Frege: Philosophy of Language

Frege analyzed the grammatical subject-term 'S' in quantified subject-predicate sentences, 'q S are P', as being logically predicative. This is in contrast to Aristotelian Logic, according to which it is a logical subject-term, like the proper name 'a' in 'a is P' – albeit a plural one, designating many particulars. I show that Frege's arguments for his analysis are unsound, and explain how he was misled to his position by the mathematical concept of function. If common nouns in this grammatical (...) subject position are indeed logical subject-terms, this should require a thorough reevaluation of the adequacy of Frege's Predicate Calculus as a tool for the analysis of the logic and semantics of natural language. (shrink)

The main thesis of this paper is that some of the most important ideas and symbolic devices that made Russell's theory of descriptions possible were already present in writings by Frege and especially Peano that Russell knew well. The paper contains a detailed comparison between the relevant parts of Russell's theory--including manuscripts recently published--and some of Frege and Peano's insights, as well as a discussion of numerous possible objections that could be posed to the main claim. Even if Russell was (...) not actually influenced by those insights, the parallelism is close enough to be worth analyzing, especially in the case of Peano, whose writings are not very well known. (shrink)

There is considerable likelihood that Gottlob Frege began writing his Foundations of Arithmetic with the expectation that he could introduce his numbers, not with sets, but through some algebraic techniques borrowed from earlier writers of the Gottingen school. These rewriting techniques, had they worked, would have required strong philosophical justification provided by Frege's celebrated "context principle," which otherwise serves little evident purpose in the published Foundations.

In the case of an actual proper name such as ‘Aristotle’ opinions as to the Sinn may differ. It might, for instance, be taken to be the following: the pupil of Plato and teacher of Alexander the Great. Anybody who does this will attach another Sinn to the sentence ‘Aristotle was born in Stagira’ than will a man who takes as the Sinn of the name: the teacher of Alexander the Great who was born in Stagira. So long as the (...) Bedeutung remains the same, such variations of Sinn may be tolerated, although they are to be avoided.. (shrink)

This paper argues for a conditional claim concerning a famous argument?developed by Church in elucidation of some remarks by Frege to the effect that the bedeutung of a sentence is the sentence?s truth-value?the Frege?Gödel?Church argument, or FGC for short. The point we make is this :if, and just to the extent that, Arthur Smullyan?s argument against Quine's use of FGC is sound, then essentially the same rejoinder disposes also of Davidson's use of FGC against ?correspondence? theories of truth. We thus (...) dispute a contention by Professor Davidson that it is coherent to accept that Smullyan?s rejoinder takes away the force of Quine?s version of FGC, while still consistently using FGC to establish that if true sentences (or utterances) correspond to anything, they all correspond to the same thing. We show that the differences between the cases discussed by Smullyan and Davidson?s version of FGC on which Davidson relies for his contention are irrelevant to the point under dispute. (shrink)

Michael Beaney has argued that Frege’s characterization of the senses of names as modes of presentation early in “On Sense and Reference” is problematic, but the problem disappears if we use the notion of modes of determination as that was deployed in the Begriffsschrift to characterize senses. It is argued that there is no philosophically interesting difference between the two notions, and no problem posed by modes of presentation that would be resolved by appeal to modes of determination.

Michael Beaney has argued that Frege’s characterization of the senses of names as modes of presentation early in “On Sense and Reference” is problematic, but the problem disappears if we use the notion of modes of determination as that was deployed in the Begriffsschrift to characterize senses. It is argued that there is no philosophically interesting difference between the two notions, and no problem posed by modes of presentation that would be resolved by appeal to modes of determination.

The analytical philosophy of the last hundred years has been heavily influenced by a doctrine to the effect that the key to the correct understanding of reality is captured syntactically in the ‘Fa’ (or, in more sophisticated versions, in the ‘Rab’) of standard firstorder predicate logic. Here ‘F’ stands for what is general in reality and ‘a’ for what is individual. Hence “f(a)ntology”. Because predicate logic has exactly two syntactically different kinds of referring expressions—‘F’, ‘G’, ‘R’, etc., and ‘a’, ‘b’, (...) ‘c’, etc.—so reality must consist of exactly two correspondingly different kinds of entity: the general (properties, concepts) and the particular (things, objects). We describe the historical influence of this view, and also show how standard first-order predicate logic can be used for the logical formalization of a more adequate “six category ontology”, which recognizes, at the level of both particulars and universals, not only things or objects but also events and qualities. (shrink)

It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there (...) is only one ultimate ontological category. This, combined with Russell's reification of propositions, ensures that he must hold concepts and objects to be of the same logical and ontological type. In this paper I argue that, while Frege's treatment of the unity of the proposition has immediate advantages over Russell's, a deeper consideration of the philosophical underpinnings and metaphysical consequences of the two approaches reveals that Frege's supposed solution is, in fact, far from satisfactory. Russell's repudiation of the Fregean position in the Principles is, I contend, convincing and Russell's own position, despite its problems, conforms to a greater extent than Frege's with common sense and, furthermore, with certain ideas which are central to our understanding of the origins of the analytical tradition. (shrink)

There is an inconsistency among claims made (or apparently made) in separate articles by Alonzo Church concerning Frege's distinction between sense and denotation taken together with plausible assertions by Frege concerning his notion of ungerade Sinn-i.e., the sense that an expression allegedly takes on in positions in which it has ungerade Bedeutung, denoting its own customary sense. As with any inconsistency, the difficulty can be avoided by relinquishing one of the joint assumptions from which contradiction may be derived. Yet what (...) seems the most plausible resolution, in light of Church's own arguments, involves abandoning the theory of sense and denotation, in the form in which it has been staunchly advocated by both Frege and Church. That theory has come under sustained criticism from several quarters. Whereas the present difficulty supplements the case against the theory, it is unlike more familiar criticisms, since it is not framed from the perspective of an alternative theory (or picture) but is based instead on an internal conflict, and therefore has special force. (shrink)

The book begins by focusing on the psychological constraints governing Frege's notion of sense, or meaning, and argues that, given these constraints, even the ...

