In diverse fictions from the second century Roman Empire, two parties with competing claims to truth hold a formal contest in a public place where, after a series of abrupt reversals, the issue is finally decided by the evidence of a dead, mutilated, or resurrected body. We can ask these corpses to tell us about the ways Roman society constructed truth. Furthermore, can we learn from the abrupt reversals in these narratives anything about the way Romans experienced shifts in truth-paradigms (...) in “real life”? (This is, of course, a question of paramount importance for appreciating the religious change propelled by Christianity). (shrink)

The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a (...) subspace of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart. (shrink)

The paper is a continuation of another paper published as Part I. Now, the case of “n=3” is inferred as a corollary from the Kochen and Specker theorem (1967): the eventual solutions of Fermat’s equation for “n=3” would correspond to an admissible disjunctive division of qubit into two absolutely independent parts therefore versus the contextuality of any qubit, implied by the Kochen – Specker theorem. Incommensurability (implied by the absence of hidden variables) is considered as dual to quantum contextuality. The (...) relevant mathematical structure is Hilbert arithmetic in a wide sense, in the framework of which Hilbert arithmetic in a narrow sense and the qubit Hilbert space are dual to each other. A few cases involving set theory are possible: (1) only within the case “n=3” and implicitly, within any next level of “n” in Fermat’s equation; (2) the identification of the case “n=3” and the general case utilizing the axiom of choice rather than the axiom of induction. If the former is the case, the application of set theory and arithmetic can remain disjunctively divided: set theory, “locally”, within any level; and arithmetic, “globally”, to all levels. If the latter is the case, the proof is thoroughly within set theory. Thus, the relevance of Yablo’s paradox to the statement of Fermat’s last theorem is avoided in both cases. The idea of “arithmetic mechanics” is sketched: it might deduce the basic physical dimensions of mechanics (mass, time, distance) from the axioms of arithmetic after a relevant generalization, Furthermore, a future Part III of the paper is suggested: FLT by mediation of Hilbert arithmetic in a wide sense can be considered as another expression of Gleason’s theorem in quantum mechanics: the exclusions about (n = 1, 2) in both theorems as well as the validity for all the rest values of “n” can be unified after the theory of quantum information. The availability (respectively, non-availability) of solutions of Fermat’s equation can be proved as equivalent to the non-availability (respectively, availability) of a single probabilistic measure as to Gleason’s theorem. (shrink)

Einstein wrote his famous sentence "God does not play dice with the universe" in a letter to Max Born in 1920. All experiments have confirmed that quantum mechanics is neither wrong nor “incomplete”. One can says that God does play dice with the universe. Let quantum mechanics be granted as the rules generalizing all results of playing some imaginary God’s dice. If that is the case, one can ask how God’s dice should look like. God’s dice turns out to be (...) a qubit and thus having the shape of a unit ball. Any item in the universe as well the universe itself is both infinitely many rolls and a single roll of that dice for it has infinitely many “sides”. Thus both the smooth motion of classical physics and the discrete motion introduced in addition by quantum mechanics can be described uniformly correspondingly as an infinite series converges to some limit and as a quantum jump directly into that limit. The second, imaginary dimension of God’s dice corresponds to energy, i.e. to the velocity of information change between two probabilities in both series and jump. (shrink)

L'écologie préénergétique des années 1905-1935 est à la recherche de ses objets d'étude. Des unités fondamentales de la nature (telles que formation végétale, association végétale, climax, biome, communauté biotique, écosystème) se trouvent en compétition et se succèdent les unes aux autres. Autour des années 1920 et 1930, la philosophie organiciste d'Alfred N. Whitehead, ainsi que la perspective évolutionniste d'Herbert Spencer et les propositions émergentistes de Samuel Alexander et Conwy L. Morgan, deviennent des références sous-jacentes au débat épistémologique concernant les unités (...) de base de l'écologie. Des auteurs comme Frederic E. Clements et John Phillips soutiendront plusieurs formes d'organicisme écologique, tandis que Henry A. Gleason interprétera l'association végétale comme le résultat d'une juxtaposition fortuite d'individus. Enfin, et paradoxalement, l'écosystème de Arthur G. Tansley, tout en faisant partie, à l'origine, d'une perspective anti-organiciste, deviendra l'unité fondamentale de programmes de recherche qui se voudront, au moins dans leurs intentions, émergentistes. (shrink)

Not long after the 2001 invasion of Afghanistan, an American citizen was captured by U.S. soldiers on he battlefield carrying a weapon and wearing the dress of a Taliban soldier. Heralded by the news media as the “American Taliban,” he became a spectacle, bound, gagged, naked and blind-folded on a stretcher in a photo taken soon after his capture. The story of how the homeschooled twenty-year-old from a middle-class Northern California family became an enemy combatant in the Afghani desert piqued (...) the popular imagination. After converting to Islam, he went to Yemen, learned Arabic, returned home and then left again to attend a madrassa (or Islamic religious school) before receiving training at an Al-Qaeda training camp in Afghanistan. Some Americans reacted to the young man’s story with wonder; others with loathing. How did this youth stray from the values that most Americans hold dear? In fact, he did not. Similar to Paul Maud’dib who, at the end of Dune Messiah, wandered into the desert a blind holy man, the American Taliban had acted in accordance with values that most American prize: self-reliance, ingenuity, spirituality and practical know-how. It is widely believed that the Fremen culture derives from their religion, Zensunni , an imaginative blending of Zen Buddhism and Sunni Muslim beliefs. However, a closer look reveals that the Fremen (similar to the American Taliban) were shockingly American in their core values. To demonstrate this, I begin by discussing the weirdness of Dune’s Fremen, their religion, customs and lifestyle. Then, I give a brief summary of American philosopher Ralph Waldo Emerson’s famous essay “Self-Reliance” followed by a similar treatment of John Dewey’s notion of democracy as a way of life. The essay returns to paint a clearer picture of the American Fremen and their exhilarating though dangerous faith in jihad as a way of life. (shrink)

There are numerous theoretical reasons which are usually said to undermine the case for mental causation. But in recent years, Libet‘s experiment on readiness potentials (Libet, Wright, and Gleason 1982; Libet, Gleason, Wright, and Pearl 1983), and a more recent replication by a research team led by John Dylan Haynes (Soon, C.S., Brass, M., Heinze, H.J., and Haynes, J.-D. [2008]) are often singled out because they appear to demonstrate empirically that consciousness is not causally involved in our choices (...) and actions. In this paper, an alternative interpretation of these studies is offered; one which is in accordance both with the empirical evidence and also with the phenomenology of the will, demonstrating that the two opposing views of agency – both the ones that deny the reality of free will and the ones that affirm it – are equally compatible with the outcomes of these two experiments. On this basis, it is shown that the claim that the results on the timing of readiness potential tip the scales in favour of one or the other view cannot be justified - neither from a neurological, nor from a philosophical perspective. (shrink)

This chapter argues that the human right to water entails specific moral limits to commodifying water. While free-market economists have generally recognized no such limits, the famous Canadian environmental thinker Maude Barlow has claimed that the human right to water entails that no water markets should be permitted. With a Lockean conception of the human right to water, this chapter argues that both views are mistaken. If water markets prevent people from obtaining some minimal and proportional share of water, by (...) charging a prohibitively high price, or otherwise, then they put the human right to water in jeopardy and, therefore, should be blocked. (shrink)

A commentary is given on Trevena and Miller . The comparability of their experimental task and of the potential they recorded with those used and recorded by Libet, Gleason, Wright, and Pearl is questioned. An interpretation is given for the similarity of event-related potentials recorded when subjects decided to move and when they decided not to move.