Frege's conception of numbers as objects pdf download

Zaltay center for the study of language and information and philosophy department stanford university in this paper, i derive a theory of numbers from a more generaltheory of abstract objects. Jul 06, 2007 project euclid mathematics and statistics online. 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 truthvalues develops. The solution is conceptually tighter in the sense that it retains the fregean principle of separating sharply between concepts and objects, it retains. The considerable interest in this thesis among the contemporary philosophy of mathematics community stands in marked contrast to kreisels folk. A companion to the philosophy of language, 2 volume set.

He has published widely in the philosophy of mathematics, logic and language including freges conception of numbers as objects 1983, truth and objectivity 1992, and realism, meaning, and. Profiles in the origins of twentieth century thought, chicago. So, i learned from this book that when i instantiate my predicate i am in frege s words finding the content of the concept, saturating the concept, finding its meaning, its bedeudung, returning thoughts to my user. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.

The oxford handbook of philosophy of mathematics and logic. The two main components in freges mathematical philosophy were his platonism and his logicism the claims, respectively, that mathematics is a body of knowledge about independently existing objects, and that this knowledge may be acquired on the basis of general logical laws and suitable definitions. Freges conception of numbers as objects scots philosophical monographs. Aberdeen university press 1983 abstract this article has no associated abstract. Freges conception here is, however, far from clear. Together they form an accessible and authoritative introduction to aspects of frege s thought that have, until now, been largely missed by the philosophical community. Frege s other program antonelli, aldo and may, robert, notre dame journal of formal logic, 2005. Pdf dummett and the origins of analytical philosophy. This is in full accord with the criterion 1 gavethat the singular definite article always indicates an object, whereas the indefinite article accompanies a conceptword. Fregean onetoone correspondence and numbers as object properties 335 are two by two coordinated entities while there are actually not and there is just one a entity on the one side put in oneto. Mathematics and logic have been central topics of concern since the dawn of philosophy.

Freges conception of numbers as objects tiles 1984. His father, alexander, a headmaster of a secondary school for girls, and his mother, auguste nee bialloblotzky, brought him up in the. Notice that humes principle bears an obvious formal resemblance to basic law v. Freges famous definition of number infamously uses the concept of extension. Freges conception of numbers as objects crispin wright. Freges conception of numbers as objects scots philosophical. Abstractionism, which is a development of frege s original logicism, is a recent and much debated position in the philosophy of mathematics. This volume contains 16 original papers by leading scholars on the philosophical and mathematical aspects of abstractionism. But crispin wright claimed, in his book freges conception of numbers as objects 1983, that. A partial reconstruction of freges grundgesetze in object theory, journal of philosophical logic, 286 1999. In the philosophy of language, the distinction between concept and object is attributable to the german philosopher gottlob frege overview. Since a statement of number based on counting contains an assertion about a concept, in. One was the use of definite descriptions like the number of the planets, which we saw above could also be.

Extensions, numbers and freges project of logic as. The moving wall represents the time period between the last issue available in jstor and the most recently published issue of a journal. Canadian journal of philosophy volume xiv, number 4, december. A logicomathematical enquiry into the concept of number. Re ections on freges and dedekinds logicisms, springer, pp. Many of these papers are of great value for the study of frege, and it was thought desirable to assemble some of them in a single volume. Application of dummetts model of history of ideas in freges philosophy is proving a fertile research for the history of philosophy. A few years ago, richard heck showed that the ramified predicative secondorder fragment of the grundgesetze is consistent. Everyday low prices and free delivery on eligible orders. According to frege, any sentence that expresses a singular thought consists of an expression a proper name or a general term plus the definite article that signifies an object together with a predicate the copula is, plus a general term accompanied. Buy frege s conception of numbers as objects scots philosophical monographs by crispin wright isbn. First, she examines frege s understanding and use of conceptual analysis, and how this notion plays out methodologically in frege s logicist philosophy of mathematics. Frege s conception of numbers as objects scots philosophical monographs crispin wright on.

