Showing papers in "Synthese in 1974"

Special sciences (or: The disunity of science as a working hypothesis)

Abstract: A typical thesis of positivistic philosophy of science is that all true theories in the special sciences should reduce to physical theories in the long run. This is intended to be an empirical thesis, and part of the evidence which supports it is provided by such scientific successes as the molecular theory of heat and the physical explanation of the chemical bond. But the philosophical popularity of the reductivist program cannot be explained by reference to these achievements alone. The development of science has witnessed the proliferation of specialized disciplines at least as often as it has witnessed their reduction to physics, so the widespread enthusiasm for reduction can hardly be a mere induction over its past successes. I think that many philosophers who accept reductivism do so primarily because they wish to endorse the generality of physics vis d vis the special sciences: roughly, the view that all events which fall under the laws of any science are physical events and hence fall under the laws of physics. 1 For such philosophers, saying that physics is basic science and saying that theories in the special sciences must reduce to physical theories have seemed to be two ways of saying the same thing, so that the latter doctrine has come to be a standard construal of the former. In what follows, I shall argue that this is a considerable confusion. What has traditionally been called 'the unity of science' is a much stronger, and much less plausible, thesis than the generality of physics. If this is true it is important. Though reductionism is an empirical doctrine, it is intended to play a regulative role in scientific practice. Reducibility to physics is taken to be a constraint upon the acceptability of theories in the special sciences, with the curious consequence that the more the special sciences succeed, the more they ought to disappear. Methodological problems about psychology, in particular, arise in just this way: the assumption that the subject-matter of psychology is part of the subject-matter of physics is taken to imply that psychological theories must reduce to physical theories, and it is this latter principle

Belief and the basis of meaning

Abstract: A theory of radical interpretation gives the meanings of all sentences of a language, and can be verified by evidence available to someone who does not understand the language. Such evidence cannot include detailed information concerning the beliefs and intentions of speakers, and therefore the theory must simultaneously interpret the utterances of speakers and specify (some of) his beliefs. Analogies and connections with decision theory suggest the kind of theory that will serve for radical interpretation, and how permissible evidence can support it.

Formulation des bétons autoplaçants : Optimisation du squelette granulaire par la méthode graphique de Dreux - Gorisse

Abstract: La formulation d'un beton autoplacant (BAP) est une operation complexe qui necessite de trouver une bonne combinaison de materiaux compatibles et le dosage convenable de chacun de ses constituants afin d'obtenir une formulation repondant aux proprietes des BAP (fluidite et homogeneite). De multiples approches se sont developpees a travers le monde pour la formulation d'un beton autoplacant. La plupart des methodes de formulation sont concues actuellement de maniere empirique. Ces methodes se basent essentiellement sur des approches diphasiques du beton autoplacant. Elles sont divisees en deux categories : celles qui sont axees sur l'optimisation du volume de pate (sous forme de pate pure ou de mortier) et celles qui sont focalisees sur l'optimisation du squelette granulaire. Notre contribution est d'apprehender la problematique de la formulation des BAP de facon globale en integrant a la fois l'optimisation du volume de pate par l'ajout de filler calcaire avec trois dosages et l'optimisation du squelette granulaire par la methode graphique de Dreux - Gorisse. Les resultats obtenus montrent qu'il existe un volume de pate optimum et que la composition du squelette granulaire par la methode graphique de Dreux - Gorisse est applicable par le choix des fractions granulaires et leurs analyses granulometriques qui permet de mettre en evidence les classes manquantes Mots Cles : BAP - Optimisation - Granulats -Additions - Caracterisation The mix design of a self-compacting concrete (SCC) is a complex operation that requires finding a good combination of compatible materials, and the proper dosage of each of these components in order to obtain a formulation that meets the properties of SCC(fluidity and homogeneity). Multiple approaches have been developed in the world wide for the formulation of a self-compacting concrete. Most methods of formulation are currently designed empirically. These methods are mainly based on the fact that the BAP is a two-phase material. These methods are divided into two categories: those that focus on optimizing the volume of paste (paste form pure or mortar) and those that focus on optimizing the granular skeleton. Our contribution is to apprehend the problem formulation sec in a comprehensive manner, integrating both the optimization of the paste volume by adding the limestone filler with three dosages and optimizing the skeleton by the graphical method Dreux - Gorisse. The results obtained show that to formulate a self-compacting concrete, there is an optimum paste volume. Whereas the composition of the granular skeleton by the graphical method of Dreux - Gorisse is applicable by the choice of granular fractions and particle size analysis which allows highlighting the missing classes Keywords : SCC - Formulation - Optimization -Aggregate -Additions - Characterization

