Concepts: Contemporary and Historical Perspectives

ProtoSociology Volume 30

Gerhard Preyer, Gerhard Preyer

• Verlag: Books on Demand
• Jahr: 2015
• ISBN:
  9783739258973
• Auflage: 1
• Thema: Philosophie
• Thema: Histoire et théorie de la philosophie

"Concept" in a historic and systematic perspectiveIn his paper "What Happened to the Sense of a Concept-Word?", Carlo Penco deals with the boundary between semantics and pragmatics and discusses some misunderstandings in the shift from the sense/reference distinction in Frege to the intension/extension distinction in semantics. Building on Fodor, Margolis and Laurence Jacob Beck defends in "Sense, Mentalese, and Ontology" the latter Fregean view on concepts by arguing that the mind-independence of Fregean senses renders them ontologically suspect in a way that mentalese symbols are not. Maria C. Amoretti explores the model of Davidson's triangulation and its specific role in concept acquisition. In "A Critique of David Chalmers' and Frank Jackson's Account of Concepts" Ingo Brigandt suggests a more pragmatic approach to natural kind term meaning, arguing that the epistemic goal pursued by a term's use is an additional semantic property. Agustin Vicente, Fernando Martinez-Manrique discuss whether this variability in the languages generates a corresponding variability in the conceptual structure of the speakers of those languages in "The Influence of Language on Conceptualization: Three Views". The connection between "Views of Concepts and of Philosophy of Mind—From Representationalism to Contextualism" is explored by Sofia Miguens, in respect of Edmund Husserl to Jocelyn Benoist. Richard Manning argues some "Changes in View: Concepts in Experience" with the main thesis that the content of perceptual experience must be conceived as concept-involving. In "Concepts and Fat Plants" Marcello Frixione suggests that typicality effects are more plausibly the consequence of some "ecological constraints" acting on the mind. What does cognitive neuroscience contribute to our philosophical under-standing of concepts? That is the main question for Joseph B. McCaffrey in "Con-cepts in the Brain: Neuroscience, Embodiment, and Categorization". The volume is completed by articles on the historical perspective on concept, starting with "Conceptual Distinctions and the Concept of Substance in Descartes" by Alan Nelson. "The Concept of Body in Hume's Treatise" is examined by Miren Boehm. Lewis Powell argues the "Conceiving without Concepts: Reid vs. The Way of Ideas". And Thomas Vinci asks: "Why the 'Concept' of Spaces is not a Concept for Kant", while Sonja Schierbaum reconstructs "Ockham on Concepts of Beings".Content and abstracts: www.protosociology.de

Concepts, Sense, and Ontology

What Happened to the Sense of a Concept-Word?

Carlo Penco

Abstract

In this paper I shall outline a short history of the ideas concerning sense and reference of a concept-word from Frege to model theoretic semantics. I claim that, contrary to what is normally supposed, a procedural view of sense may be compatible with model theoretic semantics, especially in dealing with problems at the boundary between semantics and pragmatics. A first paragraph on the paradox of the concept horse will clarify the attitude concerning the history of ideas that I assume in this paper. In the second paragraph I will discuss some misunderstandings in the shift from the sense/reference distinction in Frege to the intension/extension distinction in model theoretic semantics. In the third I will show how a particular interpretation of the Fregean sense of a concept word (and of cognitive sense in general) may be of interest for model theoretic semantics.

Introduction

Discussion on concepts both in philosophy and psychology have produced so many new ideas on the topic, that it becomes difficult to make any comparison between contemporary debates and the Fregean worries. After recent criticism of concepts as natural kinds (Frixione 2007, Macherie 2009) cognitive scientists, philosophers and psychologists are proposing new ways of treating different aspects of cognition in humans and other animals; are concepts developed from a prelinguistic ability to classify? How do they develop in children? If we do not define concepts as natural kinds, shall we define them as functional kinds? shall we define them epistemically, semantically o by their origin? (see for instance Sainsbury-Tye 2011). Although some Fregean “problems” are still confronted, the contemporary debate on concepts seems to go far away from the original terminology used by Frege, that attracts mainly exegetic confrontation (we have excellent examples in Künne 2010 and Textor 2011). A possibility to find new suggestions in Frege’s analysis of concepts may take two trends: on the one hand we may work on how his complex distinction of “levels” of concepts present psychologists and computer scientists with new problems (cf. Brandom 2009); on the other hand we may work on the history of ideas¹ and look inside the development of semantics after Frege, trying to reconstruct some of Frege’s ideas in a new setting. I will follow the second trend, pointing out a blind spot in contemporary semantics, due to a failure to engage with the Frege’s conception of the sense of a predicate—or in his terminology, a “concept-word” (Begriffswort).²

