Alternative Statements Research Articles

Optional Rules in the Formation of the Old Church Slavonic Aorist

BACKGROUND.1 Traditionally, the Old Church Slavonic verb is considered to be capable of forming three types of aorist. The so-called root aorist is presumably formed by adding personal endings directly to the stem (Diels2 ?114.1), as in the forms of the verb 'to fall' with the basic stem in pad-: 1st sg. padb, 2d and 3d sg. pade, 1st du. padove, 2d du. padeta, 3d du. padete, 1st pl. padomb, 2d pl. padete, 3d pl. padQ. The so-called s-aorist (Diels ?114.2) is presumably formed by adding the element s (which under certain conditions alternates with x) directly to the stem, as in the respective forms of ved'lead' and rek'speak': vesz, vede, vesove, vesta, veste, vesomzb, veste, ve`s, and rexb,, re ree, rxov, resta, reste, rexomb, rtste, rese. The so-called x-aorist (Diels ?114.3) is formed by adding the element ox, as in the x-aorist forms of ved-: vedoxz, vede, vedoxove, vedosta, vedoste, vedoxomnb, vedoste, and vedo4. In addition to automatic changes (such as x to s before a front vowel), it must be noted that the second and third persons singular are always formed on the root-aorist pattern; and that the third person plural ends in Q in the root aorist but in q in the sand x-aorists, as in the forms padQ (root aor.), resg (s-aor.), and vedog (x-aor.). The distribution of the various types of aorist among stem classes is the following: class 1.1 (cf. Diels ?105-6) has all three types in stems that end in an obstruent, as in the forms padb, vesZ, and nesoxb; stems of class 1.1 that end in a sonorant take s-aorist only; stems of class 2.1 take either the root aorist or the s-aorist; stems of class 2.2 and 3-6 take the s-aorist; and stems of class 7 (irregular) require individual disposition. This paper offers an alternate statement of the OCS aorist, which differs from the previous in that it consists of a series of ordered rules which are completely general, i.e. apply to verbal stems as identified by their phonological shapes without reference to a classificatory scheme like Diels's classes. The principle here involved is simplicity of grammatical statement. This principle has been discussed elsewhere,3 and will not be formally appealed to in this paper.

The “Open Society” and its Fallacies

A little over 100 years ago John Stuart Mill wrote in his essay On Liberty that “… there ought to exist the fullest liberty of professing and discussing, as a matter of ethical conviction, any doctrine, however immoral it may be considered.” The sentence from which this is taken is not obiter: Chapter Two of his book is devoted to arguments, putatively philosophical in character, which if they were sound would warrant precisely such a conclusion; we have therefore every reason to assume that Mill meant by the sentence just what it says. The topic of Chapter Two is the entire “communications” process in civilized society (“advanced” society, as Mill puts it); and the question he raises is whether there should be limitations on that process. He treats that problem as the central problem of all civilized societies, the one to which all other problems are subordinate, because of the consequences, good or ill, that a society must bring upon itself according as it adopts this or that solution to it. And he has supreme confidence in the Tightness of the solution he offers. Presumably to avoid all possible misunderstanding, he provides several alternative statements of it, each of which makes his intention abundantly clear, namely, that society must be so organized as to make that solution its supreme law. “Fullest,” that is, absolute freedom of thought and speech, he asserts by clear implication in the entire argument of the chapter, is not to be one of several competing goods society is to foster, one that on occasion might reasonably be sacrificed, in part at least, to the preservation of other goods; i.e., he refuses to recognize any competing good in the name of which it can be limited.

The “Open Society” and its Fallacies

A little over 100 years ago John Stuart Mill wrote in his essay On Liberty that “… there ought to exist the fullest liberty of professing and discussing, as a matter of ethical conviction, any doctrine, however immoral it may be considered.” The sentence from which this is taken is not obiter: Chapter Two of his book is devoted to arguments, putatively philosophical in character, which if they were sound would warrant precisely such a conclusion; we have therefore every reason to assume that Mill meant by the sentence just what it says. The topic of Chapter Two is the entire “communications” process in civilized society (“advanced” society, as Mill puts it); and the question he raises is whether there should be limitations on that process. He treats that problem as the central problem of all civilized societies, the one to which all other problems are subordinate, because of the consequences, good or ill, that a society must bring upon itself according as it adopts this or that solution to it. And he has supreme confidence in the Tightness of the solution he offers. Presumably to avoid all possible misunderstanding, he provides several alternative statements of it, each of which makes his intention abundantly clear, namely, that society must be so organized as to make that solution its supreme law. “Fullest,” that is, absolute freedom of thought and speech, he asserts by clear implication in the entire argument of the chapter, is not to be one of several competing goods society is to foster, one that on occasion might reasonably be sacrificed, in part at least, to the preservation of other goods; i.e., he refuses to recognize any competing good in the name of which it can be limited.

The associated flow rule of plasticity

The workhardening and linearity hypotheses introduced by Drucker are logically equivalent to the hypotheses of the existence of the plastic potential and of its identity with tlie yield function. Since neither of these sets of hypotheses is deducible from established physical laws, the author suggests that they are alternative statements of a new physical law.The flow rule at singular points on a yield surface is found by considering the actual yield surface as the limit of a sequence of regular surfaces. This procedure has different consequences for workhardening and nonhardening materials.