A Notion of Mechanistic Theory

Abstract: The notion in question is suggested by the words ‘mechanism’ or ‘machine’. Unlike the usual meaning of ‘mechanistic’, that is, deterministic in contrast to probabilistic, the notion here considered distinguishes among deterministic (and among probabilistic) theories.

The Conditional in Quantum Logic

Abstract: Besides the physicomathematical controversy concerning the ‘phenomenological justification’ and the specific formal structure of the calculus known as quantum logic (QL), there is a philosophical controversy concerning whether this ‘calculus of experimental propositions’ is properly speaking a logic rather than simply an algebraic structure only analogous to logic properly so called. Directly associated with this controversy is the issue of whether logic is an empirical science on the par with, e.g., physical geometry. This article is not concerned, however, with the general question of the empirical character of logic, either classical or quantal; it is rather concerned only with one seemingly decisive objection against regarding QL as logic, namely, the objection advanced by Jauch and Piron (1970, p. 176), who argue that since QL lacks an essential feature of logic — viz., a deduction scheme — it is `very questionable whether we may properly call the lattice of general quantum mechanics a logic.’ Their argument is based on what they regard to be the general failure of the lattice of QL propositions to admit a material implication connective or conditional operation by means of which the modus ponens deduction scheme can be incorporated into QL. The view of Jauch and Piron is also supported by Greechie and Gudder (1971, 1973), who examine a number of results which suggest that no reasonable material conditional exists in QL.

The Einstein-Podolsky-Rosen Paradox

Abstract: The first part of this article analyzes the ‘paradoxical’ implications of elementary quantum theory described by Einstein, Podolsky, and Rosen (1935; henceforth, EPR). At the end of the analysis we are left with a dilemma for the interpretation of quantum mechanics.

On the completeness of quantum theory

Abstract: This is an essay on the interpretation of quantum theory. I take the central interpretive problem to be the problem of completeness. Partial assignments of values to the quantities are forced out by the 0 and 1 probabilities of the theory. Can we complete the assignments so as to assign values in superposed states? What is at stake is the very capacity of quantum theory to provide an intelligible picture of the world. Thus no ‘interpretation’ of the theory that fails to build in an affirmative answer to completeness can be acceptable. I explore here the program of hidden variables as a way of completing the theory and I assess the impact on that program of recent work on ‘locality’ by Bell and Wigner. Although I do not find that this work tells against hidden variables (just as I do not find it bearing on locality), I do wind up abandoning the hidden variable program for another one, one which does seem neatly to complete the theory.

