Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Gödel's writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Gödel's three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Gödel's texts on foundations with materials from Gödel's Nachlass and from Hao Wang's discussions with Gödel. He provides discussions of Gödel's views, and develops a new (...) type of platonic rationalism that requires rational intuition, called 'constituted platonism'. (shrink)

"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as (...) if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book. (shrink)

Gödel's relation to the work of Plato, Leibniz, Kant, and Husserl is examined, and a new type of platonic rationalism that requires rational intuition, called ...

The thesis is a study of the notion of intuition in the foundations of mathematics which focuses on the case of natural numbers and hereditarily finite sets. Phenomenological considerations are brought to bear on some of the main objections that have been raised to this notion. ;Suppose that a person P knows that S only if S is true, P believes that S, and P's belief that S is produced by a process that gives evidence for it. On a phenomenological (...) view the relevant evidence is provided by intuition , and this should be the case in either ordinary perceptual knowledge or in mathematical knowledge. Intuition is to be understood in terms of fulfillments of intentions. Knowledge is a product of intuition and intention. In the case of mathematical knowledge it is said that there is a construction for a mathematical statement S if and only if the intention expressed by S is fulfilled . Constructions are thus viewed as intuition processes that could actually or possibly be carried out. In elementary parts of mathematics they might be characterized in terms of certain classes of recursive functions. This view is discussed in the case where S is taken to be a singular statement about natural numbers or finite sets, and also where S is taken to be a general statement about such objects. The distinction between intuition of and intuition that is also investigated in this context. ;It is pointed out how on a phenomenological view a number of central problems about mathematical intuition can be avoided: problems about the analogousness of perceptual and mathematical intuition, about causal accounts of knowledge in mathematics, and about structuralism in mathematics. The bearing of the account on issues concerning constructivism and platonism is also discussed. (shrink)

This book is dedicated to a classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III presents sufficient formal (...) logic to give a full development of Gödel's incompleteness theorems. Part IV considers the significance of the technical work with a discussion of Church's Thesis and readings on the foundations of mathematics. This new edition contains the timeline "Computability and Undecidability" as well as the essay "On mathematics". (shrink)

KEY TO FOOTNOTE ABBREVIATIONS MM-P. Structure Phenomenology Sense Praise Signs Visible Themes Humanism Primacy Maurice Merleau-Ponty The Structure of ...

Theories of Truth provides a clear, critical introduction to one of the most difficult areas of philosophy. It surveys all of the major philosophical theories of truth, presenting the crux of the issues involved at a level accessible to nonexperts yet in a manner sufficiently detailed and original to be of value to professional scholars. Kirkham's systematic treatment and meticulous explanations of terminology ensure that readers will come away from this book with a comprehensive general understanding of one of philosophy's (...) thorniest set of topics. -/- Included are discussions of the correspondence, coherence, pragmatic, semantic, performative, redundancy, appraisal, and truth-as-justification theories. There are also chapters or sections of chapters on the liar paradox, three-valued logic, Field's critique of Tarski, Davidson's program, Dummett's theory of linguistic competence, satisfaction, recursion, the extension/intension distinction, and an explanation of how theories of justification, properly understood, differ from theories of truth. -/- A persistent theme is that philosophers have too often failed to recognize that not all theories of truth are intended to answer the same question. When the various questions are made distinct, it is apparent that many of the "debates" in this field are really cases of philosophers talking past one another. There is much less disagreement within the field than has commonly been thought. (shrink)

In a number of essays published over the last decade or so, W. V. Quine has made some interesting suggestions concerning the ontology of theories. If I understand him correctly, one of his principal objects has been to formulate a criterion by means of which one can correctly decide what are the ontological commitments of any given theory. My aim in this paper is to reveal what I think are inadequacies in Quine's criterion and to indicate the direction in which (...) a proper formulation lies. (shrink)

