We consider two categorical syllogisms, valid or invalid, to be equivalent if they can be transformed into each other by certain transformations, going back to Aristotle, that preserve validity. It is shown that two syllogisms are equivalent if and only if they have the same models. Counts are obtained for the number of syllogisms in each equivalence class. For a more natural development, using group-theoretic methods, the space of syllogisms is enlarged to include nonstandard syllogisms, and various groups of transformations (...) on that space are studied. (shrink)

Gleason's theorem for ������³ says that if f is a nonnegative function on the unit sphere with the property that f(x) + f(y) + f(z) is a fixed constant for each triple x, y, z of mutually orthogonal unit vectors, then f is a quadratic form. We examine the issues raised by discussions in this journal regarding the possibility of a constructive proof of Gleason's theorem in light of the recent publication of such a proof.

We consider notions of boundedness of subsets of the natural numbers ℕ that occur when doing mathematics in the context of intuitionistic logic. We obtain a new characterization of the notion of a pseudobounded subset and we formulate the closely related notion of a detachably finite subset. We establish metric equivalents for a subset of ℕ to be detachably finite and to satisfy the ascending chain condition. Following Ishihara, we spell out the relationship between detachable finiteness and sequential continuity. Most (...) of the results do not require countable choice. (shrink)

The modern theory of computability is based on the works of Church, Markov and Turing who, starting from quite different models of computation, arrived at the same class of computable functions. The purpose of this paper is the show how the main results of the Church-Markov-Turing theory of computable functions may quickly be derived and understood without recourse to the largely irrelevant theories of recursive functions, Markov algorithms, or Turing machines. We do this by ignoring the problem of what constitutes (...) a computable function and concentrating on the central feature of the Church-Markov-Turing theory: that the set of computable partial functions can be effectively enumerated. In this manner we are led directly to the heart of the theory of computability without having to fuss about what a computable function is.The spirit of this approach is similar to that of [RGRS]. A major difference is that we operate in the context of constructive mathematics in the sense of Bishop [BSH1], so all functions are computable by definition, and the phrase “you can find” implies “by a finite calculation.” In particular ifPis some property, then the statement “for eachmthere isnsuch thatP” means that we can construct a functionθsuch thatP)for allm. Church's thesis has a different flavor in an environment like this where the notion of a computable function is primitive.One point of such a treatment of Church's thesis is to make available to Bishopstyle constructivists the Markovian counterexamples of Russian constructivism and recursive function theory. The lack of serious candidates for computable functions other than recursive functions makes it quite implausible that a Bishopstyle constructivist could refute Church's thesis, or any consequence of Church's thesis. Hence counterexamples such as Specker's bounded increasing sequence of rational numbers that is eventually bounded away from any given real number [SPEC] may be used, as Brouwerian counterexamples are, as evidence of the unprovability of certain assertions. (shrink)

A very weak omniscience principle is formulated, related omniscience principlesare considered, and the theorem that a function of bounded variation is the difference of two increasing functions is shown to be equivalent to the omniscience principle WLPO. It is a so shown that an arbitrary function with located variation on an interval is the difference of two increasing functions.

A form of Kripke's schema turns out to be equivalent to each of the following two statements from metric topology: every open subspace of a separable metric space is separable; every open subset of a separable metric space is a countable union of open balls. Thus Kripke's schema serves as a point of reference for classifying theorems of classical mathematics within Bishop-style constructive reverse mathematics.

A notion of completeness and completion suitable for use in the absence of countable choice is developed. This encompasses the construction of the real numbers as well as the completion of an arbitrary metric space. The real numbers are characterized as a complete Archimedean Heyting field, a terminal object in the category of Archimedean Heyting fields.

The notions of linear and metric independence are investigated in relation to the property: if U is a set of n+1 independent vectors, and X is a set of n independent vectors, then adjoining some vector in U to X results in a set of n+1 independent vectors. It is shown that this property holds in any normed linear space. A related property – that finite-dimensional subspaces are proximinal – is established for strictly convex normed spaces over the real or (...) complex numbers. It follows that metric independence and linear independence are equivalent in such spaces. Proofs are carried out in the context of intuitionistic logic without the axiom of countable choice. (shrink)

The traditional problem of evil is set forth, by no means for the first time, in Part X of Hume's Dialogues Concerning Natural Religion in these familiar words: ‘Is [God] willing to prevent evil, but not able? then he is impotent. Is he able, but not willing? then he is malevolent. Is he both able and willing? whence then is evil?’ This formulation of the problem of evil obviously suggests an argument to the effect that the existence of evil in (...) the world demonstrates that God does not exist. The purpose of this paper is to examine this argument, with a view to showing that while it is not a conclusive argument, it is much stronger than some apologists for traditional theism allow. (shrink)

