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)

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)

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)

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)

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)

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.

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.

Local Recurrency Theory (LR) holds that recurrent loops of neural activity localized to the visual cortex are necessary and sufficient for visual consciousness (if certain background conditions obtain). LR’s popularity has recently waned in favor of theories holding that higher-level types of processing are necessary for consciousness (for example, the Global Neuronal Workspace Theory and Higher-order Theory). This has been in part because of empirical evidence thought to disconfirm LR. However, these competing theories now face challenges of their own, often (...) coming in the form of evidence showing that higher-level brain areas (that is, in the prefrontal cortex) are probably not essential for consciousness. Given growing challenges to LR's competitors, it would be timely to re-assess the prospects for LR. This article carries out such an investigation, first laying out the theory precisely, then going on to survey the evidence presented against it. What will be found is that none of the evidence necessarily undermines LR, but instead just fosters its theoretical enrichment. The overall conclusion: LR remains among our most promising neuroscientific theories of visual consciousness. (shrink)

We say that A ≤LR B if every B-random number is A-random. Intuitively this means that if oracle A can identify some patterns on some real γ. In other words. B is at least as good as A for this purpose. We study the structure of the LR degrees globally and locally (i.e., restricted to the computably enumberable degrees) and their relationship with the Turing degrees. Among other results we show that whenever α in not GL₂ the LR degree of (...) α bounds $2^{\aleph _{0}}$ degrees (so that, in particular, there exist LR degrees with uncountably many predecessors) and we give sample results which demonstrate how various techniques from the theory of the c.e. degrees can be used to prove results about the c.e. LR degrees. (shrink)

Several scholars advance the ‘LR-LP thesis’: the claim that American Legal Realism presupposes Legal Positivism. Brian Leiter and Frederick Schauer, prominent scholars of Realism, delimit that thesis to a Razian version of Exclusive Legal Positivism (‘ELP’). This article nevertheless argues that Leiter and Schauer’s respective accounts of Legal Realism are difficult to square with Razian ELP. Indeed, the Realist hypotheses about alternative drivers of official decision, concerning ‘working’ rules, ‘real’ rules, and ‘situation-types’, if correct, actually threaten Razian ELP. -/- Problems (...) arise for the LR-LP thesis (as delimited to Razian ELP) irrespective of whether those three Realist alternative drivers are classified as legal or non-legal norms. If they are non-legal, merits-based norms, then (a) those alternative drivers do much more work within official decision than ELP suggests is the case for those sorts of norms, and (b), Inclusive Legal Positivism may better, and might even be required, to explain them. Alternatively, if those Realist alternative drivers are better understood as source-based legal norms, then they cannot fulfil (or even be claimed by the law to fulfil) certain core functions that ELP attributes to legal norms. (shrink)

assumptions latent in a vanilla treebank grammar. Indeed, its performance of 86.36% (LP/LR F1) is..

We demonstrate that an unlexicalized PCFG can parse much more accurately than previously shown, by making use of simple, linguistically motivated state splits, which break down false independence assumptions latent in a vanilla treebank grammar. Indeed, its performance of 86.36% (LP/LR F1) is better than that of early lexicalized PCFG models, and surprisingly close to the current state-of-theart. This result has potential uses beyond establishing a strong lower bound on the maximum possible accuracy of unlexicalized models: an unlexicalized PCFG is (...) much more compact, easier to replicate, and easier to interpret than more complex lexical models, and the parsing algorithms are simpler, more widely understood, of lower asymptotic complexity, and easier to optimize. (shrink)

