The Judgement-Stroke As A Truth-Operator: A New Interpretation Of The Logical Form Of Sentences In Frege''s Scientific Language

The syntax of Frege's scientific language iscommonly taken to be characterized by two oddities:the representation of the intended illocutionary roleof sentences by a special sign, the judgement-stroke,and the treatment of sentences as a species ofsingular terms. In this paper, an alternative view isdefended. The main theses are: (i) the syntax ofFrege's scientific language aims at an explication ofthe logical form of judgements; (ii) thejudgement-stroke is, therefore, a truth-operator, nota pragmatic operator; (iii) in Frege's first system,` ' expresses that the circumstance is a fact, and in his second system that thetruth-value - is the True; (iv) in bothsystems, the judgement-stroke is construed as a signsui generis, not as a genuine predicate; (v) itscounterpart in natural language is the syntactic ``formof assertoric sentences', not the (redundant)truth-predicate; (vi) neither in Frege's first nor inhis second system sentences are treated as singular terms.     

Accepting inconsistencies from the paradoxes

It has been proposed that the law of non-contradiction be revised to permit the simultaneous truth and falsity of the key sentences of the logical paradoxes, e.g., This sentence is false. In an attempt to show to what extent this bizarre suggestion of inconsistent models or truth-value gluts is a coherent suggestion it is proved that a first-order language for number theory can be semantically closed by having its own global truth predicate under some non-standard interpretation and thus that it actually can contain the Liar sentence. It is proved that in this interpretation the Liar sentence is both true and false, although not every sentence is.     

The formation of a semantic network by induction

Summary A semantic network describing the relations between ten words has been elaborated. The raw-data for the formation of the network were 660 natural-language sentences gained in the following experiment: The ten words were presented to 12 Ss, single, in pairs, and in triplets. Ss had to form, for each given combination, a sentence containing the presented words. The sentences gained by this method were parsed and got uniform codings. Each stimulus word then has been assigned to a node, containing all words or parts of sentences to which it was related in the sentences. Nodes with similar contents have been subsumed under a higher-level node containing the relations which are common to it's constituents. The reaction times in sentence formation strongly depend on the relations between the words in the semantic network. The correlation between association strengths and the proximities between the words in the semantic network augments to 0.70. The limitations due to the purely inductive approach in the formation of the network are discussed.

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Zusammenfassung Es wurde ein semantisehes Netzwerk aufgebaut, welches die bedeutungsmäßigen Beziehungen zwischen 10 Wörtern darstellt. Die Ausgangsdaten für die Bildung des Netzwerkes bildeten experimentell gewonnene Sätze der natürlichen Sprache: 12 Versuchspersonen erhielten die 10 Wörter einzeln, in Paaroder Dreierkombinationen dargeboten und mußten Sätze bilden, in denen diese Wörter oder Wortkombinationen vorkommen. Die so gewonnenen 660 Sätze wurden in einem einheitlichen grammatischen System kodiert. Für jedes der 10 Stimuluswörter wurde darauf ein sog. Knoten aufgebaut; dieser enthält alle Wörter und Satzteile, die bei der Satzbildung zum Stimuluswort in Beziehung gesetzt wurden. Knoten mit ähnlichem Inhalt wurden unter Oberbegriffe subsumiert. Solche Knoten höherer Ordnung enthalten alle diejenigen Wörter und Wortgruppen, die bei den Knoten niedriger Ordnung gemeinsam vorkommen. Es kann gezeigt werden, daß die Reaktionszeiten bei der Satzbildung von den Relationen zwischen den Wörtern im semantischen Netzwerk abhängen. Die Korrelation zwischen den Assoziationsstärken zwischen den Stimuluswörtern einerseits und deren Nähe im semantischen Netzwerk andererseits beträgt 0.70. Die Beschränktheit eines ausschließlich induktiven Vorgehens beim Aufbau von semantischen Netzwerken wird diskutiert.

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This research was supported by a grant of the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung.     

Choice and Logic

There is a little known paradox the solution to which is a guide to a much more thoroughgoing solution to a whole range of classic paradoxes. This is shown in this paper with respect to Berrys Paradox, Heterologicality, Russells Paradox, and the Paradox of Predication, also the Liar and the Strengthened Liar, using primarily the epsilon calculus. The solutions, however, show not only that the first-order predicate calculus derived from Frege is inadequate as a basis for a clear science, and should be replaced with Hilbert and Bernays conservative extension. Standard second-order logic, and quantified propositional logic also must be substantially modified, to incorporate, in the first place, nominalizations of predicates, and whole sentences. And further modifications must be made, so as to insist that predicates are parts of sentences rather than forms of them, and that truth is a property of propositions rather than their sentential expressions. In all, a thorough reworking of what has been called logic in recent years must be undertaken, to make it more fit for use.Portions of this paper have previously been published in Logical Studies, vol. 9, http://www.logic.ru/LogStud/09/No9-06.html, and the Australasian Journal of Logic, vol. 2, http://www.philosophy.unimelb.edu.au/ajl/2004/2004_4.pdf.     

