Natural deduction rules for English

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

Some notes on the nature of methodological indeterminacy

This paper is an attempt to extend the meaning of the concept of indeterminacy for the human sciences. The authors do this by coining the term methodological indeterminacy and arguing that indeterminacy is better understood when linked to specific methodological techniques. Paradoxically, while specific research techniques demonstrate that the issue of indeterminacy is complex, yielding the possibility of types and degrees, it does not eliminate the problem of translation first raised by Quine. However, the authors go on to argue that, from a research perspective, indeterminacy can and must be approached in such a way that it is possible to reduce cases of it, even though never completely eliminating it in the human sciences.     

Theorem counting

Consider the set of tautologies of the classical propositional calculus containing no connective other than and, or, and not. Consider the subset of this set containing tautologies in exactlyn propositional variables. This paper provides a method for determining the number of equivalence classes of each such subset modulo equivalence in the infinite-valued Lukasiewicz propositional calculus.     

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.     

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.     

Becoming: A modest proposal

In this paper I attempt a new approach to an old technical term: becoming. I show how the theory that becoming is coming-to-be could be supported by a semantic derivation of the nominalization becoming from its verbal counterpart, by investigating the properties of the present progressive constructions in which becoming as a verbal appears. My theory denies that dates, or qualitative change, play an essential role in the analysis of becoming.     

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).     

Some problems concerning the logic of grammatical modifiers

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.     

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.     

From negation to “notion”: Cognitive processes and argumentative strategies

Summary This article deals with the role of negation as a language and cognitive operation. Such a topic is treated here within the framework of the argumentative strategies which consist in making certain cognitive landmarks of the discourse flip over with the intent of imposing the necessity to choose between two types of notions, aiming at the transformation of this choice into an implication. The reference here to the Aristotelian logic of Prior Analytics appears to be more efficient than any other contemporary logic and the author intends to give account of the role of negation as contrary coming into play on an operational and cognitive basis in all the argumentative strategies which oscillate reciprocally from universal to particular.     

The Weight of Context: Headscarves in Holland

This paper explores the potential of a contextual approach to multicultural conflict. It reconstructs two cases that were hotly debated in the Netherlands—Islamic headscarves for police officers and for court officers—and asks whether a contextual approach reaches compromises and thus promotes social stability more easily than a deductive approach. The argument is that a deductive approach accepts standing interpretations of normative principles, whereas a contextual approach reinterprets these principles in the light of the circumstances and that, whether or not it promotes social stability, a contextual approach makes us attend to otherwise neglected perspectives and thus yields greater normative insights.     

Hypnotic time distortion and free-recall learning — an attempted replication

Summary Krauss, Katzell and Krauss (1974) have presented evidence suggesting that hypnosis can be used to facilitate free-recall learning. Specifically, they report that hypnotised individuals, given special time-distortion instructions, can recall as much in three minutes as waking control subjects can in ten minutes. The present study was an attempt to replicate and extend this main finding of Krauss et al. The results of the present study failed to replicate Krauss et al.'s finding; in fact, the hypnotised subjects did rather worse than waking control groups; also no relationship was found between recall scores and depths of hypnosis. Marked discrepancies were noticed between the scores of the waking control groups used in the present study, and those used by Krauss et al. It was concluded that any facilitatory effect of hypnotic time distortion on free-recall learning still awaits a definitive demonstration.     

A notorious affair called exportation

In Quantifiers and Propositional Attitudes, Quine held (a) that the rule of exportation is always admissible, and (b) that there is a significant distinction between a believes-true (Ex)Fx and (Ex) a believes-true F of x. An argument of Hintikka's, also urged by Sleigh, persuaded him that these two intuitions are incompatible; and he consequently repudiated the rule of exportation. Hintikka and Kaplan propose to restrict exportation and quantifying in to favoured contexts — Hintikka to contexts where the believer knows who or what the person or thing in question is; Kaplan to contexts where the believer possesses a vivid name of the person or thing in question. The bulk of this paper is taken up with criticisms of these proposals. Its ultimate purpose, however, is to motivate an alternative approach, which imposes no restrictions on exportation or quantifying in, but repudiates Quine's other intuition: this is the approach taken in my A Logical Form for the Propositional Attitudes.This paper is based on my doctoral dissertation (Rockefeller University, 1977). I wish to thank Susan Haack for her help in turning a draft into the present version.     

