On a problem of P(α, δ, π) concerning generalized Alexandroff s cube

Universality of generalized Alexandroff's cube plays essential role in theory of absolute retracts for the category of , -closure spaces. Alexandroff's cube. is an , -closure space generated by the family of all complete filters. in a lattice of all subsets of a set of power .Condition P(, , ) says that is a closure space of all , -filters in the lattice ( ), .Assuming that P (, , ) holds, in the paper [2], there are given sufficient conditions saying when an , -closure space is an absolute retract for the category of , -closure spaces (see Theorems 2.1 and 3.4 in [2]).It seems that, under assumption that P (, , ) holds, it will be possible to givean uniform characterization of absolute retracts for the category of , -closure-spaces.Except Lemma 3.1 from [1], there is no information when the condition P (, , ) holds or when it does not hold.The main result of this paper says, that there are examples of cardinal numbers, , , such that P (, , ) is not satisfied.Namely it is proved, using elementary properties of Lebesgue measure on the real line, that the condition P (, ₁, 2 ) is not satisfied.Moreover it is shown that fulfillment of the condition is essential assumption in, Theorems 2.1 and 3.4 from [1] i.e. it cannot be eliminated.     

Utility theory with inexact preferences and degrees of preference

a–b* c–d is taken to mean that your degree of preference for a over b is less than your degree of preference for c over d. Various properties of the strength-of-preference comparison relation * are examined along with properties of simple preferences defined from *. The investigation recognizes an individual's limited ability to make precise judgments. Several utility theorems relating a–b * c–d to u(a)–u(b) are included.     

A Translation of Intuitionistic Predicate Logic into Basic Predicate Logic

Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.     

Six-year-old children's understanding of sentences adjoined with time adverbs

The adjoining of clauses with temporal links is the basis for many sentences that convey sequence of events. The present study attempts to delineate 6-year-old children's (N=30) understanding of the meaning sequences imparted by sentences adjoined with after, before, and until. Their performance of the meaning sequence for each of 24 carefully constructed sentences is compared to an adult model. Analysis of the results (using a Wilcoxon Matched Pairs Signed Rank Test) indicated that: (1)Ss understood sentences adjoined with after according to an adult model more frequently than before adjoined sentences (P<0.01); (b) Until adjoined sentences with a negative marker in the main clause were understood according to an adult model more often than until adjoined sentences with no such negative element, but the difference was not significant at a=0.01; (3)Ss understood before adjoined sentences according to an adult model more often than until adjoined sentences, but the difference was not significant at a=0.01. In general, the results indicated that 6-year-olds have not yet completed development of an adult grammar with respect to adjoining clauses with temporal links, after, before, and until.     

Three views of demonstrative reference

Three views of demonstrative reference are examined: contextual, intentional, and quasi-intentional. According to the first, such reference is determined entirely by certain publicly accessible features of the context. According to the second, speaker intentions are criterial in demonstrative reference. And according to the third, both contextual features and intentions come into play in the determination of demonstrative reference. The first two views (both of which enjoy current popularity) are rejected as implausible; the third (originally proposed by Kaplan in Dthat) is argued to be highly plausible.     

Some problems concerning the logic of grammatical modifiers

This paper consists principally of selections from a much longer work on the semantics of English. It discusses some problems concerning how to represent grammatical modifiers (e.g. slowly in x drives slowly) in a logically perspicuous notation. A proposal of Reichenbach's is given and criticized; then a new theory (apparently discovered independently by myself, Romain Clark, and Richard Montague and Hans Kamp) is given, in which grammatical modifiers are represented by operators added to a first-order predicate calculus. Finally some problems concerning applications of adjectives to that-clauses and gerundive-clauses are discussed.     

O pojęciu zdania analitycznego

Rezultaty przedstawione w pracy niniejszej pokrywaj si czciowo z wynikami osignitymi przezR. Wójcickiego w pracy:Analityczne komponenty definicji arbitralnych. Studia Logica, t. XIV. Dotyczy to gównie rezultatów zawartych w czci pierwszej. Chciabym podkreli, i wyniki R. Wójcickiego uzyskane zostay cakowicie niezalenie od rezultatów przedstawionych w pracy obecnej.Allatum est die 16 Aprilis 1962     

Once More into the Breach of Self-Ownership: Reply to Narveson and Brenkert

In reply to Narveson, I distinguish his no-proviso argument from his liberty argument, and I show that both fail. I also argue that interference lacks the strategic status he assigns to it, because it cannot be appropriately distinguished, conceptually and morally, from prevention; that natural resources do enjoy the importance he denies they have; that laissez-faire economies lack the superiority he attributes to them; that ownership can indeed be a reflexive relation; that anti-paternalism does not entail libertarianism; and that he misrepresents the doctrines of a number of philosophers, including John Locke, Ronald Dworkin, and myself. In reply to Brenkert, I show that he seriously misconstrues my view of the nature of freedom, and of its relationship to self-ownership. I then refute his criticisms of my treatment of the contrasts between self-ownership, on the one hand, and autonomy and non-slavery, on the other. I also show that his attempt to exorcize the demon of self-ownership is multiply flawed.     

