Excerpt from Induction and Deduction: A Historical Critical Sketch of Successive Philosophical Conceptions Respecting the Relations Between Inductive and Deductive Thought and Other Essays It is a painful and pathetic task for an intimate friend of Constance Naden to be called upon to write a memoir, however brief, of her short life, instead of looking forward to years of happy and elevating intercourse, sharing in works of benevolent usefulness, and gladly watching her rise to the distinction which her intellectual (...) gifts entitled her circle of friends to anticipate. The sorrow for her loss must be lifelong. As Mrs. Browning says, "the inevitable strikes us dead," but the expression of it is unavailing. All that remains for the most devoted of her friends is to keep her memory green, by striving to let the world know what it has lost, both in promise and in fulfilment. Miss Naden's earlier life was uneventful, and almost all the details for this portion of it have been drawn from accounts published in the Birmingham papers, at the time of her death, by those associated with her school and college career. Constance Caroline Woodhill Naden was born on the 24th January, 1858, at her father's house in Edgbaston, where he still resides, and is the President of the Birmingham Architectural Association. Her mother died on the 5th February, a few days after the birth of her child. Shortly afterwards the motherless infant was domesticated with her mother's parents, Mr. and Mrs. Woodhill, of Pakenham House, Edgbaston, and here Constance lived a retired, peaceful life, adored by her grandparents, till they died, Mr. Woodhill in 1881, and his widow in 1887. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Epistemological naturalists reject the demand for a priori justification of empirical knowledge; no such thing is possible. Observation reports, being the foundation of empirical knowledge, are neither justified by other sentences, nor certain; but they may be agreed upon as starting points for inductive reasoning and they function as implicit definitions of predicates used. Making inductive generalisations from observations is a basic habit among humans. We do that without justification, but we have strong intuitions that some inductive generalisations will fail, (...) while for some other we have better hopes. Why? This is the induction problem according to Goodman. He suggested that some predicates are projectible when becoming entrenched in language. This is a step forward, but not entirely correct. Inductions result in universally generalised conditionals and these contain two predicates, one in the antecedent, one in the consequent. Counterexamples to preliminary inductive generalisations can be dismissed by refining the criteria of application for these predicates. This process can be repeated until the criteria for application of the predicate in the antecedent includes the criteria for the predicate in the consequent, in which case no further counterexample is possible. If that is the case we have arrived at a law. Such laws are implicit definitions of theoretical predicates. An accidental generalisation has not this feature, its predicates are unrelated. Laws are said to be necessary, which may be interpreted as ‘“Laws” are necessarily true’. ‘Necessarily true’ is thus a semantic predicate, not a modal operator. In addition, laws, being definitions, are necessarily true in the sense of being necessary assumptions for further use of the predicates implicitly defined by such laws. Induction, when used in science, is thus our way of inventing useful scientific predicates; it is a heuristic, not an inference principle. (shrink)

Modern Empiricists are typically troubled by the two following problems: (1) There is an epistemic gap between experience of individuals and understanding universals such that empiricist accounts of concept formation seem to beg the question. (2) There needs to be an answer to the skeptic who denies that sensory experience warrants our belief in the existence of the material substances that underlie sensible qualities. Although Aristotle’s account of induction is subject to these problems prima facie, his theory (...) of perception, his teleologically driven reliabilism about the senses, and his broader metaphysical views concerning the relation between substance and accident serve to insulate his account of induction from the pitfalls of modern empiricism. The resolution to these problems proposed in this paper allows for a consistent reading of otherwise controversial Aristotelian texts, while recommending a defense of realism about material substance against the claims of the Humean skeptic. (shrink)

The inductive category formation framework, an influential set of theories of learning in psychology and artificial intelligence, is deeply flawed. In this framework a set of necessary and sufficient features is taken to define a category. Such definitions are not functionally justified, are not used by people, and are not inducible by a learning system. Inductive theories depend on having access to all and only relevant features, which is not only impossible but begs a key question in learning. The (...) crucial roles of other cognitive processes (such as explanation and credit assignment) are ignored or oversimplified. Learning necessarily involves pragmatic considerations that can only be handled by complex cognitive processes.We provide an alternative framework for learning according to which category definitions must be based on category function. The learning system invokes other cognitive processes to accomplish difficult tasks, makes inferences, analyses and decides among potential features, and specifies how and when categories are to be generated and modified. We also examine the methodological underpinnings of the two approaches and compare their motivations. (shrink)

"With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics."--Carl B. Boyer, Brooklyn College. This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition. Contents include examinations of arithmetic and geometry; the rigorous construction of the theory of integers; the rational numbers and their foundation in arithmetic; and the rigorous construction of elementary (...) arithmetic. Advanced topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers. 1959 ed. 27 Figures. Index. (shrink)

S.J. Cyril Barrett; VI—Concepts and Concept Formation, Proceedings of the Aristotelian Society, Volume 63, Issue 1, 1 June 1963, Pages 127–144, https://doi.org/.

