Logic as the Universal Science : Bertrand Russell's Early Conception of Logic and Its Philosophical Context

Bertrand Russell (1872 1970) introduced the English-speaking philosophical world to modern, mathematical logic and foundational study of mathematics. The present study concerns the conception of logic that underlies his early logicist philosophy of mathematics, formulated in The Principles of Mathematics (1903). In 1967, Jean van Heijenoort published a paper, Logic as Language and Logic as Calculus, in which he argued that the early development of modern logic (roughly the period 1879 1930) can be understood, when considered in the light of a distinction between two essentially different perspectives on logic. According to the view of logic as language, logic constitutes the general framework for all rational discourse, or meaningful use of language, whereas the conception of logic as calculus regards logic more as a symbolism which is subject to reinterpretation. The calculus-view paves the way for systematic metatheory, where logic itself becomes a subject of mathematical study (model-theory). Several scholars have interpreted Russell s views on logic with the help of the interpretative tool introduced by van Heijenoort,. They have commonly argued that Russell s is a clear-cut case of the view of logic as language. In the present study a detailed reconstruction of the view and its implications is provided, and it is argued that the interpretation is seriously misleading as to what he really thought about logic. I argue that Russell s conception is best understood by setting it in its proper philosophical context. This is constituted by Immanuel Kant s theory of mathematics. Kant had argued that purely conceptual thought basically, the logical forms recognised in Aristotelian logic cannot capture the content of mathematical judgments and reasonings. Mathematical cognition is not grounded in logic but in space and time as the pure forms of intuition. As against this view, Russell argued that once logic is developed into a proper tool which can be applied to mathematical theories, Kant s views turn out to be completely wrong. In the present work the view is defended that Russell s logicist philosophy of mathematics, or the view that mathematics is really only logic, is based on what I term the Bolzanian account of logic . According to this conception, (i) the distinction between form and content is not explanatory in logic; (ii) the propositions of logic have genuine content; (iii) this content is conferred upon them by special entities, logical constants . The Bolzanian account, it is argued, is both historically important and throws genuine light on Russell s conception of logic.

Bilingual Notaries in Hellenistic Egypt : A Study of Language Use

The impact of Greek-Egyptian bilingualism on language use and linguistic competence is the key issue in this dissertation. The language use in a corpus of 148 Greek notarial contracts is analyzed on phonological, morphological and syntactic levels. The texts were written by bilingual notaries (agoranomoi) in Upper Egypt in the later Hellenistic period. They present, for the most part, very good administrative Greek. On the other hand, their language contains variation and idiosyncrasies that were earlier condemned as ungrammatical and bad Greek, and were not subjected to closer analysis. In order to reach plausible explanations for those phenomena, a thorough research into the sociohistorical and linguistic context was needed before the linguistic analysis. The general linguistic landscape, the population pattern and the status and frequency of Greek literacy in Ptolemaic Egypt in general, and in Upper Egypt in particular, are presented. Through a detailed examination of the notaries themselves (their names, families and handwriting), it became evident that there were one to three persons at the notarial office writing under the signature of one notary. Often the documents under one notary's name were written in the same hand. We get, therefore, exceptionally close to studying idiolects in written material from antiquity. The qualitative linguistic analysis revealed that the notaries made relatively few orthographic mistakes that reflect the ongoing phonological changes and they mastered the morphological forms. The problems arose at the syntactic level, for example, with the pattern of agreement between the noun groups or a noun with its modifiers. The significant structural differences between Greek and Egyptian can be behind the innovative strategies used by some of the notaries. Moreover, certain syntactic structures were clearly transferred from the notaries first language, Egyptian. This is obvious in the relative clause structure. Transfer can be found in other structures, as well, although, we must not forget the influence of parallel Greek structures. Sometimes these can act simultaneously. The interesting linguistic strategies and transfer features come mostly from the hand of one notary, Hermias. Some other notaries show similar patterns, for example, Hermias' cousin, Ammonios. Hermias' texts reveal that he probably spoke Greek more than his predecessors. It is possible to conclude, then, that the notaries of the later generations were more fluently bilingual; their two languages were partly integrated in their minds as an interlanguage combining elements from both languages. The earlier notaries had the two languages functionally separated and they followed the standardized contract formulae more rigidly.