This paper presents a natural deduction system for orthomodular quantum logic. The system is shown to be provably equivalent to Nishimura’s quantum sequent calculus. Through the Curry–Howard isomorphism, quantum $$\lambda $$ -calculus is also introduced for which strong normalization property is established.

It was shown recently that epimorphisms need not be surjective in a variety K of Heyting algebras, but only one counter-example was exhibited in the literature until now. Here, a continuum of such examples is identified, viz. the variety generated by the Rieger-Nishimura lattice, and all of its (locally finite) subvarieties that contain the original counter-example K . It is known that, whenever a variety of Heyting algebras has finite depth, then it has surjective epimorphisms. In contrast, we show (...) that for every integer $n \geq 2$ , the variety of all Heyting algebras of width at most n has a non-surjective epimorphism. Within the so-called Kuznetsov-Gerčiu variety (i.e., the variety generated by finite linear sums of one-generated Heyting algebras), we describe exactly the subvarieties that have surjective epimorphisms. This yields new positive examples, and an alternative proof of epimorphism surjectivity for all varieties of Gödel algebras. The results settle natural questions about Beth-style definability for a range of intermediate logics. (shrink)

A logic |$\mathcal{L}$| is said to satisfy the descending chain condition, DCC, if any descending chain of formulas in |$\mathcal{L}$| with ordering induced by |$\vdash _{\mathcal{L}};$| eventually stops. In this short note, we first establish a general theorem, which states that if a propositional logic |$\mathcal{L}$| satisfies both DCC and has the Craig Interpolation Property, CIP, then it satisfies the Uniform Interpolation Property, UIP, as well. As a result, by using the Nishimura lattice, we give a new simply proof (...) of uniform interpolation for |$\textbf{IPL}_2$|⁠, the two-variable fragment of Intuitionistic Propositional Logic; and one-variable uniform interpolation for |$\textbf{IPL}$|⁠. Also, we will see that the modal logics |$\textbf{S}_4$| and |$\textbf{K}_4$| do not satisfy atomic DCC. (shrink)

Argues against D. Hume's (1825) treatise "Of Miracles," which is often used to disprove the existence of psi. Hume states that a miracle is a violation of the laws of nature which are proved to be true by common experience, and that the only sufficient testimony for a miracle would be testimony whose falsehood would be even more miraculous than the miracle itself. The primary objections to Hume's argument are that (1) it is tautological, since it presupposes the nonexistence of (...) miraculous events, and (2) as a metaphysical statement, it is inappropriate when considering empirical evidence, which should be judged by its own rule. (shrink)

It has often been remarked that science is a young man's game. Thomas Kuhn, for example, claims that revolutionary changes in science are almost always initiated by either young scientists or those new to a field. I subject Kuhn's hypothesis to testing. I examine 24 revolutionary scientific figures mentioned in The Structure of Scientific Revolutions to determine if young scientists are more likely to make revolutionary discoveries than older scientists. My analysis suggests that middle-aged scientists are responsible for initiating more (...) scientific revolutions than young scientists, given the proportion of each group in the total population of scientists. I argue that the popular myth about the correlation between youth and scientific discovery fails to take into account the proportion of young scientists in the population of scientists. (shrink)

A crucial debate currently raging in the fields of cognitive and social science centers around general and specific approaches to understanding the actions of others. When we understand the actions of another person, do we do so on the basis of a general theory of psychology, or on the basis of an effort to place ourselves in the particular position of that specific person? Hans Herbert Kögler and Karsten R. Stueber's Empathy and Agency addresses this other issues vital to current (...) social science in an advanced and diverse analysis of the foundations of social-scientific methodology based on recent cognitive psychology. The book serves as both an introduction to the debate for non-academic audiences and as a catalyst for further discussion for serious theorists. Empathy and Agency provides a solid foundation of the fundamental issues in social and cognitive science, but also presents the most influential paradigms in the field at this time. (shrink)

Written by leading researchers in educational and social psychology, learning science, and neuroscience, this edited volume is suitable for a wide-academic readership. It gives definitions of key terms related to motivation and learning alongside developed explanations of significant findings in the field. It also presents cohesive descriptions concerning how motivation relates to learning, and produces a novel and insightful combination of issues and findings from studies of motivation and/or learning across the authors' collective range of scientific fields. The authors provide (...) a variety of perspectives on motivational constructs and their measurement, which can be used by multiple and distinct scientific communities, both basic and applied. (shrink)

