Frege On ‘I’, ‘Now’, ‘Today’ And Some Other Linguistic Devices

In this paper, I argue against an influential view of Frege's writings on indexical and other context-sensitive expressions, and in favour of an alternative. The centrepiece of the influential view, due to (among others) Evans and McDowell, is that according to Frege, context-sensitiveword-meaning plus context combine to express senses which are essentially first person, essentially present tense and so on, depending on the context-sensitive expression in question. Frege's treatment of indexicals thus fits smoothly with his Intuitive Criterion of difference of sense. On my view, by contrast, Frege stuck by the view which he held in his unpublished 1897 Logic, namely that the senses expressed by the combination of context-sensitive word-meaning and context could just as well be expressed by means of non-context-sensitive expressions: being first person, present tense and so on are properties, in Frege's view, only of language, not of thought. Given the irreducibility of indexicals – a phenomenon noticed by Castañeda, Perry and others – Frege's treatment of indexicals thus turns out to be inconsistent with the Intuitive Criterion. I argue that Frege was not aware of the inconsistency because he was not aware of the irreducibility of indexicals. This oversight was possible because the source of Frege's interest in indexicals, as inother context-sensitive expressions, differed from that of contemporary theorists. Whereas contemporary theorists are most often interested in indexicals (and in Frege's treatment of them) because they are interested in the indexical versions of Frege's Puzzle and their relation to psychological explanation, Frege himself was interested in them because they pose a prima facie threat to his general conception of thoughts. The only indexical expression Frege's view of which the above account does not cover is I insofar as it is associated with special and primitive senses, but Frege did not introduce such senses with a view to explaining theirreducibility of I his real reason for introducing them remains obscure.     

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.     

Realismbei Frege: Reply to Burge

Frege is celebrated as an arch-Platonist and arch-realist. He is renowned for claiming that truths of arithmetic are eternally true and independent of us, our judgments and our thoughts; that there is a third realm containing nonphysical objects that are not ideas. Until recently, there were few attempts to explicate these renowned claims, for most philosophers thought the clarity of Frege's prose rendered explication unnecessary. But the last ten years have seen the publication of several revisionist interpretations of Frege's writings — interpretations on which these claims receive a very different reading. In Frege on Knowing the Third Realm, Tyler Burge attempts to undermine this trend. Burge argues that Frege is the very Platonist most have thought him — that revisionist interpretations of Frege's Platonism, mine among them, run afoul of the words on Frege's pages. This paper is a response to Burge's criticisms. I argue that my interpretation is more faithful than Burge's to Frege's texts.     

Consistent Fragments of Grundgesetze and the Existence of Non-Logical Objects

In this paper, I consider two curious subsystems ofFrege's Grundgesetze der Arithmetik: Richard Heck's predicative fragment H, consisting of schema V together with predicative second-order comprehension (in a language containing a syntactical abstraction operator), and a theory T in monadic second-order logic, consisting of axiom V and ¹ ₁-comprehension (in a language containing anabstraction function). I provide a consistency proof for the latter theory, thereby refuting a version of a conjecture by Heck. It is shown that both Heck and T prove the existence of infinitely many non-logical objects (T deriving,moreover, the nonexistence of the value-range concept). Some implications concerning the interpretation of Frege's proof of referentiality and the possibility of classifying any of these subsystems as logicist are discussed. Finally, I explore the relation of T toCantor's theorem which is somewhat surprising.     

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).     

“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.     

La Evolucion de la filosofia de Wittgenstein

Summary The author claims that there is a basic difference between theTractatus and thePhilosophical Investigations; despite Bernstein's and O'Brien's claims to the contrary, there are, indeed, two Wittgensteins. Yet, to ascertain the difference between both we must look at Wittgenstein's conceptions of philosophy rather than at his views on logic and language. Wittgenstein's different, and even divergent, views on logic and language are grounded on his two views on philosophy and not the other way around. At the same time, Wittgenstein's views on philosophy are caused by his ways of conceiving the scope of philosophical activity in regard to language. Both in theTractatus and in thePhilosophical Investigations, Wittgenstein points out what is important in language for philosophy, but in each case he reaches very different conclusions. Now, when all is said, there remains one unifying factor in all of Wittgenstein's investigations: it is the question of the logic of language, which shifts positions from theTractatus to theInvestigations, so that what was earlier a hidden structure becomes later the grammar of its indefinitely complexe uses.     

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.     

On finite approximability of ψ-intermediate logics

The aim of this note is to show (Theorem 1.6) that in each of the cases: = {, }, or {, , }, or {, , } there are uncountably many -intermediate logics which are not finitely approximable. This result together with the results known in literature allow us to conclude (Theorem 2.2) that for each : either all -intermediate logics are finitely approximate or there are uncountably many of them which lack the property.     

Rules in relevant logic — II: Formula representation

This paper surveys the various forms of Deduction Theorem for a broad range of relevant logics. The logics range from the basic system B of Routley-Meyer through to the system R of relevant implication, and the forms of Deduction Theorem are characterized by the various formula representations of rules that are either unrestricted or restricted in certain ways. The formula representations cover the iterated form,A ₁ .A ₂ . ... .A _n B, the conjunctive form,A ₁&A ₂ & ...A _n B, the combined conjunctive and iterated form, enthymematic version of these three forms, and the classical implicational form,A ₁&A ₂& ...A _n B. The concept of general enthymeme is introduced and the Deduction Theorem is shown to apply for rules essentially derived using Modus Ponens and Adjunction only, with logics containing either (A B)&(B C) .A C orA B .B C .A C.I acknowledge help from anonymous referees for guidance in preparing Part II, and especially for the suggestion that Theorem 9 could be expanded to fully contraction-less logics.     

