Are Knowledge Claims Indexical?

David Lewis, Stewart Cohen, and Keith DeRose have proposed that sentences of the form S knows P are indexical, and therefore differ in truth value from one context to another.¹ On their indexical contextualism, the truth value of S knows P is determined by whether S meets the epistemic standards of the speakers context. I will not be concerned with relational forms of contextualism, according to which the truth value of S knows P is determined by the standards of the subject Ss context, regardless of the standards applying to the speaker making the knowledge claim. Relational contextualism is a form of normative relativism. Indexical contextualism is a semantic theory. When the subject is the speaker, as when S is the first person pronoun I, the two forms of contextualism coincide. But otherwise, they diverge. I critically examine the principal arguments for indexicalism, detail linguistic evidence against it, and suggest a pragmatic alternative.     

On Extensions of Intermediate Logics by Strong Negation

In this paper we will study the properties of the least extension n() of a given intermediate logic by a strong negation. It is shown that the mapping from to n() is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n (). This summarizes results that can be found already in [13,14] and [4]. Furthermore, we determine the structure of the lattice of extensions of n(LC).     

Lexical insertion,inflection, and derivation: Creative processes in word production

This study examines the distinction between creative and noncreative behavior as applied to the production of words and sentences. Under one hypothesis words such as governor and government are stored as independent units and produced by rote, but under another these nouns are not produced as fully integrated units but are generated by rules for combining stems (govern) and affixes (-ment and -or). Analyses of German and English speech errors supported the generation-by-rule thesis and indicated that word stems, prefixes, and suffixes must be separately stored in the internal lexicon and marked as to syntactic function in combining with other word components. The data also suggested a three-stage model of lexical processes in the production of speech: a lexical insertion stage whereby abstract lexical formatives are called on or introduced into sentences by means of abstract syntactic and semantic features; a rule application stage whereby feature agreement rules are applied to the formative and then inflectional, derivational, and phonological rules are applied to derive the phonetic string; finally a serial output stage whereby the phonetic string is translated into serially ordered motor commands.This research was supported by NIMH Grant RO 19964 to Donald Mackay.     

False Though Partly True – An Experiment in Logic

We explore in an experimental spirit the prospects for extending classical propositional logic with a new operator P intended to be interpreted when prefixed to a formula as saying that formula in question is at least partly true. The paradigm case of something which is, in the sense envisaged, false though still partly true is a conjunction one of whose conjuncts is false while the other is true. Ideally, we should like such a logic to extend classical logic – or any fragment thereof under consideration – conservatively, to be closed under uniform substitution (of arbitrary formulas for sentence letters or propositional variables), and to allow the substitutivity of provably equivalent formulas salva provabilitate. To varying degrees, we experience some difficulties only with this last (congruentiality) desideratum in the two four-valued logics we end up giving our most extended consideration to.     

On the relation provable equivalence and on partitions in effectively inseparable sets

We generalize a well-knownSmullyan's result, by showing that any two sets of the kindC _a = {x/ xa} andC _b = {x/ xb} are effectively inseparable (if I b). Then we investigate logical and recursive consequences of this fact (see Introduction).     

A notorious affair called exportation

In Quantifiers and Propositional Attitudes, Quine held (a) that the rule of exportation is always admissible, and (b) that there is a significant distinction between a believes-true (Ex)Fx and (Ex) a believes-true F of x. An argument of Hintikka's, also urged by Sleigh, persuaded him that these two intuitions are incompatible; and he consequently repudiated the rule of exportation. Hintikka and Kaplan propose to restrict exportation and quantifying in to favoured contexts — Hintikka to contexts where the believer knows who or what the person or thing in question is; Kaplan to contexts where the believer possesses a vivid name of the person or thing in question. The bulk of this paper is taken up with criticisms of these proposals. Its ultimate purpose, however, is to motivate an alternative approach, which imposes no restrictions on exportation or quantifying in, but repudiates Quine's other intuition: this is the approach taken in my A Logical Form for the Propositional Attitudes.This paper is based on my doctoral dissertation (Rockefeller University, 1977). I wish to thank Susan Haack for her help in turning a draft into the present version.     

A Revenge-Immune Solution to the Semantic Paradoxes

The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema True(A)A, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in ordinary contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are defective. We can in fact define a hierarchy of defectiveness predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (revenge problems) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various levels of defectiveness can all be made coherent together within a single object language.     

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).     

On seeing oneself as “left out”: The chronically complaining patient in psychotherapy

A clinical observation regarding patients who complain about feeling left out and/or second best provides the framework for this paper. What is expressed is a form of separation anxiety coupled with a loser self-concept. It is suggested that these patients represent a milder form of the moral masochism. Early theoretical formulations include Freud and his emphasis on the superego and Reich's emphasis on the masochist's fear of being left alone. Kramer's little man phenomenon is an example of a more current theoretical formulation which takes account of the complexities of the ego, and composite self and identity in the clinical phenomena observed. A case of a latency-aged child is provided.     

