Philosophical conceptual analysis is an experimental method. Focusing on this helps to justify it from the skepticism of experimental philosophers who follow Weinberg, Nichols & Stich. To explore the experimental aspect of philosophical conceptual analysis, I consider a simpler instance of the same activity: everyday linguistic interpretation. I argue that this, too, is experimental in nature. And in both conceptual analysis and linguistic interpretation, the intuitions considered problematic by experimental philosophers are necessary but epistemically irrelevant. They are like variables introduced (...) into mathematical proofs which drop out before the solution. Or better, they are like the hypotheses that drive science, which do not themselves need to be true. In other words, it does not matter whether or not intuitions are accurate as descriptions of the natural kinds that undergird philosophical concepts; the aims of conceptual analysis can still be met. (shrink)

I argue that a basic similarity analysis of analogical reasoning handles many apparent cases of visual analogy. I consider how the visual and verbal elements interact in analogical cases. Finally, I offer two analyses of visual elements. One analysis is evidential. The visual elements are evidence for their ver-bal counterparts. One is non-evidential: the visual elements link to verbal elements without providing evi-dence for those elements. The result is to make more room for the logical analysis of visual argumentation.

A survey of contemporary philosophical and scientific literatures reveals that different authors employ the term ‘heuristic’ in ways that deviate from, and are sometimes inconsistent with, one another. Given its widespread use in philosophy and cognitive science generally, it is striking that there appears to be little concern for a clear account of what phenomena heuristics pick out or refer to. In response, I consider several accounts of ‘heuristic’, and I draw a number of distinctions between different sorts of heuristics (...) in order to make sense of various research programmes. I then develop a working characterization of ‘heuristic’ which is shown to be coherent and robust enough to serve as a kind within philosophy and cognitive science broadly. My intent is not to pursue a unified account of ‘heuristic’, but to highlight some features of certain kinds of heuristics that are important for theorizing about cognition in order to proceed with a science of the mind/brain. 1 Why We Need an Appropriate Characterization of ‘Heuristic’2 Inadequate Definitions2.1 A positive attempt2.2 Heuristics versus guaranteed correct outcomes3 A Taxonomy of Heuristics3.1 Stimulus-driven versus heuristic3.2 Perceptual versus cognitive heuristics3.3 Computational versus cognitive heuristics3.4 Methodological versus inferential heuristics3.5 Summary of distinctions4 Characterizing Cognitive Heuristics4.1 Heuristics as rules of thumb4.2 Beyond rules of thumb: exploiting information5 Concluding Remarks. (shrink)

In this paper I investigate two notions of concepts that have played a dominant role in 20th century philosophy of mathematics. According to the first, concepts are definite and fixed; in contrast, according to the second notion concepts are open and subject to modifications. The motivations behind these two incompatible notions and how they can be used to account for conceptual change are presented and discussed. On the basis of historical developments in mathematics I argue that both notions of concepts (...) capture important aspects of mathematical and scientific reasoning, and, consequently, that a pluralistic approach that allows for representing both of these aspects is most useful for an adequate account of investigative practices. (shrink)

On the basis of a wide range of historical examples various features of axioms are discussed in relation to their use in mathematical practice. A very general framework for this discussion is provided, and it is argued that axioms can play many roles in mathematics and that viewing them as self-evident truths does not do justice to the ways in which mathematicians employ axioms. Possible origins of axioms and criteria for choosing axioms are also examined. The distinctions introduced aim at (...) clarifying discussions in philosophy of mathematics and contributing towards a more refined view of mathematical practice. (shrink)

Three big philosophical problems about consciousness are: Why does it exist? How do we explain and understand it? How can we explain brain-consciousness correlations? If functionalism were true, all three problems would be solved. But it is false, and that means all three problems remain unsolved (in that there is no other obvious candidate for a solution). Here, it is argued that the first problem cannot have a solution; this is inherent in the nature of explanation. The second problem is (...) solved by recognizing that (a) there is an explanation as to why science cannot explain consciousness, and (b) consciousness can be explained by a different kind of explanation, empathic or “personalistic” explanation, compatible with, but not reducible to, scientific explanation. The third problem is solved by exploiting David Chalmers“principle of structural coherence”, and involves postulating that sensations experienced by us–visual, auditory, tactile, and so on–amount to minute scattered regions in a vast, multi dimensional “space” of all possible sensations, which vary smoothly, and in a linear way, throughout the space. There is also the space of all possible sentient brain processes. There is just one, unique one-one mapping between these two spaces that preserves continuity and linearity. It is this which provides the explanation as to why brain processes and sensations are correlated as they are. I consider objections to this unique-matching theory, and consider how the theory might be empirically confirmed. (shrink)

