Semantic holism

A bivalent valuation is snt iff sound (standard PC inference rules take truths only into truths) and non-trivial (not all wffs are assigned the same truth value). Such a valuation is normal iff classically correct for each connective. Carnap knew that there were non-normal snt valuations of PC, and that the gap they revealed between syntax and semantics could be jumped as follows. Let VAL _snt be the set of snt valuations, and VAL _nrm be the set of normal ones. The bottom row in the table for the wedge is not semantically determined by VAL _snt, but if one deletes from VAL _snt all those valuations that are not classically correct at the aforementioned row, one jumps straights to VAL _nrm and thus to classical semantics. The conjecture we call semantic holism claims that the same thing happens for any semantic indeterminacy in any row in the table of any connective of PC, i.e., to remove it is to jump straight to classical semantics. We show (i) why semantic holism is plausible and (ii) why it is nevertheless false. And (iii) we pose a series of questions concerning the number of possible steps or jumps between the indeterminate semantics given by VAL _snt and classical semantics given by VAL _nrm.     

Inferential Intensionality

The paper is a study of properties of quasi-consequence operation which is a key notion of the so-called inferential approach in the theory of sentential calculi established in [5]. The principal motivation behind the quasi-consequence, q-consequence for short, stems from the mathematical practice which treats some auxiliary assumptions as mere hypotheses rather than axioms and their further occurrence in place of conclusions may be justified or not. The main semantic feature of the q-consequence reflecting the idea is that its rules lead from the non-rejected assumptions to the accepted conclusions.First, we focus on the syntactic features of the framework and present the q-consequence as related to the notion of proof. Such a presentation uncovers the reasons for which the adjective inferential is used to characterize the approach and, possibly, the term inference operation replaces q-consequence. It also shows that the inferential approach is a generalisation of the Tarski setting and, therefore, it may potentially absorb several concepts from the theory of sentential calculi, cf. [10]. However, as some concrete applications show, see e.g.[4], the new approach opens perspectives for further exploration.The main part of the paper is devoted to some notions absent, in Tarski approach. We show that for a given q-consequence operation W instead of one W-equivalence established by the properties of W we may consider two congruence relations. For one of them the current name is kept preserved and for the other the term W-equality is adopted. While the two relations coincide for any W which is a consequence operation, for an arbitrary W the inferential equality and the inferential equivalence may differ. Further to this we introduce the concepts of inferential extensionality and intensionality for q-consequence operations and connectives. Some general results obtained in Section 2 sufficiently confirm the importance of these notions. To complete a view, in Section 4 we apply the new intensionality-extensionality distinction to inferential extensions of a version of the ukasiewicz four valued modal logic.     

First-order indefinite and uniform neighbourhood semantics

The main purpose of this paper is to define and study a particular variety of Montague-Scott neighborhood semantics for modal propositional logic. We call this variety the first-order neighborhood semantics because it consists of the neighborhood frames whose neighborhood operations are, in a certain sense, first-order definable. The paper consists of two parts. In Part I we begin by presenting a family of modal systems. We recall the Montague-Scott semantics and apply it to some of our systems that have hitherto be uncharacterized. Then, we define the notion of a first-order indefinite semantics, along with the more specific notion of a first-order uniform semantics, the latter containing as special cases the possible world semantics of Kripke. In Part II we prove consistency and completeness for a broad range of the systems considered, with respect to the first-order indefinite semantics, and for a selected list of systems, with respect to the first-order uniform semantics. The completeness proofs are algebraic in character and make essential use of the finite model property. A by-product of our investigations is a result relating provability in S-systems and provability in T-systems, which generalizes a known theorem relating provability in the systems S 2° and C 2.The author would like to thank Prof. Nuel D. Belnap of the University of Pittsburg for many indispensable contributions to earlier versions of this work. The author also thanks the referee for several helpful comments and corrections.     

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.     