Comparatal dispersion,a measure of accuracy of judgment

It is suggested that the ambiguity of aset of paired comparison judgments may be measured by the quantity _i ² + _j ² – 2r _{ij ii}, This quantity is termed thecomparatal dispersion. A simultaneous solution for scale values and ratios of comparatal dispersions has been presented and applied to some data on food preferences.This research was jointly supported in part by Princeton University, the Office of Naval Research under contract Nonr-1858(15), and the National Science Foundation under grant NSF G-642, and in part by Educational Testing Service. Reproduction in whole or in part is permitted for any purpose of the United States Government.     

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.     

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.     

Universality of the closure space of filters in the algebra of all subsets

In this paper we show that some standard topological constructions may be fruitfully used in the theory of closure spaces (see [5], [4]). These possibilities are exemplified by the classical theorem on the universality of the Alexandroff's cube for T ₀-closure spaces. It turns out that the closure space of all filters in the lattice of all subsets forms a generalized Alexandroff's cube that is universal for T ₀-closure spaces. By this theorem we obtain the following characterization of the consequence operator of the classical logic: If is a countable set and C: P() P() is a closure operator on X, then C satisfies the compactness theorem iff the closure space ,C is homeomorphically embeddable in the closure space of the consequence operator of the classical logic.We also prove that for every closure space X with a countable base such that the cardinality of X is not greater than 2 there exists a subset X of irrationals and a subset X of the Cantor's set such that X is both a continuous image of X and a continuous image of X.We assume the reader is familiar with notions in [5].     

Natural deduction rules for English

A system of natural deduction rules is proposed for an idealized form of English. The rules presuppose a sharp distinction between proper names and such expressions as the c, a (an) c, some c, any c, and every c, where c represents a common noun. These latter expressions are called quantifiers, and other expressions of the form that c or that c itself, are called quantified terms. Introduction and elimination rules are presented for any, every, some, a (an), and the, and also for any which, every which, and so on, as well as rules for some other concepts. One outcome of these rules is that Every man loves some woman is implied by, but does not imply, Some woman is loved by every man, since the latter is taken to mean the same as Some woman is loved by all men. Also, Jack knows which woman came is implied by Some woman is known by Jack to have come, but not by Jack knows that some woman came.     

Theor of free choice permission

I argue that the conjunctive distribution of permissibility over or, which is a puzzling feature of free-choice permission is just one instance of a more general class of conjunctive occurrences of the word, and that these conjunctive uses are more directly explicable by the consideration that or is a descendant of oper than by reference to the disjunctive occurrences which logicalist prejudices may tempt us to regard as semantically more fundamental. I offer an account of how the disjunctive uses of or may have come about through an intermediate discourse-adverbial use of or, drawing a parallel with but, which, etymologically, is disjunctive rather than conjunctive and whose conjunctive uses seem to represent just such a discourse-adverbial application.     

On reduced matrices

It is shown that the class of reduced matrices of a logic is a 1 ^st order -class provided the variety associated with has the finite replacement property in the sense of [7]. This applies in particular to all 2-valued logics. For 3-valued logics the class of reduced matrices need not be 1 ^st order.     

Responsibility and the explanatory view of consequences

Conclusion I conclude that the explanatory view of consequences is a fruitful one.This view accounts for our common sense view that actions are, in some sense, sufficient for their consequences. It shows in a concrete and illuminating manner that we are or may be responsible for a vast number of events no matter how innocently our actions may be described. It allows for the fact that individuals lack responsibility for consequences of collective actions, thereby explaining a generally felt double effect built into our social morality. It brings into light and explains the fact that some degree of determinism seems to be presupposed if people are ever morally responsible for any events whatsoever. Finally, the explanatory view of consequences yields precise and attractive interpretations of the open and the closed views of responsibility.     

New lower and upper bounds for communality in factor analysis

We derive several relationships between communalities and the eigenvalues for ap ×p correlation matrix under the usual factor analysis model. For suitable choices ofj, _j (), where _j () is thej-th largest eigenvalue of , provides either a lower or an upper bound to the communalities for some of the variables. We show that for at least one variable, 1 - _p () improves on the use of squared mulitiple correlation coefficient as a lower bound.This research was done while the second author was at Tokyo Institute of Technology.     

Les “règles de la discussion légitime” dans la logique de Port-Royal

In the XVIIth century the conflict which opposed the jansenists to the jesuits involved the problem of the due process in theological matter. The jesuits heralded the thesis that the infallibility of the Church has to be extended from dogmatics (quaestio iuris) to the historical facts (quaestio facti). On the opposite side Arnauld maintained that such an opinion was monstruous: also in religious matters the fact has to be proved according to the principles of a due process, and not by authority. In this article the thesis pleaded by the jansenists is considered in connection with the model of argumentative procedure offered by the Port-Royal logic.The Logique ou Art de penser (1622) by Antoine Arnauld and Pierre Nicole seems to have rediscovered the classical principles of the theory of argumentation: from the burden of proof to the idea of probable truth. But really a new model of adversary-system has been introduced into the modern mind, which is very different in concept from the topical tradition. The basic metaphor of combat, implying that the truth will prevail in the fight, is compatible with the epistemological premises of the modern logic (as the separation between fact and value). Therefore the problem of the fact-finding seems to be attracted into the area of the logic of information, and not of the theory of argumentation.