Cognitive Significance in Science

The sheer multitude of criteria of empirical significance has been taken as evidence that the pre-analytic notion being explicated is too vague to be useful. I show instead that a significant number of these criteria—by Ayer, Popper, Przełęcki, Suppes, and David Lewis, among others—not only form a coherent whole, but also connect directly to the theory of definition, the notion of empirical content as explicated by Ramsey sentences, and the theory of measurement; two criteria by Carnap and Sober are trivial, (...) but can be saved and connected to the other criteria by slight modifications. A corollary is that the ordinary language defense of Lewis, the conceptual arguments by Ayer and Popper, the theoretical considerations by Przełęcki, and the practical considerations by Suppes all apply to the same criterion or closely related criteria. Furthermore, the equivalence of some criteria allows for their individual justifications to be taken cumulatively and, together with the entailment relations between nonequivalent criteria, suggest criteria for general auxiliary assumptions, comparative criteria, and more liberal conceptions of observation. (shrink)

Science and mathematics continually change in their tools, methods, and concepts. Many of these changes are not just modifications but progress---steps to be admired. But what constitutes progress? This dissertation addresses one central source of intellectual advancement in both disciplines: reformulating a problem-solving plan into a new, logically compatible one. For short, I call these cases of compatible problem-solving plans "reformulations." Two aspects of reformulations are puzzling. First, reformulating is often unnecessary. Given that we could already solve a problem using (...) an older formulation, what do we gain by reformulating? Second, some reformulations are genuinely trivial or insignificant. Merely replacing one symbol with another does not lead to intellectual progress. What distinguishes significant reformulations from trivial ones? According to what I call "conceptualism" (or "conceptual empiricism"), reformulations are intellectually significant when they provide a different plan for solving problems. Significant reformulations provide inferentially different routes to the same solution. In contrast, trivial reformulations provide exactly the same problem-solving plans, and hence they do not change our understanding. This answers the second question about what distinguishes trivial from significant reformulations. However, the first question remains: what makes a new way of solving an old problem valuable? Here, a bevy of practical considerations come to mind: one formulation might be faster, less complicated, or use more familiar concepts. According to "instrumentalism," these practical benefits are all there is to reformulating. Some reformulations are simply more instrumentally valuable for meeting the aims of science than others. At another extreme, "fundamentalism" contends that a reformulation is valuable when it provides a more fundamental description of reality. According to this view, some reformulations directly contribute to the metaphysical aim of carving reality at its joints. Conceptualism develops a middle ground between instrumentalism and fundamentalism, preserving their benefits without their costs. I argue that the epistemic value of significant reformulations does not reduce to either practical or metaphysical value. Reformulations are valuable because they are a constitutive part of problem-solving. Both science and mathematics aim at solving all possible problems within their respective domains. Meeting this aim requires being able to plan for any possible problem-solving context, and this requires reformulating. By reformulating, we clarify what we need to know to solve problems. Still, one might wonder whether the value of reformulations requires underlying differences in explanatory power. According to "explanationism," a reformulation is valuable only when it provides a better explanation. Explanationism stands as a rival middle ground position to my own. However, it faces numerous counterexamples. In many cases, two reformulations provide the same explanation while nonetheless providing different ways of understanding a phenomenon. Hence, reformulating can be valuable even when neither formulation is more explanatory. Methodologically, I draw on a variety of case studies to support my account of reformulation. These range from classical mechanics to quantum chemistry, along with examples from mathematics. Symmetry arguments provide a paradigmatic example: the mathematics of symmetry groups radically recasts quantum mechanics and quantum chemistry. Nevertheless, elementary approaches exist that eschew this additional mathematical apparatus, solving problems in a more tedious but less mathematically-demanding manner. Further examples include reformulations of quantum field theory, Arabic vs. Roman numerals, and Fermat's little theorem in number theory. In each case, my account identifies how reformulations change and improve our understanding of science and mathematics. (shrink)

