PROXY FUNCTIONS,TRUTH AND REFERENCE

Quines ontological relativity is related to Tarskis theory of truth in two ways: Quine repudiates term-by-term-correspondence, as does Tarskis rule of truth; and Quines proxy argument in support of relativity finds exact formulation in Tarskis truth definition.Unfortunately, relativity is threatened by the fact that the proxy argument doesnt comply with the rule of truth (Tarskis celebrated condition (T)). Despite Quines express allegiance to (T), use of proxy schemes does not generate all of the true sentences condition (T) requires.A possible adjustment is to drop (T), retain the satisfaction definition and proxy argument, and appeal to the theory of observation and indeterminacy of reference as grounds of relativity. But as we shall see Quines theories of assent to observation sentences and of reference-learning dont square easily with his naturalism. The first attributes intentional attitudes to observers; and the second assumes a holistic context principle and a concept of individuation which do not withstand scrutiny as empirical notions. Both appear to violate Quines behavorist canon.A saving alternative is a theory of term-reference that appears in Roots of Reference and affords a return to behaviorism, and reinstatement of the proxy argument and relativity in a way compatible with Tarskis (T).     

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     

Независимость одной системы аксиом и правила вывода пропозиционального исчисления

- Allatum est die 5 Martii 1970     

Complete Infinitary Type Logics

For each regular cardinal , we set up three systems of infinitary type logic, in which the length of the types and the length of the typed syntactical constructs are < . For a fixed , these three versions are, in the order of increasing strength: the local system ₍₎, the global system g₍₎ (the difference concerns the conditions on eigenvariables) and the -system ₍₎ (which has anti-selection terms or Hilbertian -terms, and no conditions on eigenvariables). A full cut elimination theorem is proved for the local systems, and about the -systems we prove that they admit cut-free proofs for sequents in the -free language common to the local and global systems. These two results follow from semantic completeness proofs. Thus every sequent provable in a global system has a cut-free proof in the corresponding -systems. It is, however, an open question whether the global systems in themselves admit cut elimination.     

My sister's keeper: Negative effects of social welfare and affirmative action programs on black women

The campaign rhetoric of a former neo-Nazi and Klan grand wizard who won a seat in the Louisiana state legislature in 1989 encapsulated two of this article's key points: that black women on welfare bear the brunt of derision, anger, and calls for their forcible control, and that black women who use affirmative action programs for advancement bear the brunt of derision, anger, and calls for their systematic devaluation. This white backlash is one of the negative effects of social welfare and affirmative action programs described in the article, which focuses on black women because of their particular vulnerability in a sexist and racist society. The article is both a warning to black women of an insidious widening gap between their haves and have-nots, and a plea that they work hard together to close this gap by acknowledging the fundamental similarities of their struggles to survive, and by recognizing that they and their children need each other to effectively continue the struggle.     

“Non-Natural” Qualities in G.E. Moore: Inherent or Contingent?

G.E. Moore's theory of the nature of the quality referred to by the word good asserts that this quality is non-natural. If it is, further, supposed that this non-natural quality belongs necessarily and exclusively to those events, human acts, entities, etc., which possess certain strictly determined natural qualities, and those qualities only, then it becomes difficult to explain the relation and the supposed interdependence allegedly existing between the two so disparate categories of qualities. This paper purports to show that, in fact, any mutual dependence of natural and non-natural qualities, including the causal one, is unconceivable. To deny this would allow no less but the possibility of deriving an ought from an is. A final consequence of this is that a non-natural quality, denoted by the predicate good, does, in fact, attach to a strictly delineated and limited morally relevant behaviour (and whatever else we may consider morally relevant), and to it only. But it is attached there in randomly; it is contingent, not inherent; it is there without regard to, and not as a consequence of, the natural qualities of what is the subject of moral judgment ... whether we like it or not.     

Third Men: The Logic of the Sophisms at Arist. SE 22, 178b36–170a10

This article aims at elucidating the logic of Arist. SE 22, 178b36–179a10 and, in particular, of the sophism labelled "Third Man" discussed in it. I suggest that neither the sophistic Walking Man argument, proposed by ancient commentators, nor the Aristotelian Third Man of the , suggested by modern interpreters, can be identified with the fallacious argument Aristotle presents and solves in the passage. I propose an alternative reconstruction of the Third Man sophism and argue that an explanation of the lines regarding the identity of Coriscus and Coriscus the musician (178b39–179a3) is indispensable for its correct understanding, since they hint at another sophism in some important aspects analogous. Finally, I show that two contradictions concerning spotted by scholars in the passage are only apparent and can be dissolved once the assumption that the anti-Platonic Third Man argument is at stake here is discarded, and once the passage is read in the light of its agonistic context.     