The claim that visually masked, unidentifiable words are analyzed at the level of whole word meaning has been challenged by recent findings indicating that instead, analysis occurs mainly at the subword level. The present experiments examined possible limits on subword analysis. Experiment 1 obtained semantic priming from pleasant- and unpleasant-meaning subliminal words in which no individual letter contained diagnostic information about a word’s evaluative valence; thus analysis must operate on information more complex than that contained in individual letters. Experiments 2 (...) and 3 showed that analysis must operate on information more complex than that represented by individual bigrams or trigrams . These findings suggest that while subliminal priming is driven by subword analysis, the effective units of analysis are distributed widely across at least short words. (shrink)

Peter Geach has said that Russell's use of ‘propositional function’ is ‘hopelessly confused and inconsistent’. Geach is right, and attempts to say what exactly a Russellian propositional function is, or is supposed to be, are bound to end in frustration. Nevertheless, it may be worthwhile to pursue an account of propositional functions that accommodates a good deal of what Russell says about them and that can provide some of what he expected of them.

The critics of Schleiermacher's hermeneutic are legion and its defenders few – due, to a great extent, to the popularity of Gadamer's Truth and Method and its attack on Schleiermacher. I believe that the critics of Schleiermacher have not understood him very well and the failure of his hermeneutics to gain very much respect lies, at least partially, to a lack of understanding of what he had to say. Besides, if we look at contemporary scholars who focus on the study (...) of language and how it functions we will find that they often have views very much like those found in Schleiermacher's discussion of hermeneutics. (shrink)

I defend mereological nihilism, the view that there are no composite objects, against a challenge from ontological emergence, the view that some things have properties that are ‘something over and above’ the properties of their parts. As the nihilist does not believe in composite wholes, there is nothing in the nihilist's ontology to instantiate emergent properties – or so the challenge goes. However, I argue that some simples can collectively instantiate an emergent property, so the nihilist's ontology can in fact (...) accommodate emergent properties. Furthermore, I show that employing plural instantiation does not bloat the nihilist's ontology or ideology. (shrink)

In a recent book, J. R. Lucas presents an argument to show that if God has infallible knowledge of the future, our will is not free. Thus, Lucas concludes, like the medieval Jewish philosopher Gersonides, that God in creating beings with genuinely free will, abdicates some of his omniscience as well as some of his omnipotence. God could, but will not, determine our choices, since such an exercise of his power would rob us of free will. Similarly, Lucas holds, God (...) could but does not foreknow our future choices since this also would rob us of free will. This argument, from so formidable a foe of determinism as Lucas, merits our most serious attention. However, I believe that there is a way to evade its conclusion, a way which Lucas considers but rejects. (shrink)

In a recent paper in Psychological Science, Kouider and Dupoux reported obtaining unconscious Stroop priming only when subjects had partial awareness of the masked distractor words . Kouider and Dupoux conjectured that semantic priming occurs only when such partial awareness is present. The present experiments tested this conjecture in an affective categorization priming task that differed from Kouider and Dupoux’s in using masked distractors that subjects had practiced earlier as visible words. Experiment 1 showed priming from practiced words when subjects (...) had no partial awareness of those words. Experiment 2 showed that, in the absence of partial awareness, practiced words yielded priming but not-practiced words did not. Experiment 3 corroborated Experiment 1 and 2s results using a different test of partial awareness. These results suggest that unconscious processing of subword elements drives masked semantic priming by practiced words. (shrink)

We propose a framework for including information‐processing bounds in rational analyses. It is an application of bounded optimality (Russell & Subramanian, 1995) to the challenges of developing theories of mechanism and behavior. The framework is based on the idea that behaviors are generated by cognitive mechanisms that are adapted to the structure of not only the environment but also the mind and brain itself. We call the framework computational rationality to emphasize the incorporation of computational mechanism into the definition of (...) rational action. Theories are specified as optimal program problems, defined by an adaptation environment, a bounded machine, and a utility function. Such theories yield different classes of explanation, depending on the extent to which they emphasize adaptation to bounds, and adaptation to some ecology that differs from the immediate local environment. We illustrate this variation with examples from three domains: visual attention in a linguistic task, manual response ordering, and reasoning. We explore the relation of this framework to existing “levels” approaches to explanation, and to other optimality‐based modeling approaches. (shrink)

