We discuss mathematical and physical arguments against continuity and in favor of discreteness, with particular emphasis on the ideas of Émile Borel.

This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no ...

MATHEMATICS is a wonderful, mad subject, full of imagination, fantasy and creativity that is not limited by the petty details of the physical world, but only by the strength of our inner light. Does this sound familiar? Probably not from the mathematics classes you may have attended. But consider the work of three famous earlier mathematicians: Leonhard Euler, Georg Cantor and Srinivasa Ramanujan.

The theory of lower previsions is designed around the principles of coherence and sure-loss avoidance, thus steers clear of all the updating anomalies highlighted in Gong and Meng's "Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss, and Simpson's Paradox" except dilation. In fact, the traditional problem with the theory of imprecise probability is that coherent inference is too complicated rather than unsettling. Progress has been made simplifying coherent inference by demoting sets of probabilities from fundamental building blocks to secondary representations (...) that are derived or discarded as needed. (shrink)

This is a book about the nature of film: about the nature of moving images, about the viewer's relation to film, and about the kinds of narrative that film is capable of presenting. It represents a very decisive break with the semiotic and psychoanalytic theories of film which have dominated discussion. The central thesis is that film is essentially a pictorial medium and that the movement of film images is real rather than illusory. A general theory of pictorial representation is (...) presented, which insists on the realism of pictures and the impossibility of assimilating them to language. It criticizes attempts to explain the psychology of film viewing in terms of the viewer's imaginary occupation of a position within the world of film. On the contrary, film viewing is nearly always impersonal. (shrink)

In this paper, we defend the view that Spinoza is committed to allowing for the existence of a plurality of possible worlds, that his necessitarianism is merely moderate, not strict enough to exclude the possibility of other worlds. To show that evidence for attributing strict necessitarianism to Spinoza is lacking, we shall concentrate on Don Garrett's article, “Spinoza's Necessitarianism,” in the conviction that his case for attributing strict necessitarianism to Spinoza is the strongest one available.

The information-theoretic point of view proposed by Leibniz in 1686 and developed by algorithmic information theory (AIT) suggests that mathematics and physics are not that different. This will be a first-person account of some doubts and speculations about the nature of mathematics that I have entertained for the past three decades, and which have now been incorporated in a digital philosophy paradigm shift that is sweeping across the sciences.

Hi everybody! It's a great pleasure for me to be back here at the new, improved Santa Fe Institute in this spectacular location. I guess this is my fourth visit and it's always very stimulating, so I'm always very happy to visit you guys. I'd like to tell you what I've been up to lately. First of all, let me say what algorithmic information theory is good for, before telling you about the new version of it I've got.

Since educators are always looking for ways to improve their practice, and since empirical science is now accepted in our worldview as the final arbiter of truth, it is no surprise they have been lured toward cognitive neuroscience in hopes that discovering how the brain learns will provide a nutshell explanation for student learning in general. I argue that identifying the person with the brain is scientism (not science), that the brain is not the person, and that it is the (...) person who learns. In fact the brain only responds to the learning of embodied experience within the extra-neural network of intersubjective communications. Learning is a dynamic, cultural activity, not a neural program. Brain-based learning is unnecessary for educators and may be dangerous in that a culturally narrow ontology is taken for granted, thus restricting our creativity and imagination, and narrowing the human community. (shrink)

A re-issue of Gregory Bateson's classic work. It summarizes Bateson's thinking on the subject of the patterns that connect living beings to each other and to their environment.

One of the most intractable contemporary problems in the USSR is the Soviet federal dilemma. The late 1980s witnessed competing claims among the national minority groups of the USSR to rights of voice, representation, and cultural, economic, and even political sovereignty. Since the onset of perestrojka, the principle of 'national-statehood' has acquired a new legitimacy. Nationality is one of the pillars of the federal reform. The drive to create a 'new Soviet federalism' has become an important component of perestrojka. But, (...) according to Leninist doctrine, the 'nation' is a transitional formation. Unless there is a significant departure from Leninist theory, the new acknowledgement of the 'rights of nations' in the USSR can only be a political -- and thus temporary -- concession. Can the ideology evolve in such a way as to provide ideologically-based political legitimacy to the notion of national-statehood? Is Gorbachev's 'dynamic' interpretation of Leninism capable of rejecting one of Lenin's most fundamental concepts? The thesis of this article is that Soviet federal reform requires a substantial departure from the Leninist tradition. The extent to which Soviet leaders are prepared to do this casts light on one of the perennial concerns of socialist thought, namely whether ideology matters at all. (shrink)

A comprehensive introduction to current research on the psychology of concept formation and use.