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.     

意义理论

Research into logical syntax provides us the knowledge of the structure of sentences, while logical semantics provides a window into uncovering the truth of sentences. Therefore, it is natural to make sentences and truth the central concern when one deals with the theory of meaning logically. Although their theories of meaning differ greatly, both Michael Dummett’s theory and Donald Davidson’s theory are concerned with sentences and truth and developed in terms of truth. Logical theories and methods first introduced by G. Frege underwent great developments during the past century and have played an important role in expanding these two scholars’ theories of meaning. Translated by Ma Minghui from Zhexue Yanjiu 哲学研究 (Philosophical Research), 2006, (7): 53–61     

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.     

Context and strategy in acquiring temporal connectives

There has been considerable debate over the role of comprehension strategies in the acquisition of temporal connectives. This study examined the role of caluse logic and interpretational strategies in the acquisition of temporal words; age-related changes were also considered. Thirty-two children between 3 and 5 years of age served as subjects. Sentences with a variety of temporal words were used to tap children's comprehension of before, after, when, while, just before that, and and after that. Clause logic was found to significantly improve the understanding of these sentences. However, the order of mention and main clause first strategies were used infrequently. Apparently, when children respond to sentences that describe information in a way that is consistent with that they normally hear, these strategies are seldom applied.I wish to express my thanks to Janice Bogen, who assisted in data collection, and to Erika Hoff-Ginsberg, who assisted in some of the data analysis.     

Modality,invariance, and logical truth

Conclusion Let us sum up. We began with the question, What is the interest of a model-theoretic definition of validity? Model theoretic validity consists in truth under all reinterpretations of non-logical constants. In this paper, we have described for each necessity concept a corresponding modal invariance property. Exemplification of that property by the logical constants of a language leads to an explanation of the necessity, in the corresponding sense, of its valid sentences. I have fixed upon the epistemic modalities in characterizing the logical constants: to be a logical constant in the language of a population is to be invariant over a modality describing complete possible epistemic states of that population (or an idealized analogue thereof). The grounds for this characterization are these: (1) It leads, I believe, to an extensionally reasonable demarcation of the logical constants, including clear cases and excluding clear non-cases. It gives a principled criterion for deciding unclear cases. (2) It provides an analysis of the topic-neutrality of logic. (3) It leads to an explanation of the epistemic necessity of the logical truths in terms of the topic-neutrality of the logical constants.All the same, it is reasonable to ask, even if the suggested demarcation of logic is extensionally correct, whether it can reasonably be expected to be fundamental. The epistemic invariance of an expression is a rather striking property, one which we should want to explain. What is missing, then, is an explanation of the distinguishing epistemic properties of the constants in terms of more fundamental properties involving their understanding and use. It would be these that properly define the nature, not just the extent, of logic.     

A new theory of content I: Basic content

Philosophers of science as divergent as the inductivist Carnap and the deductivist Popper share the notion that the (logical) content of a proposition is given by its consequence class. I claim that this notion of content is (a) unintuitive and (b) inappropriate for many of the formal needs of philosophers of science. The basic problem is that given this notion of content, for any arbitraryp andq, (p Vq) will count as part of the content of bothp andq. In other words, any arbitraryp andq share some common content. This notion of content has disastrous effects on, for instance, Carnap's attempts to explicate the notion of confirmation in terms of probabilistic favorable relevance, and Popper's attempts to define verisimilitude. After briefly reviewing some of the problems of the traditional notion of content I present an alternative notion of (basic) content which (a) better fits our intuitions about content and (b) better serves the formal needs of philosophers of science.     

Given-New Ordering Effects on the Production of Scrambled Sentences in Japanese

Across many languages, speakers tend to produce sentences so that given (previously referred to) arguments are mentioned before new arguments; this is termed given-new ordering. We explored the nature of such given-new effects in Japanese using a procedure following Bock and Irwin (1980). Speakers encoded and then recalled canonical (e.g., okusan-ga otetsudaisan-ni purezento-o okutta, the housewife gave the housekeeper a present) or scrambled (okusan-ga purezento-o otetsudaisan-ni okutta) dative targets when prompted by a statement-question sequence. The prompting statement established one nonsubject argument of the dative target as given, leaving the other nonsubject argument as new. Previous mention was either with lexically identical content (e.g., otetsudaisan or purezento) or with lexically distinct but nearly synonymous content (meidosan, housemaid or okurimono, gift). Results showed that speakers produced canonical or scrambled word orders so that given arguments were mentioned before new, but especially when the previous mention of the given argument occurred with lexically identical content (replicating Bock and Irwin's English effect). These results show that the production of Japanese scrambled and canonical word orders is sensitive to given versus new status (as in English), implying that given-new ordering arises at the stage of sentence production where scrambling effects are realized.     

