An investigation of Frege’s various contributions to the study of language, focusing on three of his most famous doctrines: that concepts are unsaturated, that sentences refer to truth-values, and that sense must be distinguished from reference.
Chapter. 1. Logical. Form. as. a. Level. of. Linguistic. Representation. What is the relation of a sentence's syntactic form to its logical form? This issue has been of central concern in modern inquiry into the semantic properties of natural ...
We attempt here to trace the evolution of Frege's thought about truth. What most frames the way we approach the problem is a recognition that hardly any of Frege's most familiar claims about truth appear in his earliest work. We argue that Frege's mature views about truth emerge from a fundamental re-thinking of the nature of logic instigated, in large part, with a sustained engagement with the work of George Boole and his followers, after the publication of Begriffsschrift and the (...) appearance of critical reviews by members of the Boolean school. (shrink)
Frege's logicist program requires that arithmetic be reduced to logic. Such a program has recently been revamped by the "neologicist" approach of Hale and Wright. Less attention has been given to Frege's extensionalist program, according to which arithmetic is to be reconstructed in terms of a theory of extensions of concepts. This paper deals just with such a theory. We present a system of second-order logic augmented with a predicate representing the fact that an object x is the extension of (...) a concept C, together with extra-logical axioms governing such a predicate, and show that arithmetic can be obtained in such a framework. As a philosophical payoff, we investigate the status of the so-called Hume's Principle and its connections to the root of the contradiction in Frege's system. (shrink)
Are Fregean thoughts compositionally complex and composed of senses? We argue that, in Begriffsschrift, Frege took 'conceptual contents' to be unstructured, but that he quickly moved away from this position, holding just two years later that conceptual contents divide of themselves into 'function' and 'argument'. This second position is shown to be unstable, however, by Frege's famous substitution puzzle. For Frege, the crucial question the puzzle raises is why "The Morning Star is a planet" and "The Evening Star is a (...) planet" have different contents, but his second position predicts that they should have the same content. Frege's response to this antinomy is of course to distinguish sense from reference, but what has not previously been noticed is that this response also requires thoughts to be compositionally complex, composed of senses. That, however, raises the question just how thoughts are composed from senses. We reconstruct a Fregean answer, one that turns on an insistence that this question must be understood as semantic rather than metaphysical. It is not a question about the intrinsic nature of residents of the third realm but a question about how thoughts are expressed by sentences. (shrink)
It is a characteristically Fregean thesis that the sense expressed by an expression is the linguistic meaning of that expression. Sense can play this role for Frege since it meets fundamental desiderata for meaning, that it be universal and invariantly expressed and objectively the same for everyone who knows the language. It has been argued,1 however, that, as a general thesis about natural languages, the identi cation of sense and meaning cannot be sustained since it is in con ict with (...) another characteristically Fregean thesis, that sense uniquely determines reference. The argument is quite simple and can be outlined as follows. Assume the two theses we have just stated. (shrink)
In this paper, we explore Fregean metatheory, what Frege called the New Science. The New Science arises in the context of Frege’s debate with Hilbert over independence proofs in geometry and we begin by considering their dispute. We propose that Frege’s critique rests on his view that language is a set of propositions, each immutably equipped with a truth value (as determined by the thought it expresses), so to Frege it was inconceivable that axioms could even be considered to be (...) other than true. Because of his adherence to this view, Frege was precluded from the sort of metatheoretical considerations that were available to Hilbert; but from this, we shall argue, it does not follow that Frege was blocked from metatheory in toto. Indeed, Frege suggests in Die Grundlagen der Geometrie a metatheoretical method for establishing independence proofs in the context of the New Science. Frege had reservations about the method, however, primarily because of the apparent need to stipulate the logical terms, those terms that must be held invariant to obtain such proofs. We argue that Frege’s skepticism on this score is not warranted, by showing that within the New Science a characterization of logical truth and logical constant can be obtained by a suitable adaptation of the permutation argument Frege employs in indicating how to prove independence. This establishes a foundation for Frege’s metatheoretical method of which he himself was unsure, and allows us to obtain a clearer understanding of Frege’s conception of logic, especially in relation to contemporary conceptions. (shrink)
