Reply to the Note by Mr . Aloys Müller , “ On Numbers as Signs ” ( 1923 )

نویسندگان

  • Aloys Müller
  • Paul Bernays
  • Paolo Mancosu
چکیده

Mr. Aloys Müller’s criticism of the conception of number theory as a theory that deals with meaningless signs (“number signs”) consists basically in three objections. A discussion of these objections is useful for clarifying the standpoint of intuitive number theory, and thereby also that of Hilbert’s proof theory. 1. The first objection is terminological and is directed against the use of the word “sign” for something meaningless [bedeutungslos]. If the objects of number theory, such as 1, 1+1, have no meaning, then they are not signs, so the objection goes, but rather figures or, “as we would rather want to say,” shapes [Gestalten]. The first part of this objection must be conceded: Indeed, it corresponds better to linguistic usage to say that the objects of intuitive number theory,

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تاریخ انتشار 2001