Remarks on the Modal Logic of Henry Bradford Smith

H. B. Smith, Professor of Philosophy at the influential Pennsylvania School was (roughly) a contemporary of C. I. Lewis who was similarly interested in a proper account of implication. His research also led him into the study of modal logic but in a different direction than Lewis was led. His account of modal logic does not lend itself as readily as Lewis' to the received possible worlds semantics, so that the Smith approach was a casualty rather than a beneficiary of the renewed interest in modality. In this essay we present some of the main points of the Smith approach, in a new guise.     

Beyond verisimilitude: A linguistically invariant basis for scientific progress

This paper proposes a solution to David Miller's Minnesotan-Arizonan demonstration of the language dependence of truthlikeness (Miller 1974), along with Miller's first-order demonstration of the same (Miller 1978). It is assumed, with Peter Urbach, that the implication of these demonstrations is that the very notion of truthlikeness is intrinsically language dependent and thus non-objective. As such, truthlikeness cannot supply a basis for an objective account of scientific progress. I argue that, while Miller is correct in arguing that the number of true atomic sentences of a false theory is language dependent, the number of known sentences (under certain straightforward assumptions) is conserved by translation; degree of knowledge, unlike truthlikeness, is thus a linguistically invariant notion. It is concluded that the objectivity of scientific progress must be grounded on the fact (noted in Cohen 1980) that knowledge, not mere truth, is the aim of science.For criticism and comments I am indebted to Noretta Koertge, David Miller, and an anonymous Synthese referee.     

Three views of demonstrative reference

Three views of demonstrative reference are examined: contextual, intentional, and quasi-intentional. According to the first, such reference is determined entirely by certain publicly accessible features of the context. According to the second, speaker intentions are criterial in demonstrative reference. And according to the third, both contextual features and intentions come into play in the determination of demonstrative reference. The first two views (both of which enjoy current popularity) are rejected as implausible; the third (originally proposed by Kaplan in Dthat) is argued to be highly plausible.     

Utility theory with inexact preferences and degrees of preference

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) are included.     

Mathematical quantum theory I: Random ultrafilters as hidden variables

The basic purpose of this essay, the first of an intended pair, is to interpret standard von Neumann quantum theory in a framework of iterated measure algebraic truth for mathematical (and thus mathematical-physical) assertions — a framework, that is, in which the truth-values for such assertions are elements of iterated boolean measure-algebras (cf. Sections 2.2.9, 5.2.1–5.2.6 and 5.3 below).The essay itself employs constructions of Takeuti's boolean-valued analysis (whose origins lay in work of Scott, Solovay, Krauss and others) to provide a metamathematical interpretation of ideas sometimes considered disparate, heuristic, or simply ill-defined: the collapse of the wave function, for example; Everett's many worlds'-construal of quantum measurement; and a natural product space of contextual (nonlocal) hidden variables.More precisely, these constructions permit us to write down a category-theoretically natural correlation between ideal outcomes of quantum measurements u of a universal wave function, and possible worlds of an Everett-Wheeler-like many-worlds-theory.The universal wave function, first, is simply a pure state of the Hilbert space (L ₂([0, 1]) ^M in a model M an appropriate mathematical-physical theory T, where T includes enough set-theory to derive all the analysis needed for von Neumann-algebraic formulations of quantum theory.The worlds of this framework can then be given a genuine model-theoretic construal: they are random models M(u) determined by M-random elements u of the unit interval [0, 1], where M is again a fixed model of T.Each choice of a fixed basis for a Hilbert space H in a model of M of T then assigns ideal spectral values for observables A on H (random ultrafilters on the range of A regarded as a projection-valued measure) to such M-random reals u. If is the universal Lebesgue measure-algebra on [0, 1], these assignments are interrelated by the spectral functional calculus with value 1 in the boolean extension (V( )) ^M , and therefore in each M(u).Finally, each such M-random u also generates a corresponding extension M(u) of M, in which ideal outcomes of measurements of all observables A in states are determined by the assignments just mentioned from the random spectral values u for the universal position-observable on L ₂([0, 1]) in M.At the suggestion of the essay's referee, I plan to draw on its ideas in the projected sequel to examine more recent modal and decoherence-interpretations of quantum theory, as well as Schrödinger's traditional construal of time-evolution. A preliminary account of the latter — an obvious prerequisite for any serious many-worlds-theory, given that Everett's original intention was to integrate time-evolution and wave-function collapse — is sketched briefly in Section 5.3. The basic idea is to apply results from the theory of iterated measure-algebras to reinterpret time-ordered processes of measurements (determined, for example, by a given Hamiltonian observable H in M) as individual measurements in somewhat more complexly defined extensions M(u) of M.In plainer English: if one takes a little care to distinguish boolean- from measure-algebraic tensor-products of the universal measure-algebra L, one can reinterpret formal time-evolution so that it becomes internal to the universal random models M(u).     

Suppositions in argumentation

The atheist who begins to argue his case by saying, Suppose there is an omniscient Being of the sort in which Christians believe ... is employing a very familiar move in argumentation. However, most books on argumentation theory ignore suppositions completely. Searle omits suppositions entirely from his taxonomy of speech acts and this appears to lead to a similar omission in Speech Acts in Argumentative Discussions by van Eemeren and Grootendorst.This paper argues that suppositional argument is elegant, powerful and extremely common, that the correct way to understand it is based on Gottlob Frege's distinction between asserted and unasserted propositions and hence that suppositions are neither assertions nor (and this is more important) assertives. The paper discusses the connections between suppositions and conditionals; it argues that argumentation theory which ignores suppositions is systematically misleading; and it concludes by indicating some possible developments in argumentation theory.Revised version of a paper delivered at the University of Amsterdam, April 3, 1987.     

Is it always fallacious to derive values from facts?

Since the time of David Hume, many philosophers have held that there is a logical Is/Ought gap. According to the doctrine of the Is/Ought gap, there are no valid (i.e., non-fallacious) arguments from purely factual premises about whatis the case to moral or normative conclusions about whatought to be. Occasionally, this doctrine has been challenged, but frequently it has been accepted without argumentation. Charles Pigden has recently argued for a logical Is/Ought gap on the grounds of the conservativeness of logic. I offer a counter-example which shows that Pigden's argument is unsound and that there need be no logical gap between Is-premises and an Ought-conclusion. My counter-example is an argument which is logically valid, has only Is-premises and an Ought-conclusion, and does not purport to violate the conservativeness of logic. Moreover, my argument does not rely, as other alleged counter-examples do, on controversial assumptions from Aristotelian biology about natures or ends, or about institutions such as promise-making.     

What was Leibniz's problem about relations?

The main purpose of the article is to get clear what Leibniz's concerns about relations were. His:

Father is true of David. Son is true of Solomon. But Being a father of is not true of any individual.

Leibniz, like modern nominalist Nelson Goodman, could not allow the ordered pair . To establish this I must argue against Hidé Ishiguro's claim that Leibniz should have straightforwardly constructed a logic of relations, and Jaakko Hintikka's claim that Leibniz could have allowed the use of relational predicates in such forms as (Ex) Rax and (Ey) Ryb. I must also argue that what they say about the windowlessness doctrine (especially the as if formulation) is beside the point.I wish to thank Susan Haack for her help in turning a draft into the present paper.     

Once More into the Breach of Self-Ownership: Reply to Narveson and Brenkert

In reply to Narveson, I distinguish his no-proviso argument from his liberty argument, and I show that both fail. I also argue that interference lacks the strategic status he assigns to it, because it cannot be appropriately distinguished, conceptually and morally, from prevention; that natural resources do enjoy the importance he denies they have; that laissez-faire economies lack the superiority he attributes to them; that ownership can indeed be a reflexive relation; that anti-paternalism does not entail libertarianism; and that he misrepresents the doctrines of a number of philosophers, including John Locke, Ronald Dworkin, and myself. In reply to Brenkert, I show that he seriously misconstrues my view of the nature of freedom, and of its relationship to self-ownership. I then refute his criticisms of my treatment of the contrasts between self-ownership, on the one hand, and autonomy and non-slavery, on the other. I also show that his attempt to exorcize the demon of self-ownership is multiply flawed.     