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)

The notion of exploratory modeling constitutes a powerful heuristic tool for historical-epistemological analysis and especially for studying concept formation. I will show this by means of a case study from the history of particle physics: the formation of the concept of “strangeness” in the early 1950s at the interface of theory and experiment. Strangeness emerged from a broad space of possibilities opened up by exploratory modeling by authors working in communication and competition, and constructing both new (...) questions and new answers. A systematic focus on exploratory modeling also helps compensate a bias towards the “right” developments still often present in historical investigations of theoretical work. (shrink)

I support Rips et al.'s critique of psychology through (1) a complementary argument about the normative, modal, constitutive nature of mathematical principles. I add two reservations about their analysis of mathematical induction, arguing (2) for constructivism against their logicism as to its interpretation and formation in childhood (Smith 2002), and (3) for Piaget's account of reasons in rule learning.

According to the standard interpretation, Aristotle has two accounts of induction (epagoge): intuitive induction (which is not an inference) and complete induction (which is not a kind of non-demonstrative inference). Hintikka has challenged the usual interpretation of Aristotle's "official account" in Analytica Priora II, 23. In this paper, Hintikka's view is compared with a similar, but in some respects perhaps even more plausible, interpretation that William Whewell gave already in 1850. Both Hintikka and Whewell argue convincingly that (...) Aristotelean induction is connected to concept formation. According to Whewell, the key to Aristotle's account is not the exhaustiveness or completeness of the sample of special cases, but rather its representativeness for the purpose of generalization. (shrink)

According to the standard interpretation, Aristotle has two accounts of induction (epagoge): intuitive induction (which is not an inference) and complete induction (which is not a kind of non-demonstrative inference). Hintikka has challenged the usual interpretation of Aristotle's "official account" in Analytica Priora II, 23. In this paper, Hintikka's view is compared with a similar, but in some respects perhaps even more plausible, interpretation that William Whewell gave already in 1850. Both Hintikka and Whewell argue convincingly that (...) Aristotelean induction is connected to concept formation. According to Whewell, the key to Aristotle's account is not the exhaustiveness or completeness of the sample of special cases, but rather its representativeness for the purpose of generalization. (shrink)

Developing tools is a crucial aspect of experimental practice, yet most discussions of scientific change traditionally emphasize theoretical over technological change. To elaborate on the role of tools in scientific change, I offer an account that shows how scientists use tools in exploratory experiments to form novel concepts. I apply this account to two cases in neuroscience and show how tool development and concept formation are often intertwined in episodes of tool-driven change. I support this view by proposing (...) common normative principles that specify when exploratory concept formation and tool development succeed to initiate scientific change. (shrink)

This encyclopedia article provides a procedural account of explication outlining each step that is part of the overall explicative effort (2). It is prefaced by a summary of the historical development of the method (1). The latter part of the article includes a rough structural theory of explication (3) and a detailed presentation of an examplary explication taken from the history of philosophy and the foundations of mathematics (4).

We argue for an example of based on Diamond and Carey's (1986) work on expertise and recognition, which is not made use of in The Origin of Concepts. This mechanism for perceptual learning seems to have all the necessary characteristics in that it is innate, domain-specific (requires stimulus sets possessing a certain structure), and demonstrably affects categorisation in a way that strongly suggests it will influence concept formation as well.

From an epistemological viewpoint, the Forms constitute the objects of true knowledge. From an ontological point of view, they are the principles that underlie the order of the universe.

3 in philosophy, and therefore in metaphilosophy, cannot be based on rules that avoid spending time on pseudo-problems. Of course, this implies that, if one succeeds in demonstrating convincingly the pseudo-character of a problem by giving its 'solution', the time spent on it need not be seen as wasted. We conclude this section with a brief statement of the criteria for concept explication as they have been formulated in several places by Carnap, Hempel and Stegmiiller. Hempel's account is still (...) very adequate for a detailed introduction. The process of explication starts with the identification of one or more vague and, perhaps, ambiguous concepts, the so-called explicanda. Next, one tries to disentangle the ambiguities. This, however, need not be possible at once. Ultimately the explicanda are to be replaced by certain counterparts, the so-called explicata, which have to conform to four requirements. They have to be as precise as possible and as simple as possible. In addition, they have to be useful in the sense that they give rise to the formulation of theories and the solution of problems. The three requirements of preciseness, simplicity and usefulness. have of course to be pursued in all concept formation. (shrink)

The control of pattern formation and the significance of gradients is reconsidered on the basis of the concept of cell sociology (which takes into account continuous exchange of information between cells and the possibility of autonomous progression in differentiation). Not all traits of a pattern are imposed by a single prepattern, which would be an organized molecular framework or a gradient. Patterns are unfolded in steps; these are readjustments of a cell population to intrinsic and extrinsic changes in (...) cell activities. Prepatterns are the various components of the programme of every readjustment and are established by information of various origins, which can be dissociated experimentally: determination (elementary social prepattern), pre-existing organization (antecedent pp.), surrounding cell populations (environmental pp.), position among other tissues (positional pp.) and the organization of inducers (imprinting pp.). Every transitory pattern formed during a readjustment serves as antecedent pp. during the next readjustment. Covert graded patterns result from various aspects of the social behaviour of cells (growth, aggregation, induction, cell renewal) and may serve as antecedent or imprinting prepatterns. They appear as water marks in the final patterns, or generate overt graded patterns. They also manifest themselves in temporal patterns, particularly in gradients of relative growth. (shrink)

In this paper, I wish to argue that an explanation is not a logical structure¸ that it cannot be characterised in syntactic terms, but that it is rather an epistemological structure, and, more specifically, a structure organising conceptual content. I will start from a trivial example and systematically look at the effects of making premises more general or more specific or of reshuffling the same content into another set of premises, thereby exposing the implicit suppositions and consequences of some commonly (...) held views and showing their untenability. (shrink)

In this paper, I provide an explication and defense of Merleau-Ponty’s theory of concept formation. I argue that at the core of this theory is a distinction between concepts proper and the kinds of generalities characteristic of perceptual experience, which I call “pre-conceptual generalities.” According to Merleau-Ponty, concepts are developed through a two-stage process: first, the establishment of such pre-conceptual generalities, and second, the clarification of these generalities into concepts. I provide phenomenological evidence for the existence of pre-conceptual (...) generalities and explain how they can serve to ground concept formation. To motivate Merleau-Ponty’s account, I consider objections raised by Husserl, Cassirer, and Sellars to the classical philosophical account of empirical concept formation, abstraction. I show that Merleau-Ponty’s distinction between concepts and pre-conceptual generalities provides a philosophically viable account of the formation of empirical concepts while avoiding the problems faced by accounts that rely on abstraction. (shrink)

A book aimed at advanced undergraduates and graduates in cognitive science and artificial intelligence, linguistics, applied mathematics and data analysis.

Forms and Concepts is the first comprehensive study of the central role of concepts and concept acquisition in the Platonic tradition. It sets up a stimulating dialogue between Plato s innatist approach and Aristotle s much more empirical response. The primary aim is to analyze and assess the strategies with which Platonists responded to Aristotle s (and Alexander of Aphrodisias ) rival theory. The monograph culminates in a careful reconstruction of the elaborate attempt undertaken by the Neoplatonist Proclus (6th (...) century AD) to devise a systematic Platonic theory of concept acquisition.". (shrink)

This paper argues that Weyl's view that scientific objectivity requires that concepts be freely created, i.e., introduced via Hilbert-style axiomatizations, led him to abandon the phenomenological view of objectivity.

What is art? What constitutes great art? Why do we value art so much and why has it been such a conspicuous feature of all human societies? These questions have been discussed at length though without satisfactory resolution. This is not surprising. Such discussions are usually held without reference to the brain, through which all art is conceived, executed and appreciated. Art has a biological basis. It is a human activity and, like all human activities, including morality, law and religion, (...) depends upon, and obeys, the laws of the brain. To understand the biological foundations of art, we must enquire into the biological foundations of knowledge, for art constitutes a form of knowledge; indeed is knowledge. We are still far from knowing the neural basis of the laws that dictate artistic creativity, achievement and appreciation, but spectacular advances in our knowledge of the visual brain allow us to make a beginning in trying to formulate neural laws of art and aesthetics; in short, to study neuroaesthetics. In this essay, I try to discuss the art of three Titanic figures in Western culture — Dante, Michelangelo and Wagner — in neurological terms. I try to show that we can trace the origins of their art to a fundamental characteristic of the brain, namely its capacity to form concepts. This capacity is itself the by-product of an essential characteristic of the brain. That characteristic is abstraction, and is imposed upon the brain by one of its chief functions, namely the acquisition of knowledge. (shrink)

