Gödel And The Intuition Of Concepts

Gödel has argued that we can cultivate the intuition or ‘perception’ of abstractconcepts in mathematics and logic. Gödel's ideas about the intuition of conceptsare not incidental to his later philosophical thinking but are related to many otherthemes in his work, and especially to his reflections on the incompleteness theorems.I describe how some of Gödel's claims about the intuition of abstract concepts are related to other themes in his philosophy of mathematics. In most of this paper, however,I focus on a central question that has been raised in the literature on Gödel: what kind of account could be given of the intuition of abstract concepts? I sketch an answer to this question that uses some ideas of a philosopher to whom Gödel also turned in this connection: Edmund Husserl. The answer depends on how we understand the conscious directedness toward ‘objects’ and the meaning of the term ‘abstract’ in the context of a theory of the intentionality of cognition.     

Quine, Putnam, and the ‘Quine–Putnam’ Indispensability Argument

Much recent discussion in the philosophy of mathematics has concerned the indispensability argument—an argument which aims to establish the existence of abstract mathematical objects through appealing to the role that mathematics plays in empirical science. The indispensability argument is standardly attributed to W. V. Quine and Hilary Putnam. In this paper, I show that this attribution is mistaken. Quine’s argument for the existence of abstract mathematical objects differs from the argument which many philosophers of mathematics ascribe to him. Contrary to appearances, Putnam did not argue for the existence of abstract mathematical objects at all. I close by suggesting that attention to Quine and Putnam’s writings reveals some neglected arguments for platonism which may be superior to the indispensability argument.

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Conditio sine qua non? Zuordnung in the early epistemologies of Cassirer and Schlick

In early major works, Cassirer and Schlick differently recast traditional doctrines of the concept and of the relation of concept to intuitive content along the lines of recent epistemological discussions within the exact sciences. In this, they attempted to refashion epistemology by incorporating as its basic principle the notion of functional coordination, the theoretical sciences' own methodological tool for dispensing with the imprecise and unreliable guide of intuitive evidence. Examining their respective reconstructions of the theory of knowledge provides an axis of comparison along which to locate Cassirer's Neo-Kantianism and Schlick's pre-positivist empiricism, and an immediate background of contrast to the subsequent rise of logical empiricism. For in the absence of intuition all our knowledge is without objects and therefore remains entirely empty. (Kant A62/B87) And how awkward is the human mind in diving the nature of things when forsaken by the analogy of what we see and touch directly? (Boltzmann 1895)     

Christopher Clavius and the classification of sciences

I discuss two questions: (1) would Duhem have accepted the thesis of the continuity of scientific methodology? and (2) to what extent is the Oxford tradition of classification/subalternation of sciences continuous with early modern science? I argue that Duhem would have been surprised by the claim that scientific methodology is continuous; he expected at best only a continuity of physical theories, which he was trying to isolate from the perpetual fluctuations of methods and metaphysics. I also argue that the evidence does not support the conclusion that early modern doctrines about mathematics and physics are continuous with the subalternation of sciences from Grosseteste, Bacon, and the theologians of fourteenth-century Oxford. The official and dominant context for early modern scientific methodology seems to have been progressive Thomism, and early modern thinkers seem to have pitted themselves against it.     

PSN: A prolog declarative model of conceptual knowledge

This paper introduces a declarative model of semantic memory, called PSN, written in Prolog. It is shown to be a descendant of Quillian’s (1969) Teachable Language Comprehender (TLC) in its structuring of knowledge as a conceptual reticulum and in its use of spreading activation as a retrieval mechanism. PSN goes beyond TLC, however, in its ability to instantiate the essential benchmark properties of human semantic retrieval. As such, it can provide cognitive science with a normative model on which to assess further research and it demonstrates the value of the Prolog language for modeling psychological processes.     

The status of psychoanalytic theory∗

What is the place of Psychoanalytic Theory on our map of knowledge and belief? Various alternatives are considered. Is it a scientific theory? — a myth? — or like a prescientific example of natural philosophy? — a branch of medical knowledge? — a premature empirical synthesis that is an approximation to the truth? Each of these answers runs into objections and difficulties, some of which are examined or noted. On the assumption that it is a provisional story which approximates to the truth, the question is then raised: what can we do to find out how much of an approximation to the truth the theory really is? The relevance and value of psychological studies are discussed; and the suggestion is made that the status of Psychoanalytic Theory will remain an ambiguous one for some time to come.     

