Fregean Approach Research Articles

Where Does Cardinality Come From?

AbstractHow do we acquire the notions of cardinality and cardinal number? In the (neo-)Fregean approach, they are derived from the notion of equinumerosity. According to some alternative approaches, defended and developed by Husserl and Parsons among others, the order of explanation is reversed: equinumerosity is explained in terms of cardinality, which, in turn, is explained in terms of our ordinary practices of counting. In their paper, ‘Cardinality, Counting, and Equinumerosity’, Richard Kimberly Heck proposes that instead of equinumerosity or counting, cardinality is derived from a cognitively earlier notion of just as many. In this paper, we assess Heck’s proposal in terms of contemporary theories of number concept acquisition. Focusing on bootstrapping theories, we argue that there is no evidence that the notion of just as many is cognitively primary. Furthermore, since the acquisition of cardinality is an enculturated process, the cognitive primariness of these notions, possibly including just as many, depends on various external cultural factors. Therefore, being possibly a cultural construction, just as many could be one among several notions used in the acquisition of cardinality and cardinal number concepts. This paper thus challenges those accounts which seek for a fundamental concept underlying all aspects of numerical cognition.

Against Fregean Quantification

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege’s distinction between sense and reference.

Ritornare a Schlick: semantica modellistica e uso descrittivo del linguaggi

In this article, I argue that fregean approach to semantics, like that of modelling semantics, doesn’t have the conceptual tools to define the notions of truth and reference. The reason is that these programs ignore what Wittgenstein taught us, namely the link between meaning and use. More specifically, I intend to show how a theory of descriptive language can only be constructed by clarifying the connection between the notions of linguistic game, meaning and description. But how can this connection be clarified? Wittgenstein, in the second phase of his thought, had never been interested in a theory of this type (ie the construction of a theory of descriptive use), and all his reflections on use and meaning had the sole purpose of “curing” from that essentialist attitude (the claim to capture the essence of the terms) that had characterized the Tractatus , and which still today characterizes almost the whole analytic philosophy. This means that it is not in Wittgenstein's thought that we can find such a theory, but in Moritz Schlick’s works, who attempted to build a theory of linguistic meaning based on the connection between the notions of image, use and verification.

On The Liar Sentence: A Fregean Analysis

The liar paradox, attributed to Eubulides, a fifth century BC Greek philosopher, has been debated over two millennia. In the history of philosophy, various attempts have been made to resolve and dissolve the paradox. Nevertheless, the paradox remains as a live area of exploration in logic and philosophy. The present paper is an analytical exploration into the validity of the strengthened liar sentence, which is considered as an acid test for all versions of liar paradoxes. The main method used in this analysis is the Fregean distinction between sign, sense and reference. The Fregean approach towards attributing the truth value as the predicate of the sentence is also used in this analysis. The analysis shows that the liar sentence is essentially meaningless and in a strict sense, it does not qualify as a sentence at all. Considering the liar sentence as meaningful, further analysis of the formal representation of liar sentence again proves it to be necessarily an inconsistent one. The formal analysis brings out the implicit contradiction within the liar sentence.