Recently Carrie S. Jenkins formulated an epistemology of mathematics, or rather arithmetic, respecting apriorism, empiricism, and realism. Central is an idea of concept grounding. The adequacy of this idea has been questioned e.g. concerning the grounding of the mathematically central concept of set (or class), and of composite concepts. In this paper we present a view of concept formation in mathematics, based on ideas from Carnap, leading to modifications of Jenkins’s epistemology that may solve some problematic (...) issues with her ideas. But we also present some further problems with her view, concerning the role of proof for mathematical knowledge. (shrink)

This tribute to Carlos Steel, director of the De Wulf-Mansion Centre and former Dean of Philosophy at Leuven University, offers a full bibliography of this eminent scholar's research in areas of ancient thought, critical editions of medieval texts, and central issues dealt with by prominent medieval speculators. This is followed by eleven essays arranged in three major groupings.

In recent years there has been considerable discussion and controversy concerning the concepts of mental health and mental illness. The controversy has centered around the problem of providing criteria for an adequate conception of mental health and illness, as well as difficulties in specifying a clear and workable system for the classification, understanding, and treatment of psychological and emotional disorders. In this paper I shall examine a cluster of these complex and important issues, focusing on attempts to define ‘mental health’ (...) and ‘mental illness’; diverse factors influencing the ascription of the predicates ‘is mentally ill’ and ‘is mentally healthy’; and some specific problems concerning these concepts as they appear in various theories of psychopathology. The approach here will be in the nature of a survey, directed at the specification of a number of problems—conceptual, methodological, and pragmatic—as they arise in various attempts to define and to provide criteria for applying the concepts of mental health and mental illness. (shrink)

The subject of this essay is the classical problem of induction, which is sometimes attributed to David Hume and called “the Humean Problem of Induction.” Here, I examine a certain sort of Neo-Aristotelian solution to the problem, which appeals to the concept of natural kinds in its response to the inductive skeptic. This position is most notably represented by Howard Sankey and Marc Lange. The purpose of this paper is partly destructive and partly constructive. I raise two (...) questions. The first is: Are the natural kind solutions to the problem successful? The first thesis of this paper is that they are not, and I will show how and why they fail. And the second question I raise here is: Is there nonetheless some alternative Neo-Aristotelian solution to the problem which is successful and can overcome the shortcomings endemic to the Sankey-Lange account? The second thesis is that there is, and I’ll attempt to sketch one. My stance here may be summarized by saying that, while I agree with Sankey and Lange that the problem of induction can be adequately resolved, and while I am on the whole sympathetic with the Aristotelian spirit of their account, I am, for all that, dissatisfied with the letter of them. Nothing short of a more thoroughgoing Aristotelianism about the epistemology of induction will do. (shrink)

We analyze two problems in mathematics – the first (stated in our title) is extracted from Wittgenstein’s “Philosophy for Mathematicians”; the second (“What set of numbers is non-denumerable?”) is taken from Cantor. We then consider, by way of comparison, a problem in musical aesthetics concerning a Brahms variation on a theme by Haydn. Our aim is to bring out and elucidate the essentially riddle-like character of these problems.

This article will consider the claim that the possession of concepts is innate rather than learned. Innatism about concept learning is explained through consideration of the work of Fodor and Chomsky. First, an account of concept formation is developed. Second the argument against the claim that concepts are learned through the construction of a learning paradox developed by Fodor is considered. It is argued that, despite initial plausibility, the learning paradox is not, in fact, a paradox at (...) all as it rests on eliding the distinction between recognising something and recognising it as a something. The plausibility of eliding this distinction rests, in turn, on begging the question as to whether concept possession is a necessary condition for recognition of objects, events, properties etc. Fodor's positive arguments for innatism, as set out in LOT2 are considered and parallels with his account of stereotype formation and associationist accounts of concept formation are considered. The explanatory persuasiveness of this revised account of concept activation through the generation of stereotypes is weak. The article then examines the distinction between concept possession and concept mastery in greater detail, arguing that innatists have difficulty in accounting for the phenomenon of concept mastery, including within the contexts of formal and professional education. (shrink)

Botha notes that metaphors are pervasive both in thought and in language and in human subjective experience in general: in conceptual metaphor theory metaphors are analyzed as stable and systematic relation- ships between two conceptual domains. Mittelberg explores the semiotic work gestures perform in visualizing abstract concepts and structures, insisting on the different types of iconic modes discernable in gestural representations of the metaphorically conceptualized domain of grammar. Evans considers the cognitive preadaptations that may have paved the way for the (...) emergence of semantic knowledge. (shrink)