W. V. Quine calls some general methods of science maxims: general defeasible principles that call on us to approximate, maximize, or minimize a state and that are interpreted and weighed in context-sensitive ways. On my reading, his empiricism asks us to maximize accepting overall theories empirically equivalent to ours but to minimize accepting sentences that both do not affect the empirical content of our overall theory and do not simplify our overall theory. His naturalism asks us to maximize accepting sentences (...) that are solely supported by standards that support our best current scientific theory. Drawing on the Quine archive at Houghton Library at Harvard, I support and apply these interpretations by investigating his rapidly evolving later work on empirical content and empirical equivalence, including some of his views on translation in this later work and his vacillation between what he calls the ecumenical and sectarian attitudes. (shrink)

I offer an interpretation of Carnap and Quine’s views on cognitive significance and insignificance. The basic idea behind their views is as follows: to judge an expression is insignificant is to recommend it not be used in or explicated into languages used to express truth-valued judgments in inquiry; to judge an expression is significant is to recommend it be used in or explicated into such languages. These judgments are pragmatic judgments, made in light of purposes for language use in inquiry. (...) For Carnap at least, these pragmatic judgments are non-cognitive. This basic idea is only a roughly correct statement of their views. This is because the details of the scientific languages they recommend for inquiry are necessary to understand their views and the way they understand their own views. Even so, I offer two reasons to suggest that this basic idea is worthy of our consideration today. First, it provides a conception of significance that captures the natural thought that epistemological concerns can lead us to consider expressions to be insignificant without requiring an objectionable form of verificationism. Second, if we appeal also to Carnap and Quine’s pluralistic attitude toward explication, we can make a pragmatic judgment that an expression is insignificant while judging it to be significant on a distinct explication of significance fit for describing and explaining natural language. (shrink)

Carnap suggests that philosophy can be construed as being engaged solely in conceptual engineering. I argue that since many results of the sciences can be construed as stemming from conceptual engineering as well, Carnap’s account of philosophy can be methodologically naturalistic. This is also how he conceived of his account. That the sciences can be construed as relying heavily on conceptual engineering is supported by empirical investigations into scientific methodology, but also by a number of conceptual considerations. I present a (...) new conceptual consideration that generalizes Carnap’s conditions of adequacy for analytic–synthetic distinctions and thus widens the realm in which conceptual engineering can be used to choose analytic sentences. I apply these generalized conditions of adequacy to a recent analysis of scientific theories and defend the relevance of the analytic–synthetic distinction against criticisms by Quine, Demopoulos, and Papineau. (shrink)

Criteria of empirical significance are supposed to state conditions under which reference to an unobservable object or property is “empirically meaningful”. The intended kind of empirical meaningfulness should be necessary for admissibility into the selective contexts of scientific inquiry. I defend Justus’s recent argument that the reasons generally given for rejecting the project of defining a significance criterion are unpersuasive. However, as I show, this project remains wedded to an overly narrow conception of its subject matter. Even the most cutting (...) edge significance criteria identify empirical significance with predictive power, and thereby rule out vocabulary with legitimate scientific functions. In a nutshell, the problem is that there are terms that reduce the computational burden of extracting predictions from theory, and that may therefore be scientifically useful, but that do not produce any additional predictions, and so are ruled scientifically inadmissibility by existing significance criteria. I spell out this objection by specifying terms of this kind that are ruled inadmissible by Creath’s and Schurz’s criteria. Having objected in this way to extant criteria, and to the equation of empirical significance with predictive power in general, I discuss an approach to defining empirical significance that is capable of avoiding my objection and, more ambitiously, that may break the cycle of “punctures and patches” that has plagued the project from the beginning: I gloss Goldfarb and Ricketts’s idea of “case-by-case” delineations of empirically significant terms as the provision of special rather than general explications of the informal concept of empirical significance. (shrink)

Carnap’s search for a criterion of empirical significance is usually considered a failure. I argue that the results from two out of his three different approaches are at the very least problematic, but that one approach led to success. Carnap’s criterion of translatability into logical syntax is too vague to allow for definite results. His criteria for terms—introducibility by chains of reduction sentences and his criterion from “The Methodological Character of Theoretical Concepts”—are almost trivial and have no clear relation to (...) the empirical significance of sentences. However, his criteria for sentences—translatability, verifiability, falsifiability, confirmability—are usable, and under the assumptions needed for the Carnap sentence approach, verifiability, falsifiability, and translatability become equivalent. As a result of the Carnap sentence approach, metaphysics is rendered analytic. (shrink)

Carnap’s analysis of the language of science had presupposed too close a connection between the semantics and testability. The core problem of the logical empiricist tradition was to show how to provide the interpretation of theoretical terms and hence the explanation of their application to observable entities by means of observation terms. It is argued that the utilization of a much more expressive semantic theory which identifies meanings with hyperintensional entities leads to a clarification of the competencies of semantics and (...) methodology. It is claimed that the observability or unobservability of term’s referents does not determine the meaning of the term. Carnap’s reduction sentences are therefore conceived only as methodological devices for the determination of unobservables via the theory-presupposed observable aspects. (shrink)

This article considers the development of Philipp Frank’s opposition to metaphysics in the light of the contention that there also was a long-standing pragmatic strand to the theorizing about science in the Vienna Circle. It is argued that the later Frank did not only distinguish metaphysical statements from those deemed simply cognitively meaningless by a substantive criterion but that in order to identify the latter he also sought to employ a practical rather than a formal criterion with which he and (...) Neurath had long been acquainted. (shrink)

The first theory of confirmation that Carnap developed in detail is to be found in "Testability and Meaning". In this paper, he addressed the issue of a definition of empiricism, several years after abandoning the quest for a unique and universal logical framework supposed to be the basis of a clear distinction between the meaningful sentences of science and the pseudo-sentences of metaphysics. The principle of tolerance (according to which everyone is free to build up his own form of language (...) as he wishes) had been adopted near the end of 1932, at a time when it was already obvious to Carnap that a strictly verificationist criterion of meaning was inadequate. He therefore considered a variety of empiricisms and a variety of choices for the language of science. As Carnap put it, "there are many different possibilities in framing an empiricist language" and, correspondingly, several degrees of liberalization of the criterion of meaning. It was in this context that Carnap provided both a logical (syntactical) and an empirical analysis of confirmation (and of testing), before distinguishing requirements of different strengths which served the purpose of defining several versions of empiricism. (shrink)

Recent scholarship (by mainly Michael Friedman, but also by Thomas Uebel) on the philosophy of Rudolf Carnap covering the period from the publication of Carnap’s’ 1928 book Der Logische Aufbau der Welt through to the mid to late 1930’s has tended to view Carnap as espousing a form of conventionalism (epitomized by his adoption of the principle of tolerance) and not a form of empirical foundationalism. On this view, it follows that Carnap’s 1934 The Logical Syntax of Language is the (...) pinnacle of his work during this era, this book having developed in its most complete form the conventionalist approach to dissolving the pseudoproblems that often attend philosophical investigation. My task in this paper, in opposition to this trend, is to resuscitate the empiricist interpretation of Carnap’s work during this time period. The crux of my argument is that Carnap’s 1934 book, by eschewing for the most part the empiricism he espouses in the Aufbau and in his 1932 The Unity of Science, is led to a form of conventionalism that faces the serious hazard of collapsing into epistemological relativism. My speculation is that Carnap came to recognize this deficiency in his 1934 book, and in subsequent work (“Testability and Meaning”, published in 1936/37) felt the need to re-instate his empiricist agenda. This subsequent work provides a much improved empiricist epistemology from Carnap’s previous efforts and, ashistory informs us, sets the standard for future research in the theory of confirmation. (shrink)

I argue that Wittgenstein’s short-lived verificationism (c.1929-30) differed from that of his contacts in the Vienna Circle in not being a reductionist view. It lay the groundwork for his later views that the meaning of a word is determined by its use and that certain "propositions of the form of empirical propositions" (On Certainty, §§96, 401, 402) act as "norm[s] of description" (On Certainty,§§167, 321). He gave it up once he realized that it contradicted his rejection of logical atomism, and (...) that he ever held such a view at all says something about his respect for the leader of the Vienna Circle, Moritz Schlick. (shrink)

The connection between scientific knowledge and our empirical access to realityis not well explained within the structuralist approach to scientific theories. I arguethat this is due to the use of a semantics not rich enough from the philosophical pointof view. My proposal is to employ Sellars–Brandom's inferential semantics to understand how can scientific terms have empirical content, and Hintikka's game-theoretical semantics to analyse how can theories be empirically tested. The main conclusions are that scientific concepts gain their meaning through `basic (...) theories' grounded on `common sense, and that scientific method usually allows the pragmatic verification and falsification of scientific theories. (shrink)

The paper gives an overview of key themes of twentieth century philosophical treatment of the language of science, with special emphasis on the meaning variance of scientific terms and the comparison of alternative theories. These themes are dealt with via discussion of the topics of: (a) the logical positivist principle of verifiability and the problem of the meaning of theoretical terms, (b) the postpositivist thesis of semantic incommensurability, and (c) the scientific realist response to incommensurability based on the causal theory (...) of reference. (shrink)

That some propositions are testable, while others are not, was a fundamental idea in the philosophical program known as logical empiricism. That program is now widely thought to be defunct. Quine’s (1953) “Two Dogmas of Empiricism” and Hempel’s (1950) “Problems and Changes in the Empiricist Criterion of Meaning” are among its most notable epitaphs. Yet, as we know from Mark Twain’s comment on an obituary that he once had the pleasure of reading about himself, the report of a death can (...) be an exaggeration. The research program that began in Vienna and Berlin continues, even though many of the specific formulations that came out of those circles are flawed and need to be replaced. (shrink)

In this paper I will investigate the possibility of completing a Positivist style account of demarcation. One reason for pursuing this project is that standard criticisms of Positivism do not have the bite against the demarcation project that they are often assumed to have. To argue this will be the burden of the first part of this paper. The other reason is that new research in logic has provided machinery not available to the Positivists; machinery that shows promise for solving (...) some of the technical problems faced by Positivists' account of demarcation. To argue this will be the burden of the second part of this paper. (shrink)

In chapter VI of Language, Truth, and Logic, A.J. Ayer argues that ethical statements are not literally significant. Unlike metaphysical statements, however, ethical statements are not nonsensical: even though they are not literally significant, Ayer thinks that they possess some other sort of significance. This raises the question: by what principle or criterion can we distinguish, among the class of statements that are not literally significant, between those which are genuinely meaningless and those which possess some other, non-literal form of (...) significance. I suggest that Ayer needs a generalised version of the verification principle in order to answer this question. However, when we formulate the generalised version, it turns out that ethical statements do not satisfy it, so that the emotivist is committed to viewing ethics, like metaphysics, as meaningless verbiage. (shrink)

En este trabajo sc presenta un marco general en el que desarrollar una “ontoepistemo-semántica” para las teodas científicas y sus terminos característicos. En primer lugar, se defiende la esencialidad de los aspectos ontologicos y epistemológicos para la semantica y se hacen explícitos los principios generales que constituyen dicho marco. A continuación, se aplican estos principios al análisis ontoepistemosemántico de cada uno de los tres tipos principales de términos científicos: términos relacionales y funcionales con contenido empírico, términos matemáticos puros y términos (...) para los dominios ontológicos básicos. In this paper I offer a general framework for all “ontoepistemosemantics” of scientific theories and scientific terms. First, I argue for the essential dependence of semantics on ontological and epistemological aspects and I make explicit the general principIes that make up this frame. Then, I apply these principles to the ontoepistemosmantical analysis of the three main kinds of scientific terms: relational and functional term with empirical content, purely mathematical terms and terms for basic ontological domains. (shrink)

"Testability and Meaning" is one of Carnap's best-known works. It has been usually seen as one of the main sources of the received view of the philosophy of science, and it is normally read in the hght of the tradition it originated. Nevertheless, this reading detaches the text from the philosophical project to which it belongs. This paper aims to situate Camap's article in its proper philosophical place, which is found in the programme initiated in the Logische Syntax, a programme (...) which essentially remained alive throughout the rest of Camap's career. The paper shows how this view opens up a natural way of understanding Carnap's important article in a different light, more interesting and coherent. (shrink)

The purpose of this paper is to try to set the record a little straighter about the idea of a verifiability criterion.

