Formalizing Kant’s Rules

This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These acts are not propositions; they do not have truth-values. Our formalization is related to the input/ output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL3 as a formalization of Kant’s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant’s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL3. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant’s theoretical philosophy

Unusual Nucleophilic Addition of Grignard Reagents in the Synthesis of 4-Amino-pyrimidines

Pyrimidines have always received considerable attention because of their importance in synthesis and elucidation of biochemical roles, in particular that of vitamin B1. Herein, we describe a reaction pathway in a Grignard reagent-based synthesis of substituted pyrimidines. A general synthesis of α-keto-2-methyl-4-amino pyrimidines and their C6-substituted analogues from 4-amino-5-cyano-2-methylpyrimidine is reported. The presence of the nitrile substituent in the starting material also results in an unusual reaction pathway leading to C6-substituted 1,2-dihydropyrimidines. Grignard reagents that give normal pyrimidine products under standard reaction conditions can be 14 switched to give dihydropyrimidines by holding the reaction at 0 °C before quenching

Upper-rim monofunctionalisation in the synthesis of triazole- and disulfide-linked multicalix[4]- and -[6]arenes.

Covalently linked multiple calixarenes are valued in supramolecular chemistry. We report an easy and versatile synthetic route to covalently linked double and triple calix[4]arene and calix[6]arenes by a novel DMF‐controlled selective alkylation of a convenient and readily available upper‐rim dimethylaminomethyl‐substituted tetrahydroxy calix[4]arene and ‐[6]arenes. Synthetic routes to upper‐rim functionalised redox active disulfide‐linked double‐, tetra‐ and peptidohybrid‐calixarenes employing either redox chemistry (CH2SH) or thiolates (CH2S–) are also opened up from the same key starting material

Galactic S Stars: Investigations of Color, Motion, and Spectral Features

Known bright S stars, recognized as such by their enhanced s-process abundances and C/O ratio, are typically members of the asymptotic giant branch (AGB) or the red giant branch (RGB). Few modern digital spectra for these objects have been published, from which intermediate resolution spectral indices and classifications could be derived. For published S stars we find accurate positions using the Two-Micron All Sky Survey (2MASS), and use the FAST spectrograph of the Tillinghast reflector on Mt. Hopkins to obtain the spectra of 57 objects. We make available a digital S star spectral atlas consisting of 14 spectra of S stars with diverse spectral features. We define and derive basic spectral indices that can help distinguish S stars from late-type (M) giants and carbon stars. We convolve all our spectra with the SDSS bandpasses, and employ the resulting gri magnitudes together with 2MASS JHK mags to investigate S star colors. S stars have colors similar to carbon and M stars, and are therefore difficult to distinguish by color alone. Using near and mid-infrared colors from IRAS and AKARI, we identify some of the stars as intrinsic (AGB) or extrinsic (with abundances enhanced by past mass-transfer). We also use V band and 2MASS magnitudes to calculate a temperature index for stars in the sample. We analyze the proper motions and parallaxes of our sample stars to determine upper and lower limit absolute magnitudes and distances, and confirm that most are probably giants.Comment: 11 pages. Accepted for publication in ApJS July 19, 2011. Spectra available as http://hea-www.harvard.edu/~pgreen/SStarAtlas.ta

A Gravitational Instability-Driven Viscosity in Self-Gravitating Accretion Disks

We derive a viscosity from gravitational instability in self-gravitating accretion disks, which has the required properties to account for the observed fast formation of the first super-massive black holes in highly redshifted quasars and for the cosmological evolution of the black hole-mass distribution.Comment: 14 pages, 1 figure, ApJ Letters (in press

Complex-temperature phase diagram of Potts and RSOS models

We study the phase diagram of Q-state Potts models, for Q=4 cos^2(PI/p) a Beraha number (p>2 integer), in the complex-temperature plane. The models are defined on L x N strips of the square or triangular lattice, with boundary conditions on the Potts spins that are periodic in the longitudinal (N) direction and free or fixed in the transverse (L) direction. The relevant partition functions can then be computed as sums over partition functions of an A\_{p-1} type RSOS model, thus making contact with the theory of quantum groups. We compute the accumulation sets, as N -> infinity, of partition function zeros for p=4,5,6,infinity and L=2,3,4 and study selected features for p>6 and/or L>4. This information enables us to formulate several conjectures about the thermodynamic limit, L -> infinity, of these accumulation sets. The resulting phase diagrams are quite different from those of the generic case (irrational p). For free transverse boundary conditions, the partition function zeros are found to be dense in large parts of the complex plane, even for the Ising model (p=4). We show how this feature is modified by taking fixed transverse boundary conditions.Comment: 60 pages, 16 figures, 2 table