This long-awaited study of the most enigmatic figure of Greek philosophy reclaims Socrates' ground-breaking originality. Written by a leading historian of Greek thought, it argues for a Socrates who, though long overshadowed by his successors Plato and Aristotle, marked the true turning point in Greek philosophy, religion and ethics. The quest for the historical figure focuses on the Socrates of Plato's earlier dialogues, setting him in sharp contrast to that other Socrates of later dialogues, where he is used as a (...) mouthpiece for Plato's often anti-Socratic doctrine. At the heart of the book is the paradoxical nature of Socratic thought. But the paradoxes are explained, not explained away. The book highlights the tensions in the Socratic search for the answer to the question 'How should we live?' Conceived as a divine mandate, the search is carried out through elenctic argument, and dominated by an uncompromising rationalism. The magnetic quality of Socrates' personality is allowed to emerge throughout the book. Clearly and forcefully written, philosophically sophisticated but entirely accessible to non-specialists, this book will be of major importance and interest to all those studying ancient philosophy and the history of Western thought. (shrink)

(Updated 5/23/24) This unpublished paper, which readers should feel free to cite, is posted primarily for the historical record. In recent work that has, deservedly, received some attention, Paul R. Daniels presents and defends a non-standard theory of persistence that he dubs transdurantism, according to which persisting objects are temporally extended simples. This is exactly what I do in work dating back to Spring 2004. (This work includes this version of this paper, as well as later version that was presented (...) to the University of Rochester's Philosophy Department in 2005.) While this might be a total coincidence, I doubt that it is, especially given that 'transdurantism' appears as a name for a theory of persistence associated with me in at least two places in the literature, one of which includes a citation of this paper. The paper begins with a discussion of what I call 'locative relations' (the relations borne by material objects to the regions of space and time they occupy), which draws relevant distinctions that others have failed to draw. The results of this discussion are then used in constructing spatial analogues for the three established theories of persistence--endurantism, perdurantism, and exdurantism--as well as for transdurantism. Next, these four views concerning persistence are explicitly formulated and a defense of their formulation is offered. Finally, transdurantism's advantages and disadvantages relative to the other theories are discussed. The main goal of the paper is to challenge the trichotomy between the established theories by arguing that transdurantism is also a viable view concerning persistence through time. [Note: Befitting its status as a historical document, with the exception of some light editing to fix typos that might impede understanding, no changes have been made to the paper.]. (shrink)

I yield to no one in my admiration for and appreciation of what the scientists have accomplished in the last few centuries as well as back in the days of the Greeks. Nonetheless there are certain questions that perennially recur. One might readily say that scientists have not yet reached the proper answers, but judging from what they have already accomplished satisfactory answers will be forthcoming in the revolving years. That is too facile a reply. On some things we want (...) real answers now. To put off fairly adequate explanations until some future limbo is wholly unsatisfactory. (shrink)

Groups of people are commonly said to be collectively responsible for what has happened. Sometimes the groups claimed to be responsible are vast in size, as when collective responsibility is ascribed to the class of all Americans or the class of all white males. In this book the concept of collective responsibility is analyzed. It is examined not only in the light of what philosophical proponents have said about it, but a genuine attempt is made to make sense of what (...) ordinary people say about responsibility when it is ascribed to groups of people. Accordingly, it is distinguished from related concepts such as shared responsibility and moral taint. Parallels are examined between the actions of an individual and the actions of a group or collective, parallels which seem to make ascriptions of collective responsibility more plausible. Some philosophers oppose collective responsibility and argue for an individualist type of position; in this regard the positions of Lewis and Sverdlik are critically examined. The final chapter contains the author's own position, a position which affirms that collective responsibility is possible but which also preserves some of the central intuitions of the individualist. (shrink)

Discusses mental processes, the role of humans in nature, experience, and the connection between myth, religion, and science.

