Frege: Singular Terms

Evans famosamente declarou que Frege não aceitou a possibilidade de sentido sem referente, o que significa que ele não foi tão tolerante com nomes vazios quanto comumente se pensa. Um problema central para a tese de Evans é que Frege diz explicitamente que aceita esta possibilidade, e parece que ele de fato foi tolerante com nomes vazios. Neste artigo, defendo que a solução de Evans para este problema implica que Frege estava comprometido com uma explicação implausível das frases contendo nomes (...) vazios. (shrink)

É bem conhecida a divergência entre as posições de Gottlob Frege e Bertrand Russell com relação ao tratamento semântico dado a sentenças contendo termos singulares indefinidos, ou seja, termos singulares sem referência ou com referência ambígua, tais como ‘Papai Noel’ ou ‘o atual rei da França’ ou ‘1/0 ’ ou ‘√4’ ou ‘o autor de Principia Mathematica’. Para Frege, as sentenças da linguagem natural que contêm termos indefinidos não formam declarações e portanto não são nem verdadeiras nem falsas. Já para (...) as sentenças da matemática, Frege defende que elas precisam ser corrigidas através da convenção forçada de uma referência não ambígua. Russell, por outro lado, aceita os termos indefinidos e propõe, através de sua teoria das descrições definidas, uma maneira de avaliar as sentenças em que eles ocorrem; e Quine amplia a teoria de Russell para abranger também os nomes com problemas de referência. Na prática da matemática são comuns os termos singulares indefinidos, sem referência, tais como ‘1/0 ’, ou com referência ambígua, tais como ‘√4’. Apesar de não haver uma sistematização rigorosa desta situação entre os matemáticos, há, no entanto, um conjunto de regras convencionais que tradicionalmente costumam ser aplicadas no tratamento matemático dos termos indefinidos. Nossa proposta é tomar a convenção matemática como inspiração e modelo para apresentar uma interpretação semântica formal para as descrições definidas e os nomes e utilizá-la como um argumento que favorece a abordagem de Russell relativamente à de Frege. (shrink)

It is generally accepted that Mill’s classification of names as nonconnotative terms is incompatible with Frege’s thesis that names have senses. However, Milldescribed the senses of nonconnotative terms—without being aware that he was doing so. These are the senses for names that were sought in vain by Frege. When Mill’s and Frege’s doctrines are understood as complementary, they constitute a fully satisfactory theory of names.

Bertrand Russell in his essay On Denoting [1905] presented a theory of description developed in response to the one proposed by Gottlob Frege in his paper Über Sinn und Bedeutung [1892]. The aim of our work will be to show that Russell underestimated Frege three times over in presenting the latter’s work: in relation to the Gray’s Elegy argument, to the Ferdinand argument, and to puzzles discussed by Russell. First, we will discuss two claims of Russell’s which do not do (...) justice to Frege: that we speak of a sense by means of quotation marks, and that all Frege does to cope with phrases that might denote nothing is define an arbitrary object as their reference. Second, we will show that Russell omitted the fact that Frege’s theory provided some answers for the puzzles presented by Russell in his essay. (shrink)

What is the relationship between Frege’s puzzle and the puzzle of the de se? An increasingly influential view claims that the de se puzzle is merely an instance of Frege’s puzzle and that the idea that de se attitudes pose a distinctive theoretical challenge rests on a myth. Here we argue that this view is misguided. There are important differences between the two puzzles. First, unlike Frege puzzle cases, de se puzzle cases involve unshareable Fregean senses. Second, unlike Frege puzzle (...) cases, de se puzzle cases cannot be resolved by objective information alone. Further, there seem to be pure cases of each puzzle: instances of the de se puzzle which do not have a Fregean structure, and instances of Frege’s puzzle, which do not involve de se attitudes. We conclude that the two puzzles are fundamentally different and that the traditional theory of attitudes needs to be amended. (shrink)

There are two common reactions to Frege’s claim that some senses and thoughts are private. Privatists accept both private senses and thoughts, while intersubjectivists don’t accept either. Both sides agree on a pair of tacit assumptions: first, that private senses automatically give rise to private thoughts; and second, that private senses and thoughts are the most problematic entities to which Frege’s remarks on privacy give rise. The aim of this paper is to show that both assumptions are mistaken. This will (...) motivate a so far neglected, reconciliatory position between privatism and intersubjectivism according to which all thoughts are public while some senses are private. (shrink)

