Frege distinguished two truthvalues, the true and the false, which he took to be objects. Thus, the object reading is still arguably a tenable reading of freges conception of truth. Freges work for they invoke patterns of reasoning that he developed in 1884 and 1893. Pdf frege and numbers as selfsubsistent objects gregory. Frege, in the appendix to the second volume, rephrased the paradox in terms of his own system. This point has fundamental consequences in frege s view.
Philosophers today still find that work insightful. On the contemporary conception, logical properties such as validity and consequence are metalinguistic properties of schemata determined by the truth values that result from interpretations of their placeholders. Aberdeen university press, aberdeen 1983, also distributed by humanities press, atlantic highlands, n. Thus, frege s conclusion is that the number words are like adjectives for concepts, i. One might expect frege to define the number 1 by giving a description that picks out the object that the numeral 1 already names. It might be objected that if 5556 do not consider the radical adjectival. The paper critically examines an unpopular line of freges view on. My view, in short, is that frege understood this definition. The contextualistic approach is characteristic already of freges conception.
A s he n g ph indicates, ita s en in s e to n o s htes on intuitio n nd ts al,ch ed in he al fro m 85 to 1,h e nd nd th s, in r,icizin g s s. Pdf gottlob frege on number development of his conception. Frege refutes other theories of number and develops his own theory of numbers. If valueranges were classes, cardinal numbers would now be classes of classes, rather than classes of concepts. Frege s conception of numbers as objects aberdeen university press 1983. Freges theorem and foundations for arithmetic stanford. First, he invented quantification theory and this was the first step toward making precise the notion of a purely logical deduction. Thus talk about numbers as objects and strict arithmetical truth is only possible as a systeminternal discourse, and concept script.
The book was not well received and was not read widely when it was published. Frege s conception of numbers as objects by crispin wright. Frege, concept and object co, in the frege reader,michael beaney, ed. See for example crispin wright, frege s conception of numbers as objects aberdeen university press, 1983, at pp. Tait there can be no doubt about the value of frege s contributions to the philosophy of mathematics. I begin by arguing against the claim, recently defended by several frege scholars, that the firstorder domain in grundgesetze is restricted to valueranges including the truthvalues, but conclude that there is an irresolvable tension in freges view. The formalization turns on the interaction of a nonstandard but still firstorder cardinality quantifier with an abstraction operator assigning objects to predicates. However, the derivation of the claim that every number has a successor does not follow freges plan, but rather exploits the logic of modality that is embedded in the system. Bolzano, frege, and husserl on reference and object. They are included here for those who wish to have a more complete understanding of what frege in fact attempted to do. Canadian journal of philosophy volume xiv, number 4, december. Greimanns criticisms are not sufficient to refute the object reading of freges conception of truth. Dec 23, 2020 in what follows, however, we shall continue to use the notation of the modern predicate calculus instead of freges notation.
On concept and object 1 thi s er as sted in 92 in he vierteljahrsschrift fur. Freges conception of numbers as objects by crispin wright. See heck and may for further discussion of freges contribution to the philosophy of language. If one takes the framework of freges theory to be essentially secondorder predicate logic and adopts hp with a primitive operator the number belonging to, attaching to concept expressions as an axiom, all of secondorder peano arithmetic becomes derivable, using the exact definitions and proofs employed by frege who used the explicit. Natural numbers and natural cardinals as abstract objects. But crispin wright claimed, in his book freges conception of numbers as objects 1983, that, even though hp is not a logical truth, it nonetheless has the epistemological virtues that were really central to freges logicism. When we say mars has two satellites, we express the fact that the concept satellite of mars is instantiated by two objects. A more fregean reading of this thesis might state that in locke. One such conception criticized by him holds that number is a property of objects. The tension has a direct impact on the semantics of the concept script, not least on the. The horizontal in freges begriffsschrift springerlink. Since a statement of number based on counting contains an assertion about a concept, in.
Hales deflationary conception of properties and freges. One final important difference between freges conception of logic and kants concerns the question of whether logic has any content unique to itself. Husserls notion of the intentional object may be compared and contrasted with bolzanos and freges views on the reference of linguistic expressions, especially since bolzano was a main influence on the development of husserls views. Wright, c 1983, frege s conception of numbers as objects, aberdeen university press.
I trace changes to freges understanding of numbers, arguing in. But everything is identical to itself, and so it is trivial to assert that a. A systematic exposition and a scoperestricted defense of frege s grundlagen conception of numbers. A short introduction to gottlob freges begriffsschrift. Use the link below to share a fulltext version of this article with your friends and colleagues. Aberdeen university press 1983 authors crispin wright university of stirling abstract this article has no associated abstract. I need help understanding freges definition of number. If we take a to be 0 and p to be the relation of predecessionread pxyas. Freges objects of a quite special kind springerlink. 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.
