Showing papers in "Synthese in 1970"

Linguistics and Natural Logic

Abstract: Evidence is presented to show that the role of a generative grammar of a natural language is not merely to generate the grammatical sentences of that language, but also to relate them to their logical forms. The notion of logical form is to be made sense of in terms a ‘natural logic’, a logical for natural language, whose goals are to express all concepts capable of being expressed in natural language, to characterize all the valid inferences that can be made in natural language, and to mesh with adequate linguistic descriptions of all natural languages. The latter requirement imposes empirical linguistic constraints on natural logic. A number of examples are discussed.

Proper names and identifying descriptions

Abstract: There is an extremely plausible principle about proper names that many philosophers up to the present have either assumed or argued for. I will call it the ‘principle of identifying descriptions’. One illustration of it is in this passage from Strawson’s Individuals: ...it is no good using a name for a particular unless one knows who or what is referred to by the use of the name. A name is worthless without a backing of descriptions which can be produced on demand to explain the application.1

Pragmatics and intensional logic

Abstract: The word ‘pragmatics’ was used in Morris [1] for that branch of philosophy of language which involves, besides linguistic expressions and the objects to which they refer, also the users of the expressions and the possible contexts of use. The other two branches, syntax and semantics, dealing respectively with expressions alone and expressions together with their reference, had already been extensively developed by the time at which Morris wrote, the former by a number of authors and the latter in Tarski [1].

Methodological reflections on current linguistic theory

Abstract: I want to make some broadly methodological remarks on a variety of issues. To begin with I’ll talk of rules, and dwell a while on the distinction between fitting and guiding.

Opacity, coreference, and pronouns

Abstract: The problem discussed here is to find a basis for a uniform treatment of the relation between pronouns and their antecedents, taking into account both linguists' and philosophers' approaches The two main candidates would appear to be the linguists' notion of coreference and the philosophers' notion of pronouns as variables The notion of coreference can be extended to many but not all cases where the antecedent is non-referential The pronouns-as-variables approach appears to come closer to full generality, but there are some examples of ‘pronouns of laziness’ which appear to resist either of the two approaches

A Program for Syntax

Abstract: The program for syntax which I describe here is not one I can claim as specially my own. The two basic ideas are due to Frege: analysis of an expression into a main functor and its argument(s), and distinction among categories of functors according to the categories of arguments and values. The development of a handy notation for categories, and of an algorithm to test whether a string of expressions will combine into a complex expression that belongs to a definite category, is due to the Polish logicians, particularly Ajdukiewicz. My own contribution has been confined to working out details. So my program is not original, but I think it is right in essentials; and I am making propaganda for it by working it out in some particular instructive examples. I think this is all the more called for because some recent work in syntax seems to have ignored the insights I am trying to convey.

Some Problems Concerning the Logic of Grammatical Modifiers

Abstract: This paper consists principally of selections from a much longer work on the semantics of English. It discusses some problems concerning how to represent grammatical modifiers (e.g. ‘slowly’ in ‘x drives slowly’) in a logically perspicuous notation. A proposal of Reichenbach’s is given and criticized; then a ‘new’ theory (apparently discovered independently by myself, Romain Clark, and Richard Montague and Hans Kamp) is given, in which grammatical modifiers are represented by operators added to a first-order predicate calculus. Finally some problems concerning applications of adjectives to that-clauses and gerundive-clauses are discussed.

Deep Structure as Logical Form

Abstract: A transformational derivationof a sentence is a sequence of labeled phrase structure trees. The last tree in the sequence represents the surface structureof the sentence. The first tree represents the deep structureof the sentence.1Each later tree is derived from its predecessor via the application of exactly one transformational rule. The surface structure tree represents that syntactic structure relevant to the way in which the sentence is pronounced. It will be assumed here that the deep structure tree is a full semantic representation of the sentence.2

Subjects, speakers, and roles

Abstract: This report is a record of issues in the semantics of natural languages that have concerned me in the past few years, some of the things I have had to say about them, and some of the things that others have had to say about them There is nothing new in these pages, and there is much that is borrowed I use numbered paragraphs mostly to create favorable associations — but also to make it obvious that I do not expect the reader to perceive here any structure beyond that of sheer sequence

