The source, status, and significance of the derivation of the necessity of identity at the beginning of Kripke’s lecture “Identity and Necessity” is discussed from a logical, philosophical, and historical point of view.

Wittgenstein's conception of logical and conceptual truth is often thought to rival that of the logical positivists. This paper argues that there are important respects in which these conceptions complement each other. Analyticity, in the positivists' sense, coincides, not with Wittgenstein's notion of a grammatical proposition, but rather with his notion of a tautology. Grammatical propositions can usually be construed as analyticity postulates in Carnap's sense of the term. This account of grammatical and analytic propositions will be illustrated by appeal (...) to logical, conceptual and arithmetic truths. Its consequences for an analysis of corresponding modal notions will be indicated. (shrink)

Several natural languages such as English contain prima facie different kinds of referential and quantificational expressions. In particular, natural languages.

Defenders of the prosentential theory of truth claim that the English language contains prosentences which function analogously to their better known cousins – pronouns. Statements such as ‘That is true’ or ‘It is true’, they claim, inherit their content from antecedent statements, just as pronouns inherit their reference from antecedent singular terms. Prosentential theorists claim that the content of these prosentences is exhausted by the content of their antecedents. They then use the notion of the inheritance of content from an (...) antecedent to explain the various functions of the predicate ‘. . . is true’. Defenders of the prosentential theory of truth are mistaken, I claim, in thinking that in order to oppose the view that ‘. . . is true’ is used to ascribe a substantive truth property to propositions they need to claim that no uses of ‘. . . is true’ ever attribute any property. I identify an ‘attributive’ use of prosentences in which reliability is implicitly attributed to a subject. I then use the capacity of prosentences to serve as implicit attributions of reliability as a basis for explicating the logical structure of explicit attributions of reliability. The identification of an attributive use of prosentences does not constitute a fundamental change in the prosentential theory. (shrink)

Let us call a statement of the form ‘If A was, is, or will be the case, then C was, is, or will be the case’ an indicative conditional. And let us call a statement of the form ‘If A had been, were, or were to be the case, then C would have been, would be, or would come to be the case’ a subjunctive, or counterfactual, conditional.

A conditional takes the form ‘If A, then C’. On the truth-conditional view of conditionals, conditional statements state things with truth-conditions. On the suppositional view, conditional statements involve the expression of a supposition. I develop and defend a view on which conditional statements both state things with truth-conditions and express suppositions. On this view, something is fundamentally right about standard truth-conditional and standard suppositional views. Considerations in favor of conditional contents lead us to attribute truth-conditional contents to conditional statements; considerations (...) in favor of the suppositional view then lead us to an unexpected account of these contents. The resulting view has a number of benefits, including a unified treatment of conditional speech acts, a plausible account of our practice of ascribing truth-values to conditional statements, a simple explanation of the apparent equivalence between probabilities of conditionals and conditional probabilities, an intuitive treatment of ‘Gibbardian stand-offs’, a plausible logic of conditionals, and an explanation of why theorizing about conditionals has proved so difficult. (shrink)

Psychological research on people’s understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is (...) false (whatever the value of C). This was called the “psychological defective table of the conditional.” Here we show that far from being anomalous the “defective” table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants’ truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people’s interpretations of natural language connectives. We find that de Finetti’s (1936/1995) three-valued system is the best approximation to participants’ truth tables. (shrink)

Counterfactual Entailment is the view that a counterfactual conditional is true just in case its antecedent entails its consequent. I present an argument for Counterfactual Entailment, and I develop a strategy for explaining away apparent counterexamples to the view. The strategy appeals to the suppositional view of counterfactuals, on which a counterfactual is essentially a statement, made relative to the supposition of its antecedent, of its consequent.