We examine how Frege’s contrast between identity judgments of the forms “a=a” vs. “a=b” would fare in the special case where ‘a’ and ‘b’ are complex mental representations, and ‘a’ stands for an introspected ‘I’-thought. We first argue that the Fregean treatment of I-thoughts entails that they are what we call “one-shot thoughts”: they can only be thought once. This has the surprising consequence that no instance of the “a=a” form of judgment in this specific case comes out true, let (...) alone a priori true. This further reinforces Glezakos’s objections against the set-up of Frege’s puzzle, while also raising what we think is an acute problem for Fregeans, insofar as I-thought (and indexical thinking more generally), understood in their way, turns out to be incompatible with some basic features of rationality. (shrink)

In his book The Things We Mean, Stephen Schiffer advances a subtle defence of what he calls the ‘face-value’ analysis of attributions of belief and reports of speech. Under this analysis, ‘Harold believes that there is life on Venus’ expresses a relation between Harold and a certain abstract object, the proposition that there is life on Venus. The present essay first proposes an improvement to Schiffer’s ‘pleonastic’ theory of propositions. It then challenges the face-value analysis. There will be such things (...) as propositions only if they possess conditions of identity and distinctness. By analyzing Frege’s theory of propositions (Gedanken), I argue that such conditions may be found for the special case of beliefs and sayings advanced as premises and conclusions of deductive arguments. These conditions, however, are not applicable to most ordinary beliefs and sayings. Ordinary attributions and reports, then, do not place thinkers and speakers in relations to propositions. A bonus is exposure of the fallacy in the Putnam-Taschek objection to Frege’s theory of sense and reference. (shrink)

Demonstratives seem to have posed a severe difficulty for Frege’s philosophy of language, to which his doctrine of incommunicable senses was a reaction. In “The Thought,” Frege briefly discusses sentences containing such demonstratives as “today,” “here,” and “yesterday,” and then turns to certain questions that he says are raised by the occurrence of “I” in sentences (T, 24-26). He is led to say that, when one thinks about oneself, one grasps thoughts that others cannot grasp, that cannot be communicated. However, (...) nothing could be more out of the spirit of Frege’s account of sense and thought than an incommunicable, private thought. In the first part of the paper, I explain the problem demonstratives pose for Frege, and explore three ways he might have dealt with it. I argue that none of these ways provides Frege with a solution to his problem consistent with his philosophy of language. The first two are plausible as solutions, but contradict his identification of the sense expressed by a sentence with a thought. The third preserves the identification, but is implausible. In the second part, I suggest that Frege was led to his doctrine of incommunicable senses as a result of some appreciation of the difficulties his account of demonstratives faces, for these come quickly to the surface when we think about “I.” I argue that incommunicable senses won’t help. I end by trying to identify the central problem with Frege’s approach, and sketching an alternative. (shrink)

Gödel’s slingshot-argument proceeds from a referential theory of definite descriptions and from the principle of compositionality for reference. It outlines a metasemantic proof of Frege’s thesis that all true sentences refer to the same object—as well as all false ones. Whereas Frege drew from this the conclusion that sentences refer to truth-values, Gödel rejected a referential theory of definite descriptions. By formalising Gödel’s argument, it is possible to reconstruct all premises that are needed for the derivation of Frege’s thesis. For (...) this purpose, a reference-theoretical semantics for a language of first-order predicate logic with identity and referentially treated definite descriptions will be defined. Some of the premises of Gödel’s argument will be proven by such a reference-theoretical semantics, whereas others can only be postulated. For example, the principle that logically equivalent sentences refer to the same object cannot be proven but must be assumed in order to derive Frege’s thesis. However, different true (or false) sentences can refer to different states of affairs if the latter principle is rejected and the other two premises are maintained. This is shown using an identity criterion for states of affairs according to which two states of affairs are identical if and only if they involve the same objects and have the same necessary and sufficient condition for obtaining. (shrink)

According to the principle of compositionality, the meaning of a composed expression depends only on its logical form and the meaning of its descriptive sub-expressions. This dependence can be understood as the substitutivity of expressions that have the same meaning without changing the meaning of the composed expression. In this book the hidden complexity of Frege's and Quine's conceptions of extensionality is revealed. The insights gained by this analysis as well as two versions of the principle of compositionality are used (...) in a formal reconstruction of Gödel's and Quine's versions of the slingshot argument. (shrink)

Fregean theories of descriptions as terms have to deal with improper descriptions. To save bivalence various proposals have been made that involve assigning referents to improper descriptions. While bivalence is indeed saved, there is a price to be paid. Instantiations of the same general scheme, viz. the one and only individual that is F and G is G, are not only allowed but even required to have different truth values.