On superintuitionistic logics as fragments of proof logic extensions

Coming fromI andCl, i.e. from intuitionistic and classical propositional calculi with the substitution rule postulated, and using the sign to add a new connective there have been considered here: Grzegorozyk's logicGrz, the proof logicG and the proof-intuitionistic logicI set up correspondingly by the calculiFor any calculus we denote by the set of all formulae of the calculus and by the lattice of all logics that are the extensions of the logic of the calculus, i.e. sets of formulae containing the axioms of and closed with respect to its rules of inference. In the logiclG the sign is decoded as follows: A = (A & A). The result of placing in the formulaA before each of its subformula is denoted byTrA. The maps are defined (in the definitions of x and the decoding of is meant), by virtue of which the diagram is constructedIn this diagram the maps, x and are isomorphisms, thereforex ^–1 = ; and the maps and are the semilattice epimorphisms that are not commutative with lattice operation +. Besides, the given diagram is commutative, and the next equalities take place: ^–1 = ^–1 and = ^–1 x. The latter implies in particular that any superintuitionistic logic is a superintuitionistic fragment of some proof logic extension.     

Are there human rights?

Conclusion In conclusion, I have tried to show that if there are any rights at all, legal, moral and political, there are at least the sorts of human rights cited in the Universal Declaration, rights which extend beyond the slender base provided by Hart's right to be free and which include the right to an adequate human life for everyone, rights shared by all, rights that, as rights, imply correlative duties. Even though the duties thus implied are admittedly imperfect, as rights, they confer upon right-holders, the authority to obligate others.I have argued for the most part against regarding any rights, even some human, rights (interchangable here with manifesto rights, welfare rights, rights of recipience, social and economic rights, programme rights, Fawcett calls them, positive in rem rights) as claims to rights or proposals for adoption as rights. I have argued that to have a right of any kind, including especially a human right, one shared by and held equally by all human beings,while not unconditional or unalterable, is fundamentally important, - to return once again to Feinberg's definition at the opening of this paper. A human right is fundamentally important, however, only if it, too, implies an obligation on the part of other people, one in which other people are obligated to use their power and resources to make things happen. To havea right is to be in a position to impose corresponding obligations on others. As Kant pointed out, a right of any kind gives a right holder a title to compel.

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Dowód aksjomatyzowalności pewnychn-wartościowych rachunków zdań

Praca ta zostaa wykonana pod kierunkiem prof. drJerzego Supeckiego. Jej szczególny przypadek dotyczcyn-wartociowego rachunku zda o jednej wartoci wyrónionej by referowany w Warszawie na zjedzie Grupy Logiki Instytutu Filozofii i Socjologii PAN. Streszczenie tego referatu [5] zostao wydrukowane w Sprawozdaniach Wydziau Nauk Spoecznych PAN.Allatum est die 19 Aprilis 1963     

On a certain class ofm-address machines

Conclusion It follows from the proved theorems that ifM =Q, (whereQ={0,q ₁,q ₂,...,q }) is a machine of the classM _F then there exist machinesM _i such thatM _i(1,c)=M (q _i,c) andQ _i={0, 1, 2, ..., +1} (i=1, 2, ..., ).And thus, if the way in which to an initial function of content of memorycC a machine assigns a final onecC is regarded as the only essential property of the machine then we can deal with the machines of the formM ={0, 1, 2, ..., }, and processes (t) (wheret=1,c,cC) only.Such approach can simplify the problem of defining particular machines of the classM _F , composing and simplifying them.Allatum est die 19 Januarii 1970     

Moral Responses and Moral Theory: Socially-based Externalist Ethics

The paper outlines a view called social (or two-level) response-dependency as an addition to standard alternatives in metaethics that allows for a position intermediate between standard versions of internalism and externalism on the question of motivational force. Instead of taking psychological responses as either directly supplying the content of ethics (as on emotivist or sentimentalist accounts) or as irrelevant to its content (as in classical versions of Kantian or utilitarian ethics), the view allows them an indirect role, as motivational props to moral teaching and thus to the general institution of moral discourse. However, they are not implied by any particular moral judgment (or speaker), so that amoralism comes out as possible. The response that defines the distinctively moral notion of wrong on this account is the second-level (social) response of forbidding some behavior; but this is ultimately to be understood in terms of (variable) individual reactions. Natural human emotion tendencies thereby constrain the content of ethics, while allowing for some degree of social variation in moral codes.     

