Gottlob Frege is celebrated for his distinction between the Sinn and Bedeutung – the sense and reference – of a term. The distinction is readily understood. The reference of the name ‘Plato’ is the bearer of the name, that most famous and widely revered philosopher, who lived more than two thousand years ago in ancient Greece. The sense of the name ‘Plato’, on the other hand, corresponds to what we would ordinarily recognize as belonging to its meaning: what speakers and hearers understand by the word that enables them to identify what they are talking about and to use the word intelligently. Why is Frege celebrated for this distinction? After all, just a generation or two before, Mill (1843) expounded his distinction between the connotation and denotation of a name. In The Port Royal Logic, Arnauld (1662) drew a kindred distinction between an idea and its extension. In his Summa Logicae, William of Ockham (c. 1323) distinguished between the term in mental language associated with a word and what it supposits. Earlier still, in ancient times, the Stoic logicians distinguished between an utterance, its signification, and the name-bearer. This is a very natural distinction, and we find variations on its theme reappearing throughout philosophical history. What makes Frege's distinction so noteworthy? The answer lies with his compositionality principles, one for reference and the other for sense.

The known details of the personal side of Frege's life are few. Friedrich Ludwig Gottlob Frege was born November 8, 1848, in Wismar, a town in Pomerania. His father, Karl Alexander (1809–1866), a theologian of some repute, together with his mother, Auguste (d. 1878), ran a school for girls there. Our knowledge of the remainder of Frege's personal life is similarly impoverished. He married Margarete Lieseberg (1856–1904) in 1887. They had several children together, all of whom died at very early ages. Frege adopted a child, Alfred, and raised him on his own. Alfred, who became an engineer, died in 1945 in action during the Second World War. Frege himself died July 26, 1925, at age seventy-seven.

We can say somewhat more about his intellectual life. Frege left home at age twenty-one to enter the University at Jena. He studied mathematics for two years at Jena, and then for two more at Göttingen, where he earned his doctorate in mathematics in December 1873 with a dissertation, supervised by Ernst Schering, in geometry. Although mathematics was clearly his primary study, Frege took a number of courses in physics and chemistry, and, most interestingly for us, philosophy. At Jena, he attended Kuno Fischer's course on Kant's Critical Philosophy, and in his first semester at Göttingen, he attended Hermann Lotze's course on the Philosophy of Religion. The influence and importance of Kant is evident throughout Frege's work, that of Lotze's work on logic is tangible but largely circumstantial.

Frege signed the preface to Begriffsschrift in December of 1878, and it was published the following year by George Olms. Frege did little to connect up his own work with his contemporaries, either with the logical achievements of Boole, or the mathematical investigations of Dedekind. The only explicit references are to philosophers – Aristotle, Leibniz, and Kant. His previous work, which consisted mainly of reviews, gave no indication of the direction and creativity of his thinking. Like Athena, emerging full-grown from Zeus's brow, Frege's remarkable work bore no evidence of the genesis and growth of the ideas presented therein. There is little surprise at the reception his contemporaries gave Begriffsschrift: they did not know what to make of it.

Here are some of the achievements of Begriffsschrift:

First, Frege synthesized the two otherwise opposed traditions – the Stoic logic of the propositional connectives and the Aristotelian treatment of the quantifiers – into one system, and extended the Aristotelian treatment to include relations as well as properties. His function/argument analysis of propositions supplanted the subject/predicate distinction of traditional analysis, creating one of the first extensions of mathematical forms of analysis to domains other than arithmetic and geometry.

Second, propositions (1), (2), (8), (28), (31), and (41), together with the Rule of Inference, Modus Ponens – and a suitable substitution rule that is employed but never precisely stated – constitute a complete and consistent axiomatization of truth-functional logic.

Introduction

We usually use language to speak about things other than itself. Of course, we can use language to speak about itself. The single-quote construction was devised for just this purpose, to render such speaking error free. The construction has the important characteristic that the very expression named is woven into the fabric of the sentence used to speak about it. To forestall errors of ambiguity, then, the construction takes upon itself the onus of ambiguity to assure clarity elsewhere.

