The identity predicate can be defined using second-order quantification: a=b =df ∀F(Fa↔Fb). Less familiarly, a dyadic sentential operator analogous to the identity predicate can be defined using third-order quantification: ϕ≡ψ =df ∀X(Xϕ↔Xψ), where X is a variable of the same syntactic type as a monadic sentential operator. With this notion in view, it is natural to ask after general principles governing its application. More grandiosely, how fine-grained is reality? -/- I will argue that reality is not structured in anything like (...) the way that the sentences we use to talk about it are structured. I do so by formulating a higher-order analogue of Russell’s paradox of structured propositions. I then relate this argument to the Frege-Russell correspondence. When confronted with the alleged paradox, Frege agreed that reality was not structured, but maintained that propositions (i.e. thoughts) were structured all the same. Russell replied that his paradox showed Frege’s theory of structured thoughts to be inconsistent, to which Frege replied that Russell’s argument failed to heed the distinction between sense and reference. Most recent commentators have sided with Russell. In defense of Frege, I establish the consistency of one version of his rejoinder. I then consider and reject some ways of resisting the argument against a structured conception of reality. I conclude that, if propositions are structured, this is because they correspond not to distinctions in reality, but rather to ways in which those distinctions can be represented. (shrink)

Semantics in the Montagovian tradition combines two basic tenets. One tenet is that the semantic value of a sentence is an intension, a function from points of evaluations into truth-values. The other tenet is that the semantic value of a composite expression is the result of applying the function denoted by one component to arguments denoted by the other components. Many philosophers object to intensional semantics on the grounds that intensionally equivalent sentences do not substitute salva veritate into attitude ascriptions. (...) They propose instead that the semantic values of sentences must be structured propositions. In rejecting intensional semantics, philosophers who endorse structured propositions also usually reject functional compositionality, undermining both tenets of the Montagovian programme. I defend a semantic theory that incorporates both structured propositions and functional compositionality. I argue that this semantic theory can preserve many explanatory benefits of Montague semantics. Finally, I show how treating composition functional application can resolve core problems internal to a theory of structured propositions. (shrink)

This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between objects and functions. (...) Russell understood propositional functions as what is obtained when constituents of propositions are replaced by variables, but eventually denied that they were entities in their own right. Both encountered contradictions when supposing there to exist as many objects as functions, and both adopted views about the meaningfulness of higher-order discourse that were difficult to state from within their own strictures. (shrink)

The principle of compositionality requires that the meaning of a complex expression remains the same after substitution of synonymous expressions. Alleged counterexamples to compositionality seem to force a theoretical choice: either apparent synonyms are not synonyms or synonyms do not syntactically occur where they appear to occur. Some theorists have instead looked to Frege’s doctrine of “reference shift” according to which the meaning of an expression is sensitive to its linguistic context. This doctrine is alleged to retain the relevant claims (...) about synonymy and substitution while respecting the compositionality principle. Thus, Salmon (Philos Rev 115(4):415, 2006) and Glanzberg and King (Philosophers’ Imprint 20(2):1–29, 2020) offer occurrence-based accounts of variable binding, and Pagin and Westerståhl (Linguist Philos 33(5):381–415, 2010c) argue that an occurrence-based semantics delivers a compositional account of quotation. Our thesis is this: the occurrence-based strategies resolve the apparent failures of substitutivity in the same general way as the standard expression-based semantics do. So it is a myth that a Frege-inspired occurrence-based semantics affords a genuine alternative strategy. (shrink)

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms (...) of Church’s intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin’s intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions. (shrink)

Assertion plays a crucial dual role in Frege's conception of logic, a formal and a transcendental one. A recurrent complaint is that Frege's inclusion of the judgement-stroke in the Begriffsschrift is either in tension with his anti-psychologism or wholly superfluous. Assertion, the objection goes, is at best of merely psychological significance. In this paper, I defend Frege against the objection by giving reasons for recognising the central logical significance of assertion in both its formal and its transcendental role.

Among philosophers, Fregeanism and sententialism are widely considered two of the leading theories of the semantics of attitude reports. Among linguists, these approaches have received little recent sustained discussion. This paper aims to bridge this divide. I present a new formal implementation of Fregeanism and sententialism, with the goal of showing that these theories can be developed in sufficient detail and concreteness to be serious competitors to the theories which are more popular among semanticists. I develop a modern treatment of (...) quantifying in for Fregeanism and sententialism, in the style of Heim and Kratzer, and then show how these theories can—somewhat surprisingly—account for “third readings” on the model of the “Standard Solution” from possible-worlds semantics. The resulting Fregean/sententialist proposal has a distinctive attraction: it treats data related to counterfactual attitudes —which have proven challenging to accommodate in the setting of possible worlds semantics—straightforwardly as third readings. (shrink)

The aim of this paper is to present a constructive solution to Frege's puzzle (largely limited to the mathematical context) based on type theory. Two ways in which an equality statement may be said to have cognitive significance are distinguished. One concerns the mode of presentation of the equality, the other its mode of proof. Frege's distinction between sense and reference, which emphasizes the former aspect, cannot adequately explain the cognitive significance of equality statements unless a clear identity criterion for (...) senses is provided. It is argued that providing a solution based on proofs is more satisfactory from the standpoint of constructive semantics. (shrink)