The grundlagen also helped to motivate frege s later works in logicism. Frege identified the number 0 as the number of the concept being nonselfidentical. Frege, logicism, number, extensions, functions, concepts, objects. However, if, on the other hand, frege s goal were to arrive at a concept of number usable for the purpose of science as he explicitly states it is at this very point in the text. Dec, 2020 freges view is that our understanding can grasp them as objects if their definitions can be grounded in analytic propositions governing extensions of concepts. This thesis that numbers are objects can be usefully divided into two parts. When we examine this expression for its truthvalue we see that it refers to the true and that for all other arguments the result is an expression which refers to the false e. In frege s terminology, both number and quantifiers are secondlevel concepts, i. His discussion lasts a mere two sections sections 5556 before he moves on to his more o cial portrayal of numbers as objects. See frege 1893, parsons 1965, wright 1983, and heck 1993. According to freges platonist version of logicism, i arithmetic and real analysis are true of abstract objects whose existence does not depend on the existence of any other type of entity and ii the fundamental laws of these theories are analytic, i. Thus talk about numbers as objects and strict arithmetical truth is only possible as a systeminternal discourse, and conceptscript. Volume 24, number 1, january 1983 frege s definition of number steven wagner i will interpret frege on the main issues about his definition of numbers as extensions at 8, 68\ its point, its correctness, and its implications for the nature of number. Freges analysis is to say that 2 is an argument combined with the function x is a positive square root of 4.
Frege s conception of numbers as objects scots philosophical monographs. In general, functions and numbers are not objects of the sense. Profiles in the origins of twentieth century thought, chicago. But despite appearances, there is no circularity, since frege analyzes the secondorder concept being a concept under which two objects fall without appealing to the concept two. Frege pronounced frayguhbelieved that arithmetic and all mathematics are derived from logic, and to prove this he developed a completely new approach to logic and numbers. Goldfarb depicts salient differences between freges and the contemporary philosophical conceptions of logic. Freges conception of numbers as objects tiles 1984.
He also developed analogous principles for such abstract. Pdf definite descriptions in freges theory of cardinal. In defending platonism, wright artfully intertwines considerations relevant to 1 with considerations relevant to 2, a practice that could make. Joan weiner presents a very clear outline of frege s life and ideas, showing how his thinking evolved through successive books and. They thus require a truth predicate for their expression, and, moreover. Apr 25, 2020 to see the intuitive idea behind this definition, consider how the definition is satisfied in the case of the number 1 preceding the number 2. Frege in fact identifies the cardinal number 2 with this extension, for fege contains all and only those concepts under which two objects fall. Crispin wright, freges conception of numbers as objects. Freges conception of numbers as objects scots philosophical monographs crispin wright on. Frege s conception of numbers as objects scots philosophical monographs crispin wright on.
Nov 30, 1997 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. On concept and object by gottlob frege first published in the vierteljahrsschrift fi4r wissenschaftliche philosophie, 16 1892. Aug 25, 2019 but, of course, freges view and kants view contradict each other only if they have the same conception of logic. The number 1 is the cardinal number which belongs to the concept the number 1 is the cardinal number which belongs to the concept identical with 0 the number 2 is the cardinal number which belongs to the concept the number 2 is the cardinal number which belongs to the concept identical with 0 or 1 the number 3 is the cardinal number that belongs to the concept member of the natural number series ending with 2 august 09 ozge ekin bogazici university. Frege s conception of numbers as objects wright, crispin on. G when added to classical secondorder logic but not free secondorder logic, this implies the existence of numbers, which frege regarded as logical objects. In this paper, the authors discuss frege s theory of logical objects extensions, numbers, truthvalues and the recent attempts to rehabilitate it. Volume xiv, number 4, december 1984 critical notice crispin wright. May 22, 2019 grundgesetzd still have to show that such successor cardinals are natural numbers. Number described with the use of equinumerosity of objects falling under. Crispin wright, freges conception of number as objects.
Wrights new book is a sustained defense of arithmetical platonism. 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. This paper presents a formalization of firstorder arithmetic characterizing the natural numbers as abstracta of the equinumerosity relation. Changing our notation system will not give us new numbers of functions. The topic of the paper is the public reception of gottlob freges begriffsschrift right after its publication in according to a widespread. Freges elucidatory holism 227 such that the former semantical notions can then be used to explain what judgment, inference, and assertion are. We argue that frege s mature views about truth emerge from a. Freges conception of numbers as objects scots philosophical. At the center of wrights defense is a version of frege s famous dictum that only in the context of a sentence does a word have any.
Aberdeen university press, aberdeen 1983, also distributed. It did, however, draw the attentions of bertrand russell and ludwig wittgenstein, who were. A logicomathematical enquiry into the concept of number. Also, the object reading provides a plausible understanding of freges remarks.
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