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).     

Construction of monadic three-valued Łukasiewicz algebras

The notion of monadic three-valued ukasiewicz algebras was introduced by L. Monteiro ([12], [14]) as a generalization of monadic Boolean algebras. A. Monteiro ([9], [10]) and later L. Monteiro and L. Gonzalez Coppola [17] obtained a method for the construction of a three-valued ukasiewicz algebra from a monadic Boolea algebra. In this note we give the construction of a monadic three-valued ukasiewicz algebra from a Boolean algebra B where we have defined two quantification operations and ^* such that ^*x=^*x (where ^*x=-^*-x). In this case we shall say that and ^* commutes. If B is finite and is an existential quantifier over B, we shall show how to obtain all the existential quantifiers ^* which commute with .Taking into account R. Mayet [3] we also construct a monadic three-valued ukasiewicz algebra from a monadic Boolean algebra B and a monadic ideal I of B. The most essential results of the present paper will be submitted to the XXXIX Annual Meeting of the Unión Matemática Argentina (October 1989, Rosario, Argentina).     

Ideal Epistemic Situations and the Accessibility of Realist Truth

There is a widespread opinion that the realist idea that whether a proposition is true or false typically depends on how things are independently of ourselves is bound to turn truth, in Davidson's words, into something to which humans can never legitimately aspire. This opinion accounts for the ongoing popularity of epistemic theories of truth, that is, of those theories that explain what it is for a proposition (or statement, or sentence, or what have you) to be true or false in terms of some epistemic notion, such as provability, justifiability, verifiability, rational acceptability, warranted assertibility, and so forth, in some suitably characterized epistemic situation. My aim in this paper is to show that the widespread opinion is erroneous and that the (legitimate) epistemological preoccupation with the accessibility of truth does not warrant the rejection of the realist intuition that truth is, at least for certain types of propositions, radically nonepistemic.     

Positive und negative Rückmeldung bei Alternativdiskriminationen

Zusammenfassung Die Untersuchungen befassen sich mit dem Einfluß der verbalen Rückmeldungen richtig und falsch auf das Erlernen von Alternativdiskriminationen in Blank-trial-Experimenten. Dabei wird insbesondere die Wechselwirkung der Rückmeldungskombinationen (richtig/fehlende Rückmeldung vs. falsch/fehlende Rückmeldung) mit der Rückmeldungsproportion untersucht. Die Rückmeldungsproportion ist definiert als das Verhältnis der Anzahl der S-R-Verbindungen einer Lernliste, auf die eine verbale Rückmeldung erfolgt, und der Anzahl der S-R-Verbindungen, bei denen die verbale Rückmeldung fehlt. Die Rückmeldungsproportion wird zwischen 119 und 191 systematisch variiert. Unsere Experimente ergeben u. a., daß bei kleiner Rückmeldungsproportion die Kombination richtig/fehlende Rückmeldung und bei großer Rückmeldungsproportion die Kombination falsch/fehlende Rückmeldung die Lernleistung erhöhen. Dieser Befund wurde nach theoretischen Annahmen über die Lernstrategie der Vpn erwartet. Eine alternative theoretische Interpretation der Befunde wird nach einem Zusatzexperiment verworfen. Insgesamt bestätigen die Untersuchungen, daß (a) die relative Wirksamkeit von Rückmeldungskombinationen stark von den jeweiligen experimentellen Randbedingungen abhängt, daß (b) von einer automatischen Wirksamkeit verbaler Rückmeldung keine Rede sein kann und daß (c) theoretische Annahmen über die kognitive Verarbeitung verbaler Rückmeldungen und über entsprechende Lernstrategien für die Interpretation der untersuchten Lernvorgänge erfolgversprechend sind.

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Positive and negative feedback in discrimination between alternativesFeedback proportion and learning strategy

Summary This study is concerned with the influence of the verbal feedback modes of right and wrong on the acquisition of alternative discriminations in blank-trial experiments, with special reference to the interaction between the feedback combinations (right/non-feedback as against wrong/non-feedback) and feedback proportion is investigated. Feedback proportion is defined as the ratio of the S-R connections of a learning list succeeded by verbal feedback to the S-R connections succeeded by non-feedback. Feedback proportion was systematically varied between the ratios of 119 and 191.Results showed that at a low feedback proportion learning score is increased with the combination right/non-feedback while in contrast at a high feedback proportion learning score is increased with the combination wrong/non-feedback. These results are in accordance with theoretical expectations on learning strategies of Ss. An alternative interpretation was not confirmed by the results of an additional experiment.In general, our investigations showed that (a) the relative effectiveness of feedback combinations is strongly dependent on the particular experimental conditions; (b) an automatic effect of verbal feedback cannot be assumed; (c) a cognitive interpretation of verbal feedback effects in terms of learning strategies seems very promising.