An analog of the minimax theorem for vector payoffs

for all i, j . Thus in the (two-person, zero-sum) game with matrix Λf, player I has a strategy insuring an expected gain of at least v, and player II has a strategy insuring an expected loss of at most v. An alternative statement, which follows from the von Neumann theorem and an appropriate law of large numbers is that, for any e>0, I can, in a long series of plays of the game with matrix M, guarantee, with probability approaching 1 as the number of plays becomes infinite, that his average actual gain per play exceeds v — e and that II can similarly restrict his average actual loss to v-he. These facts are assertions about the extent to which each player can control the center of gravity of the actual payoffs in a long series of plays. In this paper we investigate the extent to which this center of gravity can be controlled by the players for the case of matrices M whose elements m(i9 j) are points of ΛΓ-space. Roughly, we seek to answer the following question. Given a matrix M and a set S in iV-space, can I guarantee that the center of gravity of the payoffs in a long series of plays is in or arbitrarily near St with probability approaching 1 as the number of plays becomes infinite ? The question is formulated more precisely below, and a complete solution is given in two cases: the case JV=1 and the case of convex S. Let

A New Examination of the Laws of Thermodynamics

The first law is stated in a new, simpler form which is qualitative, and its quantitative content is proven as a corollary. This is done for both the Poincaré and the Carathéodory methods. A statement of the second law is given. Minimum requirements for statements of the laws are discussed, and new alternative statements suggested.

Osage II: Morphology

Previous articleNext article No AccessOsage II: MorphologyHans WolffHans Wolff Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by International Journal of American Linguistics Volume 18, Number 4Oct., 1952 Article DOIhttps://doi.org/10.1086/464177 Views: 7Total views on this site Citations: 2Citations are reported from Crossref PDF download Crossref reports the following articles citing this article: Lisa Conathan Osage Grammar (Quintero) Conathan, International Journal of American Linguistics 73, no.33 (Jul 2015): 370–372.https://doi.org/10.1086/521733 Mary Ruth Wise Estudio sobre la lengua machiguenga (Pío Aza) Wise, International Journal of American Linguistics 73, no.33 (Jul 2015): 372–374.https://doi.org/10.1086/521734

On the foundations of inversion geometry

Introduction. A 3-dimensional inversion geometry over an ordered field V in which every nonnegative number is a square may be defined as a partially ordered set II of objects called circles, spheres, and inversion space with the properties: (i) if p is any point, then there is an affine geometry whose points, lines, planes, and 3-space are, respectively, the points of II other than p, the containing p, the containing p, and the inversion space; (ii) the underlying field of this affine geometry is V; (iii) this affine geometry can be made a Euclidean geometry in such a way that the circles and spheres of the Euclidean geometry are, respectively, the of II not containing p and the of II not containing p. The purpose of this paper is to give axioms for II that will be sufficient to establish (i), (ii), and (iii). The only undefined relation is the ordering relation <, which means, geometrically, that all our axioms are incidence axioms. There does not seem to be any particular interest in finding alternative statements of (i), so (i) is simply assumed (1.4). Additional assumptions are added (2.11 and 2.12), and the remainder of the paper is devoted to proving that these axioms are sufficient for (ii) and (iii). The extension of this work to higher dimensions is straightforward, and we have concentrated on the 3-dimensional case for the sake of simplicity. The 2-dimensional case, however, is different in many ways('), and will be treated in a future paper. It is rather surprising that the literature contains so few investigations of the foundations of inversion geometry as an autonomous subject(2). Certainly much less is known about the postulates for inversion geometry than for other geometries. The present paper is an effort to remedy this deficiency. We wish to thank H. S. M. Coxeter, Tong Hing, and E. R. Lorch for their invaluable advice at various stages in the preparation of this manuscript. 1. The first set of postulates. In this section, we postulate that our set

The Third Law of Classical Thermodynamics

The third law, or law of limits as T→0°K, is expressed as: ``for any real phase Lim lim T→0(∂S∂xi)xj,n=0,and for any spontaneous isothermal process, Lim lim T→0Σiνi(∂S∂ni)T,y,nj≤0.''The equality sign applies to reversible processes and the inequality sign to irreversible processes. The n's represent composition variables, the x's (or T and the y's) a suitable set of state variables, and the v's the number of moles of the components entering into the reaction (positive for products, negative for reactants). Alternative statements of the third law are given and derived from the above statement. The completeness of this statement as a usable postulate for the further development of classical thermodynamics is briefly discussed.

Alternative Statements of Percentage Data in the Fitting of Logarithmic Curves

Alternative Statements of Percentage Data in the Fitting of Logarithmic Curves

Alternative Statements of Percentage Data in the Fitting of Logarithmic Curves

Alternative Statements of Percentage Data in the Fitting of Logarithmic Curves

Prevention of Transient Voltage in Windings

This paper relates to windings such as are used in transformers, reactors and the like, with particular reference to the characteristics which determine internal distributions of suddenly impressed voltages or sudden voltage changes, and the resulting internal oscillations. Ordinary lightning arresters, which limit the maximum voltages reaching the winding terminals, but cause rather than prevent the occurrence of sudden voltage changes, certainly give no protection against excessive voltages between turns or between coils. After describing the production of these transient voltages in ordinary windings, and pointing out that the treatment of symptoms by the addition of extra insulation tends to defeat itself by augmenting the cause, this paper explains these phenomena as due to faulty arrangements of inherent capacitance with the inductance of the winding. A fundamental principle is evolved indicating the constitutional remedy, which, if perfectly applied, would give only uniform internal voltage distributions, however abrupt or frequent the voltage changes at the terminals might be. Methods of application are described for the ordinary windings, by supplementing the faulty arrangements of inherent capacitance with auxiliary capacitances or condensers. Methods are given, also, for the construction of windings with the ideal distribution of inherent capacitance called for by the principle. Two alternative statements of the fundatmental principle upon which the ideal distribution of capacitance is based are emphasized in the paper, and the application of the principle is adequately illustrated in the figures, of which Fig.