Hempel's ambiguity *

Abstract: Explanation theory abandoned its pre-theoretical stage and became a respectable branch of philosophical inquiry when, in the late forties, Hempel began to develop his model of deductive nomological (D-N) explanation. In a sequence of now classic papers he succeeded in articulating an illuminating philosophical account of explanation which provided compelling evidence for the adequacy of the philosophical views captured by the D-N model. In the early sixties Hempel turned his attention to the topic of inductive explanation. Until then, it had been generally believed that the inductive model had to be understood as a generalization and a rather straightforward one at that of the deductive model. Yet, already in the HempelOppenheim paper a warning had been issued to the effect that such generalization raised \"a variety of new problems\". Indeed, when finally, in a sequence of illuminating papers on inductive explanation, Hempel decided to face one of these problems, he felt forced to propose a theory of inductive explanation which differed drastically from pre-analytic consensus on the nature of such explanations. Not the least of these departures was Hempel's implicit rejection of the claim that the deductive model is a limiting instance of the inductive model. Yet, much more than this was involved. We should like to argue that, in spite of misleading appearances of continuity, the philosophical understanding of explanations implicit in the model of inductive statistical (I-S) explanation which Hempel eventually produced is drastically different from, if not incompatible with, that which inspired his D-N model. One of the purposes of this paper is to draw attention to the nature and magnitude of the shift involved. Another is to explain why Hempel's views on inductive explanation ought not to be accepted. The evolution of Hempel's thought was causally related to his analysis of a problem which, pending more illuminating designations, we will refer to as 'Hempel's problem'. Due to it Hempel felt forced to propose an account of inductive explanation which contained a rather unexpected

Aristotle on adequate explanations

Abstract: There is a theory in Aristotle that is popularly known as the doctrine of four causes. This paper is meant as a modest beginning toward showing that the theory in question should not be construed in this manner. Properly understood it is the Stagirite's account of what constitutes an adequate explanation. For the most part, the examination of Aristotle's theory in this paper will be restricted to some key passages from Book II of the Physics. Though a full account, involving the analyses of all of the passages in which aitia is discussed is beyond the scope of this paper, I do not find at present anything in Aristotle that would contradict the sketch outlined here.

The Logic of Scientific Inquiry

Abstract: Is methodological theory a priori or a posteriori knowledge? It is perhaps a posteriori improvable, somehow. For example, Duhem discovered that since scientists disagree on methods, they do not always know what they are doing.

Where things now stand with the analytic-synthetic distinction

Abstract: The philosophy of language can be viewed as a branch of the theory of knowledge. It concerns itself with a special case in epistemology, linguistic knowledge, and the questions about such knowledge that it tries to answer have the form of classical epistemological questions, namely, what do we know about a natural language and how do we come to know it. It is no surprise, then, to find that theories about linguistic knowledge, like theories about knowledge in general, are either rationalist or empiricist. Rationalist theories like Chomsky's claim that acquisition of the complex competence of a fluent speaker must be explained as a process in which innate schemata expressing the general form of a grammar become differentiated and realized as hypotheses about the character of the particular grammar underlying a sample of speech. On a rationalist theory, the primary role of a linguistic environment is to stimulate such differentiation and to confirm or disconfirm the hypotheses resulting from these schemata. Rationalism also claims that the principles expressing these innate schemata are synthetic a priori because they constitute the framework within which environmental stimulation can be interpreted as evidence bearing on the learner's hypotheses about the grammar. 1 Empiricist theories like Quine's claim that an explanation of language acquisition needs nothing more complex or sophisticated in the way of an assumtion about innate capacities than a system of inductive procedures for forming generalizations from the limited regularities in the learner's linguistic experience. On an empiricist theory, experience plays the central role that innate schemata play on a rationalist theory. Experience teaches the language learner both the form and content of grammatical rules. Accordingly, for the empiricist, even the principles that express the invariant form and content of grammars, the linguistic universals, are synthetic a posteriori. They could have been otherwise and would have

Empirical logic and quantum mechanics

Abstract: Our purpose in this article is to discuss some of the basic notions of quantum physics within the more general framework of operational statistics and empirical logic (as developed in Foulis and Randall, 1972, and Randall and Foulis, 1973). Empirical logic is a formal mathematical system in which the notion of an operation is primitive and undefined; all other concepts are rigorously defined in terms of such operations (which are presumed to correspond to actual physical procedures).

