Showing papers in "Noûs in 1969"

An Analysis of Some Deontic Logics

Abstract: The purpose of this article is to investigate the structure and to discuss the applications of deontic logics of von Wright’s type as presented in [15] and [19]. The ‘paradoxes’ which arise in these logics seem to indicate that the axioms reflect only some special senses of the words ‘obligation’ and ‘permission’. I believe that the questions of what these special senses are can be clarified by exhibiting a simple picture of the formal structure of these logics.

Improved Formulations of Act-Utilitarianism

Abstract: Lars Bergstrom's The Alternatives and Consequences of Actions (Stockholm: 1966) is an outstanding contribution to utilitarian ethics, which definitely sets a standard of comparison for future work in the area. In the first part of his book Bergstrom deals with the following problem that seems to have been almost altogether neglected by moral philosophers: (i) how are we to understand and explicate the notion of the alternatives to an action that admittedly plays a crucial r6le in act-utilitarianism? Another problem appears to be intimately bound up with (i), viz. (ii) how is act-utilitarianism related to deontic logic? It would seem that, since act-utilitarianism provides necessary and sufficient conditions for the obligatoriness, rightness and wrongness of actions, one is entitled to expect it to validate certain principles of deontic logic "automatically", so to speak. If this were not so, it would seem that act-utilitarianism could be ruled out on purely logical grounds, provided, of course, that deontic logic is concerned with obligatoriness, etc. in a sense with which act-utilitarianism, too, is concerned, and provided also that deontic logic is a sufficiently well-established discipline (which certainly may be doubted). Now, Bergstrbm does not explicitly claim to be dealing with this problem (ii),' but its presence and relevance can be felt throughout his interesting discussion of alternatives (problem (i)). The main intent of the present paper is to give a treatment of problems (i) and (ii) in the light of Bergstrbm's work. As far as

De re et de dicto

Abstract: In Prior Analytics i, 9 Aristotle makes an interesting observation: \"It happens sometimes that the conclusion is necessary when only one premiss is necessary; not, however, either premiss taken at random, but the major premiss.\" Here Aristotle means to sanction such inferences as (1) Every human being is necessarily rational (2) Every animal in this room is a human being (3) Every animal in this room is necessarily rational. On the other hand, he means to reject inferences of the following sort: (4) Every rational creature is in Australia (5) Every human being is necessarily a rational creature *. (6) Every human being is necessarily in Australia. Aristotle would presumably accept as sound the inference of (3) from (1) and (2) (granted the truth of 2). But if so, then (3) is not to be read as (3') It is necessarily true that every animal in this room is rational ; for (3') is clearly false. Instead, (3) must be construed, if Aristotle is correct, as the claim that each animal in this room has a 235

Meaning Relations and Modalities

Abstract: The aim of this paper is to present a certain philosophical perspective on the basic concepts of modal logic. The essentials of our approach, both philosophical and formal, are found in a previous paper,2 but will be recounted briefly in sections 1 and 3. Section 2 contains an intuitive explanation of our interpretation of the modal operators, and section 4 its formal counterpart. Section 5 considers quantification and singular terms in modal contexts. In section 6 we return to philosophical issues with the question whether t-he interpretation of modal language involves metaphysical commitments.

Species, Determinates and Natural Kinds

Abstract: 1. In an article appearing in this Journal,2 John Woods offers an account of certain classificatory notions. His analysis uses a familiar technique: presentation of a truth-functional definition, which is then modified in an ad hoc manner to meet various counterexamples. In recent years, the fruits of this technique have been subjected to criticism of the most devastating sort. Woods' proposals are no exception to this, and in fact abound in crippling flaws. Below, I will list some of these, paying most attention to his account of the relation of species to genus. In a concluding section I will make some suggestions concerning a more suitable approach to these problems. 2. Woods' analysis of the determinate-determinable relation suffers from the defect that if Fx is a determinate of Gx, then Gx is a theorem of the predicate calculus. This follows at once from his condition 2*), which is built into all his later reformulations. According to 2*), if Fx is a determinate of Gx then "if there is a third term Px, distinct from Fx and Gx, such that (Gx Px) entails Fx, then Px entails Gx and Px entails Fx".3 Where Fx and Gx are any terms, let Px be ( .-Gx V Fx). Clearly, (.. Gx V Fx) is distinct from both Gx and Fx, and (Gx Px) F--Fx.4 However, Px H--Gx if