It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it (...) accommodates the many mathematical proofs that include actions on objects other than propositions; (v) this conception of logic permits the articulation of project-sized tasks for the philosophy of mathematical practice, thereby supplying a partial characterisation of normal research in the field. (shrink)

The F-twist is giving way to the methodology of scientific research programs. Milton Friedman's “Methodology for Economics” is being supplanted as the orthodox rationale for neoclassical economics by Imre Lakatos' account of scientific respectability. Friedman's instrumentalist thesis that theories are to be judged by the confirmation of their consequences and not the realism of their assumptions has long been widely endorsed by economists, under Paul Samuelson's catchy rubric “the F-twist.” It retains its popularity among economists who want no truck with (...) methodology, but among the increasing number of able economists who are writing on methodology the F-twist has been surrendered, not so much because these writers have decided it is false, as because something better has finally come along. (shrink)

The aim of this essay is a criticism of reductionism ? both in its ?static? interpretation (usually referred to as the layer model or level?picture of science) and in its ?dynamic? interpretation (as a theory of the growth of scientific knowledge), with emphasis on the latter ? from the point of view of Popperian fallibilism and Feyerabendian pluralism, but without being committed to the idiosyncrasies of these standpoints. In both aspects of criticism, the rejection is based on the proposal of (...) a global alternative. Hummell and Opp's research programme for the reduction of sociology to psychology is used as a starting?point and taken as the primary object of criticism. Following the introductory Section I, Section II analyses the three crucial notions of Hummell and Opp's research programme ? their explications of the notions of ?sociology?, ?psychology? and the concept of reduction itself ? and criticizes the authors? deficient ?logic of reduction?. Although the ?local? shortcomings of our authors? ?logic of reduction? do not affect reductionism as such, i.e. logically sound versions of reductionism as devised by Kemeny, Nagel, Oppenheim, Putnam, Woodger et al., it is argued that the logical soundness of sophisticated reductionism cannot compensate for its additional epistemological and methodological deficiencies. Section III analyses the ?dynamic? interpretation of reductionism as a particular developmental pattern of scientific growth. It is argued that even reductionism at its best can produce only cumulative progress, thus ?a priori? excluding scientific revolutions which are inevitably counter?inductive as well as counter?reductive. Section IV discusses the philosophical background of modern reductionism, and examines the effects both of reductionism and of anti?reductionistic pluralism on the autonomy of scientific fields. It is argued that pluralistic anti?reductionism undermines spurious claims for autonomy much more effectively than reductionism. As a ?local? improvement of the reductionistic research programme, the replacement of the predominant one?way reductionism by a less restrictive many?way reductionism is proposed. It is argued that the appropriate treatment for an allegedly backward science (say sociology) is not its reduction to an allegedly more advanced science (say psychology) but its non?reductive replacement by new theories (of the same or of another field) that do not incorporate the older ones. As a ?global? alternative to the reduction of sociology to psychology, the frontier?crossing direct application of psychological theories to sociological phenomena is proposed. A plea is made for a pluralistic science without reduction, based on intra? and interscientific criticism as the proper method for the advancement of knowledge. (shrink)

