Oswaldo Chateaubriand | Pontifícia Universidade Católica do Rio de Janeiro (original) (raw)

Books by Oswaldo Chateaubriand

Frege never developed a theory of senses in his published works. In particular, he did not addres... more Frege never developed a theory of senses in his published works. In particular, he did not address the question as to the status of senses as entities. Are senses objects or concepts? There is not a word about this in "On Sense and Reference" and related articles. When he contrasts objects with functions in §3 of The Basic Laws of Arithmetic, he lists numbers, truth-values, and courses-ofvalues, but not senses, as objects. 1 In one of his unpublished manuscripts, however, Frege draws a distinction for senses that parallels his distinction between objects and functions. Senses of objects, or senses that purport to be senses of objects, are objects, whereas senses of functions, or senses that purport to be senses of functions, are functions. 2

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Structuring reality: properties, sets, and states of affairs Frege's ontology can be interpreted ... more Structuring reality: properties, sets, and states of affairs Frege's ontology can be interpreted as a hierarchy of functions and objects. Objects appear exclusively at the bottom level 0 and are characterized as everything that is not a function. Functions appear at all higher levels and have as arguments and values entities of lower levels. Frege's fundamental distinction between functions and objects is that the former are incomplete and the latter complete. He also says that functions are unsaturated whereas objects are saturated. An object can be the reference of a name and a concept can have a somewhat analogous relation to a predicate. Concepts, including relations, are functions which applied to (or saturated by) appropriate arguments give as value (or result in) one of the two truth-values. 1

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The True and the False revisited: Frege's logic Frege is held to be largely responsible for debun... more The True and the False revisited: Frege's logic Frege is held to be largely responsible for debunking the traditional conception that all sentences are of subject-predicate form, partly because of his relational analysis of sentences, but mostly because of his analysis of quantification. The combination of quantifiers and connectives is not considered to be a subject-predicate combination. Although Frege explicitly rejects the traditional subject-predicate distinction in Begriffsschrift and does not separate notationally nonlogical predicates from non-logical subjects, his logical analysis is a sharpening of the traditional subject-predicate analysis. It is clear from Frege's ontological analysis that the combinations of quantifiers and connectives are properties, or concepts, or functions. And it is also clear from his notation, for he separates the logical properties from the non-logical subjects.

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Tarski suggests a characterization of truth as denotation of states of affairs in his paper "The ... more Tarski suggests a characterization of truth as denotation of states of affairs in his paper "The Semantic Conception of Truth". After formulating what he calls "the classical Aristotelian conception of truth", encapsulated by the formula

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Although in recent times the notion of fact, or of state of affairs, made something of a come bac... more Although in recent times the notion of fact, or of state of affairs, made something of a come back, for many years it was considered a disreputable notion. 1 What is it about facts, or states of affairs, or similar entities, that is so problematic? As I see it, there are three main reasons for questioning such entities. To begin with, there is the claim that various arguments show that if one ascribes denotation to sentences, then all distinctions collapse to the two truth-values. So, the most natural interpretation of facts, or states of affairs, as the denotation of sentences seems to be blocked by these arguments. By discussing in some detail the arguments given by Frege, Church, Davidson, and Gödel, I have tried to show that they do not establish that conclusion.

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COLEÇÃO CLE, 2001

The main question treated in this book is the relation between statements (sentences, proposition... more The main question treated in this book is the relation between statements (sentences, propositions) and reality. The book is the first volume of a larger work about the fundamental (ontological, epistemological, linguistic) character of logic. My viewpoint is a realistic and metaphysical view of logic and truth influenced to a very large extent by works of Plato, Aristotle, Frege, Russell, Gödel, and Hardy, among others. Hence the title "Logical Forms", inspired by Plato. I list below the titles of the chapters in lieu of an abstract.

Introduction. Logic, ontology, and epistemology.
1. Truth, description, and identification.
2. The True and the False.
3. Use, mention, and Russell's theory of descriptions.
4. Arguments for Frege's thesis.
5. Objections to facts.
6. Truth, denotation, and interpretations.
7. Tarski's semantic conception of truth.
8. The True and the False revisited: Frege's logic.
9.Structuring reality: properties, sets, and states of affairs.
10. Identity and extensionality.
11. Senses.
12. Truth and correspondence.

A translation to Spanish--Formas Lógicas I--was published by Eudeba in 2015 and I added some information and a link to Eudeba in TRANSLATIONS.

A translation to Portuguese--Lógica, ontologia e epistemologia --of the Introduction was published in 2006 and I added the pdf in TRANSLATIONS.

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Coleção CLE, 2005

This volume continues the discussion initiated in Part 1 of "Logical Forms" and deals with issues... more This volume continues the discussion initiated in Part 1 of "Logical Forms" and deals with issues of language, logic, proof, and knowledge. I list the chapter titles:
13. Language, meaning, and reference.
14. Syntax and semantics.
15 Grammar and logical form.
16. Propositional logic.
17. Predicate logic.
18. Grammar and logical truth.
19. Proof and logical deduction.
20. Proof and proving.
21. Proof and truth.
22. The tyranny of belief.
23. Ockham's razor.
24. Knowledge and justification.
25. Logic and knowledge.
Epilogue. Plato, Zeno, Parmenides, and Frege.

A translation to Portuguese of chapter 25--Lógica e conhecimento--was published in 2007 and I added the pdf in TRANSLATIONS.

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Papers by Oswaldo Chateaubriand

Trends in logic, 2014

In this chapter I discuss some traditional philosophical questions relating to propositional logi... more In this chapter I discuss some traditional philosophical questions relating to propositional logic, among which are the following: (1) Must the objects of propositional logic (propositions, sentences, thoughts, judgments, etc.) have structure? (2) What is the nature of quantification in propositional logic? (3) What is the connection between material implication and the material conditional? (4) What is the role of the material conditional in propositional logic? (5) What is the role of truth-values?

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Manuscrito, 2007

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O Que nos faz pensar, Nov 1, 1994

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Philosophia Verlag GmbH eBooks, Oct 20, 2005

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Manuscrito, 2008

In my response to Guillermo Rosado-Haddock I discuss the two main issues raised in his paper. The... more In my response to Guillermo Rosado-Haddock I discuss the two main issues raised in his paper. The first is that by allowing Henkin’s general models as a legitimate model-theoretic interpretation of second-order logic, I undermine my defense of second-order logic against Quine’s views concerning the primacy of firstorder logic. The second is that my treatment of logical truth and logical properties does not take into account various systems of logic and properties of systems of logic such as the Lowenheim-Skolem property. Resumo: Em minha replica a Guillermo Rosado-Haddock discuto as duas questoes centrais levantadas em seu artigo. A primeira e que ao permitir modelos gerais de Henkin como uma interpretacao legitima da logica de segunda ordem, desvirtuo minha defesa da logica de segunda ordem contra a visao de Quine respeito a primazia da logica de primeira ordem. A segunda e que meu tratamento da verdade logica e das propriedades logicas nao leva em consideracao diversos sistemas de logica e propriedades de sistemas de logica tais como a propriedade de Lowenheim-Skolem. Palavras chave: Verdade logica. Propriedade logica. Logica de segunda ordem. Modelos gerais.

