in comparison with some other books on the philosophy of science, which employ a syntactic approach, the author’s approach is model theoretic or structural. Properly understood, it extends the current art and science of mathematical modeling to all fields of knowledge. The link between structure and (...) algorithms is mathematics. But viewing “mathematics” as such a link is not exactly what readers most likely learned in school; thus, the task of this book is to explain what “mathematics” should actually mean. Chapter 1, an introductory essay, presents a general analysis of structures, algorithms and how they are to be linked. Several examples from the natural and social sciences, and from the history of knowledge, are provided in Chapters 2–6. In turn, Chapters 7 and 8 extend the analysis to include language and the mind. Structures are what the readers see. And, as abstract cultural objects, they can almost always be seen in many different ways. But certain structures, such as natural numbers and the basic theory of grammar, seem to have an absolute character. Any theory of knowledge grounded in human culture must explain how this is possible. The author’s analysis of this cultural invariance, combining insights from evolutionary theory and neuroscience, is presented in the book’s closing chapter. The book will be of interest to researchers, students and those outside academia who seek a deeper understanding of knowledge in our present-day society. (shrink)

In the recent philosophy of explanation, a growing attention to and discussion of non-causal explanations has emerged, as there seem to be compelling examples of non-causal explanations in the sciences, in pure mathematics, and in metaphysics. I defend the claim that the counterfactual theory of explanation captures the explanatory character of both non-causal scientific and metaphysical explanations. According to the CTE, scientific and metaphysical explanations are explanatory by virtue of revealing counterfactual dependencies between the explanandum (...) and the explanans. I support this claim by illustrating that CTE is applicable to Euler’s explanation and Loewer’s explanation. (shrink)

The goal of this paper is to develop a counterfactual theory of explanation. The CTE provides a monist framework for causal and non-causal explanations, according to which both causal and non-causal explanations are explanatory by virtue of revealing counterfactual dependencies between the explanandum and the explanans. I argue that the CTE is applicable to two paradigmatic examples of non-causal explanations: Euler’s explanation and renormalization group explanations of universality.

In this impressive second edition of Theory of Knowledge, Keith Lehrer introduces students to the major traditional and contemporary accounts of knowing. Beginning with the traditional definition of knowledge as justified true belief, Lehrer explores the truth, belief, and justification conditions on the way to a thorough examination of foundation theories of knowledge,the work of Platinga, externalism and naturalized epistemologies, internalism and modern coherence theories, contextualism, and recent reliabilist and causal theories. Lehrer gives all views (...) careful examination and concludes that external factors must be matched by appropriate internal factors to yield knowledge. This match of internal and external factors follows from Lehrer’s new coherence theory of undefeated justification. In addition to doing justice to the living epistemological traditions, the text smoothly integrates several new lines that will interest scholars. Also, a feature of special interest is Lehrer’s concept of a justification game.This second edition of Theory of Knowledge is a thoroughly revised and updated version that contains several completely new chapters. Written by a well-known scholar and contributor to modern epistemology, this text is distinguished by clarity of structure, accessible writing, and an elegant mix of traditional material, contemporary ideas, and well-motivated innovation. (shrink)

In this important new text, Keith Lehrer introduces students to the major traditional and contemporary accounts of knowing. Beginning with the accepted definition of knowledge as justified true belief, Lehrer explores the truth, belief and justification conditions on the way to a thorough examination of foundation theories of knowledge, externalism and naturalized epistemologies, internalism and modern coherence theories as well as recent reliabilist and causal theories. Lehrer gives all views careful examination and concludes that external factors must (...) be matched by appropriate internal ones to yield knowledge. Readers of Professor Lehrer's earlier book _Knowledge_ will want to know that this text adopts the framework of that classic text. But _Theory of Knowledge_ is a completely rewritten and updated version of that book that has been simplified throughout for student use. (shrink)

In the last couple of years a few seemingly independent debates on scientific explanation have emerged, with several key questions that take different forms in different areas. For example, the question what makes an explanation distinctly mathematical and are there any non-causal explanations in sciences (i.e. explanations that don’t cite causes in the explanans) sometimes take a form of the question what makes mathematical models explanatory, especially whether highly idealized models in science can be explanatory and in virtue of (...) what they are explanatory. These questions raise further issues about counterfactuals, modality and explanatory asymmetries, i.e. do mathematical and non-causal explanations support counterfactuals, and how to understand explanatory asymmetries in non-causal explanations. Even though these are very common issues in the philosophy of physics and mathematics, they can be found in different guises in the philosophy of biology, where there is the statistical interpretation of the Modern Synthesis theory of evolution, according to which the post-Darwinian theory of natural selection explains evolutionary change by citing statistical properties of populations and not the causes of changes. These questions also arise in philosophy of ecology or neuroscience in regard to the nature of topological explanations. The question here is whether in network models in biology, ecology, neuroscience and computer science the mathematical or more precisely topological properties can be explanatory of physical phenomena, or they are just different ways to represent causal structures. The aim of the special issue is to unify all these debates around several overlapping questions. (shrink)

Education and the collective construction of knowledge. An overview -- Teaching modality : a corpus analysis of the use of must by university Spanish learners of English -- Motivation and anxiety towards mathematical learning in primary education -- Criteria for the sequencing of contemporary music in education -- Sustainability training evaluation of Spanish university students -- Art as a means of fostering peace, communication and freedom of expression from childhood -- Culturemes vs. humoremes as translation problems in practice exemplified (...) in the German Cabaret of Marc-Uwe Kling and his Kangaroo stories -- Is there homogeneity among business students regarding the level of concern towards the sustainable development goals? A cluster analysis -- Use trends and methodological pertinence of Delphi within educational research in IberoAmerica : a systematic review in Scopus -- Gamification in the improvement of speaking competences in the English as a foreign language classroom : a case study -- Quality management in the Spanish university : an analysis of the success and performance rates in communication degree programs -- Teacher stories from the future : technology for the language and literature classroom. (shrink)

In this important new text, Keith Lehrer introduces students to the major traditional and contemporary accounts of knowing. Beginning with the accepted definition of knowledge as justified true belief, Lehrer explores the truth, belief and justification conditions on the way to a thorough examination of foundation theories of knowledge, externalism and naturalized epistemologies, internalism and modern coherence theories as well as recent reliabilist and causal theories. Lehrer gives all views careful examination and concludes that external factors must (...) be matched by appropriate internal ones to yield knowledge. Readers of Professor Lehrer's earlier book _Knowledge_ will want to know that this text adopts the framework of that classic text. But _Theory of Knowledge_ is a completely rewritten and updated version of that book that has been simplified throughout for student use. (shrink)

In this important new text, Keith Lehrer introduces students to the major traditional and contemporary accounts of knowing. Beginning with the accepted definition of knowledge as justified true belief, Lehrer explores the truth, belief and justification conditions on the way to a thorough examination of foundation theories of knowledge, externalism and naturalized epistemologies, internalism and modern coherence theories as well as recent reliabilist and causal theories. Lehrer gives all views careful examination and concludes that external factors must (...) be matched by appropriate internal ones to yield knowledge. Readers of Professor Lehrer's earlier book _Knowledge_ will want to know that this text adopts the framework of that classic text. But _Theory of Knowledge_ is a completely rewritten and updated version of that book that has been simplified throughout for student use. (shrink)

This book offers a causal-explanatory account of knowledge as true belief caused by the worldly state of affairs that explains its existence. It also defends a contextual account of epistemic reasons, arguing that both foundationalism and coherentism cannot provide a satisfactory account of such reasons. Skeptical arguments are answered against a historical background from Plato to the present day.

Paul Benacerraf’s argument that mathematical realism is apparently incompatible with mathematical knowledge has been widely thought to also show that a priori knowledge in general is problematic. Although many philosophers have rejected Benacerraf’s argument because it assumes a causal theory of knowledge, some maintain that Benacerraf nevertheless put his finger on a genuine problem, even though he didn’t state the problem in its most challenging form. After diagnosing what went wrong with Benacerraf’s argument, I argue (...) that a new, more challenging, version of Benacerraf’s problem can be constructed. The new version—what I call the Defeater Version—of Benacerraf’s problem makes use of a no-defeater condition on knowledge and justification. I conclude by arguing that the best way to avoid the problem is to construct a theory of how a priori judgments reliably track the facts. I also suggest four different kinds of theories worth pursuing. (shrink)

For millennia, knowledge has eluded a precise definition. The industrialization of knowledge (IoK) and the associated proliferation of the so-called knowledge communities in the last few decades caused this state of affairs to deteriorate, namely by creating a trio composed of data, knowledge, and information (DIK) that is not unlike the aporia of the trinity in philosophy. This calls for a general theory of knowledge (ToK) that can work as a foundation for a science (...) of knowledge (SoK) and additionally distinguishes knowledge from both data and information. In this paper, I attempt to sketch this generality via the establishing of both knowledge structures and knowledge systems that can then be adopted/adapted by the diverse communities for the respective knowledge technologies and practices. This is achieved by means of a formal–indeed, mathematical–approach to epistemological matters a.k.a. formal epistemology. The corresponding application focus is on knowledge systems implementable as computer programs. (shrink)

Theory of "conceptual pragmatism" takes into account both modern philosophical thought and modern mathematics. Stimulating discussions of metaphysics, a priori, philosophic method, much more.

Although Hume seems to suppose that natural processes occur in a deterministic way, his conception of causality prohibits us from knowing them as deterministic. The reason is that for him the idea of a necessary connection between events is purely psychological. In our analysis of this question, we argue that: a) in his main references about causality, Hume does not assume a strong ontological commitment with determinism; b) certain parts of his texts suggest that indeterminism is non eliminable, in the (...) knowledge of nature; and c) his causal conception of freedom supposes indeterminism in natural processes, and not in our knowledge of them only.Embora Hume eventualmente pareça supor que os processos naturais ocorrem de modo determinístico, sua concepção da causalidade proíbe que os conheçamos enquanto tais, pois, para ele, toda idéia de conexão necessária entre eventos é de natureza psicológica. Em nossa análise dessa questão, argumentamos que: a) nas suas principais passagens sobre a causalidade, Hume não assume um compromisso forte com o determinismo; b) certas partes de seus textos sugerem que o indeterminismo é ineliminável, no conhecimento da natureza; e c) sua concepção causal da liberdade supõe o indeterminismo dos processos naturais, e não apenas o indeterminismo em nível de seu conhecimento. (shrink)

We explore the prospects of a monist account of explanation for both non-causal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both non-causal explanations in science and mathematical explanations. In particular, a successful application of the CTE to mathematical (...) explanations requires us to rely on counterpossibles. We conclude that the CTE is a promising candidate for a monist account of explanation in both science and mathematics. (shrink)

In the last couple of years, a few seemingly independent debates on scientific explanation have emerged, with several key questions that take different forms in different areas. For example, the questions what makes an explanation distinctly mathematical and are there any non-causal explanations in sciences (i.e., explanations that don’t cite causes in the explanans) sometimes take a form of the question of what makes mathematical models explanatory, especially whether highly idealized models in science can be explanatory and in virtue (...) of what they are explanatory. These questions raise further issues about counterfactuals, modality, and explanatory asymmetries: i.e., do mathematical and non-causal explanations support counterfactuals, and how ought we to understand explanatory asymmetries in non-causal explanations? Even though these are very common issues in the philosophy of physics and mathematics, they can be found in different guises in the philosophy of biology where there is the statistical interpretation of the Modern Synthesis theory of evolution, according to which the post-Darwinian theory of natural selection explains evolutionary change by citing statistical properties of populations and not the causes of changes. These questions also arise in philosophy of ecology or neuroscience in regard to the nature of topological explanations. The question here is can the mathematical (or more precisely topological) properties in network models in biology, ecology, neuroscience, and computer science be explanatory of physical phenomena, or are they just different ways to represent causal structures. The aim of this special issue is to unify all these debates around several overlapping questions. These questions are: are there genuinely or distinctively mathematical and non-causal explanations?; are all distinctively mathematical explanations also non-causal; in virtue of what they are explanatory; does the instantiation, implementation, or in general, applicability of mathematical structures to a variety of phenomena and systems play any explanatory role? This special issue provides a platform for unifying the debates around several key issues and thus opens up avenues for better understanding of mathematical and non-causal explanations in general, but also, it will enable even better understanding of key issues within each of the debates. (shrink)

ABSTRACT When Hume, in the Treatise on Human Nature, began his examination of the relation of cause and effect, in particular, of the idea of necessary connection which is its essential constituent, he identified two preliminary questions that should guide his research: For what reason we pronounce it necessary that every thing whose existence has a beginning should also have a cause and Why we conclude that such particular causes must necessarily have such particular effects? Hume observes that our belief (...) in these principles can result neither from an intuitive grasp of their truth nor from a reasoning that could establish them by demonstrative means. In particular, with respect to the first, Hume examines and rejects some arguments with which Locke, Hobbes and Clarke tried to demonstrate it, and suggests, by exclusion, that the belief that we place on it can only come from experience. Somewhat surprisingly, however, Hume does not proceed to show how that derivation of experience could be made, but proposes instead to move directly to an examination of the second principle, saying that, "perhaps, be found in the end, that the same answer will serve for both questions". Hume's answer to the second question is well known, but the first question is never answered in the rest of the Treatise, and it is even doubtful that it could be, which would explain why Hume has simply chosen to remove any mention of it when he recompiled his theses on causation in the Enquiry concerning Human Understanding. Given this situation, an interesting question that naturally arises is to investigate the relations of logical or conceptual implication between these two principles. Hume seems to have thought that an answer to would also be sufficient to provide an answer to. Henry Allison, in his turn, argued that the two questions are logically independent. My proposal here is to try to show that there is indeed a logical dependency between them, but the implication is, rather, from to. If accepted, this result may be particularly interesting for an interpretation of the scope of the so-called "Kant's reply to Hume" in the Second Analogy of Experience, which is structured as a proof of the a priori character of, but whose implications for remain controversial. (shrink)

This work explores the conceptual and empirical issues of the concept of knowledge and its relation to the pattern of our belief change, from formal and experimental perspectives. Part I gives an analysis of knowledge (called Sustainability) that is formally represented and naturalistically plausible at the same time, which is claimed to be a synthesized view of knowledge, covering not only empirical knowledge, but also knowledge of future, practical knowledge, mathematical knowledge, knowledge (...) of general facts. Part II tries to formalize the natural pattern of belief change assumed in Sustainability in terms of a specific formal theory of belief change, after carefully examining the notions of belief, belief change, and Information, from which the cognitive function F in Chapter 3 is actually constructed, which is later implemented by a computer program and its behavior against random input is demonstrated. In Part III we proceed to examine the analysis empirically. In particular, we will investigate Sustainability from the developmental point of view. We first justify experimental approach in philosophy as a legitimate method of philosophical investigation, and then developmental approach in particular. The specific proposal of experiment here is what we call the Gettier Task, an analogue of the famous false-belief task in developmental psychology, which has been much discussed in philosophy of mind. Two versions of the Gettier Task were tested on children aged from 6 to 12, and we claim that the data obtained empirically supports our analysis of knowledge, or Sustainability. (shrink)

In 1967, Alvin Goldman proposed that 'X' knows that 'p' only if the fact that 'p' is causally connected with X's belief that 'p'. Brian Skyrms' alleged counterexample, the case of the fiend who beheads a person already deceased, has been widely accepted (by Robert Ackermann, Gilbert Harman, and Marshall Swain) as such. But it is not a counterexample. To see this, we must attend to two distinctions: between a death and being dead, and between causation and causal overdetermination. (...) The most visible objection to Goldman's analysis is then dissolved. a modified version of Skyrms' case fares no better. (shrink)