Reflexionen über die Struktur der Physikalischen Sprache

The aim of this paper is to discuss how far physics differs frommathematics, and if a philosophy of science which uses mathematics or logicsas a model for physics would be unable to be aware of many importantfeatures of that natural science.Many functions in physics differ from those of mathematics in beingfunctional dependecies and in having a lawlike character.Physical quantities have the character of "`determinables"', sets ofspecial entities which are presupposed by physical theories.One may suspect that physics also could not be formulated in anextensional language. This cannot be true, however, since every language canbe translated into an extensional version. Neverthless the existence ofdeterminables in physics shows that physics does not only talk aboutconcrete entities like space, time, spacetime, and particles, but also aboutvalues of abstract sets like determinables, and that it thus acknowledgestheir existence.     

Knowledge in Society as an Empirical Base for Indian Psychology

Indian society has enormous complexity and diversity of religion and culture. The Indian Psychology will be truly enriched if it explores and integrates these experiences at the individual and group levels. In addition there is perhaps something to learn from the Positive Psychology as to how to best utilize the knowledge in Indian society for the sake of humanity.     

Logical structuralism and Benacerraf’s problem

There are two general questions which many views in the philosophy of mathematics can be seen as addressing: what are mathematical objects, and how do we have knowledge of them? Naturally, the answers given to these questions are linked, since whatever account we give of how we have knowledge of mathematical objects surely has to take into account what sorts of things we claim they are; conversely, whatever account we give of the nature of mathematical objects must be accompanied by a corresponding account of how it is that we acquire knowledge of those objects. The connection between these problems results in what is often called “Benacerraf’s Problem”, which is a dilemma that many philosophical views about mathematical objects face. It will be my goal here to present a view, attributed to Richard Dedekind, which approaches the initial questions in a different way than many other philosophical views do, and in doing so, avoids the dilemma given by Benacerraf’s problem.     

Descartes's Regulae, mathematics, and modern psychology: "the Noblest example of all" in Light of Turing's (1936) On computable Numbers

There are surprisingly strong connections between the philosophy of mind and the philosophy of mathematics. One particular important example can be seen in the Regulae (1628) of Descartes. In "the noblest example of all," he used his new abstract understanding of numbers to demonstrate how the brain can be considered as a symbol machine and how the intellect's algebraic reasoning can be mirrored as operations on this machine. Even though his attempt failed, it is illuminating to explore it because Descartes launched 2 traditions--mechanistic philosophy of mind and abstract mathematics--that would diverge until A. Turing (1936) approached symbolic reasoning in a similar "symbol machine-existence proof" way. Descrates's and Turing's thought experiments, which mark the beginning of modern psychology and cognitive science, respectively, indicate how important the development of mathematics has been for the constitution of the science of mind.     

Scarcity,engagement, and value

Scarcity has been found to intensify value, positive or negative, rather than simply enhancing it. Some researchers have proposed that scarcity affects value by increasing how much attention is paid to a stimulus. We conceptualized sustained attention as stronger engagement and operationalized a situation of scarcity by telling participants who were choosing between two objects that the object that was chosen would then be replaced (Replenish) or not replaced (Scarce). To distinguish sustained attention-stronger engagement in a situation of scarcity from grabbing attention (salience from distinctiveness), the choice was between one option with a single instance (solitary-high salience) and a second option with several duplicates (abundant-low salience). We predicted that stronger engagement from a situation of scarcity would, first, intensify the value of the chosen item regardless of whether it was solitary or abundant, with positive items becoming more positive and negative items becoming more negative, and second, the stronger engagement from the situation of scarcity would transfer intensification to another separate object in the same setting. The results of Studies 1 and 2 supported both of these predictions. Study 3 tested a boundary condition for these scarcity–engagement effects in terms of how real participants experienced the choice items to be, where ‘realness’ is another source of engagement strength. As expected, the scarcity–engagement effect on intensifying value was replicated for participants who experienced the activity as real but was eliminated for those who did not.     

What Mary Didn't Read: On Literary Narratives and Knowledge

In the philosophy of art, one of the most important debates concerns the so‐called ‘cognitive value’ of literature. The main question is phrased in various ways. Can literary narratives provide knowledge? Can readers learn from works of literature? Most of the discussants agree on an affirmative answer, but it is contested what the relevant notions of truth and knowledge are and whether this knowledge and learning influence aesthetic or literary value. The issue takes on a wider, not only philosophical, importance as it is one of the central tenets of humanistic education that art and literature are valuable not only because the pleasure they afford. This paper offers a new line of argument in departing from propositional truth, arguing that literary narratives provide aesthetically significant knowledge, however, this knowledge cannot be captured in propositional form. My position depends crucially on Frank Jackson's influential knowledge argument. The paper describes a modified ‘What Mary Didn't Read’ case. In doing so, it is argued that the knowledge literary works provide should be understood as a type of experiential knowing of ‘what it is like’ analogous to what Mary acquires in the original case of seeing a new colour for the first time. 1 1 I would like to thank first and foremost David Weberman for his comments on the draft of this paper. Also, I am grateful to colleagues at the 7th In‐house Philosophy Graduate Conference of Central European University for a productive discussion. Thirdly, I am indebted to Howard Robinson and Philip Goff for illuminating debates about Jackson's thought experiment.
     