On the logic of conscious belief

In this paper we are discussing a version of propositional belief logic, denoted by LB, in which so-called axioms of introspection (B BB and B B B) are added to the usual ones. LB is proved to be sound and complete with respect to Boolean algebras equipped with proper filters (Theorem 5). Interpretations in classical theories (Theorem 4) are also considered. A few modifications of LB are further dealt with, one of which turns out to be S5.     

Some modifications of Scott's theorem on injective spaces

D. Scott in his paper [5] on the mathematical models for the Church-Curry -calculus proved the following theorem.A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of Scott's open sets in a continuous lattice.In this paper we prove a generalization of this theorem for the category of , -closure spaces. The main theorem says that, for some cardinal numbers , , absolute extensors for the category of , -closure spaces are exactly , -closure spaces of , -filters in , >-semidistributive lattices (Theorem 3.5).If = and = we obtain Scott's Theorem (Corollary 2.1). If = 0 and = we obtain a characterization of closure spaces of filters in a complete Heyting lattice (Corollary 3.4). If = 0 and = we obtain a characterization of closure space of all principial filters in a completely distributive complete lattice (Corollary 3.3).     

Think Before You Speak: Utterances and the Logic of Indexicals

This essay discusses some aspects of the logical behaviour of sentences in languages containing indexical and demonstrative expressions. After some preliminary remarks in section one, sections two and three focus on instances of logically true sentences that may be uttered falsely, and on cases of logically equivalent sentences whose utterances may have distinct truth-values. The logical and semantic problems taken into consideration include the validity of a Principle of Translation, the so-called puzzle of addressing, and examples related to measurement and approximation. Section four discusses the complementary phenomenon of sentences that may presumably always be uttered truly, but that do not qualify as logically true. In particular, I argue against the widespread tendency to consider I am here now or I exist as truths of the logic of indexicals.     

Логистическая система, исходными связками которой являются эквивалентность и дизъюнкция

- Allatum est die 5 Martii 1970     

Hick's interpretation of religious pluralism

Conclusion There is no question that Hick's theory rests upon multiple assumptions about a singular, transcendental grounding and the fundamental equality of the various religions that cannot be inductively verified beyond all doubt. That need not mean, however, that the attractiveness of his theory derives solely from the peculiar charm of supposing that the One and the Many are no more at odds in the realm of religion than anywhere else. For Hick's assumptions are not just an exercise in wishful thinking or wild speculation. They are based upon experience from within what he calls the benign circle of faith. Because the reality experienced is ambiguous, acceptance or rejection of his views will, of course, be a matter of choice. And, admittedly, this choice will be dictated not so much by a weighing of empirical evidence that might prove the various religions to be exactly as he sees them, as by a consideration of what we have been surveying in the preceding pages, namely, the import of seeing things as Hick does.

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Cooperation,Knowledge, and Time: Alternating-time Temporal Epistemic Logic and its Applications

Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic CTL, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expressed in CTL. Recently, CTL was generalised by Alur, Henzinger, and Kupferman in a logic known as Alternating-time Temporal Logic (ATL). The key insight in ATL is that the path quantifiers of CTL could be replaced by cooperation modalities, of the form , where is a set of agents. The intended interpretation of an ATL formula is that the agents can cooperate to ensure that holds (equivalently, that have a winning strategy for ). In this paper, we extend ATL with knowledge modalities, of the kind made popular in the work of Fagin, Halpern, Moses, Vardi and colleagues. Combining these knowledge modalities with ATL, it becomes possible to express such properties as group can cooperate to bring about iff it is common knowledge in that . The resulting logic — Alternating-time Temporal Epistemic Logic (ATEL) — shares the tractability of model checking with its ATL parent, and is a succinct and expressive language for reasoning about game-like multiagent systems.     

Was Marx an ethical humanist?