We examine the sub-field of philosophy of science using a new method developed in information science, Referenced Publication Years Spectroscopy (RPYS). RPYS allows us to identify peak years in citations in a field, which promises to help scholars identify the key contributions to a field, and revolutionary discoveries in a field. We discovered that philosophy of science, a sub-field in the humanities, differs significantly from other fields examined with this method. Books play a more important role in philosophy of science (...) than in the sciences. Further, Einstein’s famous 1905 papers created a citation peak in the philosophy of science literature. But rather than being a contribution to the philosophy of science, their importance lies in the fact that they are revolutionary contributions to physics with important implications for philosophy of science. (shrink)

Some decades ago, Heidi Hartmann lamented that “[t]he ‘marriage’ between marxism and feminism has been like the marriage of husband and wife depicted in English common law: marxism and feminism are one, and that one is marxism.”[1] By this, she meant that attempts at a feminist theory had ultimately collapsed into marxism, and so succeeded only in rendering sex inequality derivative of, hence, secondary to class inequality, and as such to be overcome only by ending class inequality. These attempts were (...) in a sense self-defeating, negating the need from which they had emerged, the need for feminism as such. In 1982, Catharine MacKinnon confronted and attempted to remedy this. She developed a theory of sexuality as to feminism what work is to marxism, and thereby elevated feminism to a theory of the kind that marxism is, parallel rather than subordinate to it. She thus made sex inequality finally the issue. But, paradoxically, at the very same time, MacKinnon paralysed feminism, for she revealed men’s oppression of women as unknowable. If men’s oppression of women is unknowable, then feminism, as the movement to end that oppression, is impossible. Susan Bernick recognised this, saying, “MacKinnon’s legacy to feminism is the impossibility of any future feminism. Her account makes feminism theoretically impossible.”[2] This makes the most urgent task for feminism that of explaining how women can know men’s oppression of them. In this thesis, I attempt such an explanation. (shrink)

Papers presented at the conference on "Cultivating Consciousness for Enhancing Human Potential, Wellness and Healing", held at Durham during 8-10 November 1991.

Written by leading researchers in educational and social psychology, learning science, and neuroscience, this edited volume is suitable for a wide-academic readership. It gives definitions of key terms related to motivation and learning alongside developed explanations of significant findings in the field. It also presents cohesive descriptions concerning how motivation relates to learning, and produces a novel and insightful combination of issues and findings from studies of motivation and/or learning across the authors' collective range of scientific fields. The authors provide (...) a variety of perspectives on motivational constructs and their measurement, which can be used by multiple and distinct scientific communities, both basic and applied. (shrink)

Context: Metaphysics of perception explores fundamental questions regarding the structure and status of the perceived world or appearance(s. By virtue of perception, the apparent world comes to existence. This, however, does not mean that the apparent world is a projection of mind, that it exists “in the head.” Implications: PL-metaphysics reconciles realism with constructivism. As such, it might be considered either an alternative to constructivism or an improvement and completion of this position. Constructivist content: The article refers to non-Cartesian movements (...) in contemporary philosophy, including radical constructivism, enactive and embodied cognition. Keywords: Perception, metaphysics, radical constructivism, realism, appearance, Jerzy Perzanowski, Plato, Gottfried Willhelm Leibniz, Ernst von Glasersfeld. (shrink)

I examine the degree of specialization in various sub-fields of philosophy, drawing on data from the PhilPapers Survey. The following three sub-fields are highly specialized: Ancient philosophy, seventeenth/eighteenth century philosophy, and philosophy of physics. The following sub-fields have a low level of specialization: metaphilosophy, philosophy of religion, philosophy of probability, philosophy of the social sciences, decision theory, and philosophy of race and gender. Highly specialized sub-fields tend to require extensive knowledge in some area beyond the typical training of a philosopher, (...) and outside of philosophy proper. In addition, there is a correlation between sub-field size and degree of specialization. Larger sub-fields tend to be more specialized. (shrink)

Open peer commentary on the article “Perception-Action Mutuality Obviates Mental Construction” by Martin Flament Fultot, Lin Nie & Claudia Carello. Upshot: We examine whether there are any irreducible contradictions between ecological psychology and radical enactivism. We concentrate on two points of contention between the two approaches: the relevance of neural structures in understanding perception and the use of semantically loaded concepts in theorizing about perception.