Im Rahmen der deduktiven Logik genügt schon ein einziger negativer Fall, um eine Allaussage als falsch zu erweisen; trotzdem bleibt bei dieser "schwachen Falsifikation" der Wahrheitswert der übrigen Fälle völlig offen. Die methodologisch relevante "starke Falsifikation", die besagt, daß auch alle künftigen Fälle negative Wahrheitswerte haben, setzt dagegen immer einen erweiternden Induktionsschluß voraus. Deshalb ist die These, daß eine wissenschaftliche Theorie ohne Bezugnahme auf das Induktionsprinzip bereits durch ein einziges Gegenbeispiel falsifiziert werden könne, nur dann haltbar, wenn man bereit ist, (...) auf jede wissenschaftliche Prognose zu verzichten. (shrink)

CONTENTS: 1 Introductory Remark; 2 Formalism of Empirical Theories; 3 Semantics of Formalized Languages; 4 Interpretation of Empirical Theories; 5 Interpretation of Observational Terms; 6 Interpretation of Theoretical Terms; 7 Main Types of Meaning Postulates for Theoretical Terms; 8 Some Other Kinds of Meaning Postulates for Theoretical Terms; 9 Main Types of Statements in an Empirical Theory; 10 Towards a More Realistic Account; 11 Concluding Remarks; 12 Bibliographical Note.

The title of this monograph needs explanation. It certainly sounds too promising. A more adequate, though more cumbersome one, would read: the logical syntax and semantics of the language of empirical theories. The treatment of this subject in the present monograph needs further qualifications. It focusses on what is characteristic of empirical theories as opposed to others, viz. mathematical ones. Now the difference between these two kinds of theories lies evidently, not in their syntax, but semantics. This is why our (...) main concern here is going to be with the problem of interpretation of empirical theories. The fundamental problem here concerns the distinction between the empirical and the a priori elements inherent in any such theory. Accordingly, our final task must include an explication of concepts such as: meaning postulate, analytic, synthetic, empirically meaningful sentence, and others related to them. (shrink)

The traditional role which correspondence rules, coordinating definitions, or semantical rules, have in a logical analysis of a scientific theory is questioned by providing an alternative analysis. The alternative account suggests that scientific theories are "meaningful" prior to the establishment of correspondence rules, and that correspondence rules are introduced to permit explanation and testing in the "observational" sector. The role of models is briefly assessed in connection with this prior or "antecedent theoretical meaning," and a causal sequence analysis of a (...) class of correspondence rules is presented which makes explicit the interdependence of scientific theories. (shrink)

In 1954 Hempel wrote “Once the idea of a partial specification of meaning is granted, it appears unnecessarily restrictive, however, to limit the sentences effecting such partial interpretation to reduction sentences in Carnap's sense. … Generally, then, a set of one or more theoretical terms, t1, t2 ⃛, tn, might be introduced by any set M of sentences such that M contains no extralogical terms other than t1, t2 ⃛, tn, and observation terms, M is logically consistent, and M is (...) not equivalent to a truth of formal logic. The last two of these conditions serve merely to exclude trivial extreme cases. A set M of this kind will be referred to briefly as an interpretative system, its elements as interpretative sentences.” This is the last move in a process in which the idea of definition has been widened beyond the explicit or equivalence definition which was the basis of earlier thought on the subject of introducing new words into a language. It would seem that the scheme proposed by Hempel must represent the final move, for it would seem difficult to conceive any more liberal description of a purely direct and verbal scheme. Among the predecessors of Hempel in this liberalising movement I will mention Ramsey and Braithwaite whose views stem ultimately from Campbell, and are based on the idea that the “interpretative system” is essentially a scientific theory, and Carnap who introduced the particular notion of a “reduction sentence”, and who was more directly the source of Hempel's own ideas. (shrink)