Zusammenfassung Während der letzten zehn Jahre wurde viel über den Humanismus des jungen Marx gesprochen. Osteuropäische Marxisten, die bemüht sind, ihren Anti-Stalinismus durch Berufung auf die Autorität von Marx selbst zu untermauern, gebrauchen den Ausdruck Humanismus in einem ungenauen Sinn, etwa gleichbedeutend mit Anthropozentrismus. Aber wenn man sagt, daß Marx Haltung anthropozentrisch sei, so sind damit die Hauptfragen erst gestellt, nicht schon gelöst.Humanismus mag etwa soviel wie Säkularismus bedeuten — der Mensch, nicht Gott, wird als im Mittelpunkt stehend gedacht. Die anthropozentrische Haltung kann verschiedene Formen annehmen, vor allem die Formen, die man als Humanismus der Ideale und als Humanismus der Prinzipien bezeichnen könnte. Der Humanismus der Ideale ist ausdrücklich an derZukunft orientiert, der Humanismus der Prinzipien aber an derGegenwart. Nur ein Humanismus der Prinzipien, dem es darum geht, den Eigenwert existierender Individuen zu behaupten und zu verteidigen, verdient es, ethischer Humanismus genannt zu werden. Marx, sogar der jüngste Marx, war kein ethischer Humanist in diesem Sinn. Und nur ein Humanismus in diesem strengen Sinn würde einen philosophischen Standort bieten, von dem aus man den Stalinismus oder Neo-Stalinismus angreifen könnte.Marx war ein Säkularist, und er entwarf ein humanistisches Ideal für die Zukunft, aber humanistische Prinzipien für die Gegenwart lehnte er ab. Er betonte, daß nur dem nicht entfremdeten, produktiven Individuum der kommunistischen Zukunft ein eigener Wert zukomme. Bis dahin haben Individuen nur einen geschichtlich instrumentalen Wert: jene, die an der Verwirklichung der kommunistischen Gesellschaft arbeiten, sind zu respektieren; diejenigen, welche dabei Widerstand leisten oder versagen, müssen ausschließlich als Hindernisse auf dem Wege des geschichtlichen Fortschritts behandelt werden.In diesem Sinn ist der Leninismus und sogar der Stalinismus und Neo-Stalinismus in dem zukunftsorientierten Humanismus der Ideale des jungen Marx einbegriffen, oder zumindest davon nicht ausgeschlossen. Selbst der jüngste Marx machte sich den Modeirrtum des 19. Jahrhunderts zu eigen — den Irrtum des aufgeschobenen Wertes oder des zeitlich verstellten Wertes und nahm damit eine mit dem ethischen Humanismus grundsätzlich unvereinbare Position ein.

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An earlier, and much shorter, version of this paper was read at a session on Marxism and Humanism at the Fourteenth International Philosophy Congress in Vienna, September 4, 1968, and published in Vol. II of the Congress Proceedings, Vienna, 1968, pp. 69–73.     

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.     

Lebenswelt structures of Galilean physics: The case of Galileo's pendulum

The aim of this paper is to give a self-reflective account of the building of Galileo's pendulum in order to discover what were the practical contingencies of building and using the pendulum for demonstrating the law of isochronism. In doing this, the unique Lebenswelt structures of Galilean physics are explicated through the ethnomethodological concepts developed by Harold Garfinkel. The presupposition is that the practical logic of Galilean physics is embedded in the instruments themselves. In building the pendulum and recovering its original use, Galilean physics becomes for ethnomethodologists a first-hand practical discovery. This is not a reconstruction of the mind of the historical Galileo but, rather, an explication of Galileo's practical perspective on the instrument as an intersubjective and interchangeable standpoint available for ethnomethodological analysis. This enables us to study historical facts from the standpoint of the practical logic of the original practice with a pedagogical eye for the instructive reproducibility of science.I would like to thank Mike Lynch, Eric Livingston, Jim MacLachlan, and Shelley Schweizer-Bjelic for their comments     

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.     

A semantical investigation into Leśniewski's axiom of his ontology

A structure A for the language L, which is the first-order language (without equality) whose only nonlogical symbol is the binary predicate symbol , is called a quasi -struoture iff (a) the universe A of A consists of sets and (b) a b is true in A ([p) a = {p } & p b] for every a and b in A, where a(b) is the name of a (b). A quasi -structure A is called an -structure iff (c) {p } A whenever p a A. Then a closed formula in L is derivable from Leniewski's axiom x, y[x y u (u x) u; v(u, v x u v) u(u x u y)] (from the axiom x, y(x y x x) x, y, z(x y z y x z)) iff is true in every -structure (in every quasi -structure).     

Quantum Mechanical Unbounded Operators and Constructive Mathematics – a Rejoinder to Bridges

As argued in Hellman (1993), the theorem of Pour-El and Richards (1983) can be seen by the classicist as limiting constructivist efforts to recover the mathematics for quantum mechanics. Although Bridges (1995) may be right that the constructivist would work with a different definition of closed operator, this does not affect my point that neither the classical unbounded operators standardly recognized in quantum mechanics nor their restrictions to constructive arguments are recognizable as objects by the constructivist. Constructive substitutes that may still be possible necessarily involve additional incompleteness in the mathematical representation of quantum phenomena. Concerning a second line of reasoning in Hellman (1993), its import is that constructivist practice is consistent with a liberal stance but not with a radical, verificationist philosophical position. Whether such a position is actually espoused by certain leading constructivists, they are invited to clarify.     

Parameter estimation in latent trait models

Latent trait models for binary responses to a set of test items are considered from the point of view of estimating latent trait parameters=( ₁, , _n ) and item parameters=( ₁, , _k ), where _j may be vector valued. With considered a random sample from a prior distribution with parameter, the estimation of (, ) is studied under the theory of the EM algorithm. An example and computational details are presented for the Rasch model.This work was supported by Contract No. N00014-81-K-0265, Modification No. P00002, from Personnel and Training Research Programs, Psychological Sciences Division, Office of Naval Research. The authors wish to thank an anonymous reviewer for several valuable suggestions.