The present article was partly inspired by G. Pollack’s book, and also Dadoloff, Saxena & Jensen (2010). As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1, No. 2, 2022), for example, things and Beings can travel between Universes, intentionally or unintentionally [4]. In this short remark, we revisit and offer short remark to Neil Boyd’s ideas and trying to connect them with geometry of musical chords as presented by D. Tymoczko (...) and others, then to Escherian staircase and then to Jacob’s ladder which seems to pointto possibility to interpret Jacob’s vision as described in the ancient book of Genesis as interdimensional staircase, e.g. an interdimensional bridge between heaven and earth (cf. classic book: Hofstadter, Godel, Escher, Bach). Jacob’s vision of angels going down to earth from that staircase has been depicted for instance in William Blake art etc. In our communication with others via physics literature and discussions etc, we came to several conclusions as follows: Firstly, possibility of wormhole effect to mirror particle universe, which sometimes it is termed non-orientable wormhole. While such mirror particles effect have been more than 50 years predicted with the so-called parity violation (cf. Lee & Yang, 1950s), and that is called symmetry breaking. Secondly, a series of extended experiments on laser irradiated cold water may suggest possible transition from a phase of water to be at least partially fourth phase of water, which may be composed of crystalline water (see e.g. Gerald Pollack, and also Harold Aspden on liquid crystalline). If we can imagine laser cooling effect can be done in protracted time, then we can achieve a physical representation of Aspden‘s liquid crystalline. Therefore, in this article we outline a series of simple experiments of laser irradiated iced-water along with beryl and selenite crystals in order to see possibility of such a quantum tunneling via quantum liquid crystalline Universe hypothesis, which may likely be modeled with iced-water. It is interesting to remark here that certain experiments by Stockholm University scientists have shown that X-ray triggered water can exhibit properties just like liquid crystal (cf. PRL, 2020). That is why we consider it possible that there can be quantum phase transition where liquid water (comprised of iced cubes and water) can exhibit effects such as tunneling in quantum liquid crystalline Universe. Last but not least, we admit that what we outlined here is just aninitial phase; and if you wish, perhaps we can call such experiments as “wormhole-at-lab” experiments (abbreviated: WHALE). (shrink)

As a senior physicist colleague and our friend, Robert N. Boyd, wrote in a journal (JCFA, Vol. 1,. 2, 2022), Our universe is but one page in a large book [4]. For example, things and Beings can travel between Universes, intentionally or unintentionally. In this short remark, we revisit and offer short remark to Neil’s ideas and trying to connect them with geometrization of musical chords as presented by D. Tymoczko and others, then to Escher staircase and then to (...) Jacob’s ladder which seems to point to possibility to interpret Jacob’s vision as described in the ancient book of Genesis as inter dimensional or heavenly staircase, e.g. an inter dimensional bridge between heaven and earth (see also classic book: Hofstadter, Godel, Escher, Bach). Jacob’s vision of angels going down to earth from that staircase has been depicted for instance in William Blake art etc. In our communication with others via physics literature and discussions etc, we came to several conclusions as follows: Firstly, possibility of quantum wormhole effect to mirror particle universe, which sometimes it is termed non-orientable wormhole. While such mirror particles effect have been more than 50 years predicted with the so-called parity violation (cf. Lee & Yang, 1950s), and that is called symmetry breaking. Secondly, a series of extended experiments on laser irradiated cold water may suggest possible transition from a phase of water to be at least partially fourth phase of water, which may be composed of crystalline water (see e.g. Gerald Pollack, and also Harold Aspden on liquid crystalline). If we can imagine laser cooling effect can be done in protracted time, then we can achieve a physical representation of Aspden’s liquid crystalline. Therefore, in subsequent article (Part II) we outlined simple model of such an effect of tunneling via quantum liquid crystalline Universe, which may likely be modeled with iced-water. It is interesting to remark here that certain experiments by Stockholm University scientists have shown that X-ray triggered water can exhibit properties just like liquid crystal (cf. PRL, 2020). That is why we consider it possible that there can be quantum phase transition where liquid water (comprised of iced cubes and water) can exhibit effects such as tunneling in quantum liquid crystalline Universe. Last but not least, we admit that what we outlined here is just an initial phase; and if you wish, perhaps we can call such experiments as “wormhole-at-lab” experiments (abbreviated: WHALE). (shrink)