Task Persistence in Early Childhood Education

This study was designed to discover developmental trends in task persistence (TP). It was hoped that the results would suggest when and for what groups a task persistence (TP) curriculum is crucial. To study this development a sample of two, four, and six year old children were given a work task. The task required 120 subjects (Ss) to sort and fold 33 items of clothing and linen. After the task instructions and demonstration, the experimenter did not intervene with reinforcers or further directions. The dependent variables investigated were time spent on the task, time spent away from the task, and number of tasks completed. The independent variables were age, race (Black and White), sex, and social class (advantaged and disadvantaged). The data were analyzed with analysis of variance, Pearson\u27s Product-Moment Correlation, and chi square. The results indicated that older children spent significantly more time on task and significantly less time away from task than younger children. Black children spent significantly more time (than White children) on and away from the task at all ages. Advantaged children spent significantly more time (than disadvantaged children) on task at all ages and significantly less time away from task at ages two and four. Advantaged and disadvantaged subjects were not differentiated by the time spent away from the task at age six. These results imply that task persistence training programs could begin as early as age two. They also suggest that certain subgroups (i.e., disadvantaged White) may require more intensive task persistence training then other subgroups (i.e., advantaged Black). Completion of tasks (CT) significantly differentiated six year olds from two and four year olds, but failed to differentiate two and four year olds. Tasks were completed significantly more often at ages two and four by males than females and by advantaged than disadvantaged children. However, these differences disappeared by age six. Since the differences faded at age six, the use of completion of tasks training as a general curriculum goal may not be warranted. Some of the most surprising results were described by the significant correlation coefficients. The total time spent on the task was negatively related to completion of task. Completion of task was positively related to the time spent away from the task and number of times away from task. These findings suggest that brief periods of absence from a task may improve the chances of completing the task. Therefore, optimal work performance for early childhood education may be realized by programming frequent, brief breaks. A secondary purpose of the study was to investigate verbalizations expressed during the experimental sessions. To study this variable, a verbatim record was established and maintained for each subject. The verbalizations were then totaled and classified as task relevant or irrelevant. The results were analyzed with an analysis of variance (age x race x sex x social class) and Pearson\u27s Product Moment Correlation. Although the number of verbalizations increased with age, the differences between ages four and six were not significant. This finding may reflect a shift to covert verbal mediation during work performance on or about age four. The developmental patterns of verbalizations were different for boys and girls. The girls used more overt verbalizations (than boys) at ages two and four; however, at age six the girls\u27 number of verbalizations decreased noticeably. The verbalizations of boys increased with age. At age six, they used more verbalizations than the girls. The writer concluded that this finding reflected advanced verbalization skills in the girls. If the conclusion is valid, the results may mean that overt verbalizations are more necessary for boys to organize their experiences. White children used significantly more task relevant verbalizations than Black children. This suggests that early childhood educational programs for predominately Black populations may need to stress task relevant verbalization training more than programs which serve predominately White populations. Disadvantaged children used more task irrelevant verbalizations at ages two and six than advantaged children. Apparently, they need extra emphasis on task oriented verbalization training. When considered with the previous paragraph, the disadvantaged Black population has the greatest need for task relevant verbalization training

Trypanocidal and leishmanicidal activity of six limonoids

Six limonoids [kotschyienone A and B (1, 2), 7-deacetylgedunin (3), 7-deacetyl-7-oxogedunin (4), andirobin (5) and methyl angolensate (6)] were investigated for their trypanocidal and leishmanicidal activities using bloodstream forms of Trypanosoma brucei and promastigotes of Leishmania major. Whereas all compounds showed anti-trypanosomal activity, only compounds 1–4 displayed anti-leishmanial activity. The 50% growth inhibition (GI 50) values for the trypanocidal and leishmanicidal activity of the compounds ranged between 2.5 and 14.9 μM. Kotschyienone A (1) was found to be the most active compound with a minimal inhibition concentration (MIC) value of 10 μM and GI 50 values between 2.5 and 2.9 μM. Only compounds 1 and 3 showed moderate cytotoxicity against HL-60 cells with MIC and GI 50 values of 100 μM and 31.5–46.2 μM, respectively. Compound 1 was also found to show activity against intracellular amastigotes of L. major with a GI 50 value of 1.5 μM. The results suggest that limonoids have potential as drug candidates for the development of new treatments against trypanosomiasis and leishmaniasis