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Manuscrito, 2008

The paper by Jairo Jose da Silva is mainly concerned with the character of mathematical proof and... more The paper by Jairo Jose da Silva is mainly concerned with the character of mathematical proof and with the nature of mathematics and its ontology. Although there is a fair amount of agreement in our views, I focus my response on three issues on which we disagree. The first is his view of mathematical proof as generally unconstrained by language and by a previous proof apparatus. The second is his discussion of Brouwer’s views on proof and formalization. The third is his nominalistic account of structuralism. Resumo:O artigo de Jairo Jose da Silva explora principalmente o carater das provas matematicas e a natureza ontologica da matematica. Apesar de haver bastante concordância em nossos pontos de vista, o foco de minha replica sao tres questoes em que discordamos. A primeira e sua visao da prova matematica como completamente livre de restricoes impostas pela linguagem e por um aparato previo de prova. A segunda e sua discussao de Brouwer em relacao a prova e a formalizacao. A terceira e sua formulacao nominalista do estruturalismo.Palavras chave: Prova matematica. Prova formal. Estruturalismo. Brouwer

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COLEÇÃO CLE, 2001

A translation to Spanish--Formas Lógicas I--was published by Eudeba in 2015 and I added some information and a link to Eudeba in TRANSLATIONS.

A translation to Portuguese--Lógica, ontologia e epistemologia --of the Introduction was published in 2006 and I added the pdf in TRANSLATIONS.

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Coleção CLE, 2005

A translation to Portuguese of chapter 25--Lógica e conhecimento--was published in 2007 and I added the pdf in TRANSLATIONS.

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Trends in logic, 2014

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Manuscrito, 2007

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O Que nos faz pensar, Nov 1, 1994

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Philosophia Verlag GmbH eBooks, Oct 20, 2005

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Manuscrito, 2008

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Manuscrito, 2008

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Heyting A.. After thirty years. Logic, methodology and philosophy of science, Proceedings of the 1960 International Congress, edited by Nagel Ernest, Suppes Patrick, and Tarski Alfred, Stanford University Press, Stanford, California, 1962, pp. 194–197

Journal of Symbolic Logic, Dec 1, 1971

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Journal of Symbolic Logic, Dec 1, 1971

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Journal of Symbolic Logic, Feb 1, 1970

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Manuscrito, 2003

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Manuscrito, 2005

In this paper I examine arguments by Benacerraf and by Chihara against Godel’s platonistic philos... more In this paper I examine arguments by Benacerraf and by Chihara against Godel’s platonistic philosophy of mathematics.

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Manuscrito, 2004

In §§1-2 I consider some issues that Guillermo raises in connection with Husserl, especially the ... more In §§1-2 I consider some issues that Guillermo raises in connection with Husserl, especially the distinction between the notion of state of affairs and the more general notion of situation of affairs conceived as a common substratum for different states of affairs. After a few remarks about Church’s slingshot argument in §3, I discuss several objections that Guillermo raises to my interpretation of Frege (§4), to Kripke’s notion of rigid designator (§5) and to my objections to Tarski’s semantic conception of truth (§6).

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Journal of Symbolic Logic, Dec 1, 1969

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Manuscrito, 2004

In §1 I explain that my rejection of possible (and impossible) states of affairs as a basis for a... more In §1 I explain that my rejection of possible (and impossible) states of affairs as a basis for an account of falsity is not part of a general rejection of modal notions but is a rejection of possible and impossible entities of any sort. I then show that my account of senses and of propositions is indeed a modal account. In §2 I examine some of Wittgenstein’s ideas about falsity, as presented by Luiz Carlos, in relation to my account of falsity and negation. In §3 I discuss the modal aspects of identification for propositions.

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Manuscrito, 2008

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Manuscrito, 2004

After some preliminary remarks in §1, I argue in §2 that Claudio’s considerations about my treatm... more After some preliminary remarks in §1, I argue in §2 that Claudio’s considerations about my treatment of Quine’s Bizet-Verdi counterfactuals do not constitute a difficulty for the structural analysis of such counterfactuals. I discuss some of his other examples and argue that counterfactuals are ambiguous both structurally and contextually. I conclude with an examination of the principle of transitivity for counterfactuals.

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Manuscrito, 2008

Javier Legris examines my views on symbolism and logical form in relation to two important distin... more Javier Legris examines my views on symbolism and logical form in relation to two important distinctions emphasized by Jean van Heijenoort—the distinction between logic as calculus and logic as universal language, and the distinction between absolutism and relativism in logic. I generally agree with his considerations and focus my response on some relevant aspects of classical logic. Resumo: Javier Legris examina minhas consideracoes sobre simbolismo e forma logica em relacao a duas distincoes enfatizadas por Jean van Heijenoort: a distincao entre logica como calculo e logica como linguagem universal, e a distincao entre absolutismo e relativismo na logica. Estou basicamente de acordo com suas observacoes e em minha replica enfoco alguns aspectos relevantes da logica classica. Palavras chave: Simbolismo. Forma logica. Calculo logico. Linguagem.

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Unpublished translation to English of the paper "Negação em Logical Forms" published in O Que Nos Faz Pensar 23, 2008., 2019

In this paper I briefly discuss some central theses of my book Logical Forms concerning the notio... more In this paper I briefly discuss some central theses of my book Logical Forms concerning the notions of negation, logical form, truth, and falsity, and some of their interconnections.

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Eudeba, 2015

Referencia a la traducción en español de Logical Forms. Part I publicada por Eudeba en 2015.

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Plenárias da ANPOF 2004/2006, 2006

Este texto é a tradução da introdução do livro Logical Forms feita por Guido Imaguire e revisada ... more Este texto é a tradução da introdução do livro Logical Forms feita por Guido Imaguire e revisada pelo próprio autor (que também fez algumas pequenas alterações no texto e é responsável por sua forma final). Muitas citações de textos originais nas notas de rodapé foram suprimidas na tradução.

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Metafísica: Ontologia e História. Atas do II Colóquio Internacional de Metafísica. Natal: Editora da UFRN, 2009

Neste artigo apresento uma teoria abstrata dos sentidos, pensamentos e verdade inspirada em idéia... more Neste artigo apresento uma teoria abstrata dos sentidos, pensamentos e verdade inspirada em idéias de Frege. "Inspirada", pois, em grande parte, não pretendo interpretar Frege em um sentido literal, mas, antes, desenvolver algumas de suas idéias de modo a preservar aspectos destas que me parecem importantes. Sentidos são caracterizados como propriedades identificadoras; i. e., grosso modo, como propriedades que, em virtude de sua estrutura lógica, se aplicam a exatamente uma coisa-caso se apliquem a alguma coisa. Quando a análise de Frege das sentenças em termos de função e argumento é combinada com sua análise da quantificação como predicação de ordem superior, todas as sentenças (tanto as formais quanto as informais) podem ser analisadas de vários modos diferentes como uma função (predicação) aplicada a um ou mais argumentos. Isto abre caminho para uma caracterização abstrata de pensamentos como sentidos que combinam outros sentidos de um modo uniforme e cuja verdade deriva de sua instanciação pelos itens correspondentes da realidade.

Nota: Em dezembro de 2005 participei de um colóquio sobre a noção de verdade em Frege na Universidade Federal de Santa Maria onde apresentei uma palestra titulada “The truth of thoughts: Variations on fregean themes”. Em novembro de 2006 participei do II Colóquio Internacional de Metafísica em Natal onde apresentei uma palestra titulada “An abstract theory of senses, propositions, and truth”, com um conteúdo semelhante ao da palestra de Santa Maria. O presente texto é uma tradução, feita por Sérgio Schultz e revisada por mim, do texto em Inglês redigido para o número especial de Grazer Philosophische Studien (Chateaubriand 2007), e é publicado aqui com a autorização dos respectivos editores.

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Analytica, 2007

Translation to Portuguese of chapter 25 of Logical Forms-Part II. Na parte inicial do texto cons... more Translation to Portuguese of chapter 25 of Logical Forms-Part II.

Na parte inicial do texto considero várias perspectivas epistemológicas sobre os problemas de fundamentos levantados pelos paradoxos da lógica e da teoria de conjuntos no início do século vinte. Esta discussão está centrada, principalmente, nos pontos de vista de Russell, Hilbert, Brouwer e Gödel. A parte final do texto consiste de um breve exame de questões filosóficas sobre a noção de prova.

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Elenchos, 2016

"On Denoting" marca un punto de inflexión fundamental en la perspectiva filosófica de Russell. Co... more "On Denoting" marca un punto de inflexión fundamental en la perspectiva filosófica de Russell. Con el análisis de las frases denotativas, la formulación de la distinción entre conocimiento por familiaridad y conocimiento por descripción, y el uso implícito de la navaja de Ockham como una herramienta eliminadora, se establecen las bases de gran parte del posterior trabajo filosófico y lógico de Russell, incluyendo el atomismo lógico, la teoría de las no-clases, y la jerarquía ramificada de los tipos. Aunque se ha dicho que Russell fue "un filósofo sin una filosofía" (Wood 1959, p. 260), pienso que a partir de 1905 la filosofía de Russell fue extraordinariamente fiel a las ideas presentadas por primera vez en "On Denoting". Estas ideas no sólo tuvieron un efecto perdurable en la filosofía de Russell, sino que también tuvieron una influencia considerable en el desarrollo de la filosofía analítica como un todo. En este artículo discutiré el tratamiento de Russell de las descripciones definidas en "On Denoting", y argumentaré que aunque tiene éxito en lograr una interesante reducción de contextos que involucran descripciones a contextos de lógica cuantificacional, contiene importantes ambigüedades.

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Unpublished Portuguese translation of the paper "Descriptions: Frege and Russell Combined" publis... more Unpublished Portuguese translation of the paper "Descriptions: Frege and Russell Combined" published in Synthese, 130, 2002.

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Manuscrito, 2004

Logic, Truth, and Description. Essays on Chateaubriand's Logical Forms is a volume of the periodi... more Logic, Truth, and Description. Essays on Chateaubriand's Logical Forms is a volume of the periodical Manuscrito with 11 critical essays on the book Logical Forms: Part I and replies by Oswaldo Chateaubriand.

Oswaldo Chateaubriand, Introduction.............9-11
Abel Lassalle Casanave, Chateaubriand's logicism......13-20
Oswaldo Chateaubriand, The logical character of number: reply to Abel Lasalle Casanave.....21-30
Arno Aurélio Viero, Correspondence and identification.....31-45
Oswaldo Chateaubriand, Realism and correspondence: reply to Arno Aurélio Viero....47-53
Claudio Pizzi, Chateaubriand on the ambiguity of counterfactual suppositions....55-64
Oswaldo Chateaubriand, Counterfactuals: reply to Claudio Pizzi.....65-77
Dirk Greimann, Chateaubriand’s view of truth as identification. Some critical remarks....79-85
Oswaldo Chateaubriand, The referring function of statements: reply to Dirk Greimann....87-94
Frank Thomas Sautter, Chateaubriand on the nature of logic....95-104
Oswaldo Chateaubriand, Logic and modality: reply to Frank Sautter.....105-114
Guillermo E. Rosado Haddock, Chateaubriand on logical form and semantics....115-128
Oswaldo Chateaubriand, Syntax, semantics and metaphysics in logic: reply to Guillermo Rosado Haddock....129-140
Jairo José da Silva, On the nature of the proposition.....141-146
Oswaldo Chateaubriand, The nature of propositions: reply to Jairo José da Silva....147-157
John Corcoran, The principle of wholistic reference....159-171
Oswaldo Chateaubriand, Boole on Reference and Universe of Discourse: Reply to John Corcoran....173-182
Luiz Carlos Pereira, The semantics of falsity and negation....183-191
Oswaldo Chateaubriand, Falsity, negation and modality: reply to Luiz Carlos Pereira...193-200
Marco Ruffino, Chateaubriand on the slingshot arguments....201-209
Oswaldo Chateaubriand, Did the slingshots hit the mark?: reply to Marco Ruffino...211-225
Richard Vallée, On not being a dentist.....227-233
Oswaldo Chateaubriand, Negation and negative properties: reply to Richard Vallée...235-242

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Manuscrito, 2004

Abstract Abel Lassalle Casanave: In his doctoral dissertation, O. Chateaubriand favored Dedekind... more Abstract Abel Lassalle Casanave:
In his doctoral dissertation, O. Chateaubriand favored Dedekind's analysis of the notion of number; whereas in Logical Forms, he favors a fregean approach to the topic. My aim in this paper is to examine the kind of logicism he defends. Three aspects will be considered: the concept of analysis; the universality of arithmetical properties and their definability; the irreducibility of arithmetical objects.

Abstract response:
In §1 I discuss Dedekind and Frege on the logical and structural analysis of natural numbers and present my view that the logical analysis of the notion of number involves a combination of their analyses. In §2 I answer some of the specific questions that Abel raises in connection with Chapter 9 of Logical Forms.

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Manuscrito, 2004

Abstract Arno Viero: In his book Logical Forms Chateaubriand proposes, among other things, a the... more Abstract Arno Viero:
In his book Logical Forms Chateaubriand proposes, among other things, a theory of truth according to which a true statement describes some aspect of the world. The aim of this paper is to assess Chateaubriand's claim that his theory of truth is compatible with the main intuition underlying the correspondence theory.

Abstract response:
In §1 I suggest that although my theory of truth as identification is not a correspondence theory of truth in the sense of these terms used by the logical positivists, it can nevertheless be naturally interpreted as a correspondence theory of truth. In §2 I argue that whereas a correspondence theory of truth need not be a realist theory of truth, any sufficiently elaborate realist theory of truth should be interpretable as a correspondence theory of truth. I illustrate this with Frege’s denotational theory of truth.

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Manuscrito, 2004

Abstract Claudio Pizzi: In Logical Forms Chateaubriand introduces a disambiguation technique tha... more Abstract Claudio Pizzi:
In Logical Forms Chateaubriand introduces a disambiguation technique that might turn out to be highly useful for analyzing important classes of sentences. In particular, he claims that this technique is relevant for analyzing counterfactual suppositions. In this paper I critically examine this claim and conclude that the ambiguity of counterfactuals is contextual rather than structural.

Abstract response:
After some preliminary remarks in §1, I argue in §2 that Claudio’s considerations about my treatment of Quine’s Bizet-Verdi counterfactuals do not constitute a difficulty for the structural analysis of such counterfactuals. I discuss some of his other examples and argue that counterfactuals are ambiguous both structurally and contextually. I conclude with an examination of the principle of transitivity for counterfactuals.

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Manuscrito, 2004

Abstract Dirk Greimann: Chateaubriand's view of truth as identification is based on the assumpti... more Abstract Dirk Greimann:
Chateaubriand's view of truth as identification is based on the assumption that there is a close parallelism between sentences and definite descriptions with regard to their connection with reality. The paper aims to show that this parallelism does not actually obtain.

Abstract response:
In §1 I discuss the pragmatic and semantic objections that Dirk raises against the claim that sentences (or statements) refer to states of affairs. In §2 I explain in which sense I maintain that true sentences identify states of affairs.

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Manuscrito, 2004

Abstract Frank Thomas Sautter: In this paper Chateaubriand's approach to solve some problems rel... more Abstract Frank Thomas Sautter:
In this paper Chateaubriand's approach to solve some problems related to the nature of logic is confronted with the traditional approaches. It is shown that his hierarchy of logical types opens up new possibilities to characterize logical properties and logical truths and that it also sheds some new light on the foundations of mathematics. The order in which a system is exhibited almost always does not correspond to the order in which it has been elaborated. The system proposed by Oswaldo Chateaubriand is no exception (see Chateaubriand 2001). Since it contains many original ideas and original interpretations of traditional ideas which were initially developed to refute the slingshot-argument, especially the variant formulated by Gödel, the first chapter of the book with regard to the order of elaboration is the fourth chapter with regard to the order of exhibition. The diverse parts of the system form an organic whole making it difficult to apprehend them in isolation; this explains also the recurrence of some ideas.

Abstract response:
In §1 I examine the connections between my account of logical properties and Tarski’s account of logical notions. In §2 I briefly present some of my views on modality and the basis for my claim that there are intensional as well as extensional relations between properties. In §3 I compare my views on the nature of logic and of mathematics with Gödel’s views.

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Manuscrito, 2004

Abstract Guillermo Rosado-Haddock: In this paper on Oswaldo Chateaubriand's book Logical Forms I... more Abstract Guillermo Rosado-Haddock:
In this paper on Oswaldo Chateaubriand's book Logical Forms I, I am mostly concerned with the critical task of indicating some shortcomings and stressing my disagreements with the distinguished scholar. The most important shortcoming of the book is Chateaubriand's unfamiliarity with Husserl's views on logic and semantics, some of which anticipate views propounded by the former--e.g., the distinction between logical law and logical necessity--, whereas others are more subtle than Chateaubriand's views--e.g. Husserl's views on the referent of statements. One of the most important contributions of Chateaubriand's book is his analysis and rejection of all forms of the so-called "slingshot argument". On the other hand, I disagree with Chateaubriand's rendering of some of Frege's views, though some of these are very common among Frege scholars. Finally, I assess Chateaubriand's criticisms of Kripke's views as well as those of Tarski. I tend to agree with his criticism of Kripke, but disagree with his assessment of Tarskian semantics.

Abstract response:
In §§1-2 I consider some issues that Guillermo raises in connection with Husserl, especially the distinction between the notion of state of affairs and the more general notion of situation of affairs conceived as a common substratum for different states of affairs. After a few remarks about Church’s slingshot argument in §3, I discuss several objections that Guillermo raises to my interpretation of Frege (§4), to Kripke’s notion of rigid designator (§5) and to my objections to Tarski’s semantic conception of truth (§6).

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Manuscrito, 2004

Abstract Jairo José da Silva: I present here my criticism of Chateaubriand's account of proposit... more Abstract Jairo José da Silva:
I present here my criticism of Chateaubriand's account of propositions as having an identifying character with respect to reality. I claim that (meaningful) propositions are better understood as pictures of possible states-of-affairs, and that this account is more natural considering the acts of judgment that are at the origin of propositions. I also present a possible way of understanding the notion of a possible state-of-affairs that takes care of the seemingly absurd case of necessarily false, but meaningful propositions (such as false mathematical propositions).

Abstract response:
In §1 I reply to Jairo’s objections to my account of truth and falsity showing that my account of falsity does not imply that false sentences refer to something. In §2 I argue that Jairo’s main objection to my account of propositions as abstract properties is based on a misunderstanding concerning the purpose of this account. In §3 I examine Jairo’s suggestion that contradictory sentences can be said to describe possible states of affairs.

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Manuscrito, 2004

Abstract John Corcoran: In its strongest, unqualified form the principle of wholistic reference ... more Abstract John Corcoran:
In its strongest, unqualified form the principle of wholistic reference is that each and every proposition refers to the whole universe of discourse as such, regardless how limited the referents of its non-logical or content terms. Even though Boole changed from a monistic fixed-universe framework in his earlier works of 1847 and 1848 to a pluralistic multiple-universe framework in his mature treatise of 1854, he never wavered in his frank avowal of the principle of wholistic reference, possibly in a slightly weaker form. Indeed, he took it as an essential accompaniment to his theory of concept formation and proposition formation. Similar views are found in later logicians, and some of the most recent formulations of standard, one-sorted first-order logic seem to be in accord with a form of it, if they do not actually imply the principle itself.

Abstract response:
In §1 I examine Boole’s “principle of wholistic reference” in relation to Frege’s postulation of truth-values as referents for sentences. I also consider in this connection Frege’s interpretation of quantification and his view that functions and concepts (of objects) must be defined for all objects. I then present my own contrasting views on the reference of sentences. In §2 I discuss Boole’s introduction of the notion of universe of discourse and consider whether one of the issues implicit in John’s paper is a confrontation between absolute interpretations of logic and relativistic interpretations of logic. I conclude with a brief examination of Tarski’s views on this issue.

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Manuscrito, 2004

Abstract Luiz Carlos Pereira: In Logical Forms Chateaubriand offers a realist semantics for fals... more Abstract Luiz Carlos Pereira:
In Logical Forms Chateaubriand offers a realist semantics for false elementary propositions and for true negative propositions that appeals to negative facts. Although he does not refer to Wittgenstein, he rules out "possibilist" solutions such as that of the Tractatus. In this paper I will critically discuss Chateaubriand's solution and compare it with the semantics of the Tractatus.

Abstract response:
In §1 I explain that my rejection of possible (and impossible) states of affairs as a basis for an account of falsity is not part of a general rejection of modal notions but is a rejection of possible and impossible entities of any sort. I then show that my account of senses and of propositions is indeed a modal account. In §2 I examine some of Wittgenstein’s ideas about falsity, as presented by Luiz Carlos, in relation to my account of falsity and negation. In §3 I discuss the modal aspects of identification for propositions.

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Manuscrito, 2004

Abstract Marco Ruffino: The purpose of this paper is to discuss Chateaubriand's criticism of the... more Abstract Marco Ruffino:
The purpose of this paper is to discuss Chateaubriand's criticism of the so-called slingshot arguments, particularly of those versions proposed by Church (1956) and by Gödel (1944). I concentrate on two critical points made by Chateaubriand, and argue that they are not decisive against these versions of the slingshot. I also discuss Chateaubriand's hybrid theory of definite descriptions and argue that, despite its intrinsic interest, it cannot avoid the conclusion of the slingshot.

Abstract response:
In §§1-2 I argue that Marco misidentifies my main objections to the Church and Gödel slingshot arguments and that his defense of these arguments does not overcome those objections. In §3 I discuss his criticisms of my theory of descriptions in relation to Church’s argument.

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Manuscrito, 2004

Abstract Richard Valée: Negative properties, like not flying, are controversial. I oppose Chatea... more Abstract Richard Valée:
Negative properties, like not flying, are controversial. I oppose Chateaubriand's view on these properties and offer semantic arguments against their inclusion in ontology. I distinguish predicate negation and sentential negation, and examine the syntactic and semantic behaviour of predicate negation. I contend that predicate negation is identical with sentential negation. If it is not, then we lose a lot of intuitive inferences found in natural languages and make no clear metaphysical gain. Other arguments based on Ockham's razor are offered. In Chapter 2 of Logical Forms, Chateaubriand accepts what I will call negative properties and negative relations. For example, the negative predicate "not sick" would express the negative property of not being sick, and the relation "not in love with" would express the negative relation of not being in love with. Chateaubriand calls negative properties and relations simply properties and relations. I add "negative" for clarification. This is a fascinating and underexplored topic. However, I do not share Chateaubriand's enthusiasm for negative properties.

Abstract response:
I argue in §1 that there is a clear distinction between predicate negation and sentential negation and that sentential negation is a special case of predicate negation operating on the predicate ‘is true’. In §2 I reply to Richard’s objections to negative properties on the basis of the conception of properties as identity conditions presented in Chapter 12 of Logical Forms.

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Manuscrito, 2008

Logic, Language, and Knowledge: Essays on Chateaubriand's Logical Forms is a volume of the period... more Logic, Language, and Knowledge: Essays on Chateaubriand's Logical Forms is a volume of the periodical Manuscrito with 21 critical essays on the book Logical Forms: Part II and replies by Oswaldo Chateaubriand.

Presentation…………………………………………………………………………. 7
Acknowlegments…………………………………………………………………… 9
ABEL Lassalle Casanave, Entre la Retórica y la Dialéctica………….. 11
OSWALDO Chateaubriand, Dialectical Rhetoric : Response to
ABEL Lassalle Casanave...............................................................19
ANDRÉ Porto, Formalization and Infinity……………………………….. 25
OSWALDO Chateaubriand, Proof and Infinity: Response to
ANDRÉ Porto………………………………………………………………45
DANIELLE Macbeth, The Truths of Logic and Logical Truth……….. 51
OSWALDO Chateaubriand, Logical Truth and Logical States of
Affairs: Response to DANIELLE Macbeth…………………………..69
DIRK Greimann, Multiplying Entities without Necessity: what does
“necessity” mean in this context?...................................................79
OSWALDO Chateaubriand, Multiplying Entities: Response to DIRK
Greimann……………………………………………………………………..95
E. G. K. López-Escobar, Chateaubriand on Propositional Logic......... 103
OSWALDO Chateaubriand, Propositional Logic: Response to KEN
López-Escobar.................................................................................115
FRANK Thomas Sautter, Chateaubriand on the Nature of
Language……………………………………………………………………..121
OSWALDO Chateaubriand, The Nature of Language: Response to
FRANK Thomas Sautter…………………………………………………131
GUIDO Imaguire, Ockham’s Razor and Chateaubriand’s Goatee… 139
OSWALDO Chateaubriand, Explanatory Reduction: Response to
GUIDO Imaguire…………………………………………………………155
GUILLERMO E. Rosado Haddock, Chateaubriand on Logical
Truth and Second-order Logic: Reflections on some Issues of
“Logical Forms II”………………………………………………………..163
OSWALDO Chateaubriand, Logical Truth and Second-Order
Logic: Response to GUILLERMO Rosado-Haddock……………..179
JAIRO José da Silva, On Proofs in Mathematics………………………….. 185
OSWALDO Chateaubriand, Proof in Mathematics: Response to
JAIRO José da Silva……………………………………………………….197
JAVIER Legris, Chateaubriand on Symbolism and Logical Form…… 203
OSWALDO Chateaubriand, Symbolism and Logical Form:
Response to JAVIER Legris……………………………………………...217
JOHN Corcoran, Meanings of Form…………………………………………. 223
OSWALDO Chateaubriand, Logical Forms and Logical Form:
Response to JOHN Corcoran…………………………………………...267
JOSÉ Seoane, Elucidando el Concepto de Demostración.
Observaciones sobre Chateaubriand………………………………….279
OSWALDO Chateaubriand, Proof and Explication: Response to
JOSÉ Seoane…………………………………………………………………293
MARCO Ruffino, Chateaubriand’s Senses............................................ 299
OSWALDO Chateaubriand, Senses: Response to MARCO
Ruffino...........................................................................................315
MARK Wilson, Which Came First: the Logic or the Math?.................. 331
OSWALDO Chateaubriand, Mathematics and Logic: Response to
MARK Wilson……………………………………………………………355
NORMA B. Goethe, Revisiting the question about formal proof:
philosophical theory, history, and mathematical practice………..361
OSWALDO Chateaubriand, Proof and Practice: Response to
NORMA Goethe…………………………………………………………...387
OSCAR M. Esquisabel, Lenguaje, Lógica y Ontología en la Perspectiva
de Oswaldo Chateaubriand………………………………………………..393
OSWALDO Chateaubriand, Language, Logic, and Ontology:
Response to OSCAR Esquisabel……………………………………….413
OTÁVIO Bueno, Truth and Proof…………………………………………… 419
OSWALDO Chateaubriand, Agnostic Nominalism: Response to
OTÁVIO Bueno……………………………………………………………441
PAUL Gochet, Chateaubriand on the Productivity of Language…….. 445
OSWALDO Chateaubriand, The Productivity of Language:
Response to PAUL Gochet……………………………………………….463
PAUL Horwich, Explaining Intentionality.......................................... 467
OSWALDO Chateaubriand, Deflationism: Response to PAUL
Horwich………………………………………………………………………483
RICHARD Vallée, Learning “Big”…………………………………………… 489
OSWALDO Chateaubriand, Properties and Truth: Response to
RICHARD Vallée…………………………………………………………507
WALTER Carnielli, The Tyranny of Knowledge……………………….. 511
OSWALDO Chateaubriand, Knowledge and Justification:
Response to WALTER Carnielli……………………………………..519

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Manuscrito, 2008

Abstract Abel Lassalle Casanave: En este artículo proponemos que el examen del concepto de demos... more Abstract Abel Lassalle Casanave:
En este artículo proponemos que el examen del concepto de demostración de Oswaldo Chateaubriand en los capítulos 19, 20 y 21 de la Parte II de Logical Forms incluye aspectos retóricos (la dependencia del auditorio y carácter enti-memático de las demostraciones) y dialécticos (estrategias de aceptación de principios de demostración).
Abstract: In this paper we argue that Oswaldo Chateaubriand’s conception of proof, in chapters 19, 20, and 21 of Part II of Logical Forms, incorporates rhetorical aspects (the dependence on the audience and the enthymematic character of proofs), and dialectical aspects (strategies for accepting principles of proof).

Abstract response:
Abel Lasalle Casanave’s comments on the rhetorical and dialectical aspects of the discussion of proof in chapters 19 to 21. I center most of my response on two issues raised in his concluding questions; the first being the hermeneutic aspect of the development of mathematics and of mathematical knowledge, and the second “the symbolic conception of mathematics” and the “algebraic mode of thought”.

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Manuscrito, 2008

Abstract André Porto: This article discusses some of Chateaubriand's views on the connections be... more Abstract André Porto:
This article discusses some of Chateaubriand's views on the connections between the ideas of formalization and infinity, as presented in chapters 19 and 20 of Logical Forms. We basically agree with his criticisms of the standard construal of these connections, a view we named "formal proofs as ultimate provings", but we suggest an alternative way of picturing that connection based on some ideas of the late Wittgenstein.

Abstract response:
The main issue André Porto raises in his paper concerns the use of dot notation to indicate an infinite set of hypotheses. Whereas I agree that one cannot extract a unique infinite expansion from a finite initial segment, in my response I argue that this holds for finite expansions as well. I further explain how my remarks on infinite proof structures are neither motivated by the impact of Gödel’s incompleteness theorems on Hilbert’s program, nor by a negative view of strict finitism.

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Manuscrito, 2008

Abstract Danielle Macbeth: A principal aim of Chateaubriand's Logical Forms II: Logic, Language,... more Abstract Danielle Macbeth:
A principal aim of Chateaubriand's Logical Forms II: Logic, Language, and Knowledge is to clarify and defend what Chateaubriand describes as the ontological conception of logic against the standard model-theoretic or "linguistic" view. Both sides to the debate accept that if logic is a science then there must be logically necessary facts that this science discovers, Chateaubriand arguing that because logic is a science, there must be logically necessary facts, and his opponent that because there are no logically necessary facts, logic cannot be a science. I argue that we can go between the horns of this dilemma by showing that, although logic is a science, it does not follow, as Chateaubriand assumes, that there are logically necessary facts. There are truths of (the science of) logic; there are no "logical truths".

Abstract response:
Danielle Macbeth disagrees with the view that there are logical truths in an ontological sense, and argues that we have no adequate epistemological account of our access to such features of reality. In my response I recall some main aspects of my ontological and epistemological formulation of logic as a science, and argue that neither Quine’s considerations against meaning, nor Benacerraf’s considerations against Gödel’s realism, show the untenability of an approach to logical truth in terms of logical propositions that denote logical states of affairs.

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Manuscrito, 2008

Abstract Dirk Greimann: The aim of this paper is to defend Ockham's razor against the objection ... more Abstract Dirk Greimann:
The aim of this paper is to defend Ockham's razor against the objection recently made by Oswaldo Chateaubriand that we do not know how to decide which entities are necessary and which are not. The main thesis defended is that this distinction can be adequately explained in terms of the notion of ontological reducibility. It is argued that Oswaldo's objections against this approach are not conclusive.

Abstract response:
In my response to Dirk Greimann I maintain that whereas one can recognize some specific appeals to “parsimony” or “simplicity” in the sciences and in philosophy as correct and legitimate, there is no precise adequate formulation of Ockham’s razor as a general methodological principle, and argue that the formulations he examines in his paper exemplify this imprecision.

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Manuscrito, 2008

Abstract Ken López Escobar: In Logical Forms Part II, Chateaubriand begins the Chapter on “Propo... more Abstract Ken López Escobar:
In Logical Forms Part II, Chateaubriand begins the Chapter on “Propositional Logic” by considering the reading of the ‘conditional’ by ‘implies’; in fact he states that:
There is a confusion, as a matter of fact, and it runs deep, but it is a confusion in propositional logic itself, and the mathematician’s reading is a rather sensible one.
After a careful, erudite analysis of various philosophical viewpoints of (two-valued propositional) logic, Chateaubriand comes to the conclusion that:
Pure propositional logic, as just characterized, belongs to ontological logic, and it does not include a theory of deduction as a human activity. This is a part of epistemological logic, and is more closely connected to the applications of pure propositional logic.
An implicit assumption in Chateaubriand’s reasoning appears to be that propositions (logic, number, etc.) have a timeless status. I will present arguments for the opposite viewpoint which leads to an analysis of Propositional Logic not covered under Chateaubriand’s monograph and perhaps resolves some conflicts therein; much as the conflict between the Intuitionist and Classical Mathematician on whether every function on the Reals is continuous is resolved by the realization that they are talking about different “entities”.

Abstract response:
Ken López-Escobar questions the timeless status of various entities—propositions, numbers, etc.—as well as my characterization of pure propositional logic as an ontological theory. In my response I argue that my characterization of propositional logic does not depend on timeless propositions, or on other abstract truth bearers, but is a characterization in terms of truth relations between any truth bearers. I also discuss his views on numbers as cultural constructs, as well as his use of quantification in propositional logic.

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Manuscrito, 2008

Abstract Frank Thomas Sautter: In the present paper, I raise some questions referring to Chateau... more Abstract Frank Thomas Sautter:
In the present paper, I raise some questions referring to Chateaubriand's discussion of the nature of language, its origin, its development and its functions in human life. These questions arise when his view is compared with the partly similar views defended by Gödel and Jørgensen, among others.

Abstract response:
Frank Sautter’s questions are directed at the precise senses of the words ‘invention’ and ‘creation’ used in my remarks on the origin of language, and at the connection between Jørgensen’s and my views on the development of language. In my response I clarify my use of the words ‘invention’ and ‘creation’ vis-à-vis Frank’s suggested interpretations, and examine Jørgensen’s distinction of stages in the development of language in relation to imperatives and the “directive use of language”.

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Manuscrito, 2008

Abstract Guido Imaguire: In Logical Forms II Chateaubriand puts the simple question: Why should ... more Abstract Guido Imaguire:
In Logical Forms II Chateaubriand puts the simple question: Why should we accept Ockham's razor? He blames the principle of reduction as an unjustified dogma of nominalism. In this paper I present a justification for it. Contrary to Russelìs conception of reduction as elimination, I propose the thesis that reduction is explanation.

Abstract response:
Guido Imaguire proposes an epistemological (and ontological) formulation of Ockham’s razor in terms of the notion of explanatory reduction. Although in my response I express reservations about some aspects of the specific formulations, I agree with the general epistemological idea.

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Manuscrito, 2008

Abstract Guillermo Rosado-Haddock: In this short paper I am concerned with basically two especia... more Abstract Guillermo Rosado-Haddock:
In this short paper I am concerned with basically two especially important issues in Oswaldo Chateaubriand's Logical Forms II; namely, the dispute between first-and higher-order logic and his conception of logical truth and related notions, like logical property, logical state of affairs and logical falsehood. The first issue was also present in the first volume of the book, but the last is privative of the second volume. The extraordinary significance of both issues for philosophy is emphasized and, though there is a basic agreement with Chateaubriand's views, some critical remarks are interspersed.

Abstract response:
In my response to Guillermo Rosado-Haddock I discuss the two main issues raised in his paper. The first is that by allowing Henkin’s general models as a legitimate model-theoretic interpretation of second-order logic, I undermine my defense of second-order logic against Quine’s views concerning the primacy of first-order logic. The second is that my treatment of logical truth and logical properties does not take into account various systems of logic and properties of systems of logic such as the Löwenheim-Skolem property.

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Manuscrito, 2008

Abstract Jairo José da Silva: In his book Chateaubriand points out some differences between the ... more Abstract Jairo José da Silva:
In his book Chateaubriand points out some differences between the mathematical and the formal notions of proof. I argue here that the contrast between both cannot be exaggerated, and that the latter fails to represent essential aspects of the former. I also sketch a view of the nature of mathematics that can accommodate one particular feature of mathematical proofs the formal notion, by its very nature, cannot: their freedom.

Abstract response:
The paper by Jairo José da Silva is mainly concerned with the character of mathematical proof and with the nature of mathematics and its ontology. Although there is a fair amount of agreement in our views, I focus my response on three issues on which we disagree. The first is his view of mathematical proof as generally unconstrained by language and by a previous proof apparatus. The second is his discussion of Brouwer’s views on proof and formalization. The third is his nominalistic account of structuralism.

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Manuscrito, 2008

Abstract Javier Legris: The aim of this paper is to frame briefly Chateaubriand's conception of ... more Abstract Javier Legris:
The aim of this paper is to frame briefly Chateaubriand's conception of logical forms in the distinction between logic and language as calculus and logic as universal language, devised by Jean van Heijenoort and later generalized by Jaakko Hintikka. The most important reasons to connect Chateaubriand's conception with this distinction are perhaps Chateaubriand's criticism of the linguistic approach to logical forms and the role Chateaubriand assigns to symbolism in his own account.

Abstract response:
Javier Legris examines my views on symbolism and logical form in relation to two important distinctions emphasized by Jean van Heijenoort—the distinction between logic as calculus and logic as universal language, and the distinction between absolutism and relativism in logic. I generally agree with his considerations and focus my response on some relevant aspects of classical logic.

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Manuscrito, 2008

Abstract John Corcoran: The expressions 'form', 'structure', 'schema', 'shape', 'pattern', 'figu... more Abstract John Corcoran:
The expressions 'form', 'structure', 'schema', 'shape', 'pattern', 'figure', 'mold', and related locutions are used in logic both as technical terms and in metaphors. This paper juxtaposes, distinguishes, and analyses uses of these expressions by logicians. No such project has been attempted previously. After establishing general terminology, we present a variant of traditional usage of the expression 'logical form' followed by a discussion of the usage found in the two-volume Chateaubriand book Logical Forms (2001 and 2005)-the most comprehensive work on the subject ever written and in many ways the focus of this paper.

Abstract response:
In his paper John Corcoran examines in detail many issues relating to logical form, and raises some questions about my formulations. In my response I emphasize two main distinctions that may clear up some of the issues. One is the distinction between logical forms, in the sense of logical properties of an abstract character, and logical form, in the sense in which we speak of the logical form (or logical structure) of a sentence, or of a proposition. Another is the distinction, emphasized by Boole, between primary propositions (about things), and secondary propositions (about propositions)—which I illustrate through the distinction between predicate negation and sentential negation.

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Manuscrito, 2008

Abstract José Seoane: Es razonable pensar que una parte relevante del trabajo del lógico consist... more Abstract José Seoane:
Es razonable pensar que una parte relevante del trabajo del lógico consiste en elucidar ciertos conceptos teóricamente valiosos pero, si se los evalúa desde el punto de vista de la claridad y el rigor, aún insatisfactoriamente caracterizados. Estos procesos elucidatorios pueden modelarse de formas muy variadas; el núcleo de los mismos, no obstante, reside en la construcción de un concepto más riguroso que funge como clarificación o elucidatum de un concepto previo. El concepto matemáticamente preciso de "demostración" puede considerarse un posible elucidatum del respectivo concepto intuitivo. ¿Es un elucidatum adecuado? ¿Bajo qué condiciones lo es? ¿Cómo repercute asumir tal éxito elucidatorio en nuestra concepción filosófica de la demostración? Chateaubriand no plantea, explícitamente, el problema en términos elucidatorios; sin embargo, sugeriremos que enmarcar su reflexión en tal contexto puede proveer una perspectiva novedosa de sus lúcidos análisis.
Abstract: A relevant aspect of a logician’s work consists in elucidating certain concepts that, however theoretically valuable, are yet to be sastifactorily characterized from the point of view of rigor and clarity. Although these elucidatory processes can be modelled on several ways, its nucleus resides in the construction of a more rigorous concept that acts as clarification or elucidatum of a previous concept. The mathematically precise concept of “demonstration” can be considered as a possible elucidatum of the respective intuitive concept. Is it an adecuate elucidatum? How does assuming such an elucidatory success affect our philosophical conception of the demonstration? Although Chateaubriand does not explicitly pose the question in elucidatory terms, I will suggest that framing his reflection in such a context can provide a new perspective of his lucid analysis.

Abstract response:
José Seoane centers his commentary on my critique of the standard formal analysis of proof as an elucidation of the informal notion of proof, and I basically agree with his considerations throughout the paper. In my response I argue that the notion of formal proof is fundamentally an analysis of the notion of logical consequence, rather than an elucidation of the informal notion of proof.

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Manuscrito, 2008

Abstract Marco Ruffino: In this paper I discuss Chateaubriand's notion of senses. His notion ret... more Abstract Marco Ruffino:
In this paper I discuss Chateaubriand's notion of senses. His notion retains the spirit of the original Fregean notion, but differs from it in some fundamental ways. I compare both notions, especially concerning the issue of indirect reference, and also concerning their explanatory power in epistemic matters. Finally, I raise some worries concerning the semantic role played by Chateaubriand's senses, as well as the notion of judgment that his notion of thoughts seems to imply.

Abstract response:
Marco Ruffino compares the notion of sense developed in my book with Frege’s notion of sense, and argues that whereas there are ontological similarities, my notion faces epistemological and semantic problems. In my response I discuss the various issues he raises, arguing that my notion of sense can confront them at least as well as Frege’s notion.

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Manuscrito, 2008

Abstract Mark Wilson: Many authors, including Oswaldo Chateaubriand, maintain that "properties" ... more Abstract Mark Wilson:
Many authors, including Oswaldo Chateaubriand, maintain that "properties" should be structured in logical grades, where the least abstract quantities comprise the lowest ranks of a hierarchy that embraces more abstract and mathematized qualities only at higher levels. But applied mathematicians warns that no quantities can be expected to possess crisp, real world extensions unless they have already been processed with a fair amount of set theoretic machinery beforehand.

Abstract response:
Mark Wilson argues that in order to make physical first-order properties suitable for inclusion in the bottom levels of a logical hierarchy of properties, their proper treatment must take into account the methods of applied mathematics. I agree that the methods of applied mathematics are essential for studying physical properties, and in my response focus on the nature of the logical hierarchy and on the requirements of classical logic.

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Manuscrito, 2008

Abstract Norma Goethe: This paper revisits some of Chateaubriand's critical considerations with ... more Abstract Norma Goethe:
This paper revisits some of Chateaubriand's critical considerations with regard to representing our reasoning practices in logic and mathematics by means of "idealized syntax". I focus on the persistently critical side of these considerations which aim to prepare the ground for "an interesting epistemology of logic and mathematics" that ought to make room for understanding the pragmatic dimensions of proofs as explanatory rational displays. First, I discuss the 20 th century "syntactic conception" of the logical and the underlying set of values it upholds. Secondly, I revisit the syntactic constraints on systematizing our formal forms of reasoning and ask about the relationship between "idealized" proofs construed as "syntactic objects" and the variety of formal forms of reasoning with its uses of the logical by the research mathematician. Finally, I consider the reasons why Chateaubriand thinks the syntactic requirements of "logical rigor" cannot be fulfilled, and why they ought not to be on the agenda. I conclude my paper by pointing to a deeper assumption which needs to be critically revisited as it stands in the way to what the author envisages as an "interesting epistemology of logic and mathematics".

Abstract response:
Norma Goethe addresses my criticisms of the notion of formal proof as a representation of the practice of proving, and in the process revisits large portions of my discussion of proof. I agree with many of her comments, and direct my response to two specific issues. The first concerns the essential features of proof, and the second the distinction between actual proofs and idealized proofs.

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Manuscrito, 2008

Abstract Oscar M. Esquisabel: En este trabajo se examinan las concepciones de Oswaldo Chateaubr... more Abstract Oscar M. Esquisabel:
En este trabajo se examinan las concepciones de Oswaldo Chateaubriand acerca de la naturaleza del lenguaje, así como las relaciones de éste con la lógica y la ontología. En primer lugar, se aborda la tematización del lenguaje como actividad humana. A continuación, se analiza la elucidación que propone Chateaubriand acerca del significado en términos de uso o condiciones sociales de identidad. En tercer lugar, se indaga la fundamentación del lenguaje y del significado en propiedades ontológicas. Finalmente, se plantean observaciones acerca de algunas tesis de Chateaubriand, tales como la distinción entre significado y sentido o el carácter innato de algunos conceptos.
Abstract: In this paper we examine Chateaubriand's views on language and on its general relation to logic and ontology. We first discuss his account of language as a human activity. Secondly, we analyze Chateaubriand's explanation of meaning as use or as social identity conditions. Thirdly, we spell out the ontological foundation of language and meaning on ontological properties. Finally, we make observations on some aspects of Chateaubriand's tenets such as the distinction between meaning and sense and the innateness of some concepts.

Abstract response:
Oscar Esquisabel gives an overview of Chapter 13, tracing connections with several philosophers and traditions in philosophy, especially with the hermeneutic tradition. In my response I address his concluding questions about hermeneutics, and about the relation between senses, meanings, and concepts.

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Manuscrito, 2008

Abstract Otávio Bueno: Current versions of nominalism in the philosophy of mathematics face a si... more Abstract Otávio Bueno:
Current versions of nominalism in the philosophy of mathematics face a significant problem to understand mathematical knowledge. They are unable to characterize mathematical knowledge as knowledge of the objects mathematical theories are taken to be about. Oswaldo Chateaubriand's insightful reformulation of Platonism (Chateaubriand 2005) avoids this problem by advancing a broader conception of knowledge as justified truth beyond a reasonable doubt, and by introducing a suitable characterization of logical form in which the relevant mathematical facts play an important role in the truth of the corresponding mathematical propositions. In this paper, I contrast Chateaubriand's proposal with an agnostic form of nominalism that is able to accommodate mathematical knowledge without the commitment to mathematical facts.

Abstract response:
Otávio Bueno gives a positive and accurate summary of my defense of Platonism, with special emphasis on the epistemological issues. He criticizes “skeptical nominalism”, and proposes instead an “agnostic nominalism”, which treats mathematical objects as “objects of thought”, and neither rejects nor accepts abstract entities. In my response I argue that the main problem for nominalism is to account for abstract properties and relations, and that treating mathematical objects as objects of thought does not provide a satisfactory solution to that end.

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Manuscrito, 2008

Abstract Paul Gochet: In this paper, Chateaubriand's account of the productivity of language is ... more Abstract Paul Gochet:
In this paper, Chateaubriand's account of the productivity of language is put to an historical perspective. Its philosophical significance is assessed. It is shown how it could be expanded to accommodate recent findings of professional linguists.

Abstract response:
Paul Gochet raises several interesting issues about my Chapter 13 discussion of productivity, compositionality, the context principle, meaning, and formalization. In my response I concentrate on the question of units of meaning in relation to the context principle, and on the question of infinity and formalization.

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Manuscrito, 2008

Abstract Paul Horwich: The goal here is to demystify the relation of aboutness that associates t... more Abstract Paul Horwich:
The goal here is to demystify the relation of aboutness that associates thoughts and their linguistic expression with particular features of the world. It is argued that the main obstacle to providing a naturalistic account of this relation is a misguided ('inflationary') view of truth. A deflationary perspective, on the other hand, enables us to see how the basic use of a mental or physical term establishes its referent, thereby determining what the sentences containing it are about.

Abstract response:
My disagreement with the deflationist treatment of truth affects my attitude to Paul Horwich’s approach to meaning and intentionality. In my response I summarize objections to the deflationist account of truth developed in some detail in chapters 2, 7, and 12, and argue that the notion of intentionality should be treated naturalistically in a broader context than the context of the referential import of the locution “means that”.

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