Hourya benissinaceur, marco panza, and gabriel sandu. At the center of wrights defense is a version of freges famous dictum that only in the context of a sentence does a word have any reference. Freges and dedekinds logicisms hourya benis, marco panza, gabriel sandu to cite this version. Patricia blanchette s excellent frege s conception of logic is focused, for the most part, on two interrelated questions. Using frege s perfect language we learn to distinguish between objects, and what we say about those objects.

One was the use of definite descriptions like the number of the planets, which we saw above could also be used for functional expressions. At the center of wright s defense is a version of frege s famous dictum that only in the context of a sentence does a word have any reference. Dummetts solution for meaning is one holistic and practicalinferential, having two parts. Some reflections on freges constraint wright, crispin, notre dame journal of formal logic, 2000.

Objectx treats concepts and objects as being of the same underlying neutral ontological category. Patricia blanchettes excellent freges conception of logic is focused, for the most part, on two interrelated questions. Gottlob frege, the concept of number, in benacerraf and putnam, pp. He has published widely in the philosophy of mathematics, logic and language including frege s conception of numbers as objects 1983, truth and objectivity 1992, and realism, meaning, and. Pdf fregean onetoone correspondence and numbers as. Fixing frege free download book urmusliaphas diary. For the first occurrence of reference is in the singular. His books include wittgenstein on the foundations of mathematics 1980, freges conception of numbers as objects 1983, truth and objectivity 1992, realism, meaning and truth 2nd edn, 1993, the blackwell companion to philosophy of language with bob hale, blackwell, 1997, the reasons proper study with bob hale, 2001, rails to infinity. Therefore, neologicist programs want to avoid the problems and to replace the classical fregean definition of number with humes principle where frege does not use extensions.

Crispin wright is professor of logic and metaphysics at the university of st andrews. A companion to the philosophy of language, 2 volume set, 2nd. Freges and dedekinds logicisms connecting repositories. Frege s conception of numbers as objects aberdeen university press 1983. Second, she carefully explicates freges views on logic and its role in both mathematical. In this paper, we show that the above fragment augmented with the axiom. The semantics of mathematics and science is quite different. Buy freges conception of numbers as objects scots philosophical monographs by crispin wright isbn.

Freges theorem in a constructive setting bell, john l. Freges conception of numbers as objects scots philosophical monographs crispin wright on. Extensions, in the fregean framework, are susceptible to bringing many difficulties, and, some say, even paradoxes. In rare instances, a publisher has elected to have a zero moving wall, so their current issues are available. The two main components in frege s mathematical philosophy were his platonism and his logicism the claims, respectively, that mathematics is a body of knowledge about independently existing objects, and that this knowledge may be acquired on the basis of general logical laws and suitable definitions. Abstract a feature of freges philosophy of arithmetic that has elicited a great deal of attention in the recent secondary literature is his contention that numbers are self. Thirteen years ago i published a short book henceforward freges conception which challenged this view, arguing that freges platonismthe conception of numbers as specific objects providing the proper subject matter of arithmetic, but given to us independently of any special intuitionadmitted of an epistemologically. Use the link below to share a fulltext version of this article with your friends and colleagues. Dummett accordingly insists that it is contrary to freges intention to claim, as did peter geach, that we are to count numerical terms as proper names because they refer to fregean objects. How did freges conception of logic differ from that of later logicians. Using freges perfect language we learn to distinguish between objects, and what we say about those objects.