Interpreting idioms

Immediate comprehension processes involved in the interpretation of idiomatic expressions were investigate. Idioms like bury the hatchet were used in sentential contexts that (1) biased the listener toward a literal interpretation, (2) biased the listener toward a figurative interpretation, or (3) left the interpretation ambiguous between the literal and figurative readings. In control sentences, the final words of the idioms were used in nonidiomatic expressions. Listeners monitored the sentences for specified targets. In all cases, the target words were the final words of the idiomatic phrases. The listeners were instructed to detect words that were identical to cue words, that rhymed with the cue words, or that were members of semantic categories specified by cue words. Thus, hatchet was cued with either hatchet, ratchet, or a tool. Reaction-time latencies from the onset of the targets to the listeners' responses were obtained. Identity, Rhyme, and Category matches were detected more rapidly in all three idiomatic contexts than in the nonidiomatic controls. These results suggest that idioms are automatically processed as discrete lexical entries, and that previously observed reaction time advantages for figurative expressions may reflect integrative processes rather than retrieval of meaning.This research was supported by PHS Training Grant T32 MH 15134-02 from the National Institute of Mental Health. A preliminary version of this paper was presented at the Annual Meeting of the American Psychological Association, Los Angeles, August 1981.     

A note on syntactical and semantical functions

We say that a semantical function is correlated with a syntactical function F iff for any structure A and any sentence we have A F A .It is proved that for a syntactical function F there is a semantical function correlated with F iff F preserves propositional connectives up to logical equivalence. For a semantical function there is a syntactical function F correlated with iff for any finitely axiomatizable class X the class ^–1X is also finitely axiomatizable (i.e. iff is continuous in model class topology).     

Test of the violation of local realism in quantum mechanics with no use of Bell's inequalities

A novel and versatile polarization-entanglement scheme is adopted to investigate the violation of the EPR local realism for a non-maximally entangled two-photon system according to the recent nonlocality proof by Lucien Hardy. In this context the adoption of a sophisticated detection method allows direct determination of any element of physical reality (viz., determined with probability equal to unity in the words of Einstein, Podolsky and Rosen) for the pair system within complete measurements that are largely insensitive to the detector quantum-efficiencies and noise.     

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.     

Possible-Worlds Semantics for Modal Notions Conceived as Predicates

If is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for predicates of sentences has not been developed very far. By introducing possible-worlds semantics for the language of arithmetic plus the unary predicate , we tackle both problems. Given a frame <W,R> consisting of a set W of worlds and a binary relation R on W, we investigate whether we can interpret at every world in such a way that A holds at a world wW if and only if A holds at every world vW such that wRv. The arithmetical vocabulary is interpreted by the standard model at every world. Several paradoxes (like Montague's Theorem, Gödel's Second Incompleteness Theorem, McGee's Theorem on the -inconsistency of certain truth theories, etc.) show that many frames, e.g., reflexive frames, do not allow for such an interpretation. We present sufficient and necessary conditions for the existence of a suitable interpretation of at any world. Sound and complete semi-formal systems, corresponding to the modal systems K and K4, for the class of all possible-worlds models for predicates and all transitive possible-worlds models are presented. We apply our account also to nonstandard models of arithmetic and other languages than the language of arithmetic.     

On the ontology of branching quantifiers

Conclusion Still, some may still want to say it. If so, my replies may gain nothing better than a stalemate against such persistence, though I can hope that earlier revelations will discourage others from persisting. But two replies are possible. Both come down, one circuitously, to an issue with us from the beginning: whether the language of the right side of (10) is suspect. For if (10) is to support instances for (6) which are about objects, that clause must itself be about objects. (These would be ones assigned by variants of I it mentions to constants it mentions.) Yet Barwise and I would call it implicitly about functions. Ironically, the discussion surrounding (10), hoping to settle that issue, could only do so if the issue were already settled, revealing decisively the ontology of (10). If irritating, this is also inevitable, given the Tarskian spirit of the ensivioned semantics for QLB.A second reply begins by noting that a QLB semantics which implies (10) cannot simply be assumed. Even a QL semantics augmented to imply (11) is not trivial to frame, as I will let readers confirm. On the QLB project, Barwise comments thus:It is not possible to explain the meaning of an essential use of branching quantification ... inductively, by treating one quantifier at a time in a first-order fashion. Some use of higher-type abstract objects is essential. (BQE75)But believers in a modest ontology for QLB can claim a non sequitur here. For (10), as they read it, succeeds without mentioning abstract objects, though not in the one quantifier at a time way which Barwise rightly finds impossible. This is not yet to say the same about a QLB semantics implying (10). But that too can be said, as it happens, with as good a conscience as with (10). A suitable treatment can begin by somehow linearizing non QL sentences like (6). Still assuming prefixes whose rows each consist, speaking loosely, of n universal quantifiers followed by a single existential, we could simply line up these rows in any order, with unique deconcatenatability being assured. From then on, it gets both tedious and complex. A full syntax is essential, and some surprising categories arose in mine. I will spare readers all details, except to say that one can indeed treat one quantifier at a time, if not in first-order fashion: schematic rules for treating n quantifiers at once can be eschewed. Unsurprisingly, heavy use is made of the depending only on idiom seen in (10). Nor does it surprise me that this semantics can succeed, with that idiom available. Roughly, if open talk about functions works in a semantics for QLF, what I read as implicit talk about them should work in a semantics for QLB.So even from a bare sketch, we can see that this new semantics settles nothing. It just leads back to the stalemate. Barwise and I will read crucial clauses as talking implicitly about functions, but this general charge against an idiom is equally deniable wherever the idiom occurs: in a reading for (6), say, or in the metalanguage can hardly repress a motherhood slogan: better dead than obscurely read. But that just denies the denial, unhelpfully. A better comment is the reminder that the claim stays alive only in a form which no one has ever imagined for it. The QLB quantifiers that cannot be shown not to range over objects are not the items anyone would ever have pointed to in illustrating the unkillable claim.

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“Motority” in three functional domains of word meaning

This article deals with relations between mental motor evoking capacity (motority, Putnoky, 1975a, b) and the sensory and affective connotations, as well as certain denotations, of words. Sensory connotation is indexed by degree of visual auditory, and tactual imagery, as assessed on a 7-point scale, while affective connotation is indexed by the usual three factors tapped by the semantic differential. The aspect of denotation used here is the abstractness value of words, also based on rating by scales. The general conclusions about motority are as follows: (1) the finding that its sensory connotations are mainly via theauditory modality of imagery, and especially in correlation with abstract words, suggests that it has a specific function that may have originated in the processing of heard language; (2) it correlates with thepotency andactivity factors of affective connotation, which suggests the existence of a nonspecific function or component in it; (3) correlations with abstractness reflect that motority must have a denotative function or component, especially in case of abstract verbal stimuli. On the basis of the results, motority is supposed to play a regulative role at higher levels of the organization of word meaning in particular.Computation of SD data was carried out under the direction and according to the programming of Professor William H. May in the Center for Comparative Psycholinguistics (Director: Charles E. Osgood), University of Illinois, Urbana-Champaign, with support provided by the National Institute of Mental Health (NIMH 07705) and National Science Foundation (NSF GS 360 and 2012-X).     

Phonological encoding and word comprehension

Summary A semantic categorization task was carried out on single words in order to determine under what circumstances a phonological code might be implicated in the process of getting from print to meaning. The subjects were asked whether or not a target word presented visually was a member of a superordinate category or sounded like a member of a category (e.g., PAIR; FRUIT). The target words were drawn from two groups, orthographically regular words (complying with grapheme-phoneme correspondences in English) and orthographically irregular words (exceptions to grapheme-phoneme correspondences).The results indicated that a phonological code may only be a necessary requirement for word comprehension in a task demanding phonological assessment (i.e., in the case of PAIR in the sounds like task). Furthermore, it was argued that some phonological effects, arising in single word comprehension, may be attributed to prelexical phonology while others may implicate postlexical phonology.     

Mind,rules, and the cognitive bin: Some implications for foreign language teaching

The cognitive model of language learning assumes that language is neither basically spoken nor written but that it pairs forms with concepts. The rules governing the ability to generate sentences are psychologically real, even if not articulated. The desire to express or extract meaning activates them. Language use draws from the native and experiential contents of mind, or the cognitive bin. These assumptions generate an instructional strategy which discards the sequencing of the audiolingual method. Instead, the ability to derive information from reading is developed first. Phonics then enables the student to read aloud what he can read silently. Aural comprehension is then derived from reading and phonics. Conversation is developed from a cognitive bin filled through reading and conversation. Writing develops from all three skills.