The concept of lying is generally assumed to be closely related to the concept of assertion. However, the literature on lying has focused almost exclusively on lies expressed by unqualified assertions. Sometimes a speaker chooses to qualify her assertion by hedging, making her utterance a hedged declarative. This paper defends the thesis that lies can be expressed by untruthful hedged declaratives, and explores the implications of this thesis for the definition of lying. Many standard approaches to the definition of lying (...) allow lies to be expressed by untruthful hedged declaratives, which may explain why these cases have been ignored in the literature. However, untruthful hedged declaratives present a problem for a recently-proposed theory that analyzes lying in terms of the Knowledge Norm of Assertion. According to this theory, a necessary condition on lying is that in asserting that p, the speaker represents herself as knowing that p; however, in making an untruthful hedged declarative a speaker represents herself as having an epistemic attitude weaker than knowledge. The fact that such a theory fails to adequately explain untruthful hedged declaratives provides a reason to prefer alternative theories of lying. The discussion draws out some important observations about the concepts of lying, assertion, belief, and the relations between them. (shrink)

This collection of essays by eminent philosopher Fred Dretske brings together work on the theory of knowledge and philosophy of mind spanning thirty years. The two areas combine to lay the groundwork for a naturalistic philosophy of mind. The fifteen essays focus on perception, knowledge, and consciousness. Together, they show the interconnectedness of Dretske's work in epistemology and his more contemporary ideas on philosophy of mind, shedding light on the links which can be made between the two. The first (...) section of the book argues the point that knowledge consists of beliefs with the right objective connection to facts; two essays discuss this conception of knowledge's implications for naturalism. The next section articulates a view of perception, attempting to distinguish conceptual states from phenomenal states. A naturalized philosophy of mind, and thus a naturalized epistemology, is articulated in the third section. This collection will be a valuable resource for a wide range of philosophers and their students, and will also be of interest to cognitive scientists, psychologists, and philosophers of biology. (shrink)

We suggest that there is confusion between why consciousness developed and what additional functions, through continued evolution, it has co-opted. Consider episodic memory. If we believe that episodic memory evolved solely to accurately represent past events, it seems like a terrible system—prone to forgetting and false memories. However, if we believe that episodic memory developed to flexibly and creatively combine and rearrange memories of prior events in order to plan for the future, then it is quite a good system. We (...) argue that consciousness originally developed as part of the episodic memory system—quite likely the part needed to accomplish that flexible recombining of information. We posit further that consciousness was subsequently co-opted to produce other functions that are not directly relevant to memory per se, such as problem-solving, abstract thinking, and language. We suggest that this theory is compatible with many phenomena, such as the slow speed and the after-the-fact order of consciousness, that cannot be explained well by other theories. We believe that our theory may have profound implications for understanding intentional action and consciousness in general. Moreover, we suggest that episodic memory and its associated memory systems of sensory, working, and semantic memory as a whole ought to be considered together as the conscious memory system in that they, together, give rise to the phenomenon of consciousness. Lastly, we suggest that the cerebral cortex is the part of the brain that makes consciousness possible, and that every cortical region contributes to this conscious memory system. (shrink)

Ethnic cleansing and other methods of political and social exclusion continue to thrive in our globalized world, complicating the idea that unity and diversity can exist in the same society. When we emphasize unity, we sacrifice heterogeneity, yet when we stress diversity, we create a plurality of individuals connected only by tenuous circumstance. As long as we remain tethered to these binaries, as long as we are unable to imagine the sort of society we want in an age of diversity, (...) we cannot achieve an enduring solution to conflicts that continue unabated despite our increasing proximity to one another. By envisioning the public as a multivoiced body, Fred Evans offers a solution to the dilemma of diversity. The multivoiced body is both one and many: heterogeneous voices that at once separate and bind themselves together through their continuous and creative interplay. By focusing on this traditionally undervalued or overlooked notion of voice, Evans shows how we can valorize simultaneously the solidarity, diversity, and richness of society. Moreover, recognition of society as a multivoiced body helps resists the pervasive countertendency to raise a chosen discourse to the level of "one true God," "pure race," or some other "oracle" that eliminates the dynamism of contesting voices. To support these views, Evans taps the major figures and themes of analytic and continental philosophy as well as modernist, postmodernist, postcolonial, and feminist thought. He also turns to sources outside of philosophy to address the implications of his views for justice, citizenship, democracy, and collective as well as individual rights. Through the seemingly simple conceit of a multivoiced body, Evans straddles both philosophy and political practice, confronting issues of subjectivity, language, communication, and identity. For anyone interested in moving toward a just society and politics, _The Multivoiced Body_ offers an innovative approach to the problems of human diversity and ethical plurality. (shrink)