What's wrong with Fodor's and Putnam's functionalism

Abstract: In their articles "Explanations in Psychology" and "The Mental Life of Some Machines"1' both Jerry Fodor and Hilary Putnam have argued that psychological properties ("memories, motives, needs, drives, desires, strategies, beliefs, etc.")2 are functional characterizations and therefore, on logical grounds, can never be identified with any physiological structures which science may discover to correspond to them. Although I agree with much that each has to say in these articles, I deny that an identity theory can be ruled out a priori by the functional/structural distinction t-hey develop. In this paper I examine the arguments each puts forward for this position and the key notion of "functional characterization" which enters into them. I argue that in order to speak of the functional organization of a system one first must fix a "boundary" for the system and agree upon a "level of abstraction" to describe its behavior. I conclude that these decisions regarding boundary and level of abstraction are made on various pragmatic grounds to meet the purpose at hand. The relativity this brings to the notion of functional characterization undercuts the argument that there is a logical distinction between functional and structural states which precludes any pos-

Tense logic! Why bother?

Abstract: THE TENSE REVOLUTION. According to historians like Thomas Kuhn, the story of a scientific revolution is a chronicle of disenchantment with a paradigm, often nurtured by nostalgia for bygone ideals, culminating in the production of a rival paradigm which ultima:tely wins the allegiance of the relevant scientific community away from the older paradigm through a process akin to American politics.1 What is thus true of revolutions in empirical science is no less true of revolutions in the formal sciences of logic and mathematics, and it so happens that a logical revolution is well underway today. Disenchanted with the usual handling (mishandling?) of time in modern logic, a dedicated band of revolutionaries under the aegis of Arthur Prior impugn the legitimacy of certain central notions of modern logic and have begun to develop and explore alternative logics, so-called tense logics, reminiscent of certain ancient and medieval logical developments.2 I propose in this paper to examine some of the principal charges directed against the standard treatment time receives in modern logic. We shall find that there are two breeds of tense logicians, identifiable by their stance vis4--vis what Prior has called the principle of comprehensive

God and other Minds

Abstract: In my judgment Professor Plantinga's book' is the most important contribution to the philosophy of religion that has appeared in several decades. The book has three main parts: I. Natural Theology-a consideration of the cosmological, ontological, and teleological arguments; II. Natural Atheology-a consideration of the problem of evil, verificationism, and other attacks against theism; III. God and Other Minds-a consideration of the problem of our knowledge of other minds and the bearing of this problem on the question of the reasonableness of theistic belief. The central question of the book is whether belief in the existence of the theistic God is rational. Plantinga considers in Part I the arguments by which natural theology endeavors to establish that theistic belief is rationally justified. He concludes that these arguments are unsuccessful and, therefore, fail to provide rational grounds for theistic belief. In Part II Plantinga investigates the major arguments employed to show that we have good reasons for believing that God does not exist. His conclusion is that these arguments, like the arguments of natural theology, are unsuccessful. Plantinga's conclusions about natural theology and atheology are not novel. Other philosophers have reached the same conclusions. But few, in my judgment, have argued for these conclusions with anything like the thoroughness, clarity, and skill that Plantinga brings to the subject. The novelty in Plantinga's study of the rationality of theistic belief is unfolded in Part III. Instead of concluding that agnosticism is the rational view to adopt concerning the existence of the theistic

Existence Entailing Attributes, Modes of Copulation and Modes of Being in Second Order Logic

Abstract: Recently, in [51, I formulated a second order logic of existence which centered around the distinction between those attributes ,that entail existence and those that do not.' The distinction provides an especially apt explication of the concept of existence and is for this reason especially pertinent to pragmatics and intensional logic, encompassing as they do such areas as tense, epistemic, deontic and modal logic.2 For example, apropos of tense logic some attributes, such as being red, being round, being hard, etc., cannot be possessed at a time except by objects existing at that time. Other attributes, especially relational attributes between objects whose "lifespans" need not overlap, such as being an ancestor of everyone (someone) now existing, being remembered by someone now existing,3 etc., may very well be possessed by objects which no longer

Chisholm's Epistemic Principles

Abstract: According to one familiar tradition in epistemology, dating at least to Descartes, propositions that describe ordinary physical objects receive their justification solely from propositions about a man's psychological states, his beliefs and the ways in which physical objects appear to him. But there is an almost equally familiar tradition that claims, on the contrary, that if we begin with propositions about a man's psychological states (henceforth, "subjective propositions"), we shall never be able to proceed beyond them to reach "the external world" and that we shall end up instead in "the coal pit" of skepticism. This claim is often supported with refutations of phenomenalism. But there are ways, alternative to phenomenalism, for proceeding from subjective propositions to propositions about physical objects. In his book Theory of Knowledge, Professor Chisholm develops such an altemative in detail.2 The clarity and precision of Chisholm's exposition will enable us, I believe, to see in a clear way the problems that confront this traditional approach to one of the large questions of epistemology. In the chapter entitled "The Indirectly Evident", Chisholm presents nine principles of evidence which, taken as a whole,