This article explores methodological issues central to the undertaking of joint Palestinian-Israeli research, work that is impacted by the violent conflict between the two peoples. Four issues are discussed: (a) collaborating under conflict, that is, how the conflict impacts relations between the researchers on either side of the border, (b) issues of power and equality, as they impact the research process, (c) relationships with participants, that is, how the conflict influences relations between the researcher and the research participants, and (d) (...) rethinking standards, that is, whether the normative standards of research quality are relevant for Palestinian-Israeli collaborative research. The article presents examples from joint research and offers preliminary ideas for dealing with these methodological issues. (shrink)

This book explores an important central thread that unifies Russell's thoughts on logic in two works previously considered at odds with each other, the Principles of Mathematics and the later Principia Mathematica. This thread is Russell's doctrine that logic is an absolutely general science and that any calculus for it must embrace wholly unrestricted variables. The heart of Landini's book is a careful analysis of Russell's largely unpublished "substitutional" theory. On Landini's showing, the substitutional theory reveals the unity of Russell's (...) philosophy of logic and offers new avenues for a genuine solution of the paradoxes plaguing Logicism. (shrink)

Gregory T. Doolan provides here the first detailed consideration of the divine ideas as causal principles. He examines Thomas Aquinas's philosophical doctrine of the divine ideas and convincingly argues that it is an essential element of his metaphysics. According to Thomas, the ideas in the mind of God are not only principles of his knowledge, but they are productive principles as well. In this role, God's ideas act as exemplars for things that he creates. As Doolan shows, this theory (...) of exemplarism is an integral part of Thomas's account of the existence and order of the created universe. It also accounts in part for the freedom of God's creative act. The volume begins with an introduction to Thomas's doctrine of exemplarism and then addresses his arguments for the existence of exemplar ideas within the mind of God. Having established the existence of divine ideas, Doolan considers how Thomas reconciles their multiplicity with God's simplicity. The work identifies the various things for which Thomas posits divine ideas. As Doolan is careful to show, Thomas does not consider all of these ideas to be exemplars because not all of them act as causal principles. After identifying the ideas that do act in this way, Doolan considers how such exemplars can be causes of natural things without compromising the causality of natural agents. The volume culminates with a consideration of the role that the divine ideas play within the structure of Thomas's theory of participation. ABOUT THE AUTHOR: Gregory T. Doolan, assistant professor of philosophy at The Catholic University of America, is a contributor to Wisdom's Apprentice: Thomistic Essays in Honor of Lawrence Dewan, O.P., and Reassessing the Liberal State: Reading Maritain's Man and the State. This is his first book. (shrink)

Landini discusses the second edition of Principia Mathematica, to show Russella (TM)s intellectual relationship with Wittgenstein and Ramsey.

Psychophysical scaling models of the form R = f, with R the response and I some intensity of an attribute, all assume that people judge the amounts of an attribute. With simple biases excepted, most also assume that judgments are independent of space, time, and features of the situation other than the one being judged. Many data support these ideas: Magnitude estimations of brightness increase with luminance. Nevertheless, I argue that the general model is wrong. The stabilized retinal image literature (...) shows that nothing is seen if light does not change over time. The classification literature shows that dimensions often combine to produce emergent properties that cannot be described by the elements in the stimulus. These and other effects cannot be adjusted for by simply adding variables to the general model because some factors do not combine linearly. The proposed alternative is that people initially judge the entire stimulus – the object in terms of its environment. This agrees with the constancy literature that shows that objects and their attributes are identified through their relations to other aspects of the scene. That the environment determines judgments is masked in scaling studies where the standard procedure is to hold context constant. In a typical brightness study the essential stimulus might be the intensity of the light or a difference between the light and the background. The two are perfectly confounded. This issue is examined in the case of audition. Judgments of the loudness of a tone depend on how much that tone differs from the previous tone in both pitch and loudness. To judge loudness people first seem to process the stimulus object in terms of differences between it and other aspects in the situation; only then do they assess the feature of interest. Psychophysical judgments will therefore be better interpreted by theories of attention that are based in biology or psychology than those that are based in classical physics. (shrink)