In this paper I will try to show the compatibility of a procedural interpretation of the Fregean sense of a predicate with contemporary model theoretic semantics. I don’t claim that Frege cannot suggest alternative perspectives in semantics and theories of meaning; however, as Eva Picardi (2005, 35) remarks, it is difficult to accept that radically different interpretations of Frege—such as representationalist vs. inferentialist theories—“did equal justice to Frege’s central concerns”. Picardi 2005 has shown some difficulties of strong inferentialism to keep some basic Fregean desiderata; on the other hand most people agree that model theoretic semantics, although it has been developed on the track of Frege through Carnap, apparently abandoned some Fregean requirements on cognitive aspects. Nevertheless I think that some of Frege’s most debated views on concepts are either preserved in new settings, like lambda calculus, or could be developed inside model theoretical semantics. I will then present (1) an assessment of one of the most famous problem concerning the Fregean theory of concepts as exemplifying a way to see its compatibility with develoments of logics after him; (2) a short historical presentation of the evolution of semantics after the Fregean distinctions of sense and reference for predicates in front of the “anomaly” of the original Fregean tripartite classification; (3) a use of the Fregean requirement on the sense of predicates that impinges upon the problem of the boundary between semantics and pragmatics.

1 Frege on Concepts as “Objects of a Special Kind”

Frege’s original theory of concept is grounded on his analogy between concepts and functions: “what is called in logic a concept is connected with what we call a function … a concept is a function whose value is always a truth value” (FC 15) Presented in this way the theory is certainly original with respect to the past; historically, it is a generalization of the idea of function. Stripped of its prose it can be considered the origin of the “classical” view, where connectives can be considered as functions from truth values to truth values and predicates as functions from individuals to truth values: Px represents a function that has the value true when completed with a singular term referring to an object falling under the concept P, or belonging to the class denoted by P.

A great deal of the philosophical discussion on Frege’s theory of concept has been devoted to his theory of the non-definability of (the notion of ) a concept. Frege gives a semantic definition of objects and concepts as what is referred to, respectively, by singular terms (proper names) and predicates (concept words). Predicates or concept words are for Frege unsaturated expressions, i.e. patterns given by a sentence fragment that needs to be completed by a singular term, as with “… is a horse”.³ However, in natural language, we are almost compelled to refer to concepts using the definite article: “the concept horse” How can we make the connection between the expressions “… is a horse” and “the concept horse”? How can we say that the concept horse is a concept? Our grammar suggests that an expression composed with the definite article “the” (a definite description) is a singular term, whose reference is an object and not a concept; therefore we should paradoxically assert “the concept horse is not a concept”.⁴ This has been called “the paradox” of the concept horse. Frege (1892b: 201) concludes that concepts are “objects of a special kind”, and asks the reader to accept this incongruence of natural language. Coming back on the issue years later, Frege (1906: 210) insists that grammar may mislead us, given that using a definite description to refer to concepts is “a mistake language forces upon us”. However informal elucidations should be enough to clarify the intention of the writer in order to understand the sharp distinction between concepts and objects (functions and arguments) on which the construction of his formal system is grounded⁵.

Frege required “a pinch of salt” of us in order to understand the difference between objects and concepts, remarking that not everything in a formal system can be explained, and that the elucidations of the signs preceding the presentation of the formal system are informal introductions, that cannot be expressed in terms of the formal system. Among many discussions (starting with Dummett 1973 until Davidson 2005⁶) we find two extreme positions: on the one hand Crispin Wright claims that the paradox is not solvable unless we reject the application of the notion of sense and reference to predicates; on the other hand New-Wittgensteinians claim that Fregean elucidations are plain and “robust” nonsense. Both criticisms seem overstated.