In this paper I present an abstract theory of senses, thoughts, and truth, inspired by ideas of Frege. "Inspired" because for the most part I shall not pretend to interpret Frege in a literal sense, but, rather, develop some of his ideas in ways that seem to me to preserve important aspects of them. Senses are characterized as identifying properties; i.e., roughly, as properties that apply, in virtue of their logical structure, to exactly one thing, if they apply to anything (...) at all. When Frege's analysis of sentences in terms of function and arguments is combined with his analysis of quantification as higher-order predication, all sentences (formal and informal) can be analyzed in various ways as a function (predicate) applied to one or more arguments. This allows for an abstract characterization of thoughts as senses that combine other senses in a uniform way, and whose truth derives from their instantiation by corresponding items of reality. (shrink)

There are two principles which bear the name Frege''sprinciple: the principle of compositionality, and the contextprinciple. The aim of this contribution is to investigate whether thisis justified: did Frege accept both principles at the same time, did hehold the one principle but not the other, or did he, at some moment,change his opinion? The conclusion is as follows. There is a developmentin Frege''s position. In the period of Grundlagen he followed to a strict form of contextuality. He repeatedcontextuality in later (...) writings, but became less strict. From 1914 on,pushed by the needs of research, he comes close to compositionality. Buthe could never make the final step toward compositionality forprincipled reasons, therefore he always would reject compositionality. (shrink)

Hintikka and Sandu have recently claimed that Frege's notion of function was substantially narrower than that prevailing in real analysis today. In the present note, their textual evidence for this claim is examined in the light of relevant historical and biographical background and judged insufficient.

Tomberlin's comparative claims about the superiority of the De Dicto-De Re Account over Guise Theory concerning referential opacity are abortively premature. Nevertheless, he may be right. Yet the order of the day is to develop the De Re-De Dicto Account to the hilt. Not until this is done can any useful dia-philosophical comparison of the two theories yield any fruit. My deep desire is, of course, for the sheer enjoyment of experiencing the world from the perspective of each of the (...) two views, indeed, from the perspective of other views — e.g., Frege's Sense/Referent Theory — that can be developed to the same data-encompassing stage as Guise Theory. (shrink)

Frege's doctrine that the demonstrative ‘I’ has a private, incommunicable sense creates tension within his theory of meaning. Fregean sense is supposed to be something objective, which exists independently of its being cognized by anyone. And the notion of a private sense corresponding to primitive aspects of an individual of which only he can be awaredoes violence both to Frege's theory of sense as well as to our notionof language as something essentially intersubjective. John Perry has arguedthat Frege was led (...) to the doctrine of private senses in spite of his beliefin the objectivity of sense through his attempt to solve a problem which indexicals posed for his theory. And while philosophers have argued about whether the notion of a private sense is in fact problematic for Frege, they have tended to share Perry's assumption about its origin. (shrink)

It is a commonplace that Frege thought ordinary language to be seriously defective. Yet his remarks about ordinary language are not always unflattering. Comparing the relation between his formal language and ordinary language to the relation between the microscope and the eye, Frege remarked: ‘[the eye], because of the range of its applicability and because of the ease with which it can adapt itself to the most varied circumstances, has a great superiority over the microscope’. The point, of course, is (...) that, for Frege, the deficiencies of ordinary language arise in connection with the scientific endeavour: ordinary language is not an acceptable medium in which to pursue truth. As he goes on to observe: ‘… viewed as an optical instrument [the eye] reveals many imperfections … as soon as scientific purposes place strong requirements upon sharpness of resolution, the eye proves to be inadequate. On the other hand, the microscope is perfectly suited for just such purposes’. (shrink)

Michael Dummett argued that Frege was a realist while Hans Sluga countered that he was an objective idealist in the rationalist tradition of Kant and Lotze. Sluga ties Frege's idealism to the context principle which he argues Frege never gave up. It is argued that Sluga has correctly interpreted the pre?1891 Frege while Dummett is correct concerning the later period. It is also claimed that the context principle was dropped prior to 1891 to be replaced by the doctrine of unsaturated (...) entities. (shrink)

One of the perennial questions of philosophy concerns the simple statements which say that an object is so and so or that such and such objects are so and so related: simple predicative statements. Do such statements have an ontological basis, and if so, what is that basis? The answer to this question determines—or in any case, is expressive of—a specific fundamental outlook on the world. In the course of the history of Western philosophy, various philosophers have given various answers (...) to the question of predication. This essay presents the main, crucial answers: the paradigms and theories of predication of the Sophists (and of all later radical relativists), of Plato, of Aristotle, of the Aristotelian-minded non-nominalists, of Leibniz, and of Frege. In addition, the essay follows (to some extent) the most influential—the Aristotelian or mereological—paradigm of predication in its continuity and modification through the many centuries of its reign. However, the essay is not content to adopt the merely historical point of view; it also poses the question of adequacy. Prior to Frege, there was no philosophically adequate theory of predication, and the essay points out the shortcomings (besides aspects that can be viewed as advantages) of each pre-Fregean predication theory considered in it. Frege, in the nineteenth century, brought the philosophy of predication on the right track, but his own theory of predication has its own deficits. The essay ends with the presentation of a theory of predication that the author himself considers adequate. (shrink)