Definite descriptions by Paul Elbourne

Reviewed by: Definite descriptions by Paul Elbourne Barbara Abbott Definite descriptions. By Paul Elbourne. (Oxford studies in semantics and pragmatics 1.) Oxford: Oxford University Press, 2013. Pp. 251. ISBN 9780199660209. $50. This book presents a development and refinement of the analysis of definite descriptions (and pronouns) that appears in Elbourne’s (2005) book Situations and individuals. That analysis is Fregean, according to which definite descriptions are referential expressions that presuppose the existence and uniqueness of a referent. The main foci of the book are reviewing and adding arguments in favor of the analysis, and addressing problems that have been raised against it. The main competitor is, of course, the Russellian, quantificational analysis, and in addition to arguing for the Fregean approach, E presents problems for this competitor. Ch. 1 (‘Introduction’, 1–16) briefly reviews not two but six analyses of definite descriptions: (i) Russell’s (1905); (ii) Donnellan’s (1966), according to which descriptions are ambiguous between a quantificational and a referential interpretation; (iii) Frege’s (1892); (iv) Graff (Fara)’s (2001) predicate analysis; (v) Heim’s (1982) familiarity view; and (vi) Szabó’s (2000) existential theory. E notes three prominent problems for the Fregean view (true negative existence statements, presupposition failures that result in falsity rather than lack of a truth value, and true sentences about propositional attitudes toward nonexistent entities) that are addressed later in the book, and then briefly argues against analyses (iv)–(vi) above. Ch. 2 (‘Situation semantics’, 17–41) gives a detailed formal presentation of the variety of situation semantics to be presupposed. This is important, because a crucial part of E’s analysis is the inclusion of situation variables in definite descriptions. Situations, following Barwise & Perry 1983, are entities possessing properties at spatiotemporal locations. (One small issue crops up occasionally: whether including a location excludes abstract entities.) Sentence meanings are sets of situations, here called ‘Kripkean propositions’. The actual utterance of a sentence on a particular occasion results in an Austinian proposition: ‘[t]he pair of a sentence meaning and the topic situation that it is meant to describe’ (18). Interestingly, E notes that he does not actually believe in the existence of nonactual situations, holding instead that ‘meanings are internal mental structures’ (19). Ch. 3 (‘The definite article’, 42–51) gives an analysis that, as E notes, is based on one given by Heim and Kratzer (1998). E’s version is below (47). (1). This makes the definite article a function from properties (expressed by the NP with which the combines) to functions from situations to entities—those that uniquely possess the property in the situation in question. Definite descriptions have the structure shown in 2. (2). [[the NP] s] Crucially, though, any particular definite description has the possibility of receiving two analyses, depending on whether the situation variable in 2 (which E refers to as a ‘situation pronoun’) is bound. Ch. 4 (‘Presupposition’, 52–103) is an extended discussion of how the presuppositions associated with definite descriptions appear or fail to appear in the contexts associated with modals, conditionals, disjunctions (assumed here to be equivalent to conditionals), negation, and sometimes just ordinary sentences. In the case of modals, the requirement of a unique referent for a definite description must be satisfied relative to the situation from which the alternative possible worlds are accessible. Similarly for conditionals, except those whose antecedents actually assert the existence and uniqueness of a referent for a definite description occurring in the consequent. In that case, the presupposition does not project. When we come to negation, presuppositions generally project, with the exception of true negative existentials. In this case E proposes implicit [End Page 762] modalization, so that the existence and uniqueness of the entity in question is satisfied relative to imaginary situations, and such an entity is asserted not to exist in the Austinian topic situation (typically one in the actual world). The longest discussion is devoted to ‘presupposition obviation’—cases like Strawson’s (1954:226) example of someone declaring that they had had lunch with the King of France, which we would judge to be false, rather than truth-valueless. Ch. 5 (‘Referential and attributive’, 104–19) shows how E’s analysis can provide...

Some Naturalistic Comments on Frege’s Philosophy of Mathematics

This paper compares Frege’s philosophy of mathematics with a naturalistic and nominalistic philosophy of mathematics developed in Ye (2010a, 2010b, 2010c, 2011), and it defends the latter against the former. The paper focuses on Frege’s account of the applicability of mathematics in the sciences and his conceptual realism. It argues that the naturalistic and nominalistic approach fares better than the Fregean approach in terms of its logical accuracy and clarity in explaining the applicability of mathematics in the sciences, its ability to reveal the real issues in explaining human epistemic and semantic access to objects, its prospect for resolving internal difficulties and developing into a full-fledged theory with rich details, as well its consistency with other areas of our scientific knowledge. Trivial criticisms such as “Frege is against naturalism here and therefore he is wrong” will be avoided as the paper tries to evaluate the two approaches on a neutral ground by focusing on meta-theoretical features such as accuracy, richness of detail, prospects for resolving internal issues, and consistency with other knowledge. The arguments in this paper apply not merely to Frege’s philosophy. They apply as well to all philosophies that accept a Fregean account of the applicability of mathematics or accept conceptual realism. Some of these philosophies profess to endorse naturalism.

The Bearable Lightness of Being

How are philosophical questions about what kinds of things there are to be understood and how are they to be answered? This paper defends broadly Fregean answers to these questions. Ontological categories—such as object, property, and relation—are explained in terms of a prior logical categorization of expressions, as singular terms, predicates of varying degree and level, etc. Questions about what kinds of object, property, etc., there are are, on this approach, reduce to questions about truth and logical form: for example, the question whether there are numbers is the question whether there are true atomic statements in which expressions function as singular terms which, if they have reference at all, stand for numbers, and the question whether there are properties of a given type is a question about whether there are meaningful predicates of an appropriate degree and level. This approach is defended against the objection that it must be wrong because makes what there depend on us or our language. Some problems confronting the Fregean approach—including Frege’s notorious paradox of the concept horse—are addressed. It is argued that the approach results in a modest and sober deflationary understanding of ontological commitments.

