Im Hinblick auf den Herbrand'schen Satz für die Prädikatenlogik der ersten Stufe und auf die Lehre vom Beweisverfahren mit Rechenautomaten, die daraus folgt, wird ein Beweis als komputazional synthetisch bezeichnet, wenn er sich auf Objekte bezieht, die im erwiesenen Satz nicht erwähnt sind. Die mathematischen Beweise sind aber auch synthetisch in einem begrifflichen Sinne: die Kontrolle oder die Begrenzung der angewandten Begriffe — die sogenannte Methodenreinheit — ist im allgemeinen unerreichbar.

Im Hinblick auf den Herbrand'schen Satz für die Prädikatenlogik der ersten Stufe und auf die Lehre vom Beweisverfahren mit Rechenautomaten, die daraus folgt, wird ein Beweis als komputazional synthetisch bezeichnet, wenn er sich auf Objekte bezieht, die im erwiesenen Satz nicht erwähnt sind. Die mathematischen Beweise sind aber auch synthetisch in einem begrifflichen Sinne: die Kontrolle oder die Begrenzung der angewandten Begriffe — die sogenannte Methodenreinheit — ist im allgemeinen unerreichbar.

One of the fundamental properties inclassical equational reasoning isLeibniz's principle of substitution. Unfortunately, this propertydoes not hold instandard epistemic logic. Furthermore,Herbrand's lifting theorem which isessential to thecompleteness ofresolution andParamodulation in theclassical first order logic (FOL), turns out to be invalid in standard epistemic logic. In particular, unlike classical logic, there is no skolemization normal form for standard epistemic logic. To solve these problems, we introduce anintensional epistemic logic, based on avariation of Kripke's possible-worlds semantics that need not have a (...) constant domain. We show how a weaker notion of substitution through indexed terms can retain the Herbrand theorem. We prove how the logic can yield a satisfibility preserving skolemization form. In particular, we present an intensional principle for unifing indexed terms. Finally, we describe asound andcomplete inference system for a Horn subset of the logic withequality, based onepistemic SLD-resolution. (shrink)

Gelfond and Lifschitz proposed the notion of a stable model of a logic program. We establish that the set of all stable models in a Herbrand universe of a recursive logic program is, up to recursive renaming, the set of all infinite paths of a recursive, countably branching tree, and conversely. As a consequence, the problem, given a recursive logic program, of determining whether it has at least one stable model, is Σ11-complete. Due to the equivalences established in the (...) authors' previous nonmonotone rule systems papers ), this applies equally to truth maintenance systems and default logics. (shrink)

A translation of the Écrits logiques, edited by Jean Van Heijenoort, published in 1968.

In February 2015 the UK became the first country to legalise high-profile mitochondrial replacement techniques, which involve the creation of offspring using genetic material from three individuals. The aim of these new cell reconstruction techniques is to prevent the transmission of maternally inherited mitochondrial disorders to biological offspring. During the UK debates, MRTs were often positioned as a straightforward and unique solution for the ‘eradication’ of mitochondrial disorders, enabling hundreds of women to have a healthy, biologically-related child. However, many questions (...) regarding future applications and potential users remain. Drawing on a current qualitative study on reproductive choices in the context of mitochondrial disorders, this article illustrates how the potential limitations of MRTs have been obscured in public debates by contrasting the claims made about the future beneficiaries with insights from families affected by mitochondrial disorders and medical experts. The analysis illuminates the complex choices with which families and individuals affected by mitochondrial disorders are faced, which have thus far remained invisible. An argument is presented for improved information for the public as well as an intensification of critical empirical research around the complex and specific needs of future beneficiaries of new reproductive biotechnologies. (shrink)

Recent studies indicate that mammalian chromosomes contain discretecis‐acting loci that control replication timing, mitotic condensation, and stability of entire chromosomes. Disruption of the large non‐coding RNA gene ASAR6 results in late replication, an under‐condensed appearance during mitosis, and structural instability of human chromosome 6. Similarly, disruption of the mouse Xist gene in adult somatic cells results in a late replication and instability phenotype on the X chromosome. ASAR6 shares many characteristics with Xist, including random mono‐allelic expression and asynchronous replication timing. (...) Additional “chromosome engineering” studies indicate that certain chromosome rearrangements affecting many different chromosomes display this abnormal replication and instability phenotype. These observations suggest that all mammalian chromosomes contain “inactivation/stability centers” that control proper replication, condensation, and stability of individual chromosomes. Therefore, mammalian chromosomes contain four types ofcis‐acting elements, origins, telomeres, centromeres, and “inactivation/stability centers”, all functioning to ensure proper replication, condensation, segregation, and stability of individual chromosomes. (shrink)

A historical investigation of the exclusion of Africa and Asia from modern histories of philosophy.

Vaesen infers unique properties of mind from the appearance of specific cultural innovation – a correlation without causal direction. Shifts in habitat, population density, and group dynamics are the only independently verifiable incentives for changes in cultural practices. The transition from Acheulean to Late Stone Age technologies requires that we consider how population and social dynamics affect cultural innovation and mental function.

The first English translation of Fichte’s second set of 1804 lectures on the Wissenschaftslehre.

Orthologic is defined by weakening the axioms and rules of inference of the classical propositional calculus. The resulting Lindenbaum-Tarski quotient algebra is an orthoimplication algebra which generalizes the author's implication algebra. The associated order structure is a semi-orthomodular lattice. The theory of orthomodular lattices is obtained by adjoining a falsity symbol to the underlying orthologic or a least element to the orthoimplication algebra.

Providing an original and systematic treatment of foundational issues in philosophy of religion, J. L. Schellenberg's new book addresses the structure of..

According to realist structuralism, mathematical objects are places in abstract structures. We argue that in spite of its many attractions, realist structuralism must be rejected. For, first, mathematical structures typically contain intra-structurally indiscernible places. Second, any account of place-identity available to the realist structuralist entails that intra-structurally indiscernible places are identical. Since for her mathematical singular terms denote places in structures, she would have to say, for example, that 1 = − 1 in the group (Z, +). We call this (...) the identity problem and conclude that nominalism is presently the safest route for the structuralist. (shrink)

Ned Block argues that the higher-order (HO) approach to explaining consciousness is ‘defunct’ because a prominent objection (the ‘misrepresentation objection’) exposes the view as ‘incoherent’. What’s more, a response to this objection that I’ve offered elsewhere (Weisberg 2010) fails because it ‘amounts to abusing the notion of what-it’s-like-ness’ (xxx).1 In this response, I wish to plead guilty as charged. Indeed, I will continue herein to abuse Block’s notion of what-it’s-like-ness. After doing so, I will argue that the HO approach accounts (...) for the sense of what-it’s-like-ness that matters in a theory of consciousness. I will also argue that the only incoherence present in the HO theory is that generated by embracing Block’s controversial notion of what-it’s-like-ness, something no theorist of any stripe ought to do. Block is famous for (among other things) having introduced the notion of ‘phenomenal consciousness’ into contemporary philosophy of mind (Block 1995). This term is widely employed in the philosophical literature and it even appears in the empirical literature. But wide-speared usage has brought about divergent interpretations of the term. We can distinguish a ‘moderate’ and a ‘zealous’ reading of ‘phenomenal consciousness’. On the moderate reading, ‘phenomenal consciousness’ just means ‘experience’. Many people have embraced this sense of the term and use it to roughly pick out conscious experience involving sensory quality (states like conscious visual experiences or conscious pains, for example).2 On the zealous reading, however, phenomenal consciousness is held to be ‘distinct from any cognitive, intentional, or functional property’ (Block 1995: 234). That is, any explanation of phenomenal consciousness in exclusively cognitive, intentional, or functional terms will fail to capture, without remainder, what is really distinctive about phenomenal consciousness. Block, of course, is fully clear about embracing the zealous reading; indeed, his initial introduction of the notion is in those terms. The same ambiguity occurs with the much-used (and abused) idea of ‘what-it’s-like-ness’.. (shrink)

Scientists and laypeople alike use the sense of understanding that an explanation conveys as a cue to good or correct explanation. Although the occurrence of this sense or feeling of understanding is neither necessary nor sufficient for good explanation, it does drive judgments of the plausibility and, ultimately, the acceptability, of an explanation. This paper presents evidence that the sense of understanding is in part the routine consequence of two well-documented biases in cognitive psychology: overconfidence and hindsight. In light of (...) the prevalence of counterfeit understanding in the history of science, I argue that many forms of cognitive achievement do not involve a sense of understanding, and that only the truth or accuracy of an explanation make the sense of understanding a valid cue to genuine understanding. (shrink)

The purpose of this text is to draw attention to eight forgotten heroes: William C. Bagley, Charles DeGarmo, David Felmley, William Torrey Harris, Isaac L. Kandel, Charles McMurry, William C. Ruediger, and Edward Austin Sheldon. They have been marginalized from our profession, and drawing upon their legacy is the best hope for restoring the profession of teaching today. This work also includes a chapter at the end of the book entitled "John Dewey's Forgotten Essays." The audience for this book includes: (...) 1) classroom teachers, 2) school administrators, 3) teacher educators, 4) deans and other university administrators, 5) college and university presidents, 6) legislators, 7) historians of education, 8) curriculum specialists, 9) specialists in teacher training, and 10) the general public. (shrink)