Probabilistic Grammars for Natural Languages

Abstract: Although a fully adequate grammar for a substantial portion of any natural language does not exist, a vigorous and controversial discussion of how to choose among several competing grammars has already developed. On occasion, criteria of simplicity have been suggested as systematic scientific criteria for selection. The absence of such systematic criteria of simplicity in other domains of science inevitably raises doubts about the feasibility of such criteria for the selection of a grammar. Although some informal and intuitive discussion of simplicity is often included in the selection of theories or models in physics or in other branches of science, there is no serious systematic literature on problems of measuring simplicity. Nor is there any systematic literature in which criteria of simplicity are used in a substantive fashion to select from among several theories. There are many reasons for this, but perhaps the most pressing one is that the use of more obviously objective criteria leaves little room for the addition of further criteria of simplicity. The central thesis of this paper is that objective probabilistic criteria of a standard scientific sort may be used to select a grammar.

On the Semantics of the Ought-To-Do

Abstract: Deontic concepts like ought, right, obligation, forbidden, and permissible have benefited from the philosophically exciting work in the semantics of modal concepts done by Kanger1, Hintikka2, Kripke3, Montague4 and others. Their semantics illuminates both the topic and the contribution of the standard axiomatic approach to deontic logic: the topic is what philosophers used to call the Ought-to-be. On the other hand, the nonstandard approach represented by early axiomatic deontic systems of ours deals with the Ought-to-do. Thus, rather than competing with the standard approach to deontic logic, our non-standard approach complements it. This can, however, be seen only by providing our nonstandard approach with a minimum of semantical foundations. This is precisely what this essay attempts to do. We shall also provide a rationale for our non-standard semantical system by formulating some proto-philosophical data that both guide the development of the system and serve as tests of adequacy for it. In fact, our concern is primarily philosophical, not technical.

Knowing that one knows and the classical definition of knowledge

Abstract: In his Essay in Modal Logic, G. H. von Wright suggested that the logic of knowledge or epistemic logic is a branch of modal logic.1 E. J. Lemmon has recommended a system of epistemic logic based on the Feys-von Wright modal system M,2 and in Knowledge and Belief Jaakko Hintikka proposed a stronger system which corresponds to Lewis's S4.3 The distinctive axiom of S4 is 'Np^NNp',* and the epistemic counter part of this formula is the principle that knowing implies knowing that one knows, that is,

Semantics of natural language: Editorial introduction

Abstract: The success of linguistics in treating natural languages as formal syntactic systems has aroused the interest of a number of linguists in a parallel or related development of semantics. For the most part quite independently, many philosophers and logicians have recently been applying formal semantic methods to structures increasingly like natural languages. While differences in training, method and vocabulary tend to veil the fact, philosophers and linguists are converging, it seems, on a common set of interrelated problems. Since philosophers and linguists are working on the same, or very similar, problems, it would obviously be instructive to compare notes. Inspired by this thought, we organized a small working conference on the semantics of natural language in August of 1969. The conference was sponsored by the Council for Philosophical Studies, and supported by the Council and the National Science Foundation. The Center for Advanced Study in the Behavioral Sciences in Stanford, California supplied a noble setting for our talks, and lent its efficient and friendly help in other ways. A number of the papers in this volume spring from talks given at that summer conference, or were written by people who were there; the rest are by people we wish could have been there. The purpose of the volume is the same as that of the conference: to encourage the active exchange of ideas among logicians, philosophers and linguists who are working on semantics for natural languages. We trust it will be agreed that there is more to this than the usual business of rubbing two or more disciplines together in the expectation of heat and the hope of light. In the present case, a common enterprise already exists; our aim is to make it a cooperative one. DONALD DAVIDSON GILBERT HARMAN

On the Frame of Reference

Abstract: In philosophy we are sometimes interested in the invariants of intelligibility. What do all good (adequate, successful, fair) interpretations of a language, or of a person, have in common? What common reality is projected by our understanding of each other?2 What do persons share that makes communication possible? Some voices in the tradition coach us to look for answers in subject matter, or ontology (physical objects, numbers, universais, propositions), in law governed relational systems such as causality, in deep logical structures such as predication and quantification, in universally applied concepts such as identity, truth, order, and in language-wide principles of interchange, such as the principle of extensionality. One may think here also of attitudes, such as belief, that every person takes toward “propositions”, of laws of deductive logic and, after Ramsey and de Finetti, of the calculus of probability.