The paper discusses the sense in which the changes undergone by normative economics in the twentieth century can be said to be progressive. A simple criterion is proposed to decide whether a sequence of normative theories is progressive. This criterion is put to use on the historical transition from the new welfare economics to social choice theory. The paper reconstructs this classic case, and eventually concludes that the latter theory was progressive compared with the former. It also briefly comments on (...) the recent developments in normative economics and their connection with the previous two stages. (Published Online April 18 2006) Footnotes1 This paper suspersedes an earlier one entitled “Is There Progress in Normative Economics?” (Mongin 2002). I thank the organizers of the Fourth ESHET Conference (Graz 2000) for the opportunity they gave me to lecture on this topic. Thanks are also due to J. Alexander, K. Arrow, A. Bird, R. Bradley, M. Dascal, W. Gaertner, N. Gravel, D. Hausman, B. Hill, C. Howson, N. McClennen, A. Trannoy, J. Weymark, J. Worrall, two annonymous referees of this journal, and especially the editor M. Fleurbaey, for helpful comments. The editor's suggestions contributed to determine the final orientation of the paper. The author is grateful to the LSE and the Lachmann Foundation for their support at the time when he was writing the initial version. (shrink)

This paper criticises necessitarianism, the thesis that there is at least one necessary truth; and defends possibilism, the thesis that all propositions are contingent, or that anything is possible. The second section maintains that no good conventionalist account of necessity is available, while the third section criticises model theoretic necessitarianism. The fourth section sketches some recent technical work on nonclassical logic, with the aim of weakening necessitarian intuitions and strengthening possibilist intuitions. The fifth section considers several a prioristic attempts at (...) demonstrating that there is at least one necessary proposition and finds them inadequate. The final section emphasises the epistemic aspect of possibilism. (shrink)

Peirce and Dewey were generally more concerned with the process of scientific activity than purely mathematical work. However, their accounts of knowledge production afford some insights into the epistemology of mathematical postulates, especially definition and axioms. Their rejection of rationalist metaphysics and their emphasis on continuity in inquiry provides the pretext for the pragmatic a priori – hypothetical and operational assumptions whose justification relies on their fruitfulness in the long run. This paper focuses on the application of this idea to (...) the epistemology of definitions and an account of progress in mathematics, although it has broader implications for the study of conceptual change and the function and basis of presuppositions in the sciences. (shrink)

The paper, analyses the role of measurable concepts in deductive explanation. It is shown that such concepts are, although imprecise in a defined sense, exact in that neutral candidates to them do not arise. An analysis is given of the way in which imprecision is related to generalisation, and it is shown how imprecise concepts are incorporated in testable deductive explanations.

It is thirty years since the last major reforms of science education. many believe that it is time for reappraisal of these earlier curricula, and for the renewal of science education-its content, aims, methods. also, and importantly, there is a renewed interest in the preparation of science teachers. this essay is a contribution to that task.

The paper offers a new understanding of induction in the empirical sciences, one which assimilates it to induction in geometry rather than to statistical inference. To make the point a system of notions, essential to logically sound induction, is defined. Notable among them are arbitrary object and particular property. A second aim of the paper is to bring to light a largely neglected set of assumptions shared by both induction and deduction in the empirical sciences. This is made possible by (...) appealing to the logic of common nouns and applying it to the logic of natural-kind terms.This strategy yields a new insight into the concept of natural kinds. While the strategy reveals deep affinity between empirical induction and deduction it also reveals two problems peculiar to induction. This helps to explain the intuition that induction is the more problematic of the two. The paper does not set out ‘to solve the problem of induction’. 1The paper has benefited from the support and critical comments of several friends: Steven Davis, Kevin Dunbar, Anil Gupta, Michael Hallett, Ray Jackendoff and Storrs McCall. Two friends, however, deserve special thanks, Michael Makkai and Gonzalo Reyes. Many of the points made in the paper, otherwise unacknowledged, are due to their generosity and patience. In fact, the paper can be seen as an application of the logic of kinds on which Gonzalo Reyes has been working for several years. (shrink)

Gödel argued that intuition has an important role to play in mathematical epistemology, and despite the infamy of his own position, this opinion still has much to recommend it. Intuitions and folk platitudes play a central role in philosophical enquiry too, and have recently been elevated to a central position in one project for understanding philosophical methodology: the so-called ‘Canberra Plan’. This philosophical role for intuitions suggests an analogous epistemology for some fundamental parts of mathematics, which casts a number of (...) themes in recent philosophy of mathematics (concerning a priority and fictionalism, for example) in revealing new light. (shrink)

Everyone appreciates a clever mathematical picture, but the prevailing attitude is one of scepticism: diagrams, illustrations, and pictures prove nothing; they are psychologically important and heuristically useful, but only a traditional verbal/symbolic proof provides genuine evidence for a purported theorem. Like some other recent writers (Barwise and Etchemendy [1991]; Shin [1994]; and Giaquinto [1994]) I take a different view and argue, from historical considerations and some striking examples, for a positive evidential role for pictures in mathematics.