The single-quote convention is to enclose a word or phrase in single quotation marks when we wish to speak about it. The convention was introduced into modern practice originally by Frege (1892c: 153–4), whose strategy was to treat direct quotation and indirect quotation in a parallel manner:

This passage immediately precedes the one with which we opened Chapter 9 and introduced the notions of customary and indirect reference.

Introduction

Begriffsschrift was, as the subtitle announced, a formula language of pure thought modeled upon the language of arithmetic. Frege borrowed the notation for functions from arithmetic, and enlarged the realm of applicability of a function beyond the domain of numbers. Then, supplanting the subject/predicate division, which was characteristic of previous logical systems, by a function/argument division, he created a logical notation, a Begriffsschrift – literally, Concept Writing – which would serve to represent thoughts about any objects whatsoever. Like the language of arithmetic, his Begriffsschrift represented thoughts so that the inferential connections between them were molded in the representations themselves. The project was enormously successful. Not only did Frege create modern quantificational logic, but he also provided the theoretical framework for many subsequent philosophical developments in logic as well as in speculative philosophy. As Dummett (1981a) correctly remarked, Frege's work shifted the central focus of philosophy from the epistemological issues raised by Descartes back to the metaphysical and ontological issues that were salient after Aristotle.

The function/argument analysis Frege (1879) presented was, however, flawed. There was a significant confusion in his operating semantic notion of the content [Inhalt] of a sentence. Frege came to recognize that repairs were needed, and after much hard philosophical work, the theory with which we are now familiar emerged in the early 1890s. It was announced first in Frege (1891), and then elaborated upon in Frege (1892c) and Frege (1892a).

In traditional grammar, adverbial and co-ordinate clauses are categorically distinguished: adverbial clauses are classified as subordinate clauses and co-ordinate clauses are considered nonembedded sentences. For English, as well as for many other languages, this analysis is problematic, because there are no sufficient criteria to establish a clear-out division between adverbial and co-ordinate clauses. Rather, adverbial subordination and clausal co-ordination form a continuum of related constructions. In what follows, I refer to the continuum of adverbial and co-ordinate clauses as conjoined clauses.

Like complement and relative clauses, conjoined clauses evolve from simple nonembedded sentences, but the development takes a different pathway: while complement and relative clauses evolve via clause expansion, conjoined clauses develop through a process of clause integration. The development originates from two independent utterances that are pragmatically combined in the ongoing discourse. Starting from such discourse structures, children gradually learn the use of complex sentences in which two or more clauses are integrated in a specific grammatical unit.

The earliest multiple-clause utterances that all five children produce include a finite verb and an infinitive that one might analyse as a nonfinite complement clause (e.g. I wanna eat). The occurrence of these constructions is initially restricted to a small number of complement-taking verbs such as want, have, and like that indicate volition or obligation. The present chapter shows that, although these verbs behave grammatically like matrix verbs, semantically they function like modals: rather than denoting an independent state of affairs, they indicate the child's desire or obligation to perform the activity denoted by the nonfinite verb. The whole utterance contains a single proposition and thus does not involve embedding. Other early infinitival and participial complements occur with aspectual verbs such as start and stop. Like the early quasi-modals, the aspectual verbs do not make reference to an independent state of affairs; rather, they elaborate the temporal structure of the activity denoted by the nonfinite verb. As children grow older, these constructions become increasingly more complex. Many of the complement-taking verbs that emerge later describe activities that are semantically more independent of the nonfinite verb than the early quasi-modals and aspectual verbs. Moreover, while children's early nonfinite complement clauses are always controlled by the matrix clause subject (e.g. I wanna sing), later nonfinite complements are often controlled by the direct object, which occurs between the finite verb and the infinitive or participle (e.g. He told him to leave).