Bertrand Russell in his essay On Denoting [1905] presented a theory of description developed in response to the one proposed by Gottlob Frege in his paper Über Sinn und Bedeutung [1892]. The aim of our work will be to show that Russell underestimated Frege three times over in presenting the latter’s work: in relation to the Gray’s Elegy argument, to the Ferdinand argument, and to puzzles discussed by Russell. First, we will discuss two claims of Russell’s which do not do (...) justice to Frege: that we speak of a sense by means of quotation marks, and that all Frege does to cope with phrases that might denote nothing is define an arbitrary object as their reference. Second, we will show that Russell omitted the fact that Frege’s theory provided some answers for the puzzles presented by Russell in his essay. (shrink)

It would be an understatement to say that Russell was interested in Cantorian diagonal paradoxes. His discovery of the various versions of Russell’s paradox—the classes version, the predicates version, the propositional functions version—had a lasting effect on his views in philosophical logic. Similar Cantorian paradoxes regarding propositions—such as that discussed in §500 of The Principles of Mathematics—were surely among the reasons Russell eventually abandoned his ontology of propositions.1 However, Russell’s reasons for abandoning what he called “denoting concepts”, and his rejection (...) of similar “semantic dualisms” such as Frege’s theory of sense and reference—at least in “On Denoting”—made no explicit mention of any Cantorian paradox. My aim in this paper is to argue that such paradoxes do pose a problem for certain theories such as Frege’s, and early Russell’s, about how definite descriptions are meaningful. My first aim is simply to lay out the problem I have in mind. Next, I shall turn to arguing that the theories of descriptions endorsed by Frege and by Russell prior to “On Denoting” are susceptible to the problem. Finally, I explore what responses a.. (shrink)

Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is genuine, we instead argue that (...) number words, like many related expressions, are polymorphic, having multiple uses whose meanings are systematically related via type shifting. (shrink)

É bem conhecida a divergência entre as posições de Gottlob Frege e Bertrand Russell com relação ao tratamento semântico dado a sentenças contendo termos singulares indefinidos, ou seja, termos singulares sem referência ou com referência ambígua, tais como ‘Papai Noel’ ou ‘o atual rei da França’ ou ‘1/0 ’ ou ‘√4’ ou ‘o autor de Principia Mathematica’. Para Frege, as sentenças da linguagem natural que contêm termos indefinidos não formam declarações e portanto não são nem verdadeiras nem falsas. Já para (...) as sentenças da matemática, Frege defende que elas precisam ser corrigidas através da convenção forçada de uma referência não ambígua. Russell, por outro lado, aceita os termos indefinidos e propõe, através de sua teoria das descrições definidas, uma maneira de avaliar as sentenças em que eles ocorrem; e Quine amplia a teoria de Russell para abranger também os nomes com problemas de referência. Na prática da matemática são comuns os termos singulares indefinidos, sem referência, tais como ‘1/0 ’, ou com referência ambígua, tais como ‘√4’. Apesar de não haver uma sistematização rigorosa desta situação entre os matemáticos, há, no entanto, um conjunto de regras convencionais que tradicionalmente costumam ser aplicadas no tratamento matemático dos termos indefinidos. Nossa proposta é tomar a convenção matemática como inspiração e modelo para apresentar uma interpretação semântica formal para as descrições definidas e os nomes e utilizá-la como um argumento que favorece a abordagem de Russell relativamente à de Frege. (shrink)

This dissertation is about the structure of thought. Following Gottlob Frege, I define a thought as the sort of content relevant to determining whether an assertion is true or false. The historical component of the dissertation involves interpreting Frege’s actual views on the structure of thought. I argue that Frege did not think that a thought has a unique decomposition into its component senses, but rather the same thought can be decomposed into senses in a variety of distinct ways. I (...) extend Frege’s position and use it to develop an account of the hierarchy of senses, the senses expressed by indexicals and demonstratives, and the distinction between logical and non-logical structure. I also discuss various connections with the nature of meta-representation, our capacity for reflective judgment, some aspects of the structure of conscious experience, the way we perceive regions of space and durations of time, and our conscious awareness of our own perceptions and events of thinking. (shrink)

What is the relationship between Frege’s puzzle and the puzzle of the de se? An increasingly influential view claims that the de se puzzle is merely an instance of Frege’s puzzle and that the idea that de se attitudes pose a distinctive theoretical challenge rests on a myth. Here we argue that this view is misguided. There are important differences between the two puzzles. First, unlike Frege puzzle cases, de se puzzle cases involve unshareable Fregean senses. Second, unlike Frege puzzle (...) cases, de se puzzle cases cannot be resolved by objective information alone. Further, there seem to be pure cases of each puzzle: instances of the de se puzzle which do not have a Fregean structure, and instances of Frege’s puzzle, which do not involve de se attitudes. We conclude that the two puzzles are fundamentally different and that the traditional theory of attitudes needs to be amended. (shrink)

