Maria Jose Frapolli

Frege is the acclaimed father of twentieth-century logic and at the same time the father of the discipline philosophy of language. Both of these paternities arise from a unique and general project grounded on a profound understanding of the many linguistic and conceptual subtleties that govern the use of language. His logical project, which set him apart from his contemporary fellows and on an underexplored path, participates in the richness of his approach to language and thought, which includes semantic and pragmatic hints that were only recognised much later in the twentieth century. I explain and develop these hints in support of an approach to logic that, far from psychological vagaries, benefits from the analytical depth of acknowledging the role of concepts in human communication.

In this introductory chapter, I set out the background against which the theses and arguments of the rest of this book must be understood. I explain my (minimal) version of pragmatism, and how I use the central concepts that this book is about. My inspiration has been some claims defended or suggested by Frege, and some further developments of Fregean inferentialism promoted by Robert Brandom. I discuss my take on assertion as an activity for whose outcome the agent is accountable. I also offer a complete characterization of the kind of item that propositions are, giving their individuation and identification criteria. In this task, I follow some Fregean insights related to Hume’s Principle and the Julius Caesar problem for the definition of number. Frege is also the source of the approach to the existence of abstract objects that I endorse. Existence is instantiation: a second-level concept. It is legitimate to discuss what is meant by existential claims in science. Nevertheless, the claim that numbers exist, or that propositions exist, is not something that is up for discussion; we simply cannot doubt it, since they are presupposed in our mathematical and assertive practices, respectively. Our very nature as producers and consumers of reasons rests on the assumption that judgeable contents, i.e., propositions, are exchanged in those discursive practices that define human rationality. Finally, in the last section, I explain what I will understand by the notions of argument, argumentation, and inference in the chapters ahead, and discuss material inferences that I contend, following Danielle Macbeth, were accepted by Frege as genuine logical inferences.

Several principles shape the pragmatist take on logic that I will defend in this book. The essential four are the Principle of Assertion (PA), the Principle of Propositional Priority (PPP), the Principle of Grammar Superseding (PGS), and the Principle of Inferential Individuation (PII). (PA) says that the bearers of logical properties are products of human discursive actions. (PPP) takes up the thesis that the primary bearers of logical properties are complete propositions. (PGS) advises not to look at the linguistic surface in search of logical insights. And finally, (PII) says that only inferential consequences, upstream and downstream, have any effect on propositional identity. In this chapter, I will explain these principles and their consequences and show that all of them can be traced back to Frege’s work. In addition, I will comment on the Fregean Principle of Context (PCont), a linguistic version of (PPP), and the semantic Principle of Compositionality (PComp), which Frege never stated. As a criterion of propositional identification, I propose the Organic Intuition (OI): ‘To be a proposition is to possess propositional properties.’ I then explain why (OI) offers a safe non-circular guide to detecting the presence of propositions, and finally compare genuine propositions with logical propositions. In the last section, I discuss the kind of discipline that logic is.

In this chapter, the structural connections between three paradoxes—Goodman’s ‘grue’, Prior’s ‘tonk’, and Russell’s—are traced. It is argued that none of them arises in a context in which the Principle of Propositional Priority holds. To derive them, a strong hypothesis is needed: that all syntactically well-formed expressions express genuine concepts that are significant regardless of the tasks that speakers (or theorists) use them to perform. These three paradoxes have been chosen for their relevance to the topic of this book. The interest of Goodman’s ‘grue’ is the introduction of two new analytical tools, the notions of projectibility as applied to hypotheses, and the notion of entrenchment as applied to terms, which neatly pinpoint what happens with the artificial introduction of new terms. Prior’s ‘tonk’ is relevant to understanding what is at issue with logical constants and, finally, our discussion of Russell’s paradox is intended to offer a further argument for the validity of Frege’s unitary project from the Begriffsschrift to the Grundgesetze. It also shows the potential of (PA), (PPP) and (PGS) for the foundation of arithmetic. In the pragmatist perspective I am developing in this book, concepts have to be identified from propositions and propositions are identified as the (actual or virtual) results of successful discursive actions. Languages, either natural or artificial, only produce senseful concepts and contents against the background of discursive practices, be they ordinary or scientific. Goodman, Prior and Frege had the instruments to tackle these paradoxes and push their proposals further, in a better and more fruitful perspective on language and science.

Truth is not one of a kind. Philosophers have widely assumed that truth is mysterious, intractable, troublesome, or else, trivial and redundant. I argue here that none of these alternatives is true. The only sense in which truth is unique is in the treatment that philosophers give to it. On the basis of the same corpus of evidence, we make assumptions and draw conclusions about truth that we do not draw about any other notion of a similar kind. Truth ascriptions work in natural languages as propositional variables. They are prosentences. To them applies all the knowledge that linguists and philosophers of language have gathered about the general class of proforms and the specific class of indexicals. The philosophy of language has the tools to explain the meaning of truth in all its depth. The air of mystery that has surrounded this notion is due in part to the Liar paradox, and in part to a lack of understanding of the variety and plurality of ways in which expressions can be meaningful. The Liar paradox is easy to explain. And a pluralistic approach to meaning that distinguishes between linguistic meaning and the content expressed can offer a correct account of this notion that answers philosophers’ doubts. At the end of this chapter, I deal with the allegedly puzzling connection between truth and assertion. I argue that truth is a reliable mark of assertive actions, and that the apparent counterexamples that come from special contexts, such as fiction or conditionals, can be explained by the appropriate theory of meaning. I also give reasons to doubt that Frege detached truth from assertion in those contexts. Truth, like logical constants, needs for its analysis a background shaped by (PA), (PPP), (PGS), and (PII). It needs an approach that pays attention to the role of agents in the use of expressions and the difference in semantics between first-level and higher-level predicables and concepts. To understand truth, we need to adopt a theoretical approach like the one I have defended in this book, or another one with similar resources. Otherwise, truth cannot be released from the confusing playground that still makes it refractory to analysis.

In this chapter I discuss the philosophical presuppositions and consequences of Tarski’s and Frege’s approaches to truth. Tarski’s is the most successful theory of truth ever proposed. Nevertheless, there are serious doubts about the actual effect of its technical details and, above all, about its philosophical significance. Despite starting with similar pre-theoretical intuitions, Frege and Tarski developed conflicting positions. Thus, neither at this point nor, in general, to any central topic in the philosophy of logic, is there a ‘Frege-Tarski approach’. I will argue that truth cannot be reached from satisfaction, which was Tarski’s strategy, while the opposite strategy of explaining satisfaction in terms of truth, which was Frege’s strategy, presents no difficulty. All the weaknesses of Tarski’s position result from his mistaken identification of sentences as the bearers of truth. Because of this, truth became linked to particular linguistic systems, with the unwelcome consequence of an infinite proliferation of truth predicates. Frege, by contrast, placed judgeable contents at the centre of the picture and explained truth via assertion. Truth is simple and thus indefinable, but not uncharacterisable. Assertion, in turn, is the most basic linguistic action, and is thus also ‘primitive’ and immediately understood. Frege’s view of truth derives from the principles I discussed in Chap. 2, i.e. the Principle of Assertion (PI), the Principle of Context (PCont), the Principle of Inferential Individuation (PII), and the Principle of Propositional Priority (PPP). In relation to the truth predicate ‘is true’, his proposal is expressive, as it is in relation to the analogous predicate ‘is a fact’. The semantic status of ‘is true’ has been confused with an alleged redundancy theory of truth, which Frege never supported.

Informal Logic and Argumentation Theory claim to accept a sense of ‘argument’ that is broader than the sense used in classical logic and mainstream philosophy of language. In this allegedly more general sense, pictures, sounds, gestures, maps, etc. can be premises of arguments, even if conclusions are usually seen as propositional. In this chapter, I argue that multimodality is a well-known phenomenon among linguists and among mathematicians. Relevance Theorists and Truth-Conditional Pragmatists have discussed the impact of gestures and body language in communication and the essential ineffability of what they call ‘expressives’. Mathematicians and philosophers of mathematics, in turn, have discussed the relevance of figures and diagrams in proofs. I will argue that perceptible items do not have logical properties. Logical properties are properties of a certain kind of abstract entities whose identification follows the organic intuition, (OI). Argumentation Theory has not provided arguments that advised a revision of Frege’s view that judgeable contents are the sole concern of logic. Still, the multimodality debate brings to the fore significant issues related to how information flows; among these issues, the insight that different representation modes open up different affordances and are differentially suitable for particular communicative aims.

In this chapter, I explain what is at issue in the debate on the meaning of the logical constants, exposing some weaknesses of the standard way in which logicians approach this subject. I present and discuss the two families of proposals that have been most successful: invariantism, which derives from (Tarski. History Philos Logic, 7, 143–154, 1986), and inferentialism, which derives from (Gentzen. Am Philosoph Quart 1(4), 288–306 1935/1964) and whose more philosophical aspects have been developed by Dummett, Hacking and Prawitz (Dummett M (1973) Frege. Philosophy of Language. New York, Harper and Row Publishers; Dummett M (1991) The logical basis of metaphysics. Cambridge, MA., Harvard University Press; Hacking. J Philos 76, 285–319 (1979); Prawitz. Synthese 148, 507–524 (2006)). I show that neither of these two approaches gets the set of logical constants right. Both have been accused of overgenerating, i.e. including notions that intuitively are not logical constants, and of undergenerating, i.e. leaving out of the picture some notions that clearly are logical constants. The constraints that their supporters have proposed to make them extensionally adequate point in the direction of taking on board the pragmatic roles that these notions play in communication. The last section of this chapter is devoted to explaining how a pragmatist account helps us to overcome the difficulties that more formalist approaches present, be they purely syntactic or semantically guided.

There are 16 bivalent binary truth functions, but only two fundamental logical relations between propositions: implying and precluding. In addition, some higher-level concepts express the scope and nature of inferential relations. In this chapter, I will explain Frege’s treatment of these two notions, which are the semantic and pragmatic support for conditionality and negation. I will also offer an explanation of Frege’s semantic account of universal and existential quantifiers, and the relations between them. The richness and originality of Frege’s semantics manifest in his treatment of the role of logical notions and related expressions. Frege’s logic is nothing more (and nothing less) than his semantics for logical terms together with an appropriate method for representing inferential transitions. The deductive system that converts a language into a calculus is the representation of the commitments and entitlements that individuate concepts and propositional contents. The very notation that Frege introduces shows that logical notions do not affect judgeable contents, which systematically occur as arguments of the former. In this chapter, I will argue that Frege defended an expressivist approach to the meaning of logical notions. Frege’s insights at this point can help in the as-yet unfinished task of giving a satisfactory semantics for logical notions. I consider Frege’s views and suggestions entirely correct.

In this chapter, I discuss an informed pragmatist proposal for characterising the class of logical constants, which I call ‘the inference-marker view’. It includes syntactic, semantic, and pragmatic aspects, all of them essential to the task that ultimately defines logical terms as expressive devices. Logical notions are not objects, nor do they refer to objects. Rather they are relational expressions whose meaning conveys some kind of movement between their arguments. The meaning of the relevant terms that represent logical notions linguistically has to reflect the dynamic function that they perform. The inference-marker view is inspired by Frege’s Begriffsschrift. The complex role of logical notions requires them to be binary higher-level predicables with propositions as their arguments. Being binary and higher-level are the syntactic aspects of logical terms. Concerning their semantics, the proposal stresses that logical terms do not stand for substantive concepts. Logical terms are expressive tools for bringing inferential commitments into the open. They are used to mark the presence of an inferential link between two propositions, or between one set of propositions and another proposition that follows from them. Alternatively, they express a blockage or a veto. The inference-marker view is in complete harmony with Brandom’s expressivism. The specific label that I use—‘inference-marker view’—is intended to make the role of logical constants more perspicuous, drawing on some contemporary linguistic positions in order to understand the role of these terms in language (or the role of these notions in our conceptual system).

The book offers a characterization of the meaning and role of the notion of truth in natural languages and an explanation of why, in spite of the big amount of proposals about truth, this task has proved to be resistant to the different analyses. The general thesis of the book is that defining truth is perfectly possible and that the average educated philosopher of language has the tools to do it. The book offers an updated treatment of the meaning of truth ascriptions from taking into account the latest views in philosophy of language and linguistics.

In this paper, I use an extension of Russell’s theory of descriptions to give further support to an analysis of truth ascriptions that stems back to Ramsey and has been further developed by Dorothy Grover and Christopher J. F. Williams. It is the view that the truth predicate vanishes in the logical form of the sentences in which it occurs in favour of a combination of quantifiers and propositional variables. I argue that Russell’s theory of descriptions can be used as a technical way of giving flesh to the sometimes-vague characterisation of truth terms as expressive. In my analysis, I assume the Fregean analysis of quantifiers, Frege’s context principle, and the Fregean distinction between grammatical structure and logical form. These three ground-breaking insights are crucial to the Russellian interpretation of denoting phrases and the analysis of truth ascriptions that I advocate. In section one, I explain the sense in which truth is a higher-level concept and which consequences follow from this claim, one of them being the linguistic flexibility of the concept of truth. In section two, I apply Russell’s insights to truth ascriptions and show that the truth predicate dissolves in their logical form in favour of propositional variables and quantifiers. The disappearance of the predicate in the logical form is the precise sense that I give to the claim that truth terms possess expressive meaning. As propositional quantification has been felt as a serious obstacle to the Ramseyian approach, I show in section three that the Quinean arguments usually addressed against higher-order quantification are weaker than the received view has taken them to be. I also address the objection that rests on the normative nature of truth. I argue in section four that the approach to truth ascriptions introduced by Ramsey provides an accurate and technically irreproachable account of the semantic expressivism associated with the concept of truth.

Mostraremos que el desacuerdo entre pesimistas y optimistas sobre la resolución racional de los desacuerdos profundos no se ubica en el nivel del contenido, de lo que están diciendo, sino en uno diferente. Para mostrar por qué es así, proponemos detenernos en el funcionamiento lógico-semántico del término clave en este desacuerdo: “racional”. Iniciaremos con el repaso de algunos argumentos que pesimistas y optimistas han esgrimido en su discusión, y comprobaremos la diferencia de estándares ya mencionada (sección 1); luego, nos detendremos en las particularidades lógico-semánticas de “racional”, y explicitaremos lo que hacen los hablantes cuando realizan movidas lingüísticas con él (sección 2); y para finalizar, volveremos sobre el desacuerdo entre pesimistas y optimistas, y mostraremos por qué, a pesar de la diferencia, permanece como un desacuerdo genuino y es importante seguir inmiscuidos en esta discusión. El análisis lógico-semántico nos mostrará que “racional” no es usado para describir un estándar de racionalidad independiente de cualquier contexto, sino para expresar ciertas actitudes respecto de lo que decimos o hacemos. A pesar de la diferencia de estándares, pesimistas y optimistas siguen inmiscuidos en un desacuerdo genuino porque discrepan acerca de ciertas actitudes que hay que adoptar con respecto a, en este caso específico, los DP.

Patrick Grim, The incomplete universe:totality, knowledge, and truth. Cambridge, Mass, and London: The MIT Press, 1991. xiv + 165pp. £22.50 Jan SebestikLogique et mathématique chez Bernard Bolzano. Paris:Vrin, 1992. 522 pp. 198Fr J. De Lorenzo, Kant y la matemâtica. El uso constructivo de la razön pura Madrid:Editorial Tecnos, 1992. 180 pp. No price stated F. Coniglione, R. Poli And J. Woleintski, Polish scientific philosophy:The Lvov-Warsaw school. Amsterdam and Atlanta, Georgia: Rodopi, 1993. xi + 358pp. No price stated I. Kant Lectures on logic. Translated and edited by J. Michael Young. Cambridge:Cambridge University Press, 1992. xxxii + 695 pp. £55.00 Michael Dummett, The seas of language. Oxford:Clarendon Press, 1993. xvii + 482 pp. £40.00 Stephen Read,, Sophisms in medieval logic and grammar. Acts of the Ninth European Symposium for Medieval Logic and Semantics held at St Andrews, June 1990. Dordrecht, Boston, London:Kluwer Academic Publishers, 1993. xvii + 421pp. $157.50 James D. McCawley, Everything that linguists have always wanted to know about logic∗ ∗but were ashamed to ask. Second edition. Chicago and London:The University of Chicago Press, 1993. xxi + 633pp. £25.95/$37.50 ; £79.25/$113.75 Theodor Ebert, Dialektiker und frühe Stoiker bei Sextus Empiricus. Untersuchungen zur Entstehung der Aussagenlogik. Göttingen:Vandenhoeck & Ruprecht, 1991. 347 pp. DM 85.00 Entre la logique et la foi. Entretiens avec Joseph-M. Bochenski recueillis par Jan Parys. Translated from the Polish by Eric Morin-Aguilar. Montricher :Editions Noir-sur-Blanc, 1990. 353 pp. SFr 40.00 Noel Balzer, The human being as a logical thinker. Amsterdam and Atlanta:Rodopi 1993, 148 pp. No price stated R. I. G. Hughes, A philosophical companion to first-order logic. Indianapolis:Hackett, 1993, viii + 309 pp. No price stated Shahid Rahman, Über Dialoge, Protologische Kategorien und andere Seltenheiten, Frankfurt, Peter Lang Verlag, 1993. 318 pp. No price stated Claire Ortiz Hill, Word and object in Husserl, Frege, and Russell. The roots of twentieth century philosophy. Athens, Ohio:Ohio University Press, 1991. xiii + 215pp., $34.95

The background of this paper is what I call “pragmatic inferentialism,” a view that I attribute to Robert Brandom. Here, I develop Brandom’s view and argue that it is a kind of subject naturalism, in Price’s sense, and that the charge of idealism sometimes addressed against it is unwarranted. Regarding, I show that pragmatic inferentialism finds support from evolutionary psychology and developmental psychology. Regarding, I present what I call “level 0 expressivism,” which I take to be the semantic counterpart of some aspects of evolutionary psychology and developmental psychology. Besides, I resort to Brandom’s defense of Hegel’s conceptual realism. The conclusion of the paper is a vindication of objective truth in the inferentialist framework.

This monograph is a defence of the Fregean take on logic. The author argues that Frege ́s projects, in logic and philosophy of language, are essentially connected and that the formalist shift produced by the work of Peano, Boole and Schroeder and continued by Hilbert and Tarski is completely alien to Frege's approach in the Begriffsschrift. A central thesis of the book is that judgeable contents, i.e. propositions, are the primary bearers of logical properties, which makes logic embedded in our conceptual system. This approach allows coherent and correct definitions of logical constants, logical consequence, and truth and connects their use to the practices of rational agents in science and everyday life.

The purpose of this paper is twofold: first we outline a version of non-descriptivism, ‘minimal expressivism’, leaving aside certain long-standing problems associated with conventional expressivist views. Second, we examine the way in which familiar expressivist results can be accommodated within this framework, through a particular interpretation that the expressive realm lends to a theory of meaning. Expressivist theories of meaning address only a portion of the classical problems attributed to this position when they seek to explain why the expressions they deal with have a given meaning. A position can nevertheless be termed ‘expressivist’ – in the minimal sense that we favor – based simply on the following key features of the meaning of these expressions: they can be used as functions of propositions, and they are not used to describe the way the world is

The purpose of this paper is to show that, pace (Field, 2009), MacFarlane’s assessment relativism and expressivism should be sharply distinguished. We do so by arguing that relativism and expressivism exemplify two very different approaches to context-dependence. Relativism, on the one hand, shares with other contemporary approaches a bottom–up, building block, model, while expressivism is part of a different tradition, one that might include Lewis’ epistemic contextualism and Frege’s content individuation, with which it shares an organic model to deal with context-dependence. The building-block model and the organic model, and thus relativism and expressivism, are set apart with the aid of a particular test: only the building-block model is compatible with the idea that there might be analytically equivalent, and yet different, propositions.