The Role of Inductive Reasoning in the Interpretation of Metaphor

Abstract: According to most current theories the semantics of a natural language should be focussed quite sharply on to the task of describing literal meanings. Metaphor, on this view, is either a pathological phenomenon that any account of normal language is right to disregard, or a rare and specialised extension of language, as in poetry, that can safely be left on one side for later analysis while the main task of explicating literal meaning proceeds. Yet this conception of semantics is false to the realities of the situation, in at least three respects. First, so far as synchronic linguistics is concerned, native speakers often move from literal to metaphorical speech, and back again, without any sense of strain or any bizarreness-reactions in their hearers. Consider, for example, a conversation in which the following sequences of sentences are uttered: Has the producer secured any new talent? Yes, Rosemary has swallowed his bait. or There is no fire burning in his belly. Yes, he is a rather uninteresting person.

New concepts in the evolution of complexity: Stratified stability and unbounded plans

Abstract: discover in inanimate matter; and although that is a vague description to serve as a premise, it is what inspires vitalists to claim (and their opponents to deny) that some phenomena of life cannot be explained by laws of this kind. The phenomena that are said to be inaccessible to physics are of two different kinds. One school of vitalists another ground for claiming that the laws of physics are biologically incomplete, namely in questions about the evolution of organisms. Michael Polanyi asks questions of this kind, though he lumps all levels together-origins, functioning of individuals, and the sequence of species. He claims, as vitalists have always done, that there must be an overall plan which directs them all, and I shall criticize the confusion of meanings in his idea of plan or purpose. I shall distinguish between two concepts, the usual concept of a closed or bounded plan (that is, a tactic or solution for a defined problem), and a new concept of an open or unbounded plan, that is, a general strategy.

The Semantics of Modal Notions and the Indeterminacy of Ontology

Abstract: Many philosophers dislike possible individuals. Professor W. V. Quine is a well-known case in point. According to him, possible individuals create an ontological slum, “a breeding ground for disorderly elements”. At one point, he elaborated his apprehensions as follows: “Take, for instance, the possible fat man in that doorway; and, again, the possible bald man in that doorway. Are they the same possible man, or two possible men? How do we decide? How many possible men are there in that doorway? Are there more possible thin ones than fat ones? How many of them are alike? Or would their being alike make them one? ... Or ... is the concept of identity simply inapplicable to unactualized possibles? But what sense can be found in talking of entities which cannot meaningfully be said to be identical with themselves and distinct from another? These elements are well-nigh incorrigible.”1

Quantum and classical logic: Their respective roles

Abstract: That quantum mechanics is different from classical mechanics, in what it says about the physical world and how it says it, needs no proof. How precisely to describe and explain these differences, and what significance to attach to them is being continually discussed. One of the claims that is being made is that the most significant difference between classical mechanics and quantum mechanics is that the latter uses or needs to use a non-classical kind of propositional logic, a logic that has been called a 'quantum logic'. The classical logic is often described as Aristotelian. More accurately, it is the propositional logic of two-valued truth-functional propositions, the logic of classes and the logic of quantification as, for example, these are developed in Russell and Whitehead's Principia Mathematica (PM). G. Birkhoff and J. von Neumann were the first in 1936 to put forward the view that the 'physical quantities' of quantum mechanics constitute an orthocomplemented non-distributive lattice, and not the Boolean algebra of classical PM logic. 1 Other proposals were made about the same time and later by Reichenbach, yon Weizs~icker, Heisenberg and others in favor of multi-valued logics in which the classical principle tertium non datur is violated. Bas C. van Fraasen has given a brief and systematic survey to the various quantum logics in his paper 'The Labyrinth of Quantum Logics'. I shall not be concerned in this paper with multi-valued quantum logics, but only with the view common to Birkhoff and von Neumann, Segal, Mackey, Finkelstein, Jauch, Putnam 2 and others, that quantum logic is a non-distributive lattice. This theory says that the basic empirical propositions of quantum mechanics obey, not the axioms and rules of classical P M logic, but those of a logic obtained from classical logic by dropping the distributive laws for 'and' and 'or' and replacing them by what looks like a weaker form of connection. In Jauch's version, the basic empirical propositions

Utility theory with inexact preferences and degrees of preference

Abstract: a - b ≺* c - d is taken to mean that ‘your’ degree of preference for a over b is less than ‘your’ degree of preference for c over d. Various properties of the strength-of-preference comparison relation ≺* are examined along with properties of simple preferences defined from ≺*. The investigation recognizes an individual’s limited ability to make ‘precise’ judgments. Several utility theorems relating a - b ≺* c - d to u(a)- u(b) < u(c) - u(d) are included.

Analytic/synthetic and semantic theory

Abstract: A somewhat simplified version of Jerrold J. Katz’s theory of the analytic/ synthetic distinction for natural languages is presented. Katz’s account is criticized on the following grounds. (1) the ‘antonymy operator’ is not well defined; it leaves certain sentences without readings. (2) The account of negation is defective; it has the consequence that certain nonsynonymous sentences are marked as synonymous. (3) The account of entailment is defective; it has the consequence that analytic sentences entail synthetic ones. (4) Katz’s account of “indeterminable sentences” is criticized; it has the consequence that certain logical truths are not marked as analytic. (5) Katz’s semantics provides no account of truth, so that he is unable to show that analytic sentences are true and that ‘indeterminable’ sentences are not.

Quantum mechanics and classical probability theory

Abstract: The mathematical formalism of quantum mechanics, via its customary interpretation, leads to a density function for each observable. Using this formalism, there is also a natural way to calculate joint density functions for two observables. However, it has been known for some time that joint density functions, obtained in this way, may be incompatible with classical probability theory [1], [10], [15]. More recently, Cohen [4] has shown that there are density functions for non-commuting observables and functions of these observables, given by the quantum mechanical formalism, which have the following property. There is no joint density function (compatible with classical probability theory) from which all these density functions may be derived as marginal densities. A somewhat more general proof of this has been given by Nelson ([11], p. 117). These results are not too surprising when one realizes that the numbers which the Copenhagen Interpretation of the quantum mechanical formalism identifies as 'probabilities' actually have the mathematical structure of probability-like measures whose domain is an ortho-complemented lattice. The ortho-complemented lattice in this case is the partially ordered set of all closed sub-spaces of a separable, infinite dimensional, complex Hilbert space [7], [8], [2]. These probability-like measures on an ortho-complemented lattice have many similarities to ordinary, classical probability measures defined on a Boolean algebra. But there are some dissimilarities which, as Varadarajan [17] has shown, make it impossible to define something like a classical joint density function for these probability-like measures. These considerations have led many people, among them yon Neumann (Birkhoff and yon Neumann [2]), Mackey [7], [8], Suppes [15], [16], and Varadarajan [17] to speculate that the formalism of quantum mechanics cannot be interpreted in a physically acceptable way which is consistent with classical probability theory. This is to say that the customary

Troubles about Actions

Abstract: In a recent, important series of papers,1Prof. Donald Davidson has proposed and illustrated a theory about theories of meaning. The theory, to put it very much more crudely than Davidson does, is simply that a theory of meaning for the (natural) language L ought to take the form of a truth definition for L. That is, such a theory ought to recursively associate each truth-valuable sentence of L with a representation of its truth conditions. Davidson says “what we require of a theory of meaning for a language L is that without appeal to any (further) semantical notions it place enough restrictions on the predicate ‘is T’ to entail all sentences got from schema [1] when ‘s’is replaced by a structural description of a sentence of L and ‘p’by that sentence.” (T & M 309)

Inference and Self-Reference

Abstract: In natural language it appears that self-reference is possible, and due to logical interest in the paradoxes of self-reference, the topic has also seen a number of formal investigations. But when the interest is in the paradoxes, rather than in self-reference itself, the exact linguistic mechanisms of self-reference are not necessarily relevant. Indeed, many analyses of the paradoxes assume the existence of statements capable of playing the inferential role of the paradoxes and inquire into the nature of languages containing such statements, omitting all discussion of how the paradoxical statements are produced.1

On the analysis of causation

Abstract: According to the regularity theory of causation, one set of conditions (or factors or events or states of affairs) causes another to occur only if a set of conditions similar to the latter occurs whenever a set of conditions similar to the former occurs. A well-known difficulty for the regularity theory is its failure to distinguish between cases of accidental correlation and causation. Thomas Reid's example of the coming of day regularly following the coming of night and Russell's example of the workmen leaving the Manchester factory regularly following the sounding of the hooter at the London factory illustrate this difficulty. The regularity theory, further, cannot be salvaged by the following sort of reply. 'Similar', in the regularity formula, means 'relevantly similar': the hooting at the London factory does not cause the workmen's leaving in Manchester because these sets of conditions lack a relevant similarity, for example, that they occur in the same general area. This attempted defense of the regularity theory fails because the resulting analysis is viciously circular. In this context 'relevantly similar' can only mean 'similar in the causally relevant respects'. Problems of this kind have led some philosophers to suggest analyses of causation in terms of natural laws. Accordingly, one set of conditions causes another to occur only if there are natural laws from which it can be deduced that the latter set of conditions occurs given that the former set occurs. Since 'whenever the hooter sounds at the London factory, the workmen leave the Manchester factory' is an accidental universal and not a law of nature, Russell's case does not constitute a counterexample to the laws-of-nature theory. However, there are difficulties for this theory that closely resemble those of the regularity theory. There are several kinds of natural laws. Consider the developmental law which states that whenever the formation of the circulatory system of an human embryo occurs, the formation of the lungs in the embryo occurs. On the laws-of-nature

What must be added to knowing to obtain knowing that one knows

Abstract: What point could there possibly be in asserting of one who knows that/?, that he knows that he knows that/?? Well, we might say, in general the sentence that results from prefixing 'he knows that' to a proposition expressing sentence V expresses a proposition that entails the propo sition expressed by *q\ So in asserting that some person knows that he knows that p there is at least the point of affirming that he knows that /?. But usually when we assert a proposition by uttering a sentence of the form 'he knows that q" we imply more than the proposition expressed by '#'. What more do we imply when V is of the form 'he knows that/?'? The flat answer 'nothing' might appeal here on either of two rather different sorts of grounds. One would be that investigation of the concept of knowledge (of the general sort undertaken by Hintikka and Hilpinen) reveals that the truth-conditions of the proposition expressed by 'he knows that q' that are ordinarily over and above those of the proposition expressed by V are, in the special case where V is of the form 'he knows that /?', necessarily already satisfied when the truth-conditions for the proposition expressed by V are satisfied. The other would be the claim that the truth-conditions of the proposition expressed by 'he knows that q* that are ordinarily over and above those of the proposition expressed by y simply become inapplicable or meaningless when '#' is of the form 'he knows that/?'. I want, however, to give a contrary answer to our question of what more is implied by asserting that some person knows that he knows that p than is implied by asserting simply that he knows that/?. My answer is: not much but something, namely, the proposition that he thinks that he knows that/?. In fact I wish to suggest the following two theses :

High bit rate optical transmission using midspan spectral inversion

Abstract: The problem of the phase noise generated by nonlinear effects and chromatic dispersion can limit the transmission distance and the bit rate for phase-shift-keying modulation formats. In this paper, the compensation of the nonlinear and linear effects by a midspan optical phase conjugation (OPC) is studied. First, we show the impacts of chromatic dispersion in an OD8PSK systems (Optical Differential 8-Level Phase-Shift Keying), then a long-haul differential 8-Level Phase-Shift Keying (OD8PSK) transmission simulation is studied in order to compare both the performance of the dispersion compensating fiber (DCF) and the midspan optical phase conjugation. OPC allow to obtain a best recovered of transmitted information especially when compared to a «conventional» transmission system; the latter uses dispersion compensating fiber (DCF). OPC performs better even if we increase the bit rate and the distance. Key words : alternative modulation formats; Optical Differential 8-Level Phase-Shift Keying (OD8PSK); dispersion compensation; fiber optics communications; nonlinear phase noise; optical phase conjugation; spectral inversion.

Statistical explanation in physics: The Copenhagen interpretation

Abstract: The statistical aspects of quantum explanation are intrinsic to quantum physics; individual quantum events are created in the interactions associated with observation and are not describable by predictive theory. The superposition principle shows the essential difference between quantum and non-quantum physics, and the principle is exemplified in the classic single-photon two-slit interference experiment. Recently Mandel and Pfleegor have done an experiment somewhat similar to the optical single-photon experiment but with two independently operated lasers; interference is obtained even with beam intensity so small that only one photon is in the apparatus at a time. The result can be understood in terms of the superposition of states; or, in terms of the Uncertainty Principle, which is found to forbid the determination of which of the two lasers is the source of a given photon (if conditions for interference are to obtain). The Mandel-Pfleegor experiment gives a physical argument against the continuous localization of a photon that is assumed in the ‘hidden variable’ theories and therefore gives further support for the generally accepted view that an observed entity (observed state) is created in the observation event. This aspect of quantum physics implies a subjectivism on the level of individual quantum-level occurrences, since there is in quantum theory no basis for asserting the existence of the event independently of observation of it. Extension of this subjectivism to large scale, non-quantum phenomena falls within the principles of quantum theory; counter considerations that argue against such an extension are noted.