The logical study of science

The relation between logic and philosophy of science, often taken for granted, is in fact problematic. Although current fashionable criticisms of the usefulness of logic are usually mistaken, there are indeed difficulties which should be taken seriously — having to do, amongst other things, with different scientific mentalities in the two disciplines (section 1). Nevertheless, logic is, or should be, a vital part of the theory of science. To make this clear, the bulk of this paper is devoted to the key notion of a scientific theory in a logical perspective. First, various formal explications of this notion are reviewed (section 2), then their further logical theory is discussed (section 3). In the absence of grand inspiring programs like those of Klein in mathematics or Hilbert in metamathematics, this preparatory ground-work is the best one can do here. The paper ends on a philosophical note, discussing applicability and merits of the formal approach to the study of science (section 4).I would like to thank David Pearce and Veikko Rantala for their helpful comments.     

Myth & Math,Part II (preliminary draft)

It is argued that there can only be a small-finite number of mathematical objects; that these objects range from the very concrete to the very abstract; and that mathematics is essentially not concerned with objects but with concepts. This viewpoint is described as mentalist and is upheld over Platonism, intuitionism, and formalism.     

On surrender,death, and the sociology of knowledge

Surrender-and-catch is a protest against [... our time] and an attempt at remembrance of what a human being can be. The sociology of knowledge is a protest against its hypocrisy and against unexamined social influences. Like surrender, the sociology of knowledge does not fear but passionately seeks what is true and thus, like surrender, is a remembrance, proclamation, and celebration of the spirit. Both ideas, that of the sociology of knowledge and that of surrender, are critical, polemical, radical [...]; so is the sociology of knowledge also in its practice, while in its practice surrender is cognitive live. Using a [...] distinction developed by Mannheim, we may also say that the sociology of knowledge is an extrinsic interpretation of its time, our time; surrender, an intrinsic one: the former is, advocates, and practices such an extrinsic (sociological) interpretation but needs the latter to overcome the relativism it encounters in its practice by its remembrance, rediscovery, reinvention, the catch, of what is common to all human beings, what is universally human (Wolff, 1982., pp. 265–266).     

Toward a systematic philosophy of medicine

Can Pellegrino and Thomasma's book, A Philosophical Basis of Medical Practice (1981), rightfully claim to be a step forward towards a systematic philosophy of medicine? We try to answer this question by focusing our comment upon three related aspects of the book, namely (1) the problem of philosophical method(s), (2) the alleged Aristotelian-Thomistic orientation, (3) the view of philosophical anthropology of the authors. It is first argued that it is doubtful whether there is as much philosophical method in the authors' book as their reflections on philosophical method suggest. Second, we argue that if Aristotelian-Thomistic philosophy is important to the authors, it is not so much because of its methods and content, as because it supplies them with a very convenient framework for didactically ordering and transmitting their views about what they consider to be — philosophically speaking — basic about medicine. Third we argue that the authors' conception of philosophical anthropology bears (in point of method and ontology) more resemblance to the humanistic naturalism of John Dewey, than to any of the European philosophical traditions (Aristotelism, (Neo)Thomism, Merleau-Pontyian phenomenology) listed in support of their philosophical enterprise.     

JOHN POLKINGHORNE AND BERNARD LONERGAN ON THE SCIENTIFIC STATUS OF THEOLOGY

On the basis of his acquaintance with theoretical elementary particle physics, and following the lead of Thomas Torrance, John Polkinghorne maintains that the data upon which a science is based, and the method by which it treats those data, must respect the idiosyncratic nature of the object with which the science is concerned. Polkinghorne calls this the “accommodation” (or “conformity”) of a discipline to its object. The question then arises: What should we expect religious experience and theological method to be like if they are accommodated to the idiosyncratic nature of God? Polkinghorne's methodological program is typical of postcritical positions in the theology‐science dialogue in holding that the fiduciary element in theological method is simply a species of the fiduciary element that is a de facto part of all knowing—in other words, theological method does not differ in fundamental kind from the methods of the natural sciences. But this program may contain the seeds of an alienation of theological method from the transcendence of God similar to the double self‐alienation of theology described by Michael Buckley in At the Origins of Modern Atheism. I contend that something like Bernard Lonergan's position on how the method of faith seeking understanding is related to the methods of the natural sciences is exactly the sort of thing that one should expect on the supposition of Polkinghorne's principle of accommodation, at least if the God who is the object of theological science is transcendent. The way in which the divine differs from all other objects ought to be disclosed or reflected in religious experience and theological method. Polkinghorne charts the course for an accommodated theology, but it seems to be Lonergan who is more intent on following it.