Comment on Wilfrid Sellars

Abstract: Sellars's theory, as Dennett reconstructs it, is that a hare is a tortoise in rabbit's clothing. I must say that I 'm in somewhat worse shape than Dan. I did not get six papers in advance. I got this one on Tuesday night and I left on Wednesday morning for North Carolina, so this comment is perhaps even more hallucinatory. I wish my hallucinations were as cogent as Dan's. Professor Sellars's paper 'Empiricism and the Philosophy of Mind' was one of the most important papers on the topic in recent decades, and I was happy to see him apply the insights of that paper to the topic of this conference. However, as Dennett has dealt with Sellars' paper as it touches on the philosophy of mind, I shall not focus on those aspects here, except for this grunt of approval. The device of dot quotation, although a bit 'spotty' at times, seems to me to be a good one. I don' t share Sellars' nominalism in general. I don' t find quantification over expressions-cure-functions preferable to quantification over plain old sets and properties, and I don' t think that the last paragraph of $ellars' paper, or rather the next to the last, answers the objections to the adequacy of nominalistic formulations that have appeared in the literature in the last ten years. But the general question of nominalism aside, I am pleased to join the happy chorus of those who don' t think meanings are objects. Not that one couldn't identify them with objects, just that the identification will be even more arbitrary and unconvincing than, say, the identification of the number 1 with singleton the null set. Moreover, as already pointed out at this conference, identification of meanings with objects can easily give an illusion of uniqueness which the linguistic facts will fail to warrant. Interpreting 'A means B' as \" ' A ' means 'B' \", with quotes around the B, is unsatisfactory, as Wilfrid points out, because (a) somehow the second just says that two words are synonymous, whereas the first seems to be intended to do a little more than that, and (b), although he didn't mention it, you run afoul of well-known objections by Church. Interpreting it as

How to think quantum-logically

Abstract: The heart of the quantum-logical interpretation of quantum mechanics is the following ‘proportion’: $$\frac{{CEOMETRY}}{{GENERALRELATITY}} = \frac{{LOGIC}}{{QUANTUMMECHANICS}}$$

New concepts in the evolution of complexity

Abstract: Vitalism is a traditional and persistent belief that the laws of physics that hold in the inanimate world will not suffice to explain the phenomena of life. Of course it is not suggested, either by those who share the belief or by those like me who reject it, that we know all the laws of physics now, or will know them soon. Rather what is silently supposed by both sides is that we know what kind of laws physics is made up of and will continue to 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.

A single case propensity theory of explanation

Abstract: Levi contends that these two desiderata cannot be simultaneously satisfied and that, as a result, the function of covering laws in Hempel's explication had better be envisioned as fulfilled by material rules of inference.2 The force of Levi's argument, of course, rests upon his contention that there is no acceptable interpretation of statistical probability which succeeds in converting statistical hypotheses into covering laws.3 Levi admits that he is unable to provide an impossibility theorem here but claims that "a review of the more obvious candidates ought, at a very minimum, to place the onus of proof very squarely on the shoulders of those who believe such statements can be constructed".4 The purpose of this paper is to demonstrate that Levi's argument is not well-founded and that, contrary to his claim, the propensity interpretation succeeds in fulfilling this goal. Implications of adopting this analysis as the standard account of statistical probability are explored, including (a) the unified theory it provides of the character of lawfulness for both universal and statistical laws and (b) the criterion it supports for the adequacy of explanations invoking laws of either kind. From this point of view, the conclusion emerges that all explanations in empirical science are es sentially theoretical in character. i

The quantum probability calculus

Abstract: Quantum mechanics has opened a vast sector of physics to probability calculus. In fact most of the physical interpretation of the formalism of quantum mechanics is expressed in terms of probability statements.1

Brouwer's constructivism

Abstract: In this respect then no one who has even a slight acquaintance with geometry will deny that the nature of this science is in fiat contradiction with the absurd language used by mathematicians, for want of better terms. They constantly talk of 'operations' like 'squaring', 'applying', 'adding' and so on, as if the object were to do something, whereas the true purpose of the whole subject is knowledge -knowledge, moreover, of what eternally exists, not of anything that comes to be this or that at some time and ceases to be. PLATO, Republic, VII, 527