Remarks on the concept of distribution in traditional logic

Abstract: In traditional logic, a term is often defined to be distributed in a given categorical proposition if the proposition says something about every instance of the term, or the whole of its extension, rather t-han merely some of its instances or part of its extension. Given the definition, subjects of universals and predicates of negatives are classified as distributed, whilst subjects of particulars and predicates of affirmatives are taken to be undistributed. The concept of distribution is then used in formulating rules for valid inference, particularly in syllogistic. As is well known however, the concept of distribution has in recent years been subject to a good deal of criticism. It is charged with being obscure to the point of incoherency. There is no apparent way of spelling out clearly just what is meant by saying that a proposition is about "the whole" or "only part" of the extension of a term. In so far as the concept can be understood at all, it seems to leave rather problematic the traditional claim that the predicates of particular negatives are distributed. Thus, it is argued, if the concept of distribution must be used in syllogistic, it should be defined in a purely enumerative way: subjects of universals, predicates of negatives. Such a view has been argued at length by P. T. Geach in his Reference and Generality (New York: Cornell University Press, 1962), and more briefly in articles in Mind LXV (1956): 67-74 and LXXVII (1968): 113-114. Related views are also expressed by L. Linsky in his review of Reference and Generality, Mind LXXIII (1964): 575-583, and appear to be widely accepted.

On the Logic of Cogito Propositions

Abstract: A cogito proposition is what a person would assert if he asserted that he himself is thinking (is conscious, or, if you prefer, is conscious of something), or if he asserted that he himself exists (is something, is not nothing). Because of the difference in the references to persons, my cogito propositions are different from yours; and because of the difference in the references to times, my cogito propositions now are different from my cogito propositions of a moment ago. However, qua cogito propositions they have three important properties that I shall explain in section II. In section III I shall show that cogito propositions possess all three of these properties. In section IV I shall explore the logical connection between cogito propositions and "Cogito, ergo, sum." Finally, in section V I shall sort out the entailments between cogito propositions and other propositions that also possess the three characteristics possessed by cogito propositions. These entailment relations, together with the three properties, determine a property that distinguishes the class consisting of cogito propositions. This is an important property. It underlies the philosophically interesting features of cogito propositions.

A fallacy of modality

Abstract: The ancient principle of distributivity of necessity (DN for short), that necessary propositions only entail necessary propositions, has acquired an upstart companion, the distributivity of contingency (DC), which threatens to borrow some plausibility from DN; violations of these principles are sometimes lumped together as "fallacies of modality".' The DC principle, according to which contingent statements only entail contingent statements, has played a specially important role in the discussion of entailment; and in particular it has taken a central part in Anderson and Belnap's important theory of entailment E. The DC principle has also had a major part in attacks on linguistic theories of logical necessity. We contend, however, that the principle and minor modifications of it, are false. We argue that the principle provides an example of a strong false thesis drawing its plausibility from its association with a weak but trivial counterpart which cannot however perform the task of the strong principle. We also explain in detail why no version of the principle can fulfill the role for which it is needed in E.

The Two Notions of the Passage of Time

Abstract: The vital point to be made before beginning to discuss the perplexing problem of what, if anything, can be made out of the talk about the passage of time is, that such talk may be attempted in two totally different senses. These two senses must, under no circumstances, be conflated. One way of talking about the flow of time can be attempted only with respect to a temporal universe in which, in addition to the relationships earlier than, simultaneous with and later than, there exist also what have been called the 'transient' temporal properties of being in the future, present and past. These latter properties have been called transient because events assume 'presentness' for an instant only, and the degree of remoteness to which an event is in the future or in the past seems to be changing continually. It is agreed by most philosophers that a statement reporting the 'transient' temporal properties of two events implies, but is not implied by, a statement relating them with respect to earlier than, simultaneous with and later than. Thus, a temporal universe admitting of the properties future, present and past is a full-fledged temporal universe since of necessity it admits the other temporal relations as well, but a more barren universe is conceivable in which all events are uniquely ordered by the 'static' relations of earlier, simultaneous and later and admit of no other temporal properties. Many philosophers maintain that a universe uninhabited by conscious beings would be such a temporally barren universe. In