Confirmation holism and semantic holism

Fodor and Lepore, in their recent book Holism, maintain that if an inference from semantic anatomism to semantic holism is allowed, certain fairly deleterious consequences follow. In Section 1 Fodor and Lepore's terminology is construed and amended where necessary with the result that the aforementioned deleterious consequences are neither so apparent nor straightforward as they had suggested. In Section 2 their Argument A is considered in some detail. In Section 3 their argument attributed to Quine is examined at length and a shorter and more perspicacious argument suggested which avoids their charge that the Quinean argument is guilty of an equivocation on the word statement.     

Embeddability,syntax, and semantics in accounts of scientific theories

Recently several philosophers of science have proposed what has come to be known as the semantic account of scientific theories. It is presented as an improvement on the positivist account, which is now called the syntactic account of scientific theories. Bas van Fraassen claims that the syntactic account does not give a satisfactory definition of empirical adequacy and empirical equivalence. He contends that his own semantic account does define these notations acceptably, through the concept of embeddability, a concept which he claims cannot be defined syntactically. Here, I define a syntactic relation which corresponds to the semantic relation of embeddability. I suggest that the critical differences between the positivist account and van Fraassen's account have nothing to do with the distinction between semantics and syntax.     

The Logical Structure of Linguistic Commitment III Brandomian Scorekeeping and Incompatibility

Curiously, though he provides in Making It Explicit (MIE) elaborate accounts of various representational idioms, of anaphora and deixis, and of quantification, Robert Brandom nowhere attempts to lay out how his understanding of content and his view of the role of logical idioms combine in even the simplest cases of what he calls paradigmatic logical vocabulary. That is, Brandom has a philosophical account of content as updating potential – as inferential potential understood in the sense of commitment or entitlement preservation – and says that the point of logical vocabulary is to make available the expressive resources to make explicit such semantic structures as arise from discursive scorekeeping practice. Thus, one would expect an account of the updating or inferential potential of sentences involving logical vocabulary, an account which is such as to assign to those sentences the inferential significance necessary for this expressive job. In short, one would expect a semantics of logical vocabulary – &, , – in terms of the difference an assertion of a sentence involving it makes to the atomic score of a linguistic agent, and a completeness proof for the logic generated by this semantics. Despite this, no such semantics is given in MIE. It is in the current paper.     

Converse Ackermann Croperty and semiclassical negation

A prepositional logic S has the Converse Ackermann Property (CAP) if (AB)C is unprovable in S when C does not contain . In A Routley-Meyer semantics for Converse Ackermann Property (Journal of Philosophical Logic, 16 (1987), pp. 65–76) I showed how to derive positive logical systems with the CAP. There I conjectured that each of these positive systems were compatible with a so-called semiclassical negation. In the present paper I prove that this conjecture was right. Relational Routley-Meyer type semantics are provided for each one of the resulting systems (the positive systems plus the semiclassical negation).     

The American plan completed: Alternative classical-style semantics,without stars,for relevant and paraconsistent logics

American-plan semantics with 4 values 1, 0, { {1, 0}} {{}}, interpretable as True, False, Both and Neither, are furnished for a range of logics, including relevant affixing systems. The evaluation rules for extensional connectives take a classical form: in particular, those for negation assume the form 1 (A, a) iff 0 (A, a) and 0 (A, a) iff 1 (A, a), so eliminating the star function *, on which much criticism of relevant logic semantics has focussed. The cost of these classical features is a further relation (or operation), required in evaluating falsity assignments of implication formulae.Two styles of 4 valued relational semantics are developed; firstly a semantics using notions of double truth and double validity for basic relevant systemB and some extensions of it; and secondly, since the first semantics makes heavy weather of validating negation principles such as Contraposition, a reduced semantics using more complex implicational rules for relevant systemC and various of its extensions. To deal satisfactorily with elite systemsR,E andT, however, further complication is inevitable; and a relation of mateship (suggested by the Australian plan) is introduced to permit cross-over from 1 to 0 values and vice versa.     

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.     