The thirty year long friendship between Imre Lakatos and the classic scholar and historian of mathematics Árpád Szabó had a considerable influence on the ideas, scholarly career and personal life of both scholars. After recalling some relevant facts from their lives, this paper will investigate Szabó's works about the history of pre-Euclidean mathematics and its philosophy. We can find many similarities with Lakatos' philosophy of mathematics and science, both in the self-interpretation of early axiomatic Greek mathematics as Szabó reconstructs it, (...) and in the general overview Szabó provides us about the turn from the intuitive methods of Greek mathematicians to the strict axiomatic method of Euclid's Elements. As a conclusion, I will argue that the correct explanation of these similarities is that in their main works they developed ideas they had in common from the period of intimate intellectual contact in Hungarian academic life in the mid-twentieth century. In closing, I will recall some relevant features of this background that deserve further research. (shrink)

In his Remarks on the Foundations of Mathematics, Wittgenstein claims, puzzlingly, that ‘the proof creates a new concept’ (RFM III-41). This paper aims to contribute to clarifying this idea, and to showing how it marks a major break with the traditional conception of proof. Moreover, since the most natural way to understand his claim is open to criticism, a secondary goal of what follows is to offer an interpretation of it that neutralizes the objection. The discussion proceeds by analysing a (...) well-known geometrical proof. (shrink)

Analogy has received attention as a form of inductive reasoning in the empirical sciences. Its role in mathematics has, instead, received less consideration. This paper provides a novel account of how an analogy with a more familiar mathematical domain can contribute to the confirmation of a mathematical conjecture. By reference to case-studies, we propose a distinction between an _incremental_ and a _non-incremental_ form of confirmation by mathematical analogy. We offer an account of the former within the popular framework of Bayesian (...) confirmation theory. As for the non-incremental notion, we defend its role in rationally informing the prior credences of mathematicians in those circumstances in which no new mathematical evidence is introduced. The resulting framework captures many important aspects of the use of analogical inference in the domain of pure mathematics. (shrink)

In this paper, we offer a descriptive theory of analogical reasoning in mathematics, stating general conditions under which an analogy may provide genuine inductive support to a mathematical conjecture (over and above fulfilling the merely heuristic role of ‘suggesting’ a conjecture in the psychological sense). The proposed conditions generalize the criteria of Hesse in her influential work on analogical reasoning in the empirical sciences. By reference to several case studies, we argue that the account proposed in this paper does a (...) better job in vindicating the use of analogical inference in mathematics than the prominent alternative defended by Bartha. (shrink)

ABSTRACTIn this paper I investigate how conceptual engineering applies to mathematical concepts in particular. I begin with a discussion of Waismann’s notion of open texture, and compare it to Shapiro’s modern usage of the term. Next I set out the position taken by Lakatos which sees mathematical concepts as dynamic and open to improvement and development, arguing that Waismann’s open texture applies to mathematical concepts too. With the perspective of mathematics as open-textured, I make the case that this allows us (...) to deploy the tools of conceptual engineering in mathematics. I will examine Cappelen’s recent argument that there are no conceptual safe spaces and consider whether mathematics constitutes a counterexample. I argue that it does not, drawing on Haslanger’s distinction between manifest and operative concepts, and applying this in a novel way to set-theoretic foundations. I then set out some of the questions that need to be engaged with to establish mathematics as involving a kind of conceptual engineering. I finish with a case study of how the tools of conceptual engineering will give us a way to progress in the debate between advocates of the Universe view and the Multiverse view in set theory. (shrink)

O tendinţă relativ nouă în filosofia contemporană a matematicii este reprezentată de nemulţumirea manifestată de un număr din ce în ce mai mare de filosofi faţă de viziunea tradiţională asupra matematicii ca având un statut special ce poate fi surprins doar cu ajutorul unei epistemologii speciale. Această nemulţumire i-a determinat pe mulţi să propună o nouă perspectivă asupra matematicii – una care ia în serios aspecte până acum neglijate de filosofia matematicii, precum latura sociologică, istorică şi empirică a cercetării matematice (...) şi care acordă astfel o atenţie deosebită practicii matematice. (shrink)