Over the years, I’ve been asked many times what “logical form” is, as applied to natural language. This is a natural enough question to address to me; after all, I’ve written a book titled Logical Form, and I’ve been asked to write any number of papers on the topic. This question, it seems to me, is certainly a “big” question, and big questions deserve big answers. I must admit, however, to being somewhat baffled as to how to do this satisfactorily, (...) since big answers to big questions unfortunately tend to the trivial. With a nod to Wittgenstein, logical form has always seemed to me to be something that you know it when you see it; it is clear enough when it pops up, but one is hard pressed to say just what it is, to define it. This is so even though the meanings of the words “logical” and “form” seem straightforward enough; what I find puzzling is how the first word is supposed to modify the second. What is it that makes a form logical, as opposed to something else that is not logical? This, it seems to me, is a very hard question to answer indeed, for if we cannot contrast logical form with some other type of form, then every form (or no form) is a logical form, and we have arrived at the triviality previously mentioned. (shrink)
1. There is only one rule of inference, modus ponens. This is true both in the presentations of Begriffsschrift and Grundgesetze. There are other ways of making transitions between propositions in proofs, but these are never labeled by Frege “rules of inference.” These pertain to scope of quantification, parsing of formulas, introduction of definitions, conventions for the use and replacement of the various letters, and certain structural reorganizations, ; cf. the list in Gg §48.
1. Nathan Salmon paper is entitled with a question: are general terms rigid? He asks this question in way of engaging the issue of the extension of the notion of rigidity beyond the domain of singular terms. While singular terms has been the province of most of the discussion of this rigidity since Naming and Necessity, it is well known that Kripke saw the notion extending to at least certain general terms such as terms for natural kinds. Scott Soames has (...) recently weighed in on this issue in the latter chapters of his book Beyond Rigidity. His conclusion is that although there are significant overlaps in the properties of singular and general terms, there is no direct extension of rigidity to the general terms, and that rigid designation is properly applied only to singular terms. Salmon disagrees. His view, based in part of views dating back to his book Reference and Essence, is that there is an extension to be had, one which allows the application of the standard Kripkean characterization of rigidity to be applied to both sorts of terms. Central to his thesis is a claim about the status of certain definite descriptions. In these remarks, I will try to outline the issues to which NS is reacting, and the proposal he posits in response. I will then consider in a more critical light his claim about definite descriptions, bringing to bear considerations of their grammar. (shrink)
Interpreted Logical Forms are objects composed of a syntactic structure annotated with the semantic values of each node of the structure. We criticize the view that ILFs are the objects of propositional attitude verbs such as believe, as this is developed by Larson and Ludlow. Our critique arises from a tension in the way that sen-.
“Choose your words wisely,” my mother used to say, “because you never know who’s listening.” Oddly, this is something about which my dear mother and Mark Richard apparently would agree. They both seem to think that the words you use say something about who you are, and if you use bad words, then you are a bad person. About this, I have no doubt that they are right - those who use slurs, at least in the context of many assertive (...) utterances, are surely racists, anti-Semites or whatever. But MR in his paper points out that matters go further than this, for our conversational interactions with slur words can show us to be of such dubious moral status even if we don’t utter them; just our normal practices of accepting the utterances of others would be sufficient for this result. But something is surely amiss here; no doubt we can know the meaning of slur-words, and so comprehend the utterances of others, without impugning our moral stature in any way. (shrink)
*I am very pleased to be able to contribute this paper to a festschrift for Andrea Bonomi. This is not however, the paper I really wanted to write; I would have much rather have contributed a paper comparing the pianistic styles of Lennie Tristano and Bill Evans, which I think Andrea would have found much more fascinating than an essay devoted to an understanding of Frege’s thinking. But I do not totally despair. Andrea’s first paper published in English was entitled (...) “On the Concept of Logical Form in Frege,” so perhaps I can maintain some hope that this paper will appeal to lingering interests that Andrea wrote of in the past. I would like to thank Johannes Brandl, Ben Caplan, Bill Demopoulos, Bob Fiengo, Mark Kalderon, Patricia Marino, Gila Sher, Michael Thau, Dan Vest and especially Aldo Antonelli for very helpful discussion. (shrink)
A general survey of Frege's views on truth, the paper explores the problems in response to which Frege's distinctive view that sentences refer to truth-values develops. It also discusses his view that truth-values are objects and the so-called regress argument for the indefinability of truth. Finally, we consider, very briefly, the question whether Frege was a deflationist.