A deterministic perspective, believing choices are a function of hereditary and environmental factors, could theoretically impact perceived moral responsibility and lead to decreased blame in judging others. However, little consistent support has been found relating individual differences in deterministic attitudes to blame/tolerance for others. Perhaps, though, providing information regarding past background hardships affecting an individual's current lifestyle could potentially mediate harsh moralistic judgments of that individual. In the two studies reported here, we further explored the relation of free will/determinism scales (...) to attitudes toward others as well as the effect of manipulating background information on the assignment of blame. As in previous research, little support was found for the relation of deterministic attitudes to tolerance toward others. However, judgments following manipulated information about hypothetical target persons supported the conclusion that target individuals are blamed less and given more sympathy if more information related to previous hardships is provided. In addition, in the second study perceived similarity to a target individual was associated with decreased blame/greater sympathy for a target with alcohol abuse problems. (shrink)

In a recent paper Anthony Flew gives an argument which can be outlined as follows: 1. Any attempt to give a ‘free will defence’ must be based either on a compatibilist notion of free will or a libertarian, incompatibilist, notion of free will. 2. A free will defence based on a compatibilist notion of free will must fail, for on a compatibilist view of free will, God could make creatures who were free but never chose evil. 3. A free will (...) defence based on a libertarian notion of free will might have other difficulties, but on a libertarian view of free will God could not both leave men free and bring it about that they never chose evil. 4. But a free will defence based on an incompatibilist, libertarian notion of free will can be rejected, since: It is not clear that the ordinary use of such key terms as ‘action’ and ‘choice’ carry any implications of libertarian free will. If such terms did carry the implication of libertarian free will it becomes hard to see how anyone could be in a position to know that a choice had been made or an action performed. The possession of libertarian free will by created beings seems to be incompatible with the essential theistic doctrine that all created beings are always utterly dependent on God as their sustaining cause. 5. Therefore the free will defence fails. (shrink)

The purpose of this paper is to examine the distinction between "negative" and "positive" duties. Special attention will be given to certain criticism raised against this distinction by Michael Tooley.

This comparative field study evaluated the choices made by U.S., Portuguese, and Hong Kong Chinese evening MBA and graduating university business students when resolving business-related moral dilemmas. The authors developed hypotheses at the country level based on Hofstede’s ratings of each country’s national culture dimensions of power distance, uncertainty avoidance, individualism, and masculinity. The more individualistic U.S. respondents resolved the dilemmas with choices indicating less self-interest and more concern for unidentified others than did their Portuguese and Hong Kong Chinese counterparts, (...) who are from more collectivist societies. The authors discuss implications for future cross-cultural research on business dilemmas and for cooperative interactions among managers from these and other countries. (shrink)

In this paper I will show that the omnitemporality of truth does indeed imply fatalism if the past is unchangeable. I then argue that it is very likely indeed that the past is unchangeable and thus, since it is very likely that fatalism is false, it is very likely that the doctrine of the omnitemporality of truth is false. I argue that the rejection of the omnitemporality of truth has no undesirable consequences for either logic or theology, that in fact (...) the logical and theological consequences of the rejection of the omnitemporality of truth are beneficial to both disciplines. (shrink)

Comparative case studies of lawyer deviance and discipline offer a unique perspective on how and why lawyers misbehave, how regulatory bodies respond, and the efficacy of those responses. Such studies also provide valuable pedagogic tools, opening the eyes of law students to the ways in which they, too, could transgress ethical rules. This special issue builds on my two books on misbehaving lawyers in New York and California by presenting vivid accounts of such lawyers in the UK, Canada, Australia, New (...) Zealand, and the Netherlands. (shrink)