My aim has been to adapt Quine's criterion of the ontological commitment of theories couched in standard quantificational idiom to a much broader class of theories by focusing on the set-theoretic structure of the models of those theories. For standard first-order theories, the two criteria coincide on simple entities. Divergences appear as they are applied to higher-order theories and as composite entities are taken into account. In support of the extended criterion, I appeal to its fruits in treating the various (...) examples considered above and to the healthy intuitions of the non-noneists among us. Don't O(m) and E(m) comprise just the things we should have though existed according to a particular interpretation m of a language or a theory? Whatever the answer (and it will hardly be unanimous), I hope to have pointed the way towards a recognition of ontology as a worthwhile branch of modern theory. (shrink)

The attempt to find usable diagrams fornterms of the sort devised by John Venn seems to have originated with Venn himself, who published diagrams for up to five classes (the fifth class, however, was shaped like a doughnut, and contained an area outside itself — like the hole in the doughnut). Venn then suggested that “if we wanted to use a diagram forsixterms (x, y, z, w, v, u) the best plan would probably be to taketwofive-term figures, one for theupart (...) and one for the non-upart of all the other combinations …” Such a method would, as Venn admits, be somewhat confusing to the eye, and thus fail to fulfil one of the major purposes of the diagram; nevertheless, it is a method which could be extended to covernclasses.Venn also suggests (but without illustration) another method for drawing diagrams fornterms: “… the rule of formation would be very simple. We should merely have to begin by drawing any closed figure, and then proceed to draw others subject to the one condition that each intersect once, and once only, all the existing subdivisions produced by those which had gone before.” Then, in a rather surprising footnote, he adds: “It will be found that when we adhere to continuous figures, instead of the discontinuous five-term figure given above, there is a tendency for the resultant outlines thus successively drawn to assume a comb-like shape after the first four or five. If we begin by circles or other rounded figures the teeth are curved, if by parallelograms then they are straight. (shrink)

Whether meaning is compositional has been a major issue in linguistics and formal philosophy of language for the last 2 decades. Semantic holism is widely and plausibly considered as an objection to the principle of semantic compositionality therein. It comes as a surprise that the holistic peculiarities of scientific language have been rarely addressed in formal accounts so far, given that semantic holism has its roots in the philosophy of science. For this reason, a model-theoretic approach to semantic holism in (...) the language of science is presented here. This approach preserves compositionality to a large extent. *Received September 2009; revised February 2010. †To contact the author, please write to: Seminar for Philosophy, Logic, and Theory of Science, Hauspostfach 49, Ludwig-Maximilians-Universität, Munich 80539, Germany; e-mail: [email protected]. (shrink)

In this paper, we claim that the problem of conditionals should be dealt with by carefully distinguishing between thinking conditional propositions and conditional thinking, i.e. thinking on the basis of some supposition. This distinction deserves further investigation, if we are to make sense of some old and new experimental data concerning the understanding and the assertion of conditional sentences. Here we will argue that some of these data seem to refute the mental models theory of conditional reasoning, setting the ground (...) for a different approach to the cognitive study of conditionals. (shrink)

The main idea or the concept of coherence can be expressed in the following way: The more the statements belonging to a given theory approximate a perfect supportive structure, the more coherent the theory. The degree of perfection of a supportive structure depends on the degree to which the following criteria of coherence are fulfilled: (1) the greatest possible number of supported statements belonging to the theory in question; (2) the greatest possible length of chains of reasons belonging to it; (...) (3) the greatest possible number of strongly supported statements belonging to the theory; (4) the greatest possible number of connections between various supportive chains belonging to the theory; (5) the greatest possible number of preference relations between various principles belonging to it; (6) the greatest possible number and complexity of reciprocal supportive relations between various statements belonging to the theory; (7) the greatest possible number of universal statements belonging to the theory; the greatest possible number of general concepts belonging to it; the highest possible degree of generality of concepts implemented within it; the greatest possible number of resemblances between concepts used within it; (8) the greatest possible number of conceptual cross‐connections between various theories; (9) the greatest possible number of cases covered by the theory; and (10) the greatest possible number of fields of life covered by the theory. (shrink)

The standard use of the propositional calculus ('P.C.?) in analyzing the validity of inferences involving conditionals leads to fallacies, and the problem is to determine where P.C. may be ?safely? used. An alternative analysis of criteria of reasonableness of inferences in terms of conditions of justification rather than truth of statements is proposed. It is argued, under certain restrictions, that P. C. may be safely used, except in inferences whose conclusions are conditionals whose antecedents are incompatible with the premises in (...) the sense that if the antecedent became known, some of the previously asserted premises would have to be withdrawn. (shrink)