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.     

Was Marx an ethical humanist?

Zusammenfassung Während der letzten zehn Jahre wurde viel über den Humanismus des jungen Marx gesprochen. Osteuropäische Marxisten, die bemüht sind, ihren Anti-Stalinismus durch Berufung auf die Autorität von Marx selbst zu untermauern, gebrauchen den Ausdruck Humanismus in einem ungenauen Sinn, etwa gleichbedeutend mit Anthropozentrismus. Aber wenn man sagt, daß Marx Haltung anthropozentrisch sei, so sind damit die Hauptfragen erst gestellt, nicht schon gelöst.Humanismus mag etwa soviel wie Säkularismus bedeuten — der Mensch, nicht Gott, wird als im Mittelpunkt stehend gedacht. Die anthropozentrische Haltung kann verschiedene Formen annehmen, vor allem die Formen, die man als Humanismus der Ideale und als Humanismus der Prinzipien bezeichnen könnte. Der Humanismus der Ideale ist ausdrücklich an derZukunft orientiert, der Humanismus der Prinzipien aber an derGegenwart. Nur ein Humanismus der Prinzipien, dem es darum geht, den Eigenwert existierender Individuen zu behaupten und zu verteidigen, verdient es, ethischer Humanismus genannt zu werden. Marx, sogar der jüngste Marx, war kein ethischer Humanist in diesem Sinn. Und nur ein Humanismus in diesem strengen Sinn würde einen philosophischen Standort bieten, von dem aus man den Stalinismus oder Neo-Stalinismus angreifen könnte.Marx war ein Säkularist, und er entwarf ein humanistisches Ideal für die Zukunft, aber humanistische Prinzipien für die Gegenwart lehnte er ab. Er betonte, daß nur dem nicht entfremdeten, produktiven Individuum der kommunistischen Zukunft ein eigener Wert zukomme. Bis dahin haben Individuen nur einen geschichtlich instrumentalen Wert: jene, die an der Verwirklichung der kommunistischen Gesellschaft arbeiten, sind zu respektieren; diejenigen, welche dabei Widerstand leisten oder versagen, müssen ausschließlich als Hindernisse auf dem Wege des geschichtlichen Fortschritts behandelt werden.In diesem Sinn ist der Leninismus und sogar der Stalinismus und Neo-Stalinismus in dem zukunftsorientierten Humanismus der Ideale des jungen Marx einbegriffen, oder zumindest davon nicht ausgeschlossen. Selbst der jüngste Marx machte sich den Modeirrtum des 19. Jahrhunderts zu eigen — den Irrtum des aufgeschobenen Wertes oder des zeitlich verstellten Wertes und nahm damit eine mit dem ethischen Humanismus grundsätzlich unvereinbare Position ein.

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An earlier, and much shorter, version of this paper was read at a session on Marxism and Humanism at the Fourteenth International Philosophy Congress in Vienna, September 4, 1968, and published in Vol. II of the Congress Proceedings, Vienna, 1968, pp. 69–73.     