This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

The nature of mathematical knowledge can be understood only by locating the knowing mathematician in an epistemic community. This claim is defended by extending Kripke's version of the Private Language Argument to include informal rules and using Godelian results to argue that such rules rules necessary in mathematics. A committed formalist might evade Kripke's original argument by positing internal mechanisms that determine rule -governed behavior. However, in the presence of informal rules, the formalist position collapses into the extreme skepticism that (...) the Private Language Argument works against. The existence of a community of rule followers provides the only viable alternative to such skepticism. (shrink)

Efficient voice leading, in which melodic lines move by short distances from chord to chord, is a hallmark of many different Western musical styles. Although musicians can often find maximally efficient voice leadings with relative ease, theorists have not adequately described general principles or procedures for doing so. This article formalises the notion of voice leading, shows how to classify voice leadings according to transpositional and inversional equivalence and supplies algorithms for identifying maximally efficient voice leadings between arbitrarily chosen chords. (...) The article also includes analytical and theoretical discussions of neo-Riemannian theory, the 'tritone substitution' in contemporary jazz, the music of Wagner and Debussy, the relation between harmony and counterpoint and the connections between scale theory and serial theory. (shrink)

Crispin Wright tried to refute classical 'Cartesian' skepticism contending that its core argument is extendible to a reductio ad absurdum (_Mind<D>, 100, 87-116, 1991). We show both that Wright is mistaken and that his mistakes are philosophically illuminating. Wright's 'best version' of skepticism turns on a concept of warranted belief. By his definition, many of our well-founded beliefs about the external world and mathematics would not be warranted. Wright's position worsens if we take 'warranted belief' to be implicitly defined by (...) the general principles governing it. Those principles are inconsistent, as shown by a variant of Godel's argument. Thus the inconsistency Wright found has nothing to do with the special premises of Cartesian skepticism, but is embedded in his own conceptual apparatus. Lastly, we show how a Cartesian skeptic could avoid Wright's critique by reconstructing a skeptical argument that does not use the claims Wright ultimately finds objectionable. (shrink)

According to quasi-empiricism, mathematics is very like a branch of natural science. But if mathematics is like a branch of science, and science studies real objects, then mathematics should study real objects. Thus a quasi-empirical account of mathematics must answer the old epistemological question: How is knowledge of abstract objects possible? This paper attempts to show how it is possible.The second section examines the problem as it was posed by Benacerraf in Mathematical Truth and the next section presents a way (...) of looking at abstract objects that purports to demythologize them. In particular, it shows how we can have empirical knowledge of various abstract objects and even how we might causally interact with them. (shrink)

The scientific transformation of the hermeneutic art has been the common goal for the various formalist-structuralist programs of interpretation that have dominated human studies in our century - such as New Criticism in literary analysis, the formalist programs in art history and musicology, the Gestalt and Freudian psychology, structuralism in linguistics and anthropology, etc. In this volume, these formalist-structuralist programs shall be called structural programs of interpretation in Europe and America.

At the very beginning of L’Homme-Machine, La Mettrie claims that Leibnizians with their monads have “rather spiritualized matter than materialized the soul”; a few years later Pierre-Louis Moreau de Maupertuis, President of the Berlin Academy of Sciences and natural philosopher with a strong interest in the modes of transmission of ‘genetic’ information, conceived of living minima which he termed molecules, “endowed with desire, memory and intelligence,” in his Système de la nature ou Essai sur les corps organisés. This text first (...) appeared in Latin in 1751 under the title Dissertatio inauguralis metaphysica de universali naturae systemate, with the pseudonym Dr Baumann; it was translated by Maupertuis in 1754 as Essai sur la formation des corps organisés and was later included in his 1756 Œuvres under the title Système de la nature. Now, it is clear that Maupertuis was a kind of Leibnizian; and that his molecule possessed higher-level, ‘mental’ properties. In that sense he falls under the first category described by La Mettrie. But he was also involved in a debate on this issue with Diderot, who put forth a sustained critique of Maupertuis’ theory of the molecule in the additions to his 1753 Pensées sur l’interprétation de la nature. Where Maupertuis attributes higher-level properties to his living minima, Diderot argues that these properties are ‘organizational’, i.e., they can only be properties of the whole. At issue here is the degree of commitment to a form of materialism. (shrink)

In his Philosophical Inquiry concerning Human Liberty (1717), the English deist Anthony Collins proposed a complete determinist account of the human mind and action, partly inspired by his mentor Locke, but also by elements from Bayle, Leibniz and other Continental sources. It is a determinism which does not neglect the question of the specific status of the mind but rather seeks to provide a causal account of mental activity and volition in particular; it is a ‘volitional determinism’. Some decades later, (...) Diderot articulates a very similar determinism, which seeks to recognize the existence of “causes proper to man” (as he says in the Réfutation d’Helvétius). The difference with Collins is that now biological factors are being taken into account. Obviously both the ‘volitional’ and the ‘biological’ forms of determinism are noteworthy inasmuch as they change our picture of the nature of determinism itself, but my interest here is to compare these two determinist arguments, both of which are broadly Spinozist in nature – and as such belong to what Jonathan Israel called in his recent book “the radical Enlightenment,” i.e. a kind of underground Enlightenment constituted by Spinozism – and to see how Collins’ specifically psychological vision and Diderot’s specifically biological vision correspond to their two separate national contexts: determinism in France in the mid-1750s was a much more medico-biological affair than English determinism, which appears to be on a ‘path’ leading to Mill and associationist psychology. (shrink)

J. Willard Gibbs derived the following equation to quantify the maximum work possible for a chemical reaction$${\text{Maximum work }} = \, - \Delta {\text{G}}_{{{\text{rxn}}}} = \, - \left( {\Delta {\text{H}}_{{{\text{rxn}}}} {-}{\text{ T}}\Delta {\text{S}}_{{{\text{rxn}}}} } \right) {\text{ constant T}},{\text{P}}$$ Maximum work = - Δ G rxn = - Δ H rxn - T Δ S rxn constant T, P ∆Hrxn is the enthalpy change of reaction as measured in a reaction calorimeter and ∆Grxn the change in Gibbs energy as measured, if (...) feasible, in an electrochemical cell by the voltage across the two half-cells. To Gibbs, reaction spontaneity corresponds to negative values of ∆Grxn. But what is T∆Srxn, absolute temperature times the change in entropy? Gibbs stated that this term quantifies the heating/cooling required to maintain constant temperature in an electrochemical cell. Seeking a deeper explanation than this, one involving the behaviors of atoms and molecules that cause these thermodynamic phenomena, I employed an “atoms first” approach to decipher the physical underpinning of T∆Srxn and, in so doing, developed the hypothesis that this term quantifies the change in “structural energy” of the system during a chemical reaction. This hypothesis now challenges me to similarly explain the physical underpinning of the Gibbs–Helmholtz equation$${\text{d}}\left( {\Delta {\text{G}}_{{{\text{rxn}}}} } \right)/{\text{dT}} = - \Delta {\text{S}}_{{{\text{rxn}}}} \left( {\text{constant P}} \right)$$ d Δ G rxn / dT = - Δ S rxn constant P While this equation illustrates a relationship between ∆Grxn and ∆Srxn, I don’t understand how this is so, especially since orbital electron energies that I hypothesize are responsible for ∆Grxn are not directly involved in the entropy determination of atoms and molecules that are responsible for ∆Srxn. I write this paper to both share my progress and also to seek help from any who can clarify this for me. (shrink)

_Sweet Reason: A Field Guide to Modern Logic, 2nd Edition_ offers an innovative, friendly, and effective introduction to logic. It integrates formal first order, modal, and non-classical logic with natural language reasoning, analytical writing, critical thinking, set theory, and the philosophy of logic and mathematics. An innovative introduction to the field of logic designed to entertain as it informs Integrates formal first order, modal, and non-classical logic with natural language reasoning, analytical writing, critical thinking, set theory, and the philosophy of (...) logic and mathematics Addresses contemporary applications of logic in fields such as computer science and linguistics A web-site linked to the text features numerous supplemental exercises and examples, enlightening puzzles and cartoons, and insightful essays. (shrink)