Fictional terms are terms that have null extensions, and in this regard pejorative terms are a species of fictional terms: although there are Jews, there are no kikes. That pejoratives are fictions is the central consequence of the Moral and Semantic Innocence (MSI) view of Hom et al. (2013). There it is shown that for pejoratives, null extensionality is the semantic realization of the moral fact that no one ought to be the target of negative moral evaluation solely in virtue (...) of their group membership. In having null extensions, pejorative terms are much like mythological terms like ‘unicorn horn’ that express concepts with empty extensions, even though it was thought otherwise: people who falsely believed the mythology were mislead into thinking that ordinary objects (i.e. whale tusks) were magical objects, and pejoratives terms work likewise. For example, the term ‘kike’ is supported by the ideology of anti-Semitism, and speakers who fall prey to its influence (perniciously or not) are mislead into thinking that ordinary people (i.e. Jews) are inherently worthy of contempt. In this paper, we explore the consequences of this parallelism, with an eye to criticisms of MSI. In particular, we will re-visit identity expressivist views - those that hold that there are kikes and that they are Jews, and hence deny null extensionality - arguing that this embeds a mistake of fiction for fact. Among the issues to be discussed are the role of fictional truth in understanding pejorative sentences and the relation of the semantics of pejoratives to offensive use of language. We conclude with meta-semantic reflections on the origins of word meanings. (shrink)
An investigation of what Frege means by his doctrine that functions (and so concepts) are 'unsaturated'. We argue that this doctrine is far less peculiar than it is usually taken to be. What makes it hard to understand, oddly enough, is the fact that it is so deeply embedded in our contemporary understanding of logic and language. To see this, we look at how it emerges out of Frege's confrontation with the Booleans and how it expresses a fundamental difference between (...) Frege's approach to logic and theirs. (shrink)
Syntax, in its most general sense, is the study of the structure of sentences in natural language. In this course, we will approach syntax from the perspective of generative transformational grammar, as pioneered through the work of Noam Chomsky, and developed over the past four decades. Our goals are three-fold. First, to understand the nature of language as viewed from the structural perspective, and to understand the sort of insight about language this perspective affords. Second, to understand the nature and (...) application of certain empirical methods to theoretical hypotheses within linguistics. And third, to understand certain general principles or laws of language which can be elucidated from the structural perspective by the empirical methods. The material in the course primarily will be drawn from English, but occasional reference will be made to other languages (although no prior knowledge is presupposed). (shrink)
The topic of this seminar will be the notion of language as it is employed in the philosophy of language. The seminar will be divided into two parts, of somewhat unequal length. The first part will be devoted to the change in the conception of language that marked the transition from structural linguistics to generative linguistics (the so-called "Chomskian revolution"). We will approach this not only as a chapter in the philosophy of language, but also as an important chapter in (...) the philosophy of science, in large part because much of the discussion centers around to what extent, and how, the study of language can be understood as a scientific inquiry, continuous with the other natural sciences. From this discussion, which will be devoted to reading some of the classic literature from the mid-50's to the mid-70's (largely by Chomsky), an articulation of the subject matter of the study of language will emerge, and in particular this will involve an articulation of the relation of syntax, semantics and pragmatics. This will lead us to explore, in the second part of the seminar, the most influential work, that of Grice, especially in "Logic and Conversation" devoted to articulating this distinction. (shrink)