Aspects of the Pragmatics of Explanation

Abstract: Much of the argumentation about explanation in recent years has been at cross purposes, because of failure to distinguish between attempts to characterize the logic of explanation and efforts to account for the pragmatics of explanation. Professor Hempel makes the distinction, characterizing pragmatic terms (or, more properly, pragmatic senses of terms) as those the proper use of which requires reference to the persons involved, e.g., in the process of explaining or of providing a proof ([5], pp. 425-8). Pragmatic features of explanation, then, are not necessarily related to purpose; rather, they are context dependent as opposed to context independent features. Hempel acknowledges the importance of the pragmatic dimension of explanation, but it is not, and has not been, his concern to explore that dimension. And the failure of many of his critics to find their mark has rested on their assumption that a logic of explanation that does not treat issues in the pragmatics of explanation is somehow deficient. My present purpose is to examine some aspects of the pragrnatics of explanation, and their connection with the logic of explanation. I shall argue that the way explanation operates in fact, as a process aimed at achieving understanding or allaying puzzlement, is closely linked to the logical structure of explanation. The material here represents additional programmatic development of the theory of causal judgment first presented in "Causal

Quine's definition of logical truth

Abstract: ? 1. There are three principal treatments of logical truth in the literature. The first is modal; the second model-theoretic; and the third a combination of model-theoretic and syntactic. The first is identified with Lewis and Langford; the second with Tarski; and the third with Quine, who in turn tracks down his indebtedness to Bolzano.1 The first splits off quite naturally from the other two, for on the modal view-at least some versions of it-logical truth is expressible within the object language by an operator designating necessity. The definitions proposed by Tarski and Quine, on the other hand, are metalinguistic. Tarski's definition is intuitive and has been well investigated. Quine's definition is also quite intuitive, but the imprecision of its formulation has led some philosophers to the view that it is defective: Hinman, Kim and Stich, in a recent article, offer a survey of objections and come to the conclusion that "it is hard to see the appeal of a notion of logical truth so curiously ill-behaved."2 In the present paper the authors offer, for what appears to be the first time, a precise account of the Quine definition. They discuss some of its

Induction: A Consistent Gamble

Abstract: The purpose of this paper is to discuss an important recent work on inductive inference, Gambling with Truth*, by Isaac Levi. We owe Professor Levi a debt of gratitude for producing a book of such excellence. His own approach to inductive inference is not only original and profound, it also clarifies and transforms the work of his predecessors. In short, the book deserves to become a classic. The book formulates new problems for research, and I hope to make some contribution to the solution of these problems. The problem that will be my primary concern is the formulation of acceptance rules for inductive logic. I shall argue that the rule Professor Levi proposes requires modification and propose an alternative analysis based on his methods. Professor Levi is concerned to provide criteria that are conditions of rational belief. He correctly maintains that we should not equate believing that something is true with acting as though it were true. A man might believe that something is true but be unwilling to act as though it were true, and he might act as though something were true but not believe it is true. However, the theory that we use for determining when behavior is rational can be modified for use in determining when belief is rational. Bayesian Decision Theory tells us that a specific action is rational when that action maximizes expected utility. Whether the action maximizes expected utility depends on the goals and objectives of the agent, on what utilities or values he assigns to various possible outcomes of his actions. Levi argues that cognitive inquiry has its own goals and objectives, distinct from those of practical action. He concludes

More on Skolem's Paradox

Abstract: The Ldiwenheim-Skolem Theorem to the effect that every consistent formal system has a countable model is often interpreted as demonstrating that prima facie uncountable sets-such as the set of all real numbers-are actually countable. In an earlier paper I questioned the arguments for this Skolemite position. The gist of my earlier contention was this. One of the Skolemite arguments is based upon an equivocation between the terms "the sets of the system" and "what can be taken as the sets of the system". The more rigorous arguments skirt the issue by dealing only with predicative subsets of the sets whose countability is in question or else by simply postulating the countability of the latter. In any case, such arguments are faced with the seemingly overwhelming difficulty of establishing that the sets that have been shown to be countable are identical with the ones that most mathematicians hold to be uncountable.' Arthur Fine's recent paper in which the Skolemite position is defended anew has prompted me to reexamine my earlier arguments.2 I now see that some of them were predicated upon the existence of the intended (prima facie) uncountable models for the

The Effectivity of Questions

Abstract: The following elementary considerations on the effectivity of questions are formulated not so much in order to establish results as to show some of the related problems. The introduction will present a general characterization of questions, as discussed in [4] and [5] ('see bibliography); it will also contain some remarks about effectivity. In the second section it will be seen that questions, as presented in the introduction, are effective or at least effectively enumerable as to decidable systems. But according to the t-hird section, questions are not even effectively enumerable as to undecidable systems. Since effective enumerability is a very desirable property, in the fourth section two alternative definitions of "question" will be presented, which will allow us to establish the effective enumerability of questions.