     

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).     

Varieties of Monadic Heyting Algebras. Part III

This paper is the concluding part of [1] and [2], and it investigates the inner structure of the lattice (MHA) of all varieties of monadic Heyting algebras. For every n , we introduce and investigate varieties of depth n and cluster n, and present two partitions of (MHA), into varieties of depth n, and into varieties of cluster n. We pay a special attention to the lower part of (MHA) and investigate finite and critical varieties of monadic Heyting algebras in detail. In particular, we prove that there exist exactly thirteen critical varieties in (MHA) and that it is decidable whether a given variety of monadic Heyting algebras is finite or not. The representation of (MHA) is also given. All these provide us with a satisfactory insight into (MHA). Since (MHA) is dual to the lattice NExtMIPC of all normal extensions of the intuitionistic modal logic MIPC, we also obtain a clearer picture of the lattice structure of intuitionistic modal logics over MIPC.     

Was sind “ek-statische Maschinen”? (Gedanken aus und zu: M. K. Mamardašvili,Wissenschaft und Kultur)

Ohne ZusammenfassungM. K. Mamardavili, Nauka i kul'tura, inMetodologieskie problemy istorikonaunych issledovanij, M., Nauka, 1982, str. 38–58. Zitate aus diesem Aufsatz werden im Text mit der in Klammern gesetzten Seitenzahl ausgewiesen.     

“The story says that” operator in story semantics

In [2] a semantics for implication is offered that makes use of stories — sets of sentences assembled under various constraints. Sentences are evaluated at an actual world and in each member of a set of stories. A sentence B is true in a story s just when B s. A implies B iff for all stories and the actual world, whenever A is true, B is true. In this article the first-order language of [2] is extended by the addition of the operator the story ... says that ..., as in The story Flashman among the Redskins says that Flashman met Sitting Bull. The resulting language is shown to be sound and complete.     

Is “some-other-time” sometimes better than “sometime” for proving partial correctness of programs?

The main result of this paper belongs to the field of the comparative study of program verification methods as well as to the field called nonstandard logics of programs. We compare the program verifying powers of various well-known temporal logics of programs, one of which is the Intermittent Assertions Method, denoted as Bur. Bur is based on one of the simplest modal logics called S5 or sometime-logic. We will see that the minor change in this background modal logic increases the program verifying power of Bur. The change can be described either technically as replacing the reflexive version of S5 with an irreflexive version, or intuitively as using the modality some-other-time instead of sometime. Some insights into the nature of computational induction and its variants are also obtained.This project was supported by the Hungarian National Foundation for Scientific Research, Grant No. 1810.     

Interpolation and amalgamation properties in varieties of equivalential algebras

Important positive as well as negative results on interpolation property in fragments of the intuitionistic propositional logic (INT) were obtained by J. I. Zucker in [6]. He proved that the interpolation theorem holds in purely implicational fragment of INT. He also gave an example of a fragment of INT for which interpolation fails. This fragment is determined by the constant falsum (), well known connectives: implication () and conjunction (), and by a ternary connective defined as follows: (p, q, r)= ^df (pq)(pr).Extending this result of J. I. Zucker, G. R. Renardel de Lavalette proved in [5] that there are continuously many fragments of INT without the interpolation property.This paper is meant to continue the research mentioned above. To be more precise, its aim is to answer questions concerning interpolation and amalgamation properties in varieties of equivalential algebras, particularly in the variety determined by the purely equivalential fragment of INT.     

Truth,Sentential Non-Compositionalit,and Ontology

The paper attempts to clarify some fundamental aspects of an explanationof the concept of truth which is neither deflationary nor substantive.The main aspect examined in detail concerns the ontological dimension of truth, the mind/language-world connection traditionally associated with the concept of truth. It is claimed that it does not make sense to defend or reject a relatedness of truth to the ontological dimension so long as the kind of presupposed or envisaged ontology is not made explicit and critically examined. In particular, it is shown that generally an objectual ontology is – often only implicitly – presupposed, i.e., an ontology admitting objects (substances), properties, relations, sometimes also facts, events, and the like. The paper demonstrates that such an ontology derives from the Principle of Semantic Sentential Compositionality and that this principle should be rejected. It introduces instead the Principle of Semantic Sentential Contextuality (or Context Principle) as the semantic basis of a new ontology, an ontology of primary states of affairs. After sketching such an ontology, it is shown that the relatedness of truth to the ontological dimension becomes intelligible.