Freges conception of numbers as objects by crispin wright freges conception of numbers as objects by crispin wright pp. An answer to the first question sets the stage for answering the second. Some reflections on frege s constraint wright, crispin, notre dame journal of formal logic, 2000. As frege s writings became more widely read, a number of articles were written about various aspects of frege s workhis ontology, semantics, logic. In this paper i offer a conceptually tighter, quasifregean solution to the concept horse paradox based on the idea that the unterfallen relation is asymmetrical. Extensions, numbers and freges project of logic as universal. According to wright, however wright 1983, 11, there were three more specific considerations which were involved in frege s judgement that numbers were abstract objects. Wright s new book is a sustained defense of arithmetical platonism. According to wright, however wright 1983, 11, there were three more specific considerations which were involved in freges judgement that numbers were abstract objects. In frege s conception of numbers as objects crispin wright defends modernised versions of the responses to them of the great german mathamatician and philosopher, gottlob frege, who held that numbers are a kind of logical object and that our knowledge about them, and its relevance to the ral world, is to be seen as a product of our faculty of.

Freges conception of numbers as objects aberdeen university press 1983. Freges theorem and foundations for arithmetic stanford. Taking this early theory to have been an account of cardinals as secondlevel functions, this paper works out the significance of the fact that freges cardinal numbers as objects is a theory. In essays on freges basic laws of arithmetic, edited by p. And despite freges clear distinction from lagrange in rejecting the idea of functions as pieces of language, panza finds in frege a similar deep reliance on language in freges understanding of functions. Abstractionism, which is a development of freges original logicism, is a recent and much debated position in the philosophy of mathematics. His books include wittgenstein on the foundations of mathematics 1980, frege s conception of numbers as objects 1983, truth and objectivity 1992, realism, meaning and truth 2nd edn, 1993, the blackwell companion to philosophy of language with bob hale, blackwell, 1997, the reason s proper study with bob hale, 2001, rails to infinity. He is also author of abstract objects blackwell publishers, 1997. It also discusses his view that truthvalues are objects and the socalled regress argument for the indefinability of truth. In the final section of the paper, there is a brief philosophical discussion of how the present theory relates to the work of other philosophers attempting to reconstruct freges conception of numbers and logical objects.

Joan weiner 2007 has argued that freges definitions of numbers constitute linguistic stipulations that carry no ontological commitment. Crispin wright, freges conception of numbers as objects. Scribd is the worlds largest social reading and publishing site. A systematic exposition and a scoperestricted defense of freges grundlagen conception of numbers. Request pdf the measure of scottish neologicism the scottish neologicist project began with the development of arithmetic in c. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. This system is, except for minor differences, secondorder logic together with an abstraction operator governed by freges axiom v. Other readers will always be interested in your opinion of the books youve read. A general survey of freges views on truth, the paper explores the problems in response to which freges distinctive view that sentences refer to truthvalues develops. In other words, the number n would be a concept that could truly be predicated of. His discussion lasts a mere two sections sections 5556 before he moves on to his more o cial portrayal of numbers as objects. According to the curriculum vitae that the 26year old frege filed in 1874 with his habilitationsschrift, he was born on november 8, 1848 in wismar, a town then in mecklenburgschwerin but now in mecklenburgvorpommern.

This paper offers a critical discussion of this view, showing that it is vitiated by. Freges conception of numbers as objects crispin wright, c. You can read online frege s theorem here in pdf, epub, mobi or docx formats. If the inline pdf is not rendering correctly, you can download the pdf file here. The logic of freges theorem richard g heck jr department of philosophy, brown university. Frege s conception of numbers as objects scots philosophical monographs. Freges theorem is mandatory reading for anybody wishing to learn about the. One of the most important differences between kant and frege concerns the resources available to logic. In freges conception of numbers as objects crispin wright defends modernised versions of the responses to them of the great german mathamatician and philosopher, gottlob frege, who held that numbers are a kind of logical object and that our knowledge about them, and its relevance to the ral world, is to be seen as a product of our faculty of. Wrights new book is a sustained defense of arithmetical platonism. View enhanced pdf access article on wiley online library html view download pdf for offline viewing. Each essay attempts a sympathetic, if not uncritical, reconstruction, evaluation, or extension of a facet of frege s theory of arithmetic.