The Concept of Thinking

Abstract: According to the classical view, thinking is a particular type of mental occurrence and the concept of thinking is essentially the concept of this mental occurrence. On this view the concept of thinking is monomorphous and the implied seat of this occurrence is the mind. In sharp contrast to this traditional position, many philosophers today regard the concept of thinking as polymorphous.1 In speaking of instances of thinking, Professor Ryle, the originator of this thesis, writes: "there need be nothing going on in one of them [instances of thinking], such that something else of the same species or genus must be going on in another of them." (TL 68) There is on this view no particular type of occurrence, mental or otherwise, which is (or is an essential component of) thinking. And as A. R. White has properly inferred, there is therefore no particular, much less special, seat or organ of thinking. "We do not think with our mind, or with our brain, in the same way as we see with our eyes or hear with our ears." (PM 90) It also follows that "I might think of the same thing three times in one single day and have a different experience each time." (PM 99) These implications of the polymorphism thesis indicate its philosophical import. In this

On Entailment and Support

Abstract: It is still too widely supposed that the principle: "if p entails q and if e supports p, then e supports q at least as much as it supports p," is true. Let's make a start on showing this principle is false by considering what it is for one proposition to support another proposition. I suggest that e supports p if and only if the probability of p given e is greater than the probability of p not given e. Thus, in the familiar notation:

Thomason on Natural Kinds

Abstract: Permit me a few comments on Richard Thomason's article in this journal (Vol. III (1969), pp. 95-101) on natural kinds. 1. All classifications must be with respect to some purpose. There is no "most natural" kind of natural kinds. Consequently, Mr. Thomason must be furnishing something like an explication of the concept of natural kinds with respect to some use. I would like to argue in this paper that his explication is not satisfactory for the purpose of scientific classification. The "kinds" of science are not Thomason natural kinds. 2. According to Thomason's account, no two natural kinds of a system may overlap (i.e., share members), unless one is a species of the other. But it is not hard to show that this won't do as a general criterion of scientific classification. For instance, taking silicates as a genus, we find that among the species under that (or succeeding) headings are the species of beryl silicates and chromium silicates (some beryls, some not). Clearly, if the concept of natural kinds is to be of general use in science, we must grant that both of these categories are species of silicates, and hence natural kinds. But according to Thomason's classification scheme they are not, since the two classes overlap (emeralds being chromium beryl silicates) and neither is a species of the other. Or take the periodic table of the elements, and assume for the sake of simplicity that rows determine categories by number of electron shells and columns by number of outer shell electron gaps.

Eberle On Nominalism In Non-Atomic Systems

Abstract: where Azx if and only if z is an atom (i.e. has nothing bearing the generating relation to it) and either bears the generating relation to, or is identical to x.1 In a recent article in this journal, Yoes' has. shown that use of this criterion implies that systems without atoms, if they are nominalistic, can only be committed to one entity. Eberle,3 after criticizing proposals of Yoes' for alternative criteria notes:

Non-Atomic Systems of Individuals Revisited

Abstract: Recently, various attempts have been made to generalize Goodman's well-known principle of individuation' so as to render it appropriate to non-atomic systems of individuals with respect to the ancestral of membership. As Schuldenfrei points out2, my own efforts in this direction3 were flawed in two respects: (1) by my previous criteria all atomic individuals were identified, and (2) contrary to Goodman's demands, the atoms of set theory failed to be identified with their singletons. The easiest correction of these errors would seem to be this: throughout the former Definition (8) of "ancestral base", let the word "ancestor" refer to the improper ancestral with respect to membership (which is reflective) rather than to the proper ancestral (which is irreflexive). The revised definition reads as follows:

Skyrms on Nonderivative Knowledge

Abstract: There is a class of cases suggested by Edmund Gettier as counterexamples to the thesis that knowledge is justified true belief.' In a recent article, Brian Skyrms has proposed an analysis of this concept that avoids the Gettier problems and contains many other original and helpful suggestions.2 However, Skyrms' analysis is defective. Skyrms' primary concern is with the concept of nonbasic knowledge; that is, knowledge which is dependent on prior knowledge. He -suggests that within the realm of nonbasic knowledge a distinction should be made between derivative and nonderivative knowledge. The following conditions are given by Skyrms in making this distinction: