Kant’s early essay, Universal Natural History and Theory of the Heavens, is commonly regarded as an original contribution to the development of Newtonian cosmological ideas, and as a step in the evolution of Kant’s own thought. In this paper I try to show, firstly, that despite the recognised debt to Newton’s Principia, the young German thinker makes a personal philosophical synthesis of several ancient and modern sources of cosmological thought; secondly, that besides the novelty of the exposed conjectures about the (...) mechanical production and systematic constitution of the Universe as a whole, and beyond the boldness of the proposed perspectives on the origins and continuous formation or creation of the Cosmos, this essay is also an interesting example of the manner how the young Kant works in such matters as cosmology and cosmogony. There, we can perceive and identify the epistemic presuppositions he puts in action, which are founded in the principle of analogy, used largely as a heuristic principle when the direct observation of phenomena is not possible or the propositions of natural philosophy cannot reach the mathematical precision and geometrical rigour. (shrink)

From the time of Locke, discussions of personal identity have often ignored the question of our basic metaphysical nature: whether we human people are biological organisms, spatial or temporal parts of organisms, bundles of perceptions, or what have you. The result of this neglect has been centuries of wild proposals and clashing intuitions. What Are We? is the first general study of this important question. It beings by explaining what the question means and how it differs from others, such as (...) questions of personal identity and the mind-body problem. It then examines in some depth the main possible accounts of our metaphysical nature, detailing both their theoretical virtues and the often grave difficulties they face. The book does not endorse any particular account of what we are, but argues that the matter turns on more general issues in the ontology of material things. If composition is universal–if any material things whatever make up something bigger–then we are temporal parts of organisms. If things never compose anything bigger, so that there are only mereological simples, then we too are simples–perhaps the immaterial substances of Descartes–or else we do not exist at all . The intermediate view that some things compose bigger things and others do not leads almost inevitably to the conclusion that we are organisms. So we can discover what we are by working out when composition occurs. (shrink)

Two consecution calculi are introduced: one for the implicational fragment of the logic of entailment with truth and another one for the disjunction free logic of nondistributive relevant implication. The proof technique—attributable to Gentzen—that uses a double induction on the degree and on the rank of the cut formula is shown to be insufficient to prove admissible various forms of cut and mix in these calculi. The elimination theorem is proven, however, by augmenting the earlier double inductive proof with additional (...) inductions. We also give a new purely inductive proof of the cut theorem for the original single cut rule in Gentzen’s sequent calculus $ LK $ without any use of mix. (shrink)

Two consecution calculi are introduced: one for the implicational fragment of the logic of entailment with truth and another one for the disjunction free logic of nondistributive relevant implication. The proof technique—attributable to Gentzen—that uses a double induction on the degree and on the rank of the cut formula is shown to be insufficient to prove admissible various forms of cut and mix in these calculi. The elimination theorem is proven, however, by augmenting the earlier double inductive proof with additional (...) inductions. We also give a new purely inductive proof of the cut theorem for the original single cut rule in Gentzen’s sequent calculus $ LK $ without any use of mix. (shrink)

Selon Schiller, jouer, c’est agir en étant dégagé de toute contrainte et de toute obligation, et donc tirer grand plaisir de sa liberté par rapport aux nécessités. C’est ce sentiment de liberté rattachant le jeu au phénomčne esthétique de beauté qui fait sa grande valeur éducationnelle. La qualité que nous appelons beauté procure le męme plaisir que le jeu. Dans une belle śuvre d’art, la matičre n’est pas dominée par la forme ou vice-versa. Une śuvre d’art est un jeu libre (...) entre forme et substance, entre beauté et contrainte, et représente de ce fait le summum de l’activité ludique. Les jeux sont des pas sur la voie de la beauté, car ils éduquent ceux qui jouent au plaisir de la liberté de création. Contrairement ŕ la position de Schiller, Maria Montessori rejette le jeu comme moyen d’éducation. Elle pense que les enfants doivent travailler pour trouver leur voie ŕ travers les difficultés de la réalité. Or, l’analyse de ses méthodes révčle la présence de nombreux éléments de la liberté que Schiller attribue au jeu. Les enfants peuvent choisir les choses avec lesquelles ils « travaillent ». Ils ne sont pas obligés de les utiliser exactement de la maničre que l’éducateur leur montre. Et, ce qui est le plus important, les enfants prennent un grand plaisir ŕ exécuter leur « travail ». Dans cet article, l’auteur interprčte d’abord les réflexions de Schiller sur l’éducation ŕ travers le jeu, oů l’accent est mis sur l’imagination. Dans la seconde partie, l’auteur discute la question de savoir s’il est justifié de prétendre que Maria Montessori rejette l’imagination comme moyen d’éducation. (shrink)