We identify a class of paradoxes that is neither set-theoretical nor semantical, but that seems to depend on intensionality. In particular, these paradoxes arise out of plausible properties of propositional attitudes and their objects. We try to explain why logicians have neglected these paradoxes, and to show that, like the Russell Paradox and the direct discourse Liar Paradox, these intensional paradoxes are recalcitrant and challenge logical analysis. Indeed, when we take these paradoxes seriously, we may need to rethink the commonly (...) accepted methods for dealing with the logical paradoxes. (shrink)

Certain commentators on Russell's “no class” theory, in which apparent reference to classes or sets is eliminated using higher-order quantification, including W. V. Quine and (recently) Scott Soames, have doubted its success, noting the obscurity of Russell’s understanding of so-called “propositional functions”. These critics allege that realist readings of propositional functions fail to avoid commitment to classes or sets (or something equally problematic), and that nominalist readings fail to meet the demands placed on classes by mathematics. I show that Russell (...) did thoroughly explore these issues, and had good reasons for rejecting accounts of propositional functions as extra-linguistic entities. I argue in favor of a reading taking propositional functions to be nothing over and above open formulas which addresses many such worries, and in particular, does not interpret Russell as reducing classes to language. (shrink)

Goodman and Lederman (2020) argue that the traditional Fregean strategy for preserving the validity of Leibniz’s Law of substitution fails when confronted with apparent counterexamples involving proper names embedded under propositional attitude verbs. We argue, on the contrary, that the Fregean strategy succeeds and that Goodman and Lederman’s argument misfires.

A central dispute in understanding Frege’s philosophy concerns how the sense of a complex expression relates to the senses of its component expressions. According to one reading, the sense of a complex expression is a whole built from the senses of the component expressions. On this interpretation, Frege is an early proponent of structured propositions. A rival reading says that senses compose by functional application: the sense of a complex expression is the value of the function denoted by its functional (...) component for the arguments denoted by its remaining components. I argue that two non-negotiable Fregean theses entail that senses compose by functional application. One thesis is that referents compose by functional application. The other thesis is that an expression in an indirect context refers to its customary sense. (shrink)

Theories of structured meanings are designed to generate fine-grained meanings, but they are also liable to overgenerate structures, thus drawing structural distinctions without a semantic difference. I recommend the proliferation of very fine-grained structures, so that we are able to draw any semantic distinctions we think we might need. But, in order to contain overgeneration, I argue we should insert some degree of individuation between logical equivalence and structural identity based on structural isomorphism. The idea amounts to forming an equivalence (...) class of different structures according to one or more formal criteria and designating a privileged element as a representative of all the elements, i.e., a first among equals. The proposed method helps us to a cluster of notions of co-hyperintensionality. As a test case, I consider a recent objection levelled against the act theory of structured propositions. I also respond to an objection against my methodology. (shrink)

According to Frege, we need a criterion for recognising when different sentences express the same thought to make progress in logic. He himself hedged his own equipollence criterion with a number of provisos. In the literature on Frege, little attention has been paid to the problems these provisos raise. In this paper, I will argue that Fregeans have ignored these provisos at their peril. For without these provisos, Frege’s criterion yields wrong results; but with the provisos in place, it is (...) of no use for Frege’s purposes. This is connected to what Frege took to be the ‘greatest difficulty for philosophy’: natural language sentences don’t just express thoughts; they convey evaluations and communicative hints. Because of this, Frege’s recognition criterion for thoughts cannot be applied to them and we cannot make logical progress by ‘recognising a thought in different linguistic guises’. (shrink)

The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...) universals, are exposed. Wittgenstein's and Russell's views on logical grammar are shown to be very similar. Russell's type theory does not countenance types of genuine entities nor metaphysical truths that cannot be put into words, contrary to conventional wisdom. I relate this to the debate over "inexpressible truths" in the Tractatus. I lastly comment on the changes to Russell's views brought about by Wittgenstein's influence. (shrink)

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell’s Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy (...) due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege’s extant logical system, if Frege’s system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege’s logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therein. (shrink)

Gregory Landini offers a detailed historical account of Frege's notations and the philosophical views that led Frege from Begriffssscrhrift to his mature work Grundgesetze, addressing controversial issues that surround the notations.

