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"Matter" may be defined, according to the Oxford English Dictionary, as "The substance, or the substances collectively, out of which a physical object is made or of which it consists". And while the O.E.D. is not the ultimate authority on words, nor is it, I believe, far wrong in this particular case. The definition is, as I shall argue in this paper, in substantial harmony with a tradition of some antiquity, according to which material objects do not constitute a somehow (...) |
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In his treatise Die Grundlagen der Arithmetik, Gottlob Frege tries to find a definition of number. First he rejects the idea that number could be a property of external objects. Then he comes with a suggestion that a numerical statement expresses a property of a concept, namely it indicates how many objects fall under the concept. Subsequently Frege rejects, or at least essentially modifies, also this definition, because in his view that a number cannot be a property – it should (...) |
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According to the species of neo‐logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo‐fregeanism—a general conception of the relation between language and reality; (2) the method of abstraction—a particular method for introducing concepts into language; (3) the scope of logic—second‐order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. (...) |
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In the Grundlagen , Frege offers eight main arguments, together with a series of more minor supporting arguments, against Mill’s view that numbers are “properties of external things”. This paper reviews all eight of these arguments, arguing that none are conclusive. |
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