The history of philosophy in contemporary philosophy: The view from Germany

Conclusion I have frequently mentioned objective problems and topics in the preceding sections. But what exactly is the force of objective here? As my remarks should have made clear I have been using objective to contrast with purely historical. A purely historical approach never gets beyond reproduction, commentary, and interpretation. I call an approach objective when it involves a philosopher who advances his own theses and claims.This minimal understanding of objectivity (in the context of my remarks in this paper) by no means implies that there are problems and topics, systems of concepts, methods, and similar factors that are eternal, completely independent of the contingencies of history (of philosophy, of the sciences), that are not relative to a language, to a logic, to a model, etc. Indeed whether there are problems, etc., in just this absolute, atemporal sense is itself a question for systematic philosophy. It seems clear that the formulation of a problem can only take place against a cognitive background of some sort and within some conceptual scheme.³⁴ Such an assumption is made by most if not all analytic philosophers. But the fact that a philosophical tradition recognizes conceptual schemes does not make it a purely historical, non-objective philosophy, in the sense already introduced and described. A philosopher who explicitly accepts a certain conceptual scheme proceeds in an entirely objective and systematic (and not purely historical) manner when, within this framework, he formulates his own theses.This paper is the text of a talk. the title is due to Barry Smith.     

Kenneth Strike on Liberalism,Citizenship and the Private Interest in Schooling

After indicating a number of points of agreement with the argument 0eveloped by Kenneth Strike in his article Liberalism, Citizenship and the Private Interest in Schooling, this article identifies and explores a number of queries and criticisms which arise in relation to that argument. These queries and criticisms relate especially to the nature and extent of the expansiveness involved in Strike's conception of public or common educational influence, and to the implications and justification of the claim that private educational interests enjoy a greater salience and recognition on Strike's view of public or common educational influence than on some alternative views.     

An abstract setting for Henkin proofs

A general result is proved about the existence of maximally consistent theories satisfying prescribed closure conditions. The principle is then used to give streamlined proofs of completeness and omitting-types theorems, in which inductive Henkin-style constructions are replaced by a demonstration that a certain theory respects a certain class of inference rules.     

Can Parts of Space Move? On Paragraph Six of Newton’s Scholium

Paragraph 6 of Newtons Scholium argues that the parts of space cannot move. A premise of the argument – that parts have individuality only through an order of position – has drawn distinguished modern support yet little agreement among interpretations of the paragraph. I argue that the paragraph offers an a priori, metaphysical argument for absolute motion, an argument which is invalid. That order of position is powerless to distinguish one part of Euclidean space from any other has gone virtually unremarked. It remains uncertain what the import of the paragraph is but it is not close to apparently similar arguments of Leibniz.     

Education for European citizenship: a philosophical critique

The European dimension of civic education can allow educators to promote many positive elements of internationalism. These include the promotion of general respect for the rule of law and for human rights and of commitment to democratic and egalitarian principles. This paper accepts these aspects of the European dimension in civic education. What it objects to is the attempt, through education, to change the focus of the political allegiance of young people by promoting the notion of European citizenship. Support for the valuable elements in the European dimension of civic education does not entail support for a contrived notion of citizenship for inhabitants of nations who have long civic traditions of their own. In the first section of the paper, the project of appropriating education to engineer political loyalty to the New Europe is criticized. The second part of the article draws attention to certain unacknowledged difficulties in conceptualizing the shared identity which would be required in order to animate and sustain a sense of European citizenship.     

A Translation of Intuitionistic Predicate Logic into Basic Predicate Logic

Basic Predicate Logic, BQC, is a proper subsystem of Intuitionistic Predicate Logic, IQC. For every formula in the language {, , , , , , }, we associate two sequences of formulas 0,1,... and 0,1,... in the same language. We prove that for every sequent , there are natural numbers m, n, such that IQC , iff BQC n m. Some applications of this translation are mentioned.     

Dichotic sequence discrimination: The effect of continued practice

Summary Dichotic sequence discrimination was studied by means of a three-alternative forced-choice method. Two of the alternatives (same) consisted of a single pair of dichotic clicks with the stimulus at one ear preceding the stimulus at the other ear by a given temporal separation (e.g., R-t-L). One of the alternatives consisted of a single pair of clicks with the opposite sequence (e.g., L-t-R). The subjects' task was to discriminate between the different and the same dichotic pairs. The results indicate that discrimination is a nonmonotonic function of t, i.e., V- or U-shaped, with high levels at both short and long temporal separations (t=2 and 4 ms and t=64 and 96 ms) and with lower levels of discrimination for intermediate ts. A second experiment was performed to study the effect of continued practice by subjects trained in dichotic sequence discrimination for ts 4 and 64 ms (high discrimination levels) and for t=16 ms (low discrimination level). There was no systematic trend towards improvement over 8 blocks of 50 trials for each t. Discrimination levels of these ts did not differ between Experiments 1 and 2.Dr. Babkoff is spending the 1979–1981 academic year at the Walter Reed Army Institute of Research, Department of Military Medical Psychophysiology, Forest Glen Annex, Building 189, Washington, D.C. 20012, USAThe experiments were conducted at the Bar-Ilan University, Ramat-Gan, Israel. The authors would like to thank the Bar-Ilan Research Committee for making funds available to conduct the experimentsThis material has been reviewed by the Walter Reed Army Institute of Research, and there is no objection to its presentation and/or publication. The opinions or assertions contained herein are the private views of the authors and are not to be construed as official or as reflecting the views of the Department of the Army or the Department of Defense     