Treating connectionism properly: Reflections on Smolensky

Summary In this essay, I undertake to examine the principal theses of Paul Smolensky's 1988Behavioral and Brain Sciences target article, On the proper treatment of connectionism, from the point of view of the methodology and epistemology of science, that is, the philosophical theory of theories in general. After exploring the instrumentalist and realist views of the relationships between micro- and macrotheories on their home ground in the natural sciences, the procedures by which a phenomenally described cognitive task is prepared for symbolic or subsymbolic modeling, and the contrast between the deliberate conscious reasoning processes of a novice and intuitive behavior of an expert in solving a given family of cognitive problems, I argue that although Smolensky is right about what it would take for connectionist subsymbolic models to relate to symbolic models as micro- to macrotheories, he is wrong in concluding that they do. On the contrary, it would be something of a miracle if the idealized nomological structure of the behavior of stochastic patterns of activity over large numbers of subsymbolic units in a connectionist machine corresponded even approximately to the nomological structure of the conceptual level behavior of a Von Neumann computer running off a program whose syntax had been explicitly designed to structurally operationalize a determinate fragment of intentional semantics — unless, of course, the connectionist machine had been deliberately constructed to implement the symbol processor in the first place.I conclude that the proper treatment of connectionism is to be found among the blandly ecumenical proposals for irenic cooperation and division of labor that Smolensky considers and rejects.     

What Conditional Probability Could Not Be

Kolmogorov's axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0"> Call this the ratio analysis of conditional probability. It has become so entrenched that it is often referred to as the definition of conditional probability.I argue that it is not even an adequate analysis of that concept. I prove what I call the Four Horn theorem, concluding that every probability assignment has uncountably many trouble spots. Trouble spots come in four varieties: assignments of zero togenuine possibilities; assignments of infinitesimals to such possibilities; vague assignments to such possibilities; and no assignment whatsoever to such possibilities. Each sort of trouble spot can create serious problems for the ratio analysis. I marshal manyexamples from scientific and philosophical practice against the ratio analysis. I conclude more positively: we should reverse the traditional direction of analysis. Conditional probability should be taken as the primitive notion, and unconditional probability should be analyzed in terms of it. I'd probably be famous now If I wasn't such a good waitress. Jane Siberry, Waitress     

Synonymy in sentential languages: a pragmatic view

In this note two notions of meaning are considered and accordingly two versions of synonymy are defined, weaker and stronger ones. A new semantic device is introduced: a matrix is said to be pragmatic iff its algebra is in fact an algebra of meanings in the stronger sense. The new semantics is proved to be universal enough (Theorem 1), and it turns out to be in some sense a generalization of Wójcicki's referential semantics (Theorem 3).     

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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The completeness of S

The subsystem S of Parry's AI [10] (obtained by omitting modus ponens for the material conditional) is axiomatized and shown to be strongly complete for a class of three valued Kripke style models. It is proved that S is weakly complete for the class of consistent models, and therefore that Ackermann's rule is admissible in S. It also happens that S is decidable and contains the Lewis system S4 on translation — though these results are not presented here. S is arguably the most relevant relevant logic known at this time to be decidable.I wish to thank Jill Pipher and Professora Nuel D. Belnap, Jr. and David Kaplan for their helpful comments on an earlier version of this paper.     

Paradox,truth and logic part I: Paradox and truth

Conclusion The discussion of the semantics of inconsistent truth theories now comes to a pause. The preceding is of course but a sketch; many interesting questions remain to be answered. The second part of this essay, however, will not seek to answer them. Rather, I will turn to the discussion of the proof theory of truth theory: the local and global logic of truth.Under the first heading, I show how to replace the inductive construction of models with an appropriate infinitary proof theory, and relate this on the one hand to the so-called dependence approach to inductive truth theories (Davis, 1979; Yablo, 1982) and on the other to van Fraassen's fact semantics for relevance logic.Under the second heading, I offer formals systems which capture the inferences valid in all approximate models. Not surprisingly, these turn out to be relevant logics.With formalism in hand, I discuss finally the extent to which the gap and/or glut approach can in fact be said to solve the paradoxes; that is, to allow us to say that the very language we are speaking is of the sort described in our theory.     