In theorizing about racial pejoratives, an initially attractive view is that pejoratives have the same reference as their “neutral counterparts”. Call this the identity thesis. According to this thesis, the terms “kike” and “Jew”, for instance, pick out the same set of people. To be a Jew just is to be a kike, and so to make claims about Jews just is to make claims about kikes. In this way, the two words are synonymous, and so make the same contribution (...) to the truth-conditions of sentences containing them. While the fundamental claim for the identity thesis that Jews are kikes sounds anti-semitic, it need not be actually anti-semitic. The identity thesis is usually bolstered with the further claim that the pejorative aspect of “kike” and other such terms is located elsewhere than in truth-conditional content, so what makes “kike” a bad word is a non-truth-conditional association with anti-semitism that is not shared with the word “Jew”. The exact nature and location of the negative moral content of pejoratives is a matter of some dispute among identity theorists. But whatever the intuitive appeal of the identity theory for those persuaded by such views, it is nevertheless inconsistent. (shrink)
How many senses can a given name have, with its reference held fixed? One, more than one? One answer that most would agree to is that sense is unique for each utterance of a name, that is, that a name can have no more than one sense on any given occasion. But is sense unique in any stronger sense than this? The answer that is typically attributed to Frege is that there is not, that, as Tyler Burge puts it, 1 (...) Frege “treats proper names as having different senses while applying to the same person.” There are a number of possibilities for the locus of this multiplicity of sense; the following remark by Ruth Marcus indicates the possibilities: “the sense of a term is whatever is grasped or understood by a speaker on a particular occasion of use and may vary from occasion to occasion as well as from speaker to speaker.”2 Of the views canvassed by Marcus, we can draw out a more conservative one, and one more extreme. On the more conservative view, Frege is holding that sense may vary from speaker to speaker; on the more extreme view, Frege holds not only this, but that sense may vary from context to context. Endorsements of the two views are not hard to find. For example, typical sorts of endorsement of the conservative view are found in Harold Noonan’s remark that “different senses [are] associated with the name ‘Aris-. (shrink)
The LOGICAL FORM of a sentence (or utterance) is a formal representation of its logical structure; that is, of the structure which is relevant to specifying its logical role and properties. There are a number of (interrelated) reasons for giving a rendering of a sentence's logical form. Among them is to obtain proper inferences (which otherwise would not follow; cf. Russell's theory of descriptions), to give the proper form for the determination of truth-conditions (e.g. Tarski's method of truth and satisfaction (...) as applied to quantification), to show those aspects of a sentence's meaning which follow from the logical role of certain terms (and not from the lexical meaning of words; cf. the truth-functional account of conjunction), and to formalize or regiment the language in order to show that it is has certain metalogical properties (e.g. that it is free of paradox, or that there is a sound proof procedure). (shrink)
The analysis of identity as coreference is strongly associated with Frege ; it is the view in Begriffsschrift, and, some have argued, henceforth throughout his work. This thesis is incorrect: Frege never held that identity is coreference. The case is made not by interpretation of “proof-quotes”, but rather by exploring how Frege actually deploys the concept. Two cases are considered. The first, from Grundgesetze, are the definitions of the core concepts, zero and truth; the second, from Begriffsschrift, is the validity (...) of Leibniz's Law. In both cases, if identity is coreference, results ensue that would be unacceptable to Frege. (shrink)
As the history of analytic philosophy is written, Gottlob Frege sits among the pantheon, one of the core creators of a novel way of philosophical thinking. It is a way of thinking that is notably infused with logical and semantic insights that are original to Frege. The source of these insights is well known. They arise in the context of logicism, Frege’s mathematical project that unfolded in a body of thought punctuated by three seminal works, Begriffsschrift of 1879, Die Grundlagen (...) der Arithmetik of 1884, and the two volumes of Grundgesetze der Arithmetik, published in 1893 and 1903. In these works, Frege sets out to show that arithmetic can be reduced to logic; more technically, that (a version of) the Peano-Dedekind axioms are derivable as theorems in a definitional extension of impredicative second-order logic. To achieve this goal, Frege introduced both a new logic and a new semantics; the conceptual apparatus that Frege brought to bear in these works, and in an accompanying series of classic essays, including most famously “On Sense and Reference,” has animated philosophical thought ever since. (shrink)