Epistemologische betrachtungen zu [S4, S5]

Zusammenfassung Die zahlreichen modallogischen Systeme zwischen den Standardkalkülen S4 und S5 werden vom epistemologischen Standpunkt aus untersucht, indem Notwendigkeit wahlweise als Wissen bzw. als Überzeugt-sein gedeutet wird. Dabei stellt sich heraus, daß — unter gewissen andernorts begründeten Voraussetzungen über epistemische Logik-S4.4 als Logik der wahren Überzeugungen aufgefaßt werden kann, während die Systeme S4.3.2 und S4.2 als Logiken für solche Leute erscheinen, die das Schema Wissen = wahre Überzeugung nur eingeschränkt für ganz spezielle rein doxastische bzw. rein epistemische Sätze akzeptieren. S4.2 ist dabei allem Anschein nach die Logik des Wissens.

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The numerous modal systems between S4 and S5 are investigated from an epistemological point of view by interpreting necessity either as knowledge or as (strong) belief. It is shown that-granted some assumptions about epistemic logic for which the author has argued elsewhere-the system S4.4 may be interpreted as the logic of true belief, while S4.3.2 and S4.2 may be taken to represent epistemic logic systems for individuals who accept the scheme knowledge = true belief only for certain special instances. There is strong evidence in favor of the assumption that S4.2 is the logic of knowledge.

     

Grading the ‘cultural literacy’ project

The essay examines the argument advanced by E.D. Hirsch, Jr., for instituting cultural literacy as a fundamental priority of schools. A number of confusions and equivocations in Hirsch's reasoning are identified, and the propensity of his project to indoctrinate is exposed. Among the features of Hirsch's argument shown to be troubling are his shifting construal of language, his inconsistency about the requirements of cultural literacy, and his uncritical relation to traditional images of the American past and present. The upshot is to raise the question why Hirsch's project has elicited wide support and praise.     

Incompatible empirically equivalent theories: A structural explication

The thesis of the empirical underdetermination of theories (U-thesis) maintains that there are incompatible theories which are empirically equivalent. Whether this is an interesting thesis depends on how the term incompatible is understood. In this paper a structural explication is proposed. More precisely, the U-thesis is studied in the framework of the model theoretic or emantic approach according to which theories are not to be taken as linguistic entities, but rather as families of mathematical structures. Theories of similarity structures are studied as a paradigmatic case. The structural approach further reveals that the U-thesis is related to problems of uniqueness in the representational theory of measurement, questions of geometric conventionalism, and problems of structural underdetermination in mathematics.I'd like to thank three anonymous referees for valuable comments on earlier versions of this paper and Thomas E. Uebel for linguistic advice.     

The relationship between perceived surface-lightness and perceived illumination

Summary An attempt was made to specify the relationship between perceived surface lightness and perceived illumination under the stimulus conditions where different combinations of albedo and illuminance gave 10 approximately equal-luminance levels of a test field (TF) on three different (black-, gray- and white-appearing) backgrounds. Two types of category judgments for TF-lightness and overall illumination were made on the total of 94 TFs by 5 Ss. The results indicated that under the condition where achromatic surface colors appear, the perceptual scission which produces two different perceptual dimensions (lightness and perceived illumination) from one sort of stimulation (luminance) was clearly observed. The relation between the two judgments was consistent with the lightness-illumination invariance hypothesis: As lightness judgments (A) changed from darker to lighter, illumination judgments (I) shifted form brighter to dimmer, the sum of A and I being kept nearly invariant for a given luminance of the TF; the psychological relationship between lightness and illumination, A+I, changed as a linear function of the photometric combination of albedo and illuminance, log A+log I. It was also found that the albedo of the background was an important factor determining the extent of perceptual scission between lightness and illumination.