On a complexity-based way of constructivizing the recursive functions

Let g _E(m, n)=o mean that n is the Gödel-number of the shortest derivation from E of an equation of the form (m)=k. Hao Wang suggests that the condition for general recursiveness mn(g _E(m, n)=o) can be proved constructively if one can find a speedfunction _{s s}, with _s(m) bounding the number of steps for getting a value of (m), such that mn _s(m) s.t. g _E(m, n)=o. This idea, he thinks, yields a constructivist notion of an effectively computable function, one that doesn't get us into a vicious circle since we intuitively know, to begin with, that certain proofs are constructive and certain functions effectively computable. This paper gives a broad possibility proof for the existence of such classes of effectively computable functions, with Wang's idea of effective computability generalized along a number of dimensions.We are grateful to an anonymous referee for Studia Logica for valuable advice leading to substantial improvements in the presentation of the main definitions and theorem.     

Semantic analysis of natural kind terms

This paper develops a model theoretic semantics for so called natural kind terms that reflects the viewpoint of (Kripke, 1980) and (Putnam, 1975). The semantics generates a formal counterpart of the K-mechanism investigated in (Salmon, 1981) and in unpublished work by Keith Donnellan.I would like to thank David Anderson, Bernard Linsky, Hilary Putnam, Nathan Salmon, Edward Zalta, and the participants of the 1992 SEP conference for much helpful discussion and encouragement regarding the project of this paper.     

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.     

Neue soziometrische Perspektiven

Zusammenfassung Die Hypothese, daß ein Zusammenhang besteht zwischen dem soziometrischen Wahlverhalten und einem oder mehreren Faktoren der Trias Valenz, Potenz und Erregung, konnte korrelationsstatistisch bestätigt werden. Es zeigte sich, daß die typischen soziometrischen Wahlfragen weitgehend einfaktoriell — valenzkorreliert — sind. Daneben spielt aber für bestimmte Fragen (z.B. Führerwahl) auch die Potenzdimension eine entscheidende Rolle. Die 21 in diesem Versuch verwendeten Kriterium-Fragen, unter denen sich auch soziale Meinungs-, Einstellungs- und Personwahrnehmungsfragen befanden, zeigten mit ihren Valenz-Potenz-Korrelationen eine gemeinsame funktionale Bezugsgrundlage.Das Eindrucksdifferential erwies sich als geeignetes Instrument, eine soziale Gruppe und ihre Angehörigen hinsichtlich ihrer Eigenschaften als Objekte und Subjekte sozialer Beziehungen zu kennzeichnen. Die Daten des Eindrucksdifferentials lassen eine objektive Strukturanalyse der Gruppe mit Hilfe der D-Faktormethode zu. Die Vorzüge der Methode sind zahlreich, so daß man gern bereit sein wird, ihre wenigen Nachteile (vor allem zeitlichen Aufwand) mit in Kauf zu nehmen, wenn es die Umstände erlauben. Die klassische soziometrische Methode der Vorzugswahlen wird jedoch bei jüngeren Kindern nicht durch die Differentialmethode zu ersetzen sein.

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Summary The hypothesis that sociometric choice behavior is intimately related to one or several factors of the factorial trias Valenz (evaluation), Potenz (potency) und Erregung (activity) was supported by this correlational study. It has been shown that the standard sociometric questions are correlated with Valenz. Certain other questions (leader choice questions e.g.) are further correlated with Potenz. Most of the 21 questions of a criterion questionnaire applied in this study, among them opinion, attitude and person perception items, proved to have a common functional frame of reference defined by the Valenz and Potenz coordinates.The differential method was shown to be a suitable instrument to analyze small groups and their members in terms of their intragroup relations. The data obtained by this method permit an objective subgroup analysis by the D-method of factorization. Unfortunately the procedure of differential scaling is more time consuming. But the advantages are numerous and prevail over the disadvantages. The classical sociometric test might remain the only applicable method in studies with younger children.