We prove how to validly quantify into hyperpropositional contexts de dicto in Transparent Intensional Logic. Hyperpropositions are sentential meanings and attitude complements individuated more finely than up to logical equivalence. A hyperpropositional context de dicto is a context in which only co-hyperintensional propositions can be validly substituted. A de dicto attitude ascription is one that preserves the attributee’s perspective when one complement is substituted for another. Being an extensional logic of hyperintensions, Transparent Intensional Logic validates all the rules of extensional (...) logic, including existential quantification. Yet the rules become more exacting when applied to hyperintensional contexts. The rules apply to only some types of entities, because the existence of only some types of entities is entailed by a hyperpropositional attitude de dicto. The insight that the paper offers is how a particular logic of hyperintensions is capable of validating quantifying-in in a principled and rigorous manner. This result advances the community-wide understanding of how to logically manipulate hyperintensions. (shrink)

This paper challenges a standard interpretation according to which Frege’s conception of logic (early and late) is at odds with the contemporary one, because on the latter’s view logic is formal, while on Frege’s view it is not, given that logic’s subject matter is reality’s most general features. I argue that Frege – in Begriffsschrift – retained the idea that logic is formal; Frege sees logic as providing the ‘logical cement’ that ties up together the contentful concepts of specific sciences, (...) not the most general truths. Finally, I discuss how Frege conceives of the application of Begriffsschrift, and of its status as a ‘lingua characteristica’. (shrink)

It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church's “lambda calculus” for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903–1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the lambda calculus. Russell also anticipated Schönfinkel's combinatory logic approach of treating multiargument functions as functions having other functions as value. (...) Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and “value-ranges”. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the lambda calculus. (shrink)

In these articles, I describe Cantor’s power-class theorem, as well as a number of logical and philosophical paradoxes that stem from it, many of which were discovered or considered (implicitly or explicitly) in Bertrand Russell’s work. These include Russell’s paradox of the class of all classes not members of themselves, as well as others involving properties, propositions, descriptive senses, class-intensions, and equivalence classes of coextensional properties. Part I focuses on Cantor’s theorem, its proof, how it can be used to manufacture (...) paradoxes, Frege’s diagnosis of the core difficulty, and several broad categories of strategies for offering solutions to these paradoxes. (shrink)

Many philosophers still countenance senses or meanings in the broadly Fregean vein. However, it is difficult to posit the existence of senses without positing quite a lot of them, including at least one presenting every entity in existence. I discuss a number of Cantorian paradoxes that seem to result from an overly large metaphysics of senses, and various possible solutions. Certain more deflationary and nontraditional understanding of senses, and to what extent they fare better in solving the problems, are also (...) discussed. In the end, it is concluded that one must divide senses into various ramified-orders in order to avoid antinomy, but that the philosophical justification of such orders is, as yet, still somewhat problematic. (shrink)

The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege (...) did not hold the relevant sense-identity claim regarding basic law V. (shrink)

I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning (...) of Russell's paradox, this position is a natural position for him to have retreated to, when properly understood. (shrink)

In a series of articles dating from 1903 to 1906, Frege criticizes Hilbert’s methodology of proving the independence and consistency of various fragments of Euclidean geometry in his Foundations of Geometry. In the final part of the last article, Frege makes his own proposal as to how the independence of genuine axioms should be proved. Frege contends that independence proofs require the development of a ‘new science’ with its own basic truths. This paper aims to provide a reconstruction of this (...) New Science that meets modern standards and to examine possible problems surrounding Frege’s original proposal. The paper is organized as follows: the first two sections summarize the main points of the Frege–Hilbert controversy and discuss some issues surrounding the problem of independence proofs. Section 3 contains an informal presentation of Frege’s proposal. In section 4 a more detailed reconstruction of Frege’s New Science is set out while section 5 examines what is left out. The concluding section is devoted to a discussion of Frege’s strategy and its significance from a broader perspective. (shrink)

This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church's Logic of Sense and Denotation. Church understands such senses themselves to be "sense-functions," functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or "deviant" sense-functions. Certain absurdities result, e.g., an argument can be found for equating any two (...) senses of the same type. An alternative treatment of the senses of functions is discussed, and is thought to do better justice to Frege's original theory. (shrink)

Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not be (...) thought of as a single thing, neither can the meaning/intension of any expression capable of singling out one collection (class) of things as opposed to another. If this is right, it shows that Russell’s method of solving the logical paradoxes is wholly incompatible with anything like a Fregean dualism between sense and reference or meaning and denotation. I also discuss how this realization lead to modifications in his understanding of propositions and propositional functions, and suggest that Russell’s confrontation with these issues may be instructive for ongoing research. (shrink)

This paper continues a thread in Analysis begun by Adam Rieger and Nicholas Denyer. Rieger argued that Frege’s theory of thoughts violates Cantor’s theorem by postulating as many thoughts as concepts. Denyer countered that Rieger’s construction could not show that the thoughts generated are always distinct for distinct concepts. By focusing on universally quantified thoughts, rather than thoughts that attribute a concept to an individual, I give a different construction that avoids Denyer’s problem. I also note that this problem for (...) Frege’s philosophy was discovered by Bertrand Russell as early as 1902 and has been discussed intermittently since. (shrink)

All contributions included in the present issue were originally presented at an ‘Author Meets Critics’ session organised by Richard Zach at the Pacific Meeting of the American Philosophical Association in San Diego in the Spring of 2014.

In Grundgesetze der Arithmetik, Frege tried to show that arithmetic is logical by giving gap-free proofs from what he took to be purely logical basic laws. But how do we come to judge these laws as true, and to recognize them as logical? The answer must involve giving an account of the apparent arguments Frege provides for his axioms. Following Sanford Shieh, I take these apparent arguments to instead be exhibitions: the exercise of a logical capacity in order to bring (...) us into a state of judgement. I provide an account of what sort of inferential capacities are at play in such exhibitions, and explain how they lead us to judge that Frege’s primitive laws are general and undeniable. I will also situate my account with respect to other rival interpretations, particularly the elucidatory interpretations of Joan Weiner and Thomas Ricketts. (shrink)

This paper addresses an issue with the sign ‘⊢’ in Frege’s mature version of Begriffsschrift, i.e., the version in ‘Function and Concept’ and Grundgesetze. The sign is a performative for asserting in that writing down ‘⊢p’ is equivalent to asserting that p. Frege further says that writing ‘ p’ is also equivalent to identifying the reference of ‘p’ with the truth-value True. It looks as if he holds that asserting that p consists in identifying the True with the reference of (...) ‘p’. Frege’s commitment to it, however, seems to encounter a number of tensions. This paper aims to show that these tensions can be avoided by endorsing a non-assertive conception of identification under which making an identification is not making an identity assertion. The suggested reading leads to an entirely di erent understanding of the compositionality of the sign ‘⊢’ as well as Frege’s conception of assertion and judgment. (shrink)

This essay offers a detailed philosophical criticism of Frege’s popular thesis that identity is a relation of names. I consider Frege’s position as articulated both in ‘On Sense and Reference’, and in the Grundgesetze, where he appears to take an objectual view of identity, arguing that in both cases Frege is clearly committed to the proposition that identity is a relation holding between names, on the grounds that two different things can never be identical. A counterexample to Frege’s thesis is (...) considered, and a positive thesis is developed according to which, in contradistinction to the Fregean position, identity is a reflexive, symmetric, and transitive relation holding only between a thing and itself which can be expressed as a relation between names. (shrink)

It is often claimed that the theory of function levels proposed by Frege in Grundgesetze der Arithmetik anticipates the hierarchy of types that underlies Church’s simple theory of types. This claim roughly states that Frege presupposes a type of functions in the sense of simple type theory in the expository language of Grundgesetze. However, this view makes it hard to accommodate function names of two arguments and view functions as incomplete entities. I propose and defend an alternative interpretation of first-level (...) function names in Grundgesetze into simple type-theoretic open terms rather than into closed terms of a function type. This interpretation offers a still unhistorical but more faithful type-theoretic approximation of Frege’s theory of levels and can be naturally extended to accommodate second-level functions. It is made possible by two key observations that Frege’s Roman markers behave essentially like open terms and that Frege lacks a clear criterion for distinguishing between Roman markers and function names. (shrink)

A feature of Frege's philosophy of arithmetic that has elicited a great deal of attention in the recent secondary literature is his contention that numbers are ‘self‐subsistent’ objects. The considerable interest in this thesis among the contemporary philosophy of mathematics community stands in marked contrast to Kreisel's folk‐lore observation that the central problem in the philosophy of mathematics is not the existence of mathematical objects, but the objectivity of mathematics. Although Frege was undoubtedly concerned with both questions, a goal of (...) the present paper is to argue that his success in securing the objectivity of arithmetic depends on a less contentious commitment to numbers as objects than either he or his critics have supposed. As such, this paper is an articulation and defense of both Frege's analysis of arithmetic and Kreisel's observation. (shrink)

In , Frank Ramsey separates paradoxes into two groups, now taken to be the logical and the semantical. But he also revises the logical system developed in Whitehead and Russellthe intensional paradoxess interest in these problems seriously, then the intensional paradoxes deserve more widespread attention than they have historically received.

This paper is the twin of (Duží and Jespersen, in submission), which provides a logical rule for transparent quantification into hyperprop- ositional contexts de dicto, as in: Mary believes that the Evening Star is a planet; therefore, there is a concept c such that Mary be- lieves that what c conceptualizes is a planet. Here we provide two logical rules for transparent quantification into hyperpropositional contexts de re. (As a by-product, we also offer rules for possible- world propositional contexts.) One (...) rule validates this inference: Mary believes of the Evening Star that it is a planet; therefore, there is an x such that Mary believes of x that it is a planet. The other rule validates this inference: the Evening Star is such that it is believed by Mary to be a planet; therefore, there is an x such that x is believed by Mary to be a planet. Issues unique to the de re variant include partiality and existential presupposition, sub- stitutivity of co-referential (as opposed to co-denoting or synony- mous) terms, anaphora, and active vs. passive voice. The validity of quantifying-in presupposes an extensional logic of hyperinten- sions preserving transparency and compositionality in hyperinten- sional contexts. This requires raising the bar for what qualifies as co-denotation or equivalence in extensional contexts. Our logic is Tichý’s Transparent Intensional Logic. The syntax of TIL is the typed lambda calculus; its highly expressive semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The two non-standard features we need are a hyper- intension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hy- perintensions. (shrink)

Review essay covering Godehard Link, ed. One Hundred Years of Russell’s Paradox (de Gruyter 2004).

Gottlob Frege (1848-1925) was a German logician, mathematician and philosopher who played a crucial role in the emergence of modern logic and analytic philosophy. Frege's logical works were revolutionary, and are often taken to represent the fundamental break between contemporary approaches and the older, Aristotelian tradition. He invented modern quantificational logic, and created the first fully axiomatic system for logic, which was complete in its treatment of propositional and first-order logic, and also represented the first treatment of higher-order logic. In (...) the philosophy of mathematics, he was one of the most ardent proponents of logicism, the thesis that mathematical truths are logical truths, and presented influential criticisms of rival views such as psychologism and formalism. His theory of meaning, especially his distinction between the sense and reference of linguistic expressions, was groundbreaking in semantics and the philosophy of language. He had a profound and direct influence on such thinkers as Russell, Carnap and Wittgenstein. Frege is often called the founder of modern logic, and he is sometimes even heralded as the founder of analytic philosophy. (shrink)

Alonzo Church (1903–1995) was a renowned mathematical logician, philosophical logician, philosopher, teacher and editor. He was one of the founders of the discipline of mathematical logic as it developed after Cantor, Frege and Russell. He was also one of the principal founders of the Association for Symbolic Logic and the Journal of Symbolic Logic. The list of his students, mathematical and philosophical, is striking as it contains the names of renowned logicians and philosophers. In this article, we focus primarily on (...) Church’s philosophical contributions. (For an account of his life and academic history see the Introduction to The Collected Works of Alonzo Church (2019).) However, we also discuss his mathematical results when it is desirable to do so in order to pursue a philosophical issue. (shrink)

In the last two decades, there has been increasing interest in a re-evaluation of Frege’s stance towards consistency- and independence proofs. Papers by several authors deal with Frege’s views on these topics. In this note, I want to discuss one particular problem, which seems to be a main reason for Frege’s reluctant attitude towards his own proposed method of proving the independence of axioms, namely his view that thoughts, that is, intensional entities are the objects of metatheoretical investigations. This stands (...) in contrast to more straightforward interpretations, which claim that Frege’s hesitancy is mainly due to worries concerning the logical constants or what counts as a logical inference. (shrink)

The paper reconstructs three main stages in the development of Carnap’s approach to language in the years 1931 – 1947. It starts with Carnap’s approach to metalogic in his Viennese Zirkelprotokolle and his Logische Syntax der Sprache from the point of view of one-level approach to the relation between metalanguage and its object-language. It then analyzes Tarski’s turn to semantics in his paper presented at the Paris conference in September 1935, as well as the implications of his view for Carnap’s (...) approach to semantics from 1935 until 1943. Finally, it analyzes Church’s rediscovery of Frege and its impact on Carnap’s shift to the extension/intension distinction in his semantics in the years 1943 – 1947. (shrink)

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Classic Studies in the History of Ideas. South Bend, IN: St Augustine's Press, 2001, xxxvii +388 pp., pb. no price given. Belief and its Neutralization: Husserl's System of Phenomenology in Ideas I, Marcus Brainard. SUNY Series in Contemporary Continental Philosophy. Albany, NY: State University of New York, 2002, xvii + 331 pp., $86.50, pb. $29.95. The Nature of Research: Inquiry in Academic Contexts, Angela Brew. London/new York: Routledge, 2001, v + 205 pp., pb. £18.99. Critical Thinking: A Concise Guide, Tracy Bowell and Gary Kemp. London/new York: Routledge, 2002, x + 275 pp., No price given. Fodor: Language, Mind and Philosophy, M. J. Cain. Key Contemporary Thinkers. Oxford: Polity, 2002, ix + 240 pp., £50.00, pb. £14.00. The Religious, John D. Caputo. Blackwell Readings in Continental Philosophy. Oxford/maiden, MA: Blackwell, 2002, xiii + 322 pp., £55.00, pb. £16.99. 101 Philosophy Problems, Martin Cohen. 2nd ed. London/new York: Routledge, xviii + 229 pp., pb. £8.99. Hilary Putnam: Pragmatism and Realism, James Conant and Urszula M. Zeglen. Routledge Studies in Twentieth Century Philosophy. London/new York: 2002, xii + 242 pp., £50.00. Essay on the Origin of Human Knowledge, Etienne Bonnot de Condillac. Ed. and trans. Hans Aarsleff. Cambridge Texts in the History of Philosophy. Cambridge: Cambridge University Press, 2001, xlv + 225 pp., $59.95, pb. $21.95. Theories of Democracy: A Critical Introduction, Frank Cunningham. Routledge Contemporary Political Philosophy. London/new York: Routledge, 2002, vi + 248 pp., pb. £13.99. Self-Identity and Personal Autonomy: An Analytical Anthropology, Stefaan E. Cuypers. Ashgate New Critical Thinking in Philosophy. Aldershot/burlington USA/singapore/ Sydney: Ashgate, 2001, ix + 172 pp., £37.50. Stream of Consciousness: Unity and Continuity in Conscious Experience, Barry Dainton. International Library of Philosophy. London/new York: Routledge, 2000, xvi + 254 pp. Kierkegaard After MacIntyre: Essays on Freedom, Narrative, and Virtue, John J. Davenport and Anthony Rudd. Replies by Alasdair Maclntyre and Philip L. Quinn. Chicago/la Salle, IL: Open Court, 2001, xxxix + 363 pp., £47.95, pb. £22.50. What Distinguishes Human Understanding? John Deely. South Bend, IN: St Augustine's Press, 2002, xiv + 178 pp., £17.50. Acts of Religion, Jacques Derrida. Ed. with intro. by Gil Anidjar. London/new York: Routledge, 2002, vi + 436 pp., pb. £15.99. Religion and Media, Hent de Vries and Samuel Weber. Cultural Memory in the Present. Stanford, CA: Stanford University Press, 2001, xvii + 649 pp., $69.00, pb. $29.95. Art and Value, George Dickie. Oxford: Blackwell, 2001, vi + 114 pp., £45.00, pb. £11.99. Modern Philosophy from Descartes to Nietische: An Anthology, Steven M. Emmanuel and Patrick Goold. Blackwell Philosophy Anthologies. Maiden, MA/oxford: Routledge, 2002, xvii + 525 pp. The Basic Writings of Bertrand Russell, Robert Enger and Lester Denonn, with new intro. by John Slater. London/new York: Routledge, 1992, reissue: 2001, 736 pp., pb. $26.95. Democracy, David Estlund. Blackwell Readings in Philosophy. Maiden, MA/oxford: Blackwell, 2001, xii + 310 pp., £55.00, pb. £15.99. Philosophy Goes to the Movies: An Introduction to Philosophy, Christopher Falzon. London/new York: Routledge, 2002, ix + 230 pp., pb. £11.99. Arresting Language: From Leibniz to Benjamin, Peter Fenves. Meridian: Crossing Aesthetics. Stanford, CA: Stanford University Press, 2001, xiii + 379 pp., $55.00, pb. $24.95. Richard Rorty: Critical Dialogues, Matthew Festenstein and Simon Thompson. Cambridge: Polity, 2001, ix + 241 pp., £50.00, pb. £14.99. Berkeley and the Principles of Human Knowledge, Robert J. Fogelin. Routledge Philosophy Guidebooks. London/new York: Routledge, 2001, x + 166 pp., pb. £8.99. Intellectual Trust in Oneself and Others, Richard Foley. Cambridge Studies in Philosophy. Cambridge: Cambridge University Press, 2001, x + 182 pp., $55.00. Thomas Kuhn: A Philosophical History for Our Times, Steve Fuller. Chicago/london: University of Chicago Press, 2000, pb. 2001, xvii + 472 pp., pb. $22.50, 314.50. A Common Humanity: Thinking about Love and Truth and Justice, Raimond Gaita. London/new York: Routledge, 2002, xiii + 293 pp., pb. Stochastic Causality, Maria Carla Galavotti, Patrick Suppe s and Domenieo Costantini. CSLI Publications. Chicago, IL: University of Chicago Press, xii + 275 pp., $65.00, pb. $25.00; £41.00, pb. £16.00. Introduction to Logic, Harry J. Gensler. London/new York: Routledge, 2002, ix + 399 pp., pb. £15.99. Walter Benjamin: Critical Constellations, Graeme Gilloch. Key Contemporary Thinkers. Oxford: Polity, 2002, xi + 304 pp., £50.00, pb. £14.99. Between Ethics and Aesthetics: Crossing the Boundaries, Dorota Glowacka and Stephen Boos. Albany, NY: State University of New York, 2002, v + 310 pp., $81.50, pb. $27.95. Practical Rules: When We Need Them and When We Don't, Alan H. Goldman. Cambridge Studies in Philosophy. Cambridge: Cambridge University Press, 2002, xi + 210 pp., $54.95. Manners and Violence, Ignacio L. Götz. Westport, CN/london: Praeger, 2000, xiii +131 pp., £44.50. Dummett: Philosophy of Language, Karen Green. Key Contemporary Thinkers. Cambridge: Polity, 2001, xi + 236 pp., £55.00, pb. £14.99. Wittgenstein: Connections and Controversies, P. M. S. Hacker. Oxford: Clarendon Press,2001. xxiv + 375 pp., £35.00. India: A Financial Sector for the Twenty-first Century, James A. Hanson and Sanjay Kathuria. Oxford India Paperbacks. Oxford: Oxford University Press, 2002, xv + 446 pp., pb. £13.99. Socialism, Michael W. Howard. Key Concepts in Critical Theory. New York: Humanity Books, 2001, 408 pp., pb. $29.00. Ontology and the Art of Tragedy: An Approach to Aristotle's Poetics, Martha Husain. SUNY Series in Ancient Greek Philosophy. Albany, NY: State University of New York,2002. ix + 152 pp., pb. $16.95. Why Good is Good: The Sources of Morality, Robert A. Hinde. London/new York: Routledge, 2002, xiv + 241 pp., pb. £15.99. Logical Investigations, Edmund Husserl. Two vols. trans. J. N. Findlay, revised Dermot Moran with new preface by Dermot Moran and new introduction by Michael Dummett. International Library of Philosophy. London/new York: Routledge, 2001, vol. 1, Ixxxvii + 331 pp., pb. $29.95; vol. 2, xiv + 364 pp., pb. $29.95. The Shorter Logical Investigations, Edmund Husserl. Abridged ed. and trans. J. N. Findlay, abridged and revised by Dermot Moran with new preface by Dermot Moran and new introduction by Michael Dummett. London/new York: Routledge, 2001, Ixxxv + 422 pp., pb. $27.95. The Political, David Ingram. Blackwell Readings in Philosophy. Maiden, MA/ Oxford: Blackwell, 2001, xii + 310 pp., £60.00, pb. £15.99. Hegel, M. J. In wood. Arguments of the Philosophers. London/new York: Routledge, xxxiv + 582 pp., pb. Reconsidering Michael Polanyi's Philosophy, Stefania Ruzsits Jha. Pittsburgh, PA: University of Pittsburgh Press, 2002, viii + 318 pp., $32.00. Speaking the Unspeakable: Religion, Misogyny, and the Uncanny Mother in Freud's Cultural Texts, Diane Jone-Pace. Berkeley: University of California Press, 2001, x + 190 pp., $45.00, pb. $17.95, £29.95, pb. £12.95. Free Will, Robert Kane. Blackwell Readings in Philosophy. Maiden, MA/oxford: Blackwell, 2001, xii + 310 pp., £55.00, pb. £15.99. Wittgenstein: Biography and Philosophy, James C. Klagge. Cambridge: Cambridge University Press, 2001, xv + 272 pp., $54.95, pb. $19.95. Frege and the Logic of Sense and Reference, Kevin C. Klement. Studies in Philosophy: Outstanding Dissertations. New York/london: Routledge, 2002, xiii + 260 pp., $70.00. The Presence of Myth, Leszek Kolakowski. Chicago, IL/london: University of Chicago Press, pb. ed. 2001, xii + 138 pp., $13.00, £8.50. Justifying Emotions: Pride and Jealousy, Kristján Kristjansson. Routledge Studies in Ethics and Moral Theory. London/new York: Routledge, 2001, xii + 257 pp., £50.00. Understanding Philosophy of Science, James Ladyman. London/new York: Routledge, 2002, xiii + 290 pp., pb. £12.99. Infinite Minds: A Philosophical Cosmology, John Leslie. Oxford: Clarendon Press, 2001, xi + 234 pp., £25.00. Appositions of Jacques Derrida and Emmanuel Levinas, John Llewelyn. Bloomington, IN: Indiana University Press, 2002, xx + 255 pp., $49.95, pb. $24.95. Logic, Form, and Grammar. Peter Long. International Library of Philosophy. London/new York: Routledge, 2000, x + 109 pp. Metaphysics: A Contemporary Introduction, Michael J. Loux. Routledge Contemporary Introductions to Philosophy. London/new York: Routledge, 2002, xiii + 303 pp., pb. £13.99. Metaphysics: Contemporary Readings, Michael J. Loux. Routledge Contemporary Readings in Philosophy. London/new York: Routledge, 2002, xii + 555 pp., pb. £16.99. The Metaphysicians of Meaning: Russell and Frege on Sense and Denotation, Gideon Makin. International Library of Philosophy. London/new York: Routledge, 2000, ix + 229 pp. Towards a Critical Theory of Society, Herbert Marcuse. Collected Papers of Herbert Marcuse 2. London/new York: Routledge, 2001, xiii + 242 pp., £19.99. Kierkegaard in the Present Age, Gordon Marino. Pref. by Philip Rieff. Marquette Studies in Philosophy 27. Milwaukee, WI: Marquette University Press, 2001, 124 pp. An Introduction to the Philosophy of Mind, K. T. Maslin. Cambridge: Polity, 2001, xviii + 332 pp., no price given. The Philosophy of Merleau-Ponty, Eric Matthews. Continental European Philosophy. Chesham, UK: Acumen, 2002, vi + 186 pp., £40.00, pb. £14.95. Mind and Mechanism, Drew McDermott. Bradford Books. Cambridge, MA/london: MIT Press, 2001, xv + 262 pp., $32.95. Approaches to Wittgenstein: Collected Papers, Brian McGuinness. London/new York: Routledge, 2002, xv + 299 pp., £50.00. Collective Rationality and Collective Reasoning, Christopher McMahon. Cambridge: Cambridge University Press, 2001, ix + 251 pp., $54.95, pb. $19.95. Authority and Estrangement: An Essay on Self-Knowledge, Richard Moran. Princeton, NJ: Princeton University Press, 2001, xxxv + 202 pp., £35.00, pb. £11.95. The Sublime in Kant and Beckett Aesthetic Judgement, Ethics and Literature, Bjørn K. Myskja. Kantstudien 140. Berlin/new York: Walter de Gruyter, 2002, xii + 313 pp., no price given. Spinoza's Heresy: Immortality and the Jewish Mind, Steven Nadler. Oxford: Clarendon Press, 2001, xvi + 225 pp., £22.50. Arguing About Art: Contemporary Philosophical Debates, Alex Neill and Aaron Ridley. 2nd ed. London/new York: Routledge, 2002, xiii + 479 pp. Building on Frege: New Essays on Sense, Content, and Concept, Albert Newen, Ulrich Nortmann and Rainer Stuhlmann-Laeisz. CSLI Publications. Chicago, IL: University of Chicago Press, xxiv + 351 pp., $65.00, pb. $23.00, £41.00, pb. £14.50. Naturalism and Religion, Kai Nielsen. Amherst, NY: Prometheus Books, 2001, 506 pp., $40.00. Beyond Good and Evil: Prelude to a Philosophy of the Future, Friedrich Nietzsche. Ed. Rolf-Peter Horstmann and Judith Norman; trans. Judith Norman. Cambridge Texts in the History of Philosophy. Cambridge: Cambridge University Press, 2001, xxxiv + 193 pp., $38.00, pb. $14.00. Truth Matters: Realism, Anti-Realism and Response-Dependence, Christopher Norris. Edinburgh: Edinburgh University Press, 2002, viii + 228 pp., £40.00. Naturalism and the Human Condition: Against Scientism, Frederick A. Olafson. London/ New York: Routledge, 2001, xi + 115 pp., pb. £13.99. Wittgenstein's Tractatus: A Dialectical Interpretation. Matthew B. Ostrow. Cambridge: Cambridge University Press, 2002, x + 175 pp., $55.00, pb. $20.00. Land, Value, Community: Callicott and Environmental Philosophy, Wayne Ouderkirk and Jim Hill. Albany, NY: State University of New York, 2002, ix + 358 pp., $73.50, pb. $24.95. Philosophy and the Adventure of the Virtual: Bergson and the Time of Life, Keith Ansell Pearson. London/new York: Routledge, 2002, ix + 246 pp., $80.00, pb. $38.95. Environmental Culture: The Ecological Crisis of Reason, VaI Plum wood. Environmental Philosophies. London/new York: Routledge, 2002, vii + 291 pp., pb. £13.99. Ethical Life: The Past and Present of Ethical Cultures, Harry Redner. Lanham/boulder/ New York/oxford: Rowman and Littlefield, 2001, ix + 348 pp., $80.00, pb. $32.95. Paradoxes: Their Roots, Range, and Resolution, Nicholas Rescher. Chicago/la Salle, IL: Open Court, 2001, xxiii + 293 pp., £44.50, pb. £20.95. Medicine, Magic and Religion, W. H. R. Rivers. The Fitzpatrick Lectures. Routledge Classics. Preface by G. Elliot Smith. London/new York: Routledge, 2001, viii + 136 pp.. No price given. Is it Righteous to Be? Interviews with Emannuel Levinas, Jill Robbins. Meridian: Crossing Aesthetics. Stanford, CA: Stanford University Press, 2001, ix + 305 pp., $55.00, pb. $24.95. Philosophy of Science: A Contemporary Introduction, Alex Rosenberg. Routledge Contemporary Introductions to Philosophy. London/new York: Routledge, 2000, x + 191 pp. ABC of Relativity, Bertrand Russell. 6th ed. with intro. by Peter Clark. London/ny: Routledge, 1992, reissue: 2001, xvi + 155 pp., pb. $15.95. What is Truth? Richard Schantz. Current Issues in Theoretical Philosophy 1. Berlin/ New York: Walter de Gruyter, 2002, vi + 338 pp., no price given. The BlackweU Guide to Social and Political Philosophy, Robert L. Simon. Blackwell Philosophy Guides. Maiden, MA/oxford: Blackwell, 2002, xi + 329 pp., £60.00, pb. £16.99. The Unfinished Project: Toward a Postmetaphysical Humanism, Lorenzo C. Simpson. London/ny: Routledge, 2001, xi +180 pp., $85.00, pb. $22.95. Hegel and the Phenomenology of Spirit, Robert Stern. Routledge Guidebooks. London / New York: 2001, xviii + 234 pp., pb. £8.99. Wittgenstein, Avrum Stroll. Oxford: Oneworld Publications, 2002, ix + 162 pp., pb. $14.95. Matters of Mind: Consciousness, Reason and Nature, Scott Sturgeon. International Library of Philosophy. London/new York: Routledge, 2000, x + 166 pp. Marx for a Post-Communist Era, Stefan Sullivan. London/new York: Routledge, 2002, x + 191 pp., pb. £14.99. Critical Reasoning: A Practical Introduction, Arme Thompson. 2nd ed. London/new York: Routledge, 2002, ix + 209 pp., pb. £12.99. Hyperreality: Paradigm for the Third Millennium, John Tiffin and Nobuyoshi Terashima. London/new York: Routledge, 2001, vvii +165 pp., price not given. Foucault and Latin America: Appropriations and Deployments of Discoursive Analysis, Benigno Trigo. New York/london: Routledge, 2002, xxi + 305 pp., pb. £16.99. Knowledge, Michael Welbourne. Central Problems of Philosophy. Chesham, UK: Acumen, 2001, xiii + 143 pp., £35.00, pb. £12.95. Philosophy, Literature and the Human Good, Michael Weston. London/new York: Routledge, 2001, xix + 198 pp., pb. £14.99. A Clearing in the Forest: Law, Life, and Mind, Steven L. Winter. Chicago/london: University of Chicago Press, 2001, xvii + 440 pp., $38.00/£24.00. Kant, Herder, and the Birth of Anthropology, John H. Zammito. Chicago/london: University of Chicago Press, 2002, xii + 576 pp., pb. $29.00, £18.50. (shrink)