On the one hand Wright 1998 claims that Frege’s use of a singular term to refer to concepts clashes with his requirement for which two expressions with the same reference should be inter-substitutable in all extensional sentences salva veritate, and in all sentences salva congruitate (reference principle); in fact singular terms (“the concept horse”) and concept words (“… is a horse”) have different grammatical roles and cannot substituted salva congruitate.⁷ Therefore, in the end, Frege was mistaken: singular terms refer, but predicates don’t⁸. Wright criticizes Dummett’s attempt to solve the “paradox” finding a way to express the second order expression “concept horse”, but the discussion may probably be stopped before the beginning. One problem with Wright’s interpretation is that he wonders “how exactly Frege is to communicate his semantic proposals about predicates”; he asks for a “decent semantic theory” (Wright 1998, §III) while Frege explicitly considers his elucidations something where exactness cannot be attained, because—used to introducing his formal system—they are not part of it. Instead of conceding Frege to give an informal introduction to the basic concepts of his semantics, Wright looks for a formal analysis, and comes to the conclusion that Frege’s basic mistake is the application of the sense/reference distinction to predicates (concept words). Wright requires a strict formalism exactly where Frege was supposing that no formal definition is required: we cannot give definitions for primitive elements of the system. (E.g. Frege 1906: 301; 1924: 290). Wright is correct in saying—after Frege—that singular terms and predicates behave differently, and we may refer to predicates indirectly, by giving their extension. In fact we may use extensions (classes) as the semantic value of predicates (as contemporary semantics does); but this does not abolish the possibility of speaking of concepts.⁹ We touch here a point in which—as Textor (2011, 253) remarks—“reference as what we want to speak about and reference as semantic role come apart”. Speaking of the reference of a predicate is not only defining a semantic value in a formal system, but also—basically—a reminder for the distinction between a function and its extension, distinction on which Frege was insisting in all his remarks on the idea of function. We might be content to claim that, in our informal elucidations, we need to refer to entities that are not objects, but concepts.

On the other hand, since the connection between Frege’s “elucidations” and Wittgenstein’s remarks on the unsayable discussed by Geach 1976 and later by Diamodn 1988, many authors, mainly “New Wittgensteinians”, began to theorize the “ineffability” or “nonsense” of philosophical elucidations (the elucidations of Tractatus itself, or the elucidations in the introduction to Frege’s Begriffsschrift). Certainly Frege was well aware that the basic concepts of the theory are not part of it and called the words “concept” and “function” with the term “pseudo-predicates”, and used to speak of “nonsense” (Unsinn) about attempts to define primitive elements of his system until his latest writings¹⁰. Wittgenstein in the Tractatus called “object” and “function” “formal concepts”—i.e. not genuine, empirical concepts—that “show” their function in the use of the formalism. Anticipating Quine’s motto, Wittgenstein used to say that the correct use of the word “object” is expressed in the formalism by a variable.¹¹ However, although both Frege and Wittgenstein used the term “nonsense” (“Unsinn”), it is plain that Frege used it in special cases, where the grammar of language clashes with theoretical intuitions as in the case of “the concept horse”. Instead of accepting the attempt to recognize the limitations of the grammar of our natural language to express some basic ideas of the formal system, the New Wittgensteinans consider that what elucidations attempt to say always issues in plain nonsense.

Frege’s aim (followed to the extreme in Wittgenstein’s Tractatus) was more modest, and asked for informal agreement on basic concepts of his formal theory: “since definitions are not possible for primitive elements, something else must enter in. I call it elucidation. It is this, therefore, that serves the purpose of mutual understanding among investigators, as well as of the communication of the science to others.”¹² I am not alone in thinking that the so called “paradox” of the concept horse is not really a paradox¹³, but what the “second” Wittgenstein would have called a “misunderstanding” due to the grammar of our natural language. Even in speaking of “nonsense” we should need a pinch of salt.

In what follows I suggest an attitude where some basic Fregean ideas can be considered not only as such, in contrast with logical systems developed after him, but also for their value to illuminate and being illuminated by more recent developments.

A first example is what happened of the Fregean suggestion that concepts are “objects of a special kind” (he could have said “entities”). The suggestion has been developed by Alonzo Church with the lambda notation, where we may refer to concepts by an expression with bound variables which is formally analogous to the iota operator for definite descriptions (that Frege introduces in Grundgesetze § 11). In fact, facing the problem of the paradox of “the concept horse”, somebody might attempt to use a second order description operator such as: iF: (x) (F(x) iff Horse (x)), that is “the F such that for all x, x is an F iff x is an horse”. But Frege introduced the description operator for singular terms would have not accepted it for predicates that need to be represented as insaturated expressions (see also Dummett 1973: 244). Church breaks this prohibition and invents a new kind of operator, with the expression “lx. horse (x)” as a way to expressing the concept horse. Contrary to Frege’s requirement, we have here an expression that is not literally “unsaturated”, that is with a gap. Is Church’s solution radically different from Frege’s? Certainly it is, from the point of view of strict literal interpretation, but, nevertheless other aspects of Frege’s main tenets seem to be represented, especially in lambda abstraction and lambda application, including the sharp differenc...