During the past few decades, a radical shift has occurred in how philosophers conceive of the relation between science and philosophy. A great number of analytic philosophers have adopted what is commonly called a ‘naturalistic’ approach, arguing that their inquiries ought to be in some sense continuous with science. Where early analytic philosophers often relied on a sharp distinction between science and philosophy—the former an empirical discipline concerned with fact, the latter an a priori discipline concerned with meaning—philosophers today largely (...) follow Willard Van Orman Quine (1908-2000) in his seminal rejection of this distinction. -/- This book offers a comprehensive study of Quine’s naturalism. Building on Quine’s published corpus as well as thousands of unpublished letters, notes, lectures, papers, proposals, and annotations from the Quine archives, this book aims to reconstruct both the nature (chapters 2-4) and the development (chapter 5-7) of his naturalism. As such, this book aims to contribute to the rapidly developing historiography of analytic philosophy, and to provide a better, historically informed, understanding of what is philosophically at stake in the contemporary naturalistic turn. (shrink)

Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

The ontology of decision theory has been subject to considerable debate in the past, and discussion of just how we ought to view decision problems has revealed more than one interesting problem, as well as suggested some novel modifications of classical decision theory. In this paper it will be argued that Bayesian, or evidential, decision-theoretic characterizations of decision situations fail to adequately account for knowledge concerning the causal connections between acts, states, and outcomes in decision situations, and so they are (...) incomplete. Second, it will be argues that when we attempt to incorporate the knowledge of such causal connections into Bayesian decision theory, a substantial technical problem arises for which there is no currently available solution that does not suffer from some damning objection or other. From a broader perspective, this then throws into question the use of decision theory as a model of human or machine planning. (shrink)

Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, "The logic and meaning of plurals, II", aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic and meaning of plural constructions that result (...) from the view that plural constructions are, by and large, devices for talking about many things (as such). The account of logic presented in the papers surpasses contemporary Fregean accounts in its scope. This extension of the scope of logic results from extending the range of languages that logic can directly relate to. Underlying the view of language that makes room for this is a perspective on reality that locates in the world what plural constructions can relate to. The papers suggest that reflections on plural constructions point to a broader framework for understanding logic, language, and reality that can replace the contemporary Fregean framework as this has replaced its Aristotelian ancestor. (shrink)

Inscrutability arguments threaten to reduce interpretationist metasemantic theories to absurdity. Can we find some way to block the arguments? A highly influential proposal in this regard is David Lewis’ ‘ eligibility ’ response: some theories are better than others, not because they fit the data better, but because they are framed in terms of more natural properties. The purposes of this paper are to outline the nature of the eligibility proposal, making the case that it is not ad hoc, but (...) instead flows naturally from three independently motivated elements; and to show that severe limitations afflict the proposal. In conclusion, I pick out the element of the eligibility response that is responsible for the limitations: future work in this area should therefore concentrate on amending this aspect of the overall theory. (shrink)

I construe the question Are species sets? as a question about whether species can be conceived of as sets, as the term set is understood by contemporary logicians. The question is distinct from the question Are species classes?: The conception of classes invoked by Hull and others differs from the logician's conception of a set. I argue that species can be conceived of as sets, insofar as one could identify a set with any given species and that identification would satisfy (...) three desiderata: the set would be a set of organisms, the identification would be apposite, and the identification would permit the formulation of statements about species in set-theoretic terms. One cannot, however, identify a species with any given set. Understanding the claim that species are sets in this way enables one to understand better the dispute between some who accept the claim (e.g., Kitcher 1984, 1987) and some who apparently reject it (e.g., Mayr 1987). (shrink)

In "Metaphysics" Gamma 3 Aristotle declares that the philosopher investigates things that are qua things that are and that he therefore should be able to state the firmest principles of everything. The firmest principle of all is identified as the principle of non-contradiction (PNC). The main focus of Gamma 3 is Aristotle's proof for this identification. This paper begins with remarks about Aristotle's notion of the firmness of a principle and then offers an analysis of the firmness proof for PNC. (...) It focuses on some key assumptions of the proof and on the range and force of the proof. Aristotle closes Gamma 3 with the claim that PNC is ultimate in the sense that all other principles somehow rest on it. This, rather controversial, claim is given a defensible reading and shown to be central to the chapter's effort to establish PNC as the firmest principle of all. As such it completes the firmness proof and is not simply an appended remark. (shrink)

Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much more, (...) I argue. "If you love me, kiss me", a conditional imperative, mixes a declarative antecedent ("you love me") with an imperative consequent ("kiss me"); it is satisfied if you love and kiss me, violated if you love but don't kiss me, and avoided if you don't love me. So we need a logic of three -valued imperatives which mixes declaratives with imperatives. I develop such a logic. (shrink)

Cities are mysteriously attractive. The more we get used to being citizens of the world, the more we feel the need to identify ourselves with a city. Moreover, this need seems in no way distressed by the fact that the urban landscape around us changes continuously: new buildings rise, new restaurants open, new stores, new parks, new infrastructures… Cities seem to vindicate Heraclitus’s dictum: you cannot step twice into the same river; you cannot walk twice through the same city. But, (...) as with the river, we want and need to say that it is the same city we are walking through every day. It is always different, but numerically self-identical. How is that possible? What sort of mysterious thing is a city? The answer, I submit, is that cities aren’t things. They are processes. Like rivers, cities unfold in time just as they extend in space, by having different temporal parts for each time at which they exist. And walking though one part and then again through another is, literally, walking through the same whole. (shrink)

I argue that there are some causal relata for which it is indeterminate whether one caused the other. Positing indeterminacy in causation helps us defend contested principles in the logic of causation and makes possible new ways of thinking about the theoretical impact of symmetric causal overdetermination. I close by discussing amendments of current theories of causation that would help explain causal indeterminacy.

I argue that there are some causal relata for which it is indeterminate whether one caused the other. Positing indeterminacy in causation helps us defend contested principles in the logic of causation and makes possible new ways of thinking about the theoretical impact of symmetric causal overdetermination. I close by discussing amendments of current theories of causation that would help explain causal indeterminacy.

Achinstein, Putnam, and others have urged the rejection of the received view on theories (which construes theories as axiomatic calculi where theoretical terms are given partial observational interpretations by correspondence rules) because (i) the notion of partial interpretation cannot be given precise formulation, and (ii) the observational-theoretical distinction cannot be drawn satisfactorily. I try to show that these are the wrong reasons for rejecting the received view since (i) is false and it is virtually impossible to demonstrate the truth of (...) (ii). Nonetheless, the received view should be rejected because it obscures a number of epistemologically important features of scientific theorizing. I show this by sketching an alternative analysis which reveals some of these features and gives a more faithful picture of scientific theorizing. (shrink)

The notion of similarity plays a central role in Quine's theory of Universals and it is with the help of this notion that Quine intends to define the concept of kind which also plays a central role in the theory. But as Quine has admitted, his attempts to define kinds in terms of similarities were unsuccessful and it is mainly because of this shortcoming that Quine's theory has been ignored by several philosophers. Nominalism and realism: Universals and Scientific realism. Cambridge: (...) Cambridge University Press). In the present paper, I propose an alternative framework that accounts for the phenomena that Quine intends to explain with his resemblance theory. The framework agrees with Quine's austere ontology; in particular, it does not assume the existence of properties and of possible worlds.. Resemblance nominalism: A solution to the problem of Universals. Oxford: Clarendon Press.) Moreover, the framework is extensionalist since the abstract entities it assumes are classes and these can be individuated extensionally, for classes are identical if their members are identical. Finally, I will refute some of the objections to Quine's approach that have been raised by Armstrong and Oliver [. The metaphysics of properties. Mind, 105, 1-80.] and I will argue that, contrary to what has been claimed by Oliver in a comment on Lewis [. On the plurality of worlds. Oxford: Blackwell.], Quine is able to specify an important set of sparse properties. (shrink)

Early sections of the paper develop a view of the natural numbers and a view of counting which are suggested by the remarks of several modern philosophers. Further investigation of these views leads to one of the main theses of the paper: a special kind of quantifier, the "numerical quantifier" is essential to counting. The remainder of the paper suggests the rudiments of a new view of the natural numbers, a view which maintains that numerical quantifiers are one kind of (...) natural number. (shrink)