This chapter tries to answer the following question: How should we conceive of the method of mathematics, if we take a naturalist stance? The problem arises since mathematical knowledge is regarded as the paradigm of certain knowledge, because mathematics is based on the axiomatic method. Moreover, natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some authors tried to naturalize (...) mathematics by relying on evolutionism. But several difficulties arise when we try to do this. This chapter suggests that, in order to naturalize mathematics, it is better to take the method of mathematics to be the analytic method, rather than the axiomatic method, and thus conceive of mathematical knowledge as plausible knowledge. (shrink)

The aim of this paper is to generalize a pair of concepts that are widely used in the history of science, in art history and in historical linguistics – the concept of internal and external history – and to replace the often very vague talk of ‘historical narratives’ with this conceptual framework of internal versus external history. I argue that this way of framing the problem allows us to see the possible alternatives more clearly – as a limited number of (...) possible relations between internal and external history. Finally, I argue that while external history is metaphysically prior to internal history, when it comes to historical explanations, we need both. (shrink)

The aim of this dissertation is to outline and defend the view here dubbed “anti-foundational categorical structuralism” (henceforth AFCS). The program put forth is intended to provide an answer the question “what is mathematics?”. The answer here on offer adopts the structuralist view of mathematics, in that mathematics is taken to be “the science of structure” expressed in the language of category theory, which is argued to accurately capture the notion of a “structural property”. In characterizing mathematical theorems as both (...) conditional and schematic in form, the program is forced to give up claims to securing the truth of its theorems, as well as give up a semantics which involves reference to special, distinguished “mathematical objects”, or which involves quantification over a fixed domain of such objects. One who wishes—contrary to the AFCS view—to inject mathematics with a “standard” semantics, and to provide a secure epistemic foundation for the theorems of mathematics, in short, one who wishes for a foundation for mathematics, will surely find this view lacking. However, I argue that a satisfactory development of the structuralist view, couched in the language of category theory, accurately represents our best understanding of the content of mathematical theorems and thereby obviates the need for any foundational program. (shrink)

The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...) and (3) the specific forms of representation and notation shared and selected by the practitioners. Moreover, it is claimed that a broadening of the notion of ‘permissible action’ as introduced by Larvor (2012) with respect to mathematical arguments, allows for a consideration of all these three elements simultaneously. Second, a case from topology – the proof of Alexander’s theorem – is presented to illustrate a concrete analysis of a mathematical practice and to exemplify the proposed method. It is discussed that the attention to the three elements of the practice identified above brings to the emergence of philosophically relevant features in the practice of topology: the need for a revision in the definition of criteria of validity, the interest in tracking the operations that are performed on the notation, and the constant and fruitful back-and-forth from one representation to another in dealing with mathematical content. Finally, some suggestions for further research are given in the conclusions. (shrink)

From the pre-Socratics to the present, one primary aim of philosophy has been to learn from arguments. Philosophers have debated whether we could indeed do this, but they have by and large agreed on how we would use arguments if learning from argument was at all possible. They have agreed that we could learn from arguments either by starting with true premises and validly deducing further statements which must also be true and therefore constitute new knowledge, or that we could (...) start from putative premises and validly deduce false consequences thereby showing that our premises were false. Our aim in this paper is to suggest a third alternative: we can learn from plausible arguments through criticism of such arguments which enable us to discover new problems. (shrink)

Derivationists, those wishing to explain the correctness and rigour of informal proofs in terms of associated formal proofs, are generally held to be supported by the success of the project of translating informal proofs into computer-checkable formal counterparts. I argue, however, that this project is a false friend for the derivationists because there are too many different associated formal proofs for each informal proof, leading to a serious worry of overgeneration. I press this worry primarily against Azzouni's derivation-indicator account, but (...) conclude that overgeneration is a major obstacle to a successful account of informal proofs in this direction. (shrink)

Suppose we were to ask some students of philosophy to imagine a typical book of classical German philosophy and describe its general style and character, how might they reply? I suspect that they would answer somewhat as follows. The book would be long and heavy, it would be written in a complicated style which employed only very abstract terms, and it would be extremely difficult to understand. At all events a description of this kind does indeed fit many famous works (...) of German philosophy. Let us take for example Hegel's Phenomenology of Spirit of 1807. The 1977 English translation published by Oxford has 591 pages, and as for style here is a typical passage: Self-consciousness found the Thing to be like itself, and itself to be like a Thing; i.e., it is aware that it is in itself the objectively real world. It is no longer the immediate certainty of being all reality, but a certainty for which the immediate in general has the form of something superseded, so that the objectivity of the immediate still has only the value of something superficial, its inner being and essence being self-consciousness itself. The object, to which it is positively related, is therefore a self-consciousness. It is in the form of thinghood, i.e. it is independent ; but it is certain that this independent object is for it not something alien, and thus it knows that it is in principle recognized by the object. It is Spirit which, in the duplication of its self-consciousness and in the independence of both, has the certainty of its unity with itself. This certainty has now to be raised to the level of truth; what holds good for it in principle , and in its inner certainty, has to enter into its consciousness and become explicit fork. (shrink)

In the spirit of James and Dewey, I ask what one might want from a theory of knowledge. Much Anglophone epistemology is centered on questions that were once highly pertinent, but are no longer central to broader human and scientific concerns. The first sense in which epistemology without history is blind lies in the tendency of philosophers to ignore the history of philosophical problems. A second sense consists in the perennial attraction of approaches to knowledge that divorce knowing subjects from (...) their societies and from the tradition of socially assembling a body of transmitted knowledge. When epistemology fails to use the history of inquiry as a laboratory in which methodological claims can be tested, there is a third way in which it becomes blind. Finally, lack of attention to the growth of knowledge in various domains leaves us with puzzles about the character of the knowledge we have. I illustrate this last theme by showing how reflections on the history of mathematics can expand our options for understanding mathematical knowledge. (shrink)

Cauchy’s contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, (...) the seeds of the theory of rates of growth of functions as developed by Paul du Bois-Reymond. One sees, with E. G. Björling, an infinitesimal definition of the criterion of uniform convergence. Cauchy’s foundational stance is hereby reconsidered. (shrink)

Kaposy (2010) argues that contemporary neuroscience cannot provide rational reasons for abandoning folk psychological concepts like self, personhood, or free will because these concepts are necessa...

Douglas W. Hands's “What Economics Is Not: An Economist's Response to Rosenberg“ is an unsympathetic criticism of the explanatory hypotheses of “If Economics Isn't Science, What Is It?”. Before replying to his objection, I summarize the claims of that paper.

ABSTRACT Recent discussions of practice in this Journal have appealed to what they describe as the classical concept of practice. In this paper, it is argued that if there is a single classical concept of practice, it has not been described with sufficient clarity for it to be of use in illuminating or correcting anything, even our ‘radically ambiguous’ common-sense understanding of educational practice; and that there are writers today whose understanding of practical wisdom is far superior to that of (...) the modern philosophers whose treatment of the topic has been relied upon. (shrink)

Reasoners compare problems to prior cases to draw conclusions about a problem and guide decision making. All Case-Based Reasoning (CBR) employs some methods for generalizing from cases to support indexing and relevance assessment and evidences two basic inference methods: constraining search by tracing a solution from a past case or evaluating a case by comparing it to past cases. Across domains and tasks, however, humans reason with cases in subtly different ways evidencing different mixes of and mechanisms for these components.In (...) recent CBR research in Artificial Intelligence (AI), five paradigmatic approaches have emerged: statistically-oriented, model-based, planning/design-oriented, exemplar-based, and adversarial or precedent-based. The paradigms differ in the assumptions they make about domain models, the extent to which they support symbolic case comparison, and the kinds of inferences for which they employ cases. (shrink)

. Heuristic is a central concept of Lakatos' philosophy both in his early works and in his later work, the methodology of scientific research programs. The term itself, however, went through significant change of meaning. In this paper I study this change and the ‘metaphysical’ commitments behind it. In order to do so, I turn to his mathematical heuristic elaborated in Proofs and Refutations. I aim to show the dialogical character of mathematical knowledge in his account, which can open a (...) door to hermeneutic studies of mathematical practice. (shrink)

The fallibility of deduction is the thesis that a thoughtful speaker-reasoner can wrongly believe that an inference is deductively valid. The author presents an argument to the effect that the fallibility of deduction is incompatible with the widespread view that deduction is epistemically unfruitful (the conclusion is contained in the premises, and the transition from premises to conclusion never extends knowledge). If the fallibility of deduction is a fact, the argument presented is a refutation of the doctrine of the unfruitfulness (...) of deduction. But its relevance goes further, because the argument reveals a connection between two different problems: a solution to the problem of fruitfulness (how can deductive inferences increase our knowledge?) is a starting point for a solution to the problem of fallibility (how can deductive inferences be wrong?). To solve the problem of fruitfulness, Michael Dummett proposed some general ideas concerning meaning and inference. Starting from these meaning-theoretical ideas, one can develop an explanation of the fallibility of deduction. The general explanatory strategy does not depend on the choice between a theory of meaning centered on truth, verification, inferential role, or on other key notions. (shrink)

Some of the problem areas in which British philosophers of science have recently been engaged are described and some of the major contributions noted. Two sets of problems are given special attention: one concerned with the analysis of probability statements and one concerned with the appraisal of scientific theories. Three traditions in the approach to this second set of problems are distinguished. These might be called the Carnapian, the Popperian and the Wittgensteinian traditions.

Jim Mackenzie; Authority, Journal of Philosophy of Education, Volume 22, Issue 1, 30 May 2006, Pages 57–65, https://doi.org/10.1111/j.1467-9752.1988.tb00177.x.

. The circumstance, that the text of Imre Lakatos' doctoral thesis from the University of Debrecen did not survive, makes the evaluation of his career in Hungary and the research of aspects of continuity of his lifework difficult. My paper tries to reconstruct these newer aspects of continuity, introducing the influence of László Kalmár the mathematician and his fellow student, and Sándor Karácsony the philosopher and his mentor on Lakatos' work. The connection between the understanding of the empirical basis of (...) exact ideas—which is a common feature in the papers of the members of the Karácsonycircle—and Lakatos' way of thinking regarding mathematics is more direct and can be documented through his connection to Kalmár. The central element of Lakatos' philosophy of mathematics is criticism of formalism and his tendency is to use the empirical view. Discussions at the 1965 International Colloquium in the Philosophy of Science in London were very helpful in clarifying the quasi-empirical conception. Kalmár's lecture in London, based on one of his papers published by Karácsony in 1942, emphasized the empirical character of mathematics. After this colloquium some elements of the heritage of the Karácsony-circle were integrated again in the development of Lakatos' way of thinking. First I will analyze the Kalmár lecture of 1965 at the Colloquium of Philosophy of Science and Lakatos's reflections on the problem of the foundation of mathematics. Then I will present their common Hungarian background, their education and the beginning of their career, which have many important common features; third I draw attention to the network of contacts of Karácsony-disciples. (shrink)

The last century has seen many disciplines place a greater priority on understanding how people reason in a particular domain, and several illuminating theories of informal logic and argumentation have been developed. Perhaps owing to their diverse backgrounds, there are several connections and overlapping ideas between the theories, which appear to have been overlooked. We focus on Peirce’s development of abductive reasoning [39], Toulmin’s argumentation layout [52], Lakatos’s theory of reasoning in mathematics [23], Pollock’s notions of counterexample [44], and argumentation (...) schemes constructed by Walton et al. [54], and explore some connections between, as well as within, the theories. For instance, we investigate Peirce’s abduction to deal with surprising situations in mathematics, represent Pollock’s examples in terms of Toulmin’s layout, discuss connections between Toulmin’s layout and Walton’s argumentation schemes, and suggest new argumentation schemes to cover the sort of reasoning that Lakatos describes, in which arguments may be accepted as faulty, but revised, rather than being accepted or rejected. We also consider how such theories may apply to reasoning in mathematics: in particular, we aim to build on ideas such as Dove’s [13], which help to show ways in which the work of Lakatos fits into the informal reasoning community. (shrink)