Language and Logical Pluralism: Some Aspects of a Wittgensteinian Perspective on the Nature of Logic

This essay examines the importance of some aspects of Wittgenstein's post-Tractatus work in the realm of discussions on the nature of logic. The first part considers a relationship between certain conceptions of language and certain positions on the nature of logical laws and logical pluralism. Supposing the rejection of mentalism in the field of meaning leads to a rejection of psychologism, it presents some alternatives different from psychologism, based on non mentalistic theories of meaning. One is the Platonistic Fregean approach to language and logic, the other is Carnap's formalist view on both topics. The second part concentrates on Wittgenstein's non mentalistic and non Platonistic proposals about language and his defense of the logical pluralism proposed by psychologists. It compares two periods on Wittgenstein's work after Tractatus -the periods of ‘calculus conception’ and ‘languange games conception’- and it shows how characteristic notions of Wittgenstein's later conception of language, like ‘use’, ‘language games’, and ‘forms of life’, work on the characterization of logic and specially on the kind of logical pluralism that the author seems to defend in his last period. In doing so, this essay offers an approach to some of the author's considerations about contradictions and the possibility of the existence of a calculus that includes them. This approach emphasizes on the idea of applicability (or use of a linguistic expression) introduced by the author in some of his last works, and in some examples of functional contradictions that can help to understand and complement that idea.

How Much Substitutivity?

How Much Substitutivity?

Modos de presentación y modos de determinación

In this paper I argue that, in order to make (T1) and (T2) compatible within a Fregean approach, we must reject the view that all modes of presentation are senses. (T1) There is a diversity of ways in which Venus may be presented to each subject, and which are associated with the name ‘Venus’. (T2) There is only one Fregean thought expressed by the sentence ‘Venus is a planet’. Modes of presentation are those things which are essentially psychological and have causal powers on minds. The mind of a subject is sensitive to differences in modes of presentation, so that if an object is presented to a subject under different modes of presentation and she has no reason to believe that they are modes of presentation of one and the same object, then she may take opposing attitudes involving those different modes of presentation. In contrast, senses are those things which are essentially semantic. For this reason, I propose that they be understood as certain ways of determining the reference of terms, and either are given by the semantic rules for those terms or are identical to those semantic rules. I agree with McDowell that an interpretive truth-theory for a language L gives us a theory of sense for L, and that something like (V) ‘Venus’ refers to Venus will give us the axiom which assigns the semantic value for ‘Venus’ within such a theory, and which is necessary in order to derive the interpretive truth-conditions of a sentence like ‘Venus is a planet’. An axiom like ‘Venus’ refers to Hesperus will not do within a theory of sense. Nonetheless, it will do within a theory of reference, a truth-theory which delivers not interpretive truth-conditions, but purely referential truth conditions. The purely referential truth-conditions for an indicative atomic sentence are, I claim, those which are specified by specifying those features in the world (objects, properties, etc.) to which the meaningful parts of the sentence refer, representing them as related in a certain way. For the specification of such truth-conditions, the difference in cognitive value between two sentences will not matter, whereas it will matter for the specification of interpretive truth-conditions. Now, senses are introduced to allow for an explanation of the difference in cognitive value between sentences with the same purely referential truth-conditions. An indication of when two sentences differ in cognitive value is when it is possible for a subject who is rational and understands the language in question to take opposing attitudes to those sentences (or their contents —whatever those contents are); and if there is in fact such a subject who takes opposing attitudes to those sentences, then those sentences differ in their cognitive value. Given this connection between cognitive value and a subject’s attitudes, and given the purpose for which senses are introduced, we must suppose that a subject’s mind must be sensitive to differences in senses, and so, that senses must be psychologically relevant. My proposal, which aims to establish some kind of identity between some modes of presentation under certain conditions and those ways of determination which are senses, is as follows: A psychological mode of presentation M is a way of determination which is a sense relative to a particular expression e in a public language L which aids in expressing propositional attitude P if and only if i the subject who has M and who is sufficiently competent in L knows (or realizes) that M goes with e in L; ii no other proposition e′ in L is more adequate for reporting the subject’s propositional attitude P; iii M is crucial in the subject’s rational failure to make certain identifications; and iv M is an appropriate function to an appropriate reference. Only the mode of presentation associated with ‘Venus’ that satisfies conditions i-iv relative to ‘Venus’ which aids in expressing a propositional attitude like the belief that Venus is a planet, will be the sense of ‘Venus’. I argue that only the mode of presentation of Venus as Venus will do, and that such mode of presentation is implicit in the way of determination shown by (V). Other modes of presentation of Venus as being big or appearing in the sky in the evenings or being the second planet in proximity to the sun will not satisfy conditions i–iv. Thus, although a subject may have all these modes of presentation of Venus and associate them with ‘Venus’ (i.e. (T1)), only the mode of presentation of Venus as Venus will do as the sense of ‘Venus’. Hence, only one thought will be expressed by a sentence like ‘Venus is a planet’ (i.e. (T2)).