In Defense of Indexicalism:Comments on Davis

Wayne Davis (2004) argues against the thesis that knowledge claims are indexical, and he presents an alternative account of the contextual variability of our use of S knows p. In this commentary I focus on the following three points. First, I want to supplement Daviss considerations about the inability of indexicalism to deal with skeptical paradoxes by considering what the consequence would be if the indexicalists explanation of these paradoxes were satisfactory. Second, I am going to take a brief look at Daviss alternative theory. Third, in the main part of my commentary I try to show that indexicalism may be true in spite of the linguistic evidence Davis presents against it.     

The ω-rule

We prove that all proofs in -logic (a first order logic with -rule added) in which -rule is used finitely many times can be turned into proofs in which the -rule is used at most one time. Next, we prove that the word finitely above cannot be changed by the word infinitely.     

Analytic/synthetic and semantic theory

A somewhat simplified version of Jerrold J. Katz's theory of the analytic/synthetic distinction for natural languages is presented. Katz's account is criticized on the following grounds. (1) the antonymy operator is not well defined; it leaves certain sentences without readings. (2) The account of negation is defective; it has the consequence that certain nonsynonymous sentences are marked as synonymous. (3) The account of entailment is defective; it has the consequence that analytic sentences entail synthetic ones. (4) Katz's account of indeterminable sentences is criticized; it has the consequence that certain logical truths are not marked as analytic. (5) Katz's semantics provides no account of truth, so that he is unable to show that analytic sentences are true and that indeterminable sentences are not.     

O liczbach kardynalnych

Tre: Wstp. I. Niektóre pojcia i prawa teorii klas stosunków. II. O klasach abstrakcji. III. O równoskadnikowoci. IV. O kardynalnych liczbach skadników. V. O. stosowanej teorii równoskadnikowoci. VI. O relacji równej liczby elementów. VII. Stosunek obu poj liczb kardynalnych. Zakoczenie.Allatum est die 30 Augusti 1961     

An Appreciation of Hal Childs' Critique of Historical Jesus Research

Biblical scholars have been exceedingly slow to grasp the implications of the Heisenberg principle, namely, that the observer is always a part of the field being observed, and disturbs that field by the very act of observation. In terms of the interpretive task, this means that there can be no question of an objective view of Jesus as he really was. Objective view; is itself an oxymoron; every view is subjective, from a particular angle of vision. We always encounter the biblical text with interests. We always have a stake in our reading of it. We always have angles of vision that can be helpful or harmful in interpreting texts. Historical writing does not treat reality; it treats the interpreter's relation to it, according to Brian Stock. All history, said the poet Wallace Stevens, is modern history. And historical criticism is a form of criticism of the present, according to Walter Kasper. All that is true, but only partially. For historical criticism can still help us recover an understanding of that past that holds out to us present meaning.     

John Nash's Postdelusional Period: A Case of Transformed Narcissism

This article concludes the psychoanalytic study of mathematical genius John Nash begun in previous articles (Capps 2003a, 2003b) by focusing on his recovery from paranoid schizophrenia after more than a decade of being under control of his delusions. I develop the idea that Nash was a highly narcissistic personality, the primary focus of which was his beautiful mind, in the years preceding his mental breakdown. I attribute his recovery primarily to the transformation of his narcissistic personality and support this attribution by means of Heinz Kohut's identification of five major expressions of transformed narcissism in his classic essay on the forms and transformations of narcissism.     

On some structural aspects of physical problems

Bachelard's concept of the problématique is used in order to classify physical problems and their interrelations. This classification is effectuated along two dimensions. Along the horizontal dimension, physical problems are divided into the kinds that the different modes of physics' development define. These modes are themselves determined by the interplay among the conceptual system, the object and the experimentation transactions specific to physics. Along the vertical dimension, physical problems are classified according to the different stages of maturation they have to undergo before the process of their solution is effectively undertaken. To determine these maturation stages, the Althusserian conception of ideology is used. The interrelations between physical problems are examined through the introduction and elaboration of the notion interdependence network.It is a pleasure to thank Marcello Pera and Kostas Gavroglou for their very helpful comments and criticisms.