This essay consists of two parts. In the first part, I focus my attention on the remarks that Frege makes on consistency when he sets about criticizing the method of creating new numbers through definition or abstraction. This gives me the opportunity to comment also a little on H. Hankel, J. Thomae—Frege’s main targets when he comes to criticize “formal theories of arithmetic” in Die Grundlagen der Arithmetik (1884) and the second volume of Grundgesetze der Arithmetik (1903)—G. Cantor, L. E. (...) J. Brouwer and D. Hilbert (1899). Part 2 is mainly devoted to Hilbert’s proof theory of the 1920s (1922–1931). I begin with an account of his early attempt to prove directly, and thus not by reduction or by constructing a model, the consistency of (a fragment of) arithmetic. In subsequent sections, I give a kind of overview of Hilbert’s metamathematics of the 1920s and try to shed light on a number of difficulties to which it gives rise. One serious difficulty that I discuss is the fact, widely ignored in the pertinent literature on Hilbert’s programme, that his language of finitist metamathematics fails to supply the conceptual resources for formulating a consistency statement qua unbounded quantification. Along the way, I shall comment on W. W. Tait’s objection to an interpretation of Hilbert’s finitism by Niebergall and Schirn, on G. Gentzen’s allegedly finitist consistency proof for Peano Arithmetic as well as his ideas on the provability and unprovability of initial cases of transfinite induction in pure number theory. Another topic I deal with is what has come to be known as partial realizations of Hilbert’s programme, chiefly advocated by S. G. Simpson. Towards the end of this essay, I take a critical look at Wittgenstein’s views about (in)consistency and consistency proofs in the period 1929–1933. I argue that both his insouciant attitude towards the emergence of a contradiction in a calculus and his outright repudiation of metamathematical consistency proofs are unwarranted. In particular, I argue that Wittgenstein falls short of making a convincing case against Hilbert’s programme. I conclude with some philosophical remarks on consistency proofs and soundness and raise a question concerning the consistency of analysis. (shrink)

O presente manual tem como intenção constituir um guia para uma disciplina introdutória de filosofia da linguagem. Foi elaborado a partir da leccionação da disciplina de Filosofia da Linguagem I na Faculdade de Letras da Universidade do Porto desde 2001. A disciplina de Filosofia da Linguagem I ocupa um semestre lectivo e proporciona aos estudantes o primeiro contacto sistemático com a área da filosofia da linguagem. Pretende-se que este manual ofereça aos estudantes os instrumentos necessários não apenas para acompanhar uma (...) iniciação ao campo da filosofia da linguagem mas também para o estudo e a investigação autónomos posteriores. Para isso é percorrido um trajecto que conduz das intuições pré-teóricas acerca de linguagem, de que todos dispomos, até um conhecimento disciplinar específico, histórico e temático, da filosofia da linguagem. Em termos práticos, são considerados como precedentes da disciplina de Filosofia da Linguagem I – mesmo se, pelo existem actualmente precedências em sentido estrito – as disciplinas de Lógica I e II e de Filosofia do Conhecimento I e II. Os programas dessas disciplinas nos últimos anos estiveram presentes por trás da elaboração do manual. (shrink)

When reasons are given for compositionality, the arguments usually purport to establish compositionality in an almost a priori manner. I will rehearse these arguments why one could think that compositionality is a priori true, or almost a priori true, and will find all of them inconclusive. This, in itself, is no reason against compositionality, but a reason to try to establish or defend the principle on other than quasi-a priori grounds.

In this essay I will consider two theses that are associated with Frege,and will investigate the extent to which Frege really believed them.Much of what I have to say will come as no surprise to scholars of thehistorical Frege. But Frege is not only a historical figure; he alsooccupies a site on the philosophical landscape that has allowed hisdoctrines to seep into the subconscious water table. And scholars in a widevariety of different scholarly establishments then sip from thesedoctrines. I believe (...) that some Frege-interested philosophers at various ofthese establishments might find my conclusions surprising.Some of these philosophical establishments have arisen from an educationalmilieu in which Frege is associated with some specific doctrine at theexpense of not even being aware of other milieux where other specificdoctrines are given sole prominence. The two theses which I will discussillustrate this point. Each of them is called Frege''s Principle, but byphilosophers from different milieux. By calling them milieux I do not want to convey the idea that they are each located at some specificsocio-politico-geographico-temporal location. Rather, it is a matter oftheir each being located at different places on the intellectuallandscape. For this reason one might (and I sometimes will) call them(interpretative) traditions. (shrink)

The implicit-explicit distinction is applied to knowledge representations. Knowledge is taken to be an attitude towards a proposition which is true. The proposition itself predicates a property to some entity. A number of ways in which knowledge can be implicit or explicit emerge. If a higher aspect is known explicitly then each lower one must also be known explicitly. This partial hierarchy reduces the number of ways in which knowledge can be explicit. In the most important type of implicit knowledge, (...) representations merely reflect the property of objects or events without predicating them of any particular entity The dearest cases of explicit knowledge of a fact are representations of one's own attitude of knowing that fact. These distinctions are discussed in their relationship to similar distinctions such as procedural-declarative, conscious unconscious, verbalizable-nonverbalizable, direct-indirect tests, and automatic voluntary control. This is followed by an outline of how these distinctions can be used to integrate and relate the often divergent uses of the implicit-explicit distinction in different research areas. We illustrate this for visual perception, memory, cognitive development, and artificial grammar learning. (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)

This paper explores early Australasian philosophy in some detail. Two approaches have dominated Western philosophy in Australia: idealism and materialism. Idealism was prevalent between the 1880s and the 1930s, but dissipated thereafter. Idealism in Australia often reflected Kantian themes, but it also reflected the revival of interest in Hegel through the work of ‘absolute idealists’ such as T. H. Green, F. H. Bradley, and Henry Jones. A number of the early New Zealand philosophers were also educated in the idealist tradition (...) and were influential in their communities, but produced relatively little. In Australia, materialism gained prominence through the work of John Anderson, who arrived in Australia in 1927, and continues to be influential. John Anderson had been a student of Henry Jones, who might therefore be said to have influenced both main strands of Australian philosophical thought. (shrink)

The new theory of reference has won popularity. However, a number of noted philosophers have also attempted to reply to the critical arguments of Kripke and others, and aimed to vindicate the description theory of reference. Such responses are often based on ingenious novel kinds of descriptions, such as rigidified descriptions, causal descriptions, and metalinguistic descriptions. This prolonged debate raises the doubt whether different parties really have any shared understanding of what the central question of the philosophical theory of reference (...) is: what is the main question to which descriptivism and the causal-historical theory have presented competing answers. One aim of the paper is to clarify this issue. The most influential objections to the new theory of reference are critically reviewed. Special attention is also paid to certain important later advances in the new theory of reference, due to Devitt and others. (shrink)

Given the large literature on Frege, one might believe that it would be impossible to say anything essentially new on the subject. This book contradicts this belief, calling attention to Frege's in...

This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes of Grundlagen are developed: the relationship Frege envisions between arithmetic and geometry and (...) the way in which the study of reasoning is to illuminate this. In the final section, it is argued that the sorts of issues Frege attempted to address concerning the character of mathematical reasoning are still in need of a satisfying answer. (shrink)

This paper addresses the question whether introspection plus externalism about mental content warrant an a priori refutation of external-world skepticism and ontological solipsism. The suggestion is that if thought content is partly determined by affairs in the environment and if we can have non-empirical knowledge of our current thought contents, we can, just by reflection, know about the world around us -- we can know that our environment is populated with content-determining entities. After examining this type of transcendental argument and (...) discussing various objections found in the literature, I argue that the notion of privileged self-knowledge underlying this argument presupposes that we can learn, via introspection, that our so-called thoughts are propositional attitudes rather than contentless states. If, however, externalism is correct and thought content consists in the systematic dependency of internal states on relational properties, we cannot know non-empirically whether or not we have propositional attitudes. Self-knowledge (apropositional attitude) is consistent with us lacking the ability to rule out, via introspection, the possibility that we don't have any propositional attitudes. Self-knowledge provides us with knowledge of what is in our minds, but not that we have minds. Hence, the combination of externalism with the doctrine of privileged self-knowledge does not allow for an a priori refutation of skepticism and is therefore unproblematic. (shrink)

The Analytic Tradition in Philosophy is an excellent successor to an excellent book : It is a fine an example of the necromantic style in the history of philosophy where the object of the exercise is to resurrect the mighty dead in order to get into an argument with them, either because we think them importantly right or instructively wrong. However what was a pardonable a simplification and a reasonable omission in the earlier book has now metamorphosed into a sin (...) of omission and an oversimplification in its successor—the book lacks is an adequate discussion of the Ramified Theory of Types and Russell’s reasons for adopting it. I conclude with a brief meditation on Open Question Arguments and the threats that they pose to some of the analyses proposed by Russell and Moore themselves. (shrink)

In this symposium contribution I critically review the first two chapters, on Frege, in Volume 1 of The Analytic Tradition in Philosophy by Scott Soames.

This is a Festschrift volume dedicated to Jan Woleński, whose extensive work in the history of Polish logic indeed deserves one. Accordingly, it is mostly devoted to Woleński's main interests: the...

The paper discusses the emergence of Frege's puzzle and the introduction of the celebrated distinction between sense and reference in the context of Frege's logicist project. The main aim of the paper is to show that not logicism per se is mainly responsible for this introduction, but Frege's constant struggle against formalism. Thus, the paper enlarges the historical context, and provides a reconstruction of Frege's philosophical development from this broader perspective.

Two standard epistemological accounts are conflated in Dienes & Perner's account of knowledge, and this conflation requires the rejection of their four conditions of knowledge. Because their four metarepresentations applied to the explicit-implicit distinction are paired with these conditions, it follows by modus tollens that if the latter are inadequate, then so are the former. Quite simply, their account misses the link between true reasoning and knowledge.

This entry introduces the reader to the main ideas in Frege's philosophy of logic, mathematics, and language.

Gottlob Frege famously rejects the methodology for consistency and independence proofs offered by David Hilbert in the latter's Foundations of Geometry. The present essay defends against recent criticism the view that this rejection turns on Frege's understanding of logical entailment, on which the entailment relation is sensitive to the contents of non-logical terminology. The goals are (a) to clarify further Frege's understanding of logic and of the role of conceptual analysis in logical investigation, and (b) to point out the extent (...) to which his understanding of logic differs importantly from that of the model-theoretic tradition that grows out of Hilbert's work. (shrink)

This paper discusses George Boole’s two distinct approaches to the explanatory relationship between logical and psychological theory. It is argued that, whereas in his first book he attributes a substantive role to psychology in the foundation of logical theory, in his second work he abandons that position in favour of a linguistically conceived foundation. The early Boole espoused a type of psychologism and later came to adopt a type of anti-psychologism. To appreciate this invites a far-reaching reassessment of his philosophy (...) of logic. (shrink)

Existe en Frege no solo una concepción intencional de la conciencia, sino también uma concepción motivacional de su causalidad, esto es, Frege concibe la idea de una causalidade específica, diferente de la científico-natural, y que tiene como presupuesto la existência de estados intencionales. En tal sentido, existe un interesante punto de contacto entre Frege y Husserl.

This paper discusses how we understand and use a concept or the meaningof a general term to identify the objects falling under the term. There aretwo distinct approaches to research on the problems of concepts and meaningthe psychological approach and the formal (or logical) approach. My majorconcern is to consider the possibility of reconciling these two differentapproaches, and for this I propose to build a psychologically plausibleformal system of conceptualization. That is, I will develop a theory-basedaccount of concepts and propose (...) an explanation of how an agent activates aperspective (which consists of theories) in response to a situation in whichreasoning using a concept is called for. Theories are represented as sets offacts and rules, both strict and defeasible. Each theory is organized in acoherent perspective which stands for an agent's mental state or an agent'smodel of another agent's perspective. Perspectives are organized intohierarchies and the theory for a concept in one perspective may defeat thetheory for the same concept in another perspective. Which perspective issuperior is context-dependent. (shrink)