Administrative—judgment on the nature of judgment—conflict between Judges in judicial practice—claimant challenges the judicial capacity of respondent —claimant open and fluid in judicial style—respondent certain and authoritative in judicial style—insights from Psi Division on the role of judgment in the universe—whether respondent is a good judge—whether judgment closes down meaning—whether respondent is inhuman—whether judges are inhuman—whether judging is horrific—insight from twentieth century fiction on the place of humans in the universe—horror of HP Lovecraft—suppression of horrific cosmic context within judicial institution—suppression (...) for the good of society. (shrink)

Chief Judge Achilles and Judge Hera – uniqueness of proceedings – the nature of judicial decision-making – the judicial order of Mega-city One – source of judicial power – judicial styles – qualities required for judicial office – context of judicial action – requirement of reflection – interpretation and meaning in enforcement of law – adjudicative models – law as horrific – legal theories – Hans Kelsen – Justice Hercules – Jacques DerridaJudge Howard – critical assessment of judicial order of (...) Mega-city One – Hans Kelsen, positivism and democracy – merging of law fondatrice and law conservatrice – the “soul of the law” – fracture of the Rule of Law – fascism – comparisons with fascist regimes of twentieth Century Europe – signifiers in judicial uniform – consequences of dissent – reasons for, and consequences of, resignationChief Judge AchillesJudge HeraJudgement delivered 3 March 2138.Grand Hall of Justice, Mega-city One. (shrink)

Two consecution calculi are introduced: one for the implicational fragment of the logic of entailment with truth and another one for the disjunction free logic of nondistributive relevant implication. The proof technique—attributable to Gentzen—that uses a double induction on the degree and on the rank of the cut formula is shown to be insufficient to prove admissible various forms of cut and mix in these calculi. The elimination theorem is proven, however, by augmenting the earlier double inductive proof with additional (...) inductions. We also give a new purely inductive proof of the cut theorem for the original single cut rule in Gentzen’s sequent calculus \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ LK $$\end{document} without any use of mix. (shrink)

We prove a number of results in effective randomness, using methods in which Π⁰₁ classes play an essential role. The results proved include the fact that every PA Turing degree is the join of two random Turing degrees, and the existence of a minimal pair of LR degrees below the LR degree of the halting problem.

Let ω be the set of natural numbers. For functions f, g: ω → ω, we say f is dominated by g if f < g for all but finitely many n ∈ ω. We consider the standard “fair coin” probability measure on the space 2ω of in-finite sequences of 0's and 1's. A Turing oracle B is said to be almost everywhere dominating if, for measure 1 many X ∈ 2ω, each function which is Turing computable from X is (...) dominated by some function which is Turing computable from B. Dobrinen and Simpson have shown that the almost everywhere domination property and some of its variant properties are closely related to the reverse mathematics of measure theory. In this paper we exposit some recent results of Kjos-Hanssen, Kjos-Hanssen/Miller/Solomon, and others concerning LR-reducibility and almost everywhere domination. We also prove the following new result: If B is almost everywhere dominating, then B is superhigh, i. e., 0″ is truth-table computable from B ′, the Turing jump of B. (shrink)

A well known fact is that every Lebesgue measurable set is regular, i.e., it includes an F$_{\sigma}$ set of the same measure. We analyze this fact from a metamathematical or foundational standpoint. We study a family of Muchnik degrees corresponding to measure-theoretic regularity at all levels of the effective Borel hierarchy. We prove some new results concerning Nies's notion of LR-reducibility. We build some $\omega$-models of RCA$_0$which are relevant for the reverse mathematics of measure-theoretic regularity.