Contextualism and the Skeptic: Comments on Engel

Mylan Engels paper (2004) is divided into two parts: a negative part, criticizing the costs of contextualism and a constructive part proposing a noncontextualist resolution of the skeptical problem. I will only address the constructive part here. The constructive part is composed of three elements: (i) a reconstruction or reformulation of the original skeptical argument, which draws on the notion of epistemic possibility (e-possibility), (ii) a distinction between two senses of knowledge (and two corresponding kinds of e-possibility): fallibilistic and infallibilistic, and (iii) an argument which tries to hoist the skeptic by their own petard, namely the closure principle (CP). As I will argue, there are two ways to understand Engels anti-skeptical argument. Only in one interpretation does the argument depend on the proposed reconstruction of the skeptical argument in terms of e-possibility. But this version of the argument is unsound. More importantly, the skeptic has a strong prima facie objection at her disposal, which applies to both interpretations of the argument. If this objection is valid, Engels argument does not hold. But once it is invalidated, his argument is superfluous.     

Theor of free choice permission

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

Lying and intersubjective truth: A communication based approach to understanding lying

This project was undertaken as a response to a perceived deficiency regarding the role of communication in a large block of the phenomenological discourse on lying. The arguments presented here attempt to make the communication process an explicit, rather than an implicit component of this discussion. First, a lie is explained as a communicative act that is identified by making a simple comparison between two contradictory realities, the reality presented by the lie, and some sort of true reality. Existing discussions of lying are examined and judged to be deficient because they limit their explanations of this true reality to subjective and objective standards of truth. Intersubjectivity is presented as an alternative truth standard, and it is argued that lies can only be discovered and understood through a process of interpretation or negotiation (dialogue) by human interactants.     

Happiness and virtue in Socrates' moral theory

Conclusion In Section IV above we start with texts whose prima facie import speaks so strongly for the Identity Thesis that any interpretation which stops short of it looks like a shabby, timorous, thesis-saving move. What else could Socrates mean when he declares with such conviction that no evil can come to a good man (T19), that his prosecutors could not harm him (T16(a)), that if a man has not been made more unjust he has not been harmed (T20), that all of happiness is in culture and justice (T16(a)), that living well is the same as living justly (T15)? But then doubts begin to creep in. Recalling that inflation of the quantifier is normal and innocuous in common speech (that job means everything to him, he'll do anything to get it, will stick at nothing) we ask if there is really no chance at all that no evil in T19, not harmed in T20 might be meant in the same way? The shift from no harm at T16(a) to no great harm at T16(b), once noticed, strengthens the doubt. It gets further impetus in T21(b) when to explain how all of happiness is in culture and justice he depicts a relation (that recurs more elaborately in T22) which, though still enormously strong, is not quite as strong as would be required by identity. The doubt seeps into T15 when we note that current usage did allow just that relation as a respectable use of the same.At that point we begin to wonder if resort to the Identity Thesis might not be just a first approximation to a subtler, more finely nuanced, doctrine which would give Socrates as sound a foundation for what we know he wants to maintain at all costs - the Sovereignty of Virtue - without obliterating the eudaemonic value of everything else in his world. We cast about for a credible model of such a relation of virtue to happiness and hit on that multicomponent pattern sketched on p. 9 above. We ascertain that this will afford a comprehensively coherent eudaemonist theory of rational action, while its rival would not, and will fit perfectly a flock of texts in Section V which the latter will not fit at all. Are we not entitled to conclude that this is our best guide to the true relation of virtue to happiness in Socrates' thought - the one for which he would have declared if he had formulated explicitly those two alternative theses and made a reasoned choice between them?The Socrates of this paper is the protagonist of Plato's earlier dialogues. I list these (by self-explanatory abbreviations), borrowed from T. Irwin, Plato's Moral Theory [1974] (hereafter PMT): Ap., Ch., Cr., Eud., Eu., G., HMa., HMi, Ion, La., Ly., Pr., R., I. I assume, but shall not argue here, that in this segment of his corpus, Plato aims to recreate the doctrines and arguments of his teacher in dramatic scenes, all of which (except for the Ap.) may be, and most of which undoubtedly are, fictional; I shall be referring these works, under this proviso, as Plato's Socratic dialogues. (I did not include the Menexenus in the above list, since the parody of a funeral oration in this dialogue is implicitly dissociated from Socrates.)