Replies to David Lewis and W.V. Quine

Abstract: First let me respond to David Lewis' careful and useful comments and suggestions. Lewis says that ontological parsimony is not the subject we're discus sing, so we may as well assume any entities that can do us any good. I'm all for that. The question I raised was whether or not things like proposi tions, meanings as entities and objects of beliefs do do us any good in the present enterprise. Now for a more important point. The P corpus determines all the rest; in one sense that seems to me to be absolutely right and it's a dogma I accept along with David. But there's that word 'determine'. All the things that go in boxes Ao, Ak and M are supervenient on what goes into P. David gave the same characterization of supervenience I would (the same one Moore gave, although he was giving it for a special case) : you can't have two things that are exactly alike in all of the things that you would list under P and differing in the things you would list under Ao, Ak and M. This is a 'determining' I agree with completely, a mild form of mater ialism. But there's another sense of 'determining' that, it seems to me, David thinks follows from this or is even identical to it, that I would put in a different compartment. That is, for example, the idea that if you describe all of the truths about what's in P you have now given all of the evidence you will ever need or could use in deciding what goes into the other boxes. This I think is false. It isn't any part of my project to show how the entire evidential base can be drawn from P. I don't mean, in saying this, to question David's remark that there is information in P that I've thrown away or wasted. That's a different point, and it may be right. But the idea that the whole evidential base could come from P seems to be very questionable. Perhaps we don't have to argue about that. Whatever is in Ak comes from P, according to David; my question was how far we could get with what comes out of Ak. If David can show that we can, or must, use more of what comes from P than is used in Ak, then it seems to me he has scored a real point and I ought to go along with it.

Intuitionistic views on the nature of mathematics

Abstract: One of the questions which philosophers ask about mathematics is: Why are mathematical theorems so certain? Whence does mathematics take its evidence, its indubitable truth? The answer of intuitionists to these questions is: The basic notions of mathematics are so extremely simple, even trivial, that doubts about their properties do not rise at all. Intuitionism is not a philosophical system on the same level with realism, idealism, or existentialism. The only philosophical thesis of mathematical intuitionism is that no philosophy is needed to understand mathematics. On the contrary, every philosophy is conceptually much more complicated than mathematics. Logic in the usual sense does depend upon philosophical questions. One of its basic notions is that of a proposition being true. But what is a proposition? Does it coincide with the sentence by which it is expressed or is it something behind the sentence, some meaning? If so, what is the relation between the proposition and the sentence? And what does it mean that the proposition is true? Does this notion presuppose the existence of an external world in which it is true? If the proposition is the same as the sentence analogous questions can be asked. I am not going to answer them; they have been solved in a hundred different ways, none of them quite convincing, and all of them showing that logic is complicated and therefore unsuitable as a basis for mathematics. I shall come back to the relations of logic to mathematics later in this talk. We look for a basis of mathematics which is directly given and which we can immediately understand without philosophical subtleties. The first that presents itself is the process of counting. However, counting establishes a correspondence between material or non-material objects and the natural numbers, so it can only be understood if both an external world (or at least some sort of objects) and abstract numbers are given. It is still too complicated to serve as a basis for mathematics. An analysis

Some Results from the Combinatorial Approach to Quantum Logic

Abstract: The combinatorial approach to quantum logic focuses on certain interconnections between graphs, combinatorial designs, and convex sets as applied to a quantum logic (ℒ, S), that is, to a a-orthocomplete orthomodular poset ℒ and a full set of σ-additive states S on ℒ. Combinatorial results of interest in quantum logic appear in Gerelle et al. (1974), Greechie (1968, 1969, 1971a, b), Greechie and Gudder (1973), and Greechie and Miller (1970, 1972). In this article I shall be concerned only with orthomodular lattices ℒ and associated structures.

