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)

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)

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.

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 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.

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.

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 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)

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)

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)

Fred Miller offers a controversial reappraisal of the Politics, suggesting that nature, justice, and rights are central to Aristotle's political thought. He sheds new light on Aristotle's relation to modern natural rights theorists, and to the current liberalism-communitarianism debate.

"Taken as a trilogy, _consent not to be a single being_ is a monumental accomplishment: a brilliant theoretical intervention that might be best described as a powerful case for blackness as a category of analysis."—Brent Hayes Edwards, author of _Epistrophies: Jazz and the Literary Imagination_ In _The Universal Machine_—the concluding volume to his landmark trilogy _consent not to be a single being_—Fred Moten presents a suite of three essays on Emmanuel Levinas, Hannah Arendt, and Frantz Fanon in which he (...) explores questions of freedom, capture, and selfhood. In trademark style, Moten considers these thinkers alongside artists and musicians such as William Kentridge and Curtis Mayfield while interrogating the relation between blackness and phenomenology. Whether using Levinas's idea of escape in unintended ways, examining Arendt's antiblackness through Mayfield's virtuosic falsetto and Anthony Braxton's musical language, or showing how Fanon's form of phenomenology enables black social life, Moten formulates blackness as a way of being in the world that evades regulation. Throughout _The Universal Machine_—and the trilogy as a whole—Moten's theorizations of blackness will have a lasting and profound impact. (shrink)

What is death? Do people survive death? What do we mean when we say that someone is "dying"? Presenting a clear and engaging discussion of the classic philosophical questions surrounding death, this book studies the great metaphysical and moral problems of death. In the first part, Feldman shows that a definition of life is necessary before death can be defined. After exploring several of the most plausible accounts of the nature of life and demonstrating their failure, he goes on to (...) propose his own conceptual scheme for death and related concepts. In the second part, Feldman turns to ethical and value-theoretical questions about death. Addressing the ancient Epicurean ethical problem about the evil of death, he argues that death can be a great evil for those who die, even if they do not exist after death, because it may deprive them of the goods they would have enjoyed if they had continued to live. Confrontations with the Reaper concludes with a novel consequentialist theory about the morality of killing, applying it to such thorny practical issues as abortion, suicide, and euthanasia. (shrink)

"Taken as a trilogy, _consent not to be a single being_ is a monumental accomplishment: a brilliant theoretical intervention that might be best described as a powerful case for blackness as a category of analysis."—Brent Hayes Edwards, author of _Epistrophies: Jazz and the Literary Imagination_ In _Stolen Life_—the second volume in his landmark trilogy _consent not to be a single being_—Fred Moten undertakes an expansive exploration of blackness as it relates to black life and the collective refusal of social (...) death. The essays resist categorization, moving from Moten's opening meditation on Kant, Olaudah Equiano, and the conditions of black thought through discussions of academic freedom, writing and pedagogy, non-neurotypicality, and uncritical notions of freedom. Moten also models black study as a form of social life through an engagement with Fanon, Hartman, and Spillers and plumbs the distinction between blackness and black people in readings of Du Bois and Nahum Chandler. The force and creativity of Moten's criticism resonate throughout, reminding us not only of his importance as a thinker, but of the continued necessity of interrogating blackness as a form of sociality. (shrink)

Philosophical interest in situated cognition has been focused most intensely on the claim that human cognitive processes extend from the brain into the tools humans use. As we see it, this radical hypothesis is sustained by two kinds of mistakes, confusing coupling relations with constitutive relations and an inattention to the mark of the cognitive. Here we wish to draw attention to these mistakes and show just how pervasive they are. That is, for all that the radical philosophers have said, (...) the mind is still in the head. (shrink)