According to a criterion of difference for thoughts derived from Frege, two thoughts are different if it is at the same time possible for a rational subject to take conflicting epistemic attitudes toward them. But applying this criterion to perception-based demonstrative thoughts seems to slice thoughts too finely and lead to their proliferation which makes the criterion implausible. I argue that such a proliferation of thoughts is blocked by transforming this criterion into a related one that is shown to be (...) essential in individuating thoughts as they are conceived of in this paper. This has to do with the fact that what makes demonstrative sense synchronically or diachronically the same is the subject’s unreflective taking-for-granted that the object that she is perceiving is a single object that does not require her to keep track of it in the sense supposed by Evans and Campbell. (shrink)

I have three main objectives in this essay. First, in chapter 2, I shall put forward and justify what I call worldlessness, by which I mean the following: All truths (as well as falsehoods) are wholly independent of any circumstances, not only time and place but also possible worlds. It follows from this view that whatever is actually true must be taken as true with respect to every possible world, which means that all truths are (in a sense) necessary. However, (...) the account I shall propound is different from what is known in the trade as necessitarianism, i.e. the view that there is only one possible world, viz. the actual one, for the doctrine of the worldlessness of truth values, despite its commitment to the necessity of truths and falsehoods, is quite compatible with the idea of there being other possible worlds. Another important issue in chapter 2, explored in particular in section 2.12, is the claim that there is no real change in the world. Secondly, in chapter 3 I consider the eminent traditional argument for determinism, deriving from Aristotle, namely, logical determinism, i.e. determinism justified by an appeal to the logical principle of bivalence (that all proper statements, including those concerning the future, are either true or false). In this connection I try to show that, (i), the formulation of the conclusion of this argument as "Whatever will happen will happen of necessity" is implausible, at least from the modern point of view, (ii), the formulation as "Whatever will happen will happen inevitably" is more to the point, and (iii), on the basis of the worldless and timeless aspect advocated in chapter 2, this latter formulation is quite harmless, essentially amounting to the trivial statement, "Whatever will happen will happen". Thirdly, in chapter 4 I study theological determinism, or determinism that arises from God's supposed providential control over everything that happens. In this connection, I shall survey some historical accounts of the relation between human free will and determinism (not only theological but also causal determinism); the philosophers the views of whom I shall attend to include Chrysippus, St. Augustine, Boethius and Aquinas. I shall in particular consider G.W. Leibniz' theodicean aspirations, viz. his solution to the problem of evil and, especially, his compatibilist attempts to reconcile human free will with the strictly deterministic flow of actual events. I think it is important to try to explicate Leibniz' ingenious account of these matters, since it seems that it has not been fully appreciated in the literature, not even by contemporary Leibniz scholars (such as B. Mates, R.C. Sleigh, C. Wilson, R.M. Adams and D. Rutherford). In providing the Leibnizian compatibilist solution of the problem of determinism and freedom in chapter 4, I shall utilize the approach of chapter 2. (shrink)

Frege held that referring expressions in general, and demonstratives and indexicals in particular, contribute more than just their reference to what is expressed by utterances of sentences containing them. Heck first attempts to get clear about what the essence of the Fregean view is, arguing that it rests upon a certain conception of linguistic communication that is ultimately indefensible. On the other hand, however, he argues that understanding a demonstrative (or indexical) utterance requires one to think of the object denoted (...) in an appropriate way. This fact makes it difficult to reconcile the view that referring expressions are "directly referential" with any view that seeks (as Grice's does) to ground meaning in facts about communication. (shrink)

Demonstratives seem to have posed a severe difficulty for Frege’s philosophy of language, to which his doctrine of incommunicable senses was a reaction. In “The Thought,” Frege briefly discusses sentences containing such demonstratives as “today,” “here,” and “yesterday,” and then turns to certain questions that he says are raised by the occurrence of “I” in sentences (T, 24-26). He is led to say that, when one thinks about oneself, one grasps thoughts that others cannot grasp, that cannot be communicated. However, (...) nothing could be more out of the spirit of Frege’s account of sense and thought than an incommunicable, private thought. In the first part of the paper, I explain the problem demonstratives pose for Frege, and explore three ways he might have dealt with it. I argue that none of these ways provides Frege with a solution to his problem consistent with his philosophy of language. The first two are plausible as solutions, but contradict his identification of the sense expressed by a sentence with a thought. The third preserves the identification, but is implausible. In the second part, I suggest that Frege was led to his doctrine of incommunicable senses as a result of some appreciation of the difficulties his account of demonstratives faces, for these come quickly to the surface when we think about “I.” I argue that incommunicable senses won’t help. I end by trying to identify the central problem with Frege’s approach, and sketching an alternative. (shrink)