Ethnic cleansing and other methods of political and social exclusion continue to thrive in our globalized world, complicating the idea that unity and diversity can exist in the same society. When we emphasize unity, we sacrifice heterogeneity, yet when we stress diversity, we create a plurality of individuals connected only by tenuous circumstance. As long as we remain tethered to these binaries, as long as we are unable to imagine the sort of society we want in an age of diversity, (...) we cannot achieve an enduring solution to conflicts that continue unabated despite our increasing proximity to one another. By envisioning the public as a multivoiced body, Fred Evans offers a solution to the dilemma of diversity. The multivoiced body is both one and many: heterogeneous voices that at once separate and bind themselves together through their continuous and creative interplay. By focusing on this traditionally undervalued or overlooked notion of voice, Evans shows how we can valorize simultaneously the solidarity, diversity, and richness of society. Moreover, recognition of society as a multivoiced body helps resists the pervasive countertendency to raise a chosen discourse to the level of "one true God," "pure race," or some other "oracle" that eliminates the dynamism of contesting voices. To support these views, Evans taps the major figures and themes of analytic and continental philosophy as well as modernist, postmodernist, postcolonial, and feminist thought. He also turns to sources outside of philosophy to address the implications of his views for justice, citizenship, democracy, and collective as well as individual rights. Through the seemingly simple conceit of a multivoiced body, Evans straddles both philosophy and political practice, confronting issues of subjectivity, language, communication, and identity. For anyone interested in moving toward a just society and politics, _The Multivoiced Body_ offers an innovative approach to the problems of human diversity and ethical plurality. (shrink)

Ethicists, researchers and policy makers have paid increasing attention to the ethical conduct of research, especially research involving human beings. Research performed with and by undergraduates poses a specific set of ethical challenges. These challenges are often overlooked by the research community because it is assumed that undergraduate student researchers do not have a significant impact on the research community and that their projects are not host to research posing important ethical issues. This paper identifies several features characteristic of research (...) in undergraduate environments. The paper pays special attention to selective small liberal arts colleges, an important segment of higher education in the US, and advocates integrating instruction in research ethics wherever undergraduates are engaged in research. (shrink)

The most successful theory in all of science--and the basis of one third of our economy--says the strangest things about the world and about us. Can you believe that physical reality is created by our observation of it? Physicists were forced to this conclusion, the quantum enigma, by what they observed in their laboratories. Trying to understand the atom, physicists built quantum mechanics and found, to their embarrassment, that their theory intimately connects consciousness with the physical world. Quantum Enigma explores (...) what that implies and why some founders of the theory became the foremost objectors to it. Schrodinger showed that it "absurdly" allowed a cat to be in a "superposition" simultaneously dead and alive. Einstein derided the theory's "spooky interactions." With Bell's Theorem, we now know Schrodinger's superpositions and Einstein's spooky interactions indeed exist. Authors Bruce Rosenblum and Fred Kuttner explain all of this in non-technical terms with help from some fanciful stories and bits about the theory's developers. They present the quantum mystery honestly, with an emphasis on what is and what is not speculation. Physics' encounter with consciousness is its skeleton in the closet. Because the authors open the closet and examine the skeleton, theirs is a controversial book. Quantum Enigma's description of the experimental quantum facts, and the quantum theory explaining them, is undisputed. Interpreting what it all means, however, is controversial. Every interpretation of quantum physics encounters consciousness. Rosenblum and Kuttner therefore turn to exploring consciousness itself--and encounter quantum physics. Free will and anthropic principles become crucial issues, and the connection of consciousness with the cosmos suggested by some leading quantum cosmologists is mind-blowing. Readers are brought to a boundary where the particular expertise of physicists is no longer a sure guide. They will find, instead, the facts and hints provided by quantum mechanics and the ability to speculate for themselves. (shrink)

An elegant introduction to Bataille's major concepts and concerns, "Bataille: A Critical Reader" underlines the powerful impact his work has had, in different ...

This paper proposes a third meditation-category—automatic self-transcending— to extend the dichotomy of focused attention and open monitoring proposed by Lutz. Automaticself-transcending includes techniques designed to transcend their own activity. This contrasts with focused attention, which keeps attention focused on an object; and open monitoring, which keeps attention involved in the monitoring process. Each category was assigned EEG bands, based on reported brain patterns during mental tasks, and meditations were categorized based on their reported EEG. Focused attention, characterized by beta/gamma activity, (...) included meditations from Tibetan Buddhist, Buddhist, and Chinese traditions. Open monitoring, characterized by theta activity, included meditations from Buddhist, Chinese, and Vedic traditions. Automaticself-transcending, characterized by alpha1 activity, included meditations from Vedic and Chinese traditions. Between categories, the included meditations differed in focus, subject/object relation, and procedures. These findings shed light on the common mistake of averaging meditations together to determine mechanisms or clinical effects. (shrink)

This chapter discusses the flaws of Clark’s extended mind hypothesis. Clark’s hypothesis assumes that the nature of the processes internal to an object has nothing to do with whether that object carries out cognitive processing. The only condition required is that the object is coupled with a cognitive agent and interacts with it in a certain way. In making this tenuous connection, Clark commits the most common mistake extended mind theorists make; alleging that an object becomes cognitive once it is (...) connected to a cognitive agent is a “coupling-constitution fallacy.” From this fallacy, many hastily proceed to the conclusion that the object or process constitutes part of the agent’s cognitive apparatus or cognitive processing. (shrink)