منابع مشابه
Predicative Logic and Formal Arithmetic
After a summary of earlier work it is shown that elementary or