Informal axiomatization, formalization and the concept of truth

Abstract: Axiomatization is an especially thoroughgoing and rigorous instance of a process in the organization of knowledge that might be called systematization. The objective is to organize a body of knowledge (or of theory that aspires to be knowledge) in such a way as to clarify its structure and strengthen its justification as a whole. In particular, one seeks to single out certain concepts and principles as 'primitive' or 'fundamental' and others as 'defined' or 'derived'. The method of axiomatization, first applied to geometry in ancient times and epitomized by Euclid's Elements, presents a theory by singling out certain primitive notions and defining others from them, and singling out certain propositions as axioms and deriving all other propositions of the theory by deduction. These notions of definition and deduction are not without ambiguity. It is a mark of an informal axiomatic theory that a general background is used in developing it that is not itself axiomatized in the theory itself. In modern mathematics this background can include logic, arithmetic, and even some analysis and set theory. It would seem desirable to restrict this background to pure logic, since it should contain the most general rules of definition and deduction which should be applicable to all sciences. Everything else used in developing the theory would have to be axiomatized. Although Euclid may already have had such a procedure in mind, one could probably not have achieved it for any serious mathematical theory until an exact characterization of the logical inferences used in mathematics was available: that is, until the time of Frege. Increasing demands for exactness of axiomatization and for elimination of assumptions not explicitly given as axioms leads to the questioning even of logic as unaxiomatized 'background'. Even before this point is reached, the validity of the deductions in the theory comes to depend less and less on the intended meaning of the primitives: since whatever is assumed about what the theory is about is to be explicitly stated in axioms,

Adverbs and Events

Abstract: There are two basic approaches to the analysis of adverbial constructions in formalized representations of English. One is to follow Richard Montague1 and treat them as sentential operators of the same syntactical category as not.2 The other is to follow Donald Davidson3 and represent them in the predicate calculus with the aid of an extra argument place in the verb to be modified. Montague’s approach requires an intensional language and so there seems no hope of fitting his analysis into Davidson’s programme. It is, however, possible to incorporate Davidson’s analysis into an intensional language. In this paper I indicate why this may be desirable and then shew how it can be done in a way which satisfies the rather strict conditions imposed in [12] on the relation between ordinary English and the representing formal language.

A point of reference

Abstract: 83. It should now be apparent that the familiar problems of reference and modality can be satisfactorily resolved without either abandoning substitutivity of identity in modal contexts or invoking an intensional ontology. It might be argued, however, that the suggested resolution avoids invoking an intensional ontology only because the modal predicates, e.g. Nec and Believes, are left unanalysed. This may well be true but it should be appreciated that the analysis of modal predicates is an issue which is independent of both the problem of reference in modal contexts and the problem of the logical structure of propositions containing such contexts. These problems can be settled, as we have seen, without also settling how the modal predicates are to be analysed. Hence, if an intensional ontology is in the end required, it is required to analyse the modal predicates, not to solve the problems of reference and logical structure. This, we suggest, is an interesting and perhaps unexpected result.

Towards a Revised Probabilistic Basis for Quantum Mechanics

Abstract: Quantum mechanics (QM) supplies quantitative probabilities for the occurrences of physically significant events. Historically the probabilistic interpretation of the Schrodinger wave function arose almost as an afterthought. When Schrodinger proposed his equation for the wave function Ψ he had an electromagnetic analogy in mind (Jammer, 1966). When Born (1926) suggested that Ψ be given a probabilistic interpretation he only related probability to |Ψ|2 in a remark added in proof. The curious origins of the probability interpretation notwithstanding, Born’s suggestion quickly took virtually unchallenged hold throughout physics. The famous challenges by Einstein were not to a probabilistic interpretation for Ψ but rather to the completeness of the description of physical reality offered by QM (Einstein et al., 1935).