In the recent literature on confirmation there are two leading approaches to the provision of a probabilistic measure of the degree to which a hypothesis is confirmed by evidence. The first is to construe the degree to which evidence E confirms hypothesis H as a function that is directly proportional to p and inversely proportional to p . I shall refer to this as the probability approach. The second approach construes the notion as a function that is directly proportional to (...) the true-positive rate – the probability of the evidence if the hypothesis is true, p – and inversely proportional to the false-positive rate – the probability of the evidence if the hypothesis is false, p . These reverse conditional probabilities – of the evidence on the truth or falsehood of the hypothesis – are sometimes known as likelihoods. I shall refer to the approach to confirmation that uses them as the likelihood approach.For each of these approaches, there are two obvious options as to how to define the confirmation function. The first is to define it as the difference between the magnitude that is treated as increasing confirmation or p ) and the magnitude that is treated as decreasing confirmation or p ). The second is to define confirmation as the quotient of these two magnitudes.This yields four different measures of confirmation, represented in the following table: Differences RatiosProbabilities PD = p – p1 PR = Graphic2Likelihoods LD = p – p3 LR = Graphic4All these measures agree on whether or not E provides some support for H. Intuitively, we want to say that E provides some support for H just in case learning that E is true would make us assign a higher probability to H, i.e. when p(H …. (shrink)

Ladyman and Ross argue that quantum objects are not individuals and use this idea to ground their metaphysical view, ontic structural realism, according to which relational structures are primary to things. LR acknowledge that there is a version of quantum theory, namely the Bohm theory, according to which particles do have denite trajectories at all times. However, LR interpret the research by Brown et al. as implying that "raw stuff" or haecceities are needed for the individuality of particles of BT, (...) and LR dismiss this as idle metaphysics. In this paper we note that Brown et al.'s research does not imply that haecceities are needed. Thus BT remains as a genuine option for those who seek to understand quantum particles as individuals. However, we go on to discuss some problems with BT which led Bohm and Hiley to modify it. This modified version underlines that, due to features such as context-dependence and non-locality, Bohmian particles have a very limited autonomy in situations where quantum effects are non-negligible. So while BT restores the possibility of quantum individuals, it also underlines the primacy of the whole over the autonomy of the parts. The later sections of the paper also examine the Bohm theory in the general mathematical context of symplectic geometry. This provides yet another way of understanding the subtle, holistic and dynamic nature of Bohmian individuals. We finally briefly consider Bohm's other main line of research, the "implicate order", which is in some ways similar to LR's structural realism. (shrink)

There is a plethora of confirmation measures in the literature. Zalabardo considers four such measures: PD, PR, LD, and LR. He argues for LR and against each of PD, PR, and LD. First, he argues that PR is the better of the two probability measures. Next, he argues that LR is the better of the two likelihood measures. Finally, he argues that LR is superior to PR. I set aside LD and focus on the trio of PD, PR, and LR. (...) The question I address is whether Zalabardo succeeds in showing that LR is superior to each of PD and PR. I argue that the answer is negative. I also argue, though, that measures such as PD and PR, on one hand, and measures such as LR, on the other hand, are naturally understood as explications of distinct senses of confirmation. (shrink)

There are different Bayesian measures to calculate the degree of confirmation of a hypothesis H in respect of a particular piece of evidence E. Zalabardo (Analysis 69:630–635, 2009) is a recent attempt to defend the likelihood-ratio measure (LR) against the probability-ratio measure (PR). The main disagreement between LR and PR concerns their sensitivity to prior probabilities. Zalabardo invokes intuitive plausibility as the appropriate criterion for choosing between them. Furthermore, he claims that it favours the ordering of pairs evidence/hypothesis generated by (...) LR. We will argue, however, that the intuitive non-numerical example provided by Zalabardo does not show that prior probabilities do not affect the degree of confirmation. On account of this, we conclude that there is no compelling reason to endorse LR qua measure of degree of confirmation. On the other side, we should not forget some technicalities which still benefit PR. (shrink)

To the standard propositional modal system of provability logic constants are added to account for the arithmetical fixed points introduced by Bernardi-Montagna in [5]. With that interpretation in mind, a system LR of modal propositional logic is axiomatized, a modal completeness theorem is established for LR and, after that, a uniform arithmetical completeness theorem with respect to PA is obtained for LR.

A full separation theorem for the derivable rules of intuitionistic linear logic without bounds, 0 and exponentials is proved. Several structural consequences of this theorem for subreducts of (commutative) residuated lattices are obtained. The theorem is then extended to the logic LR+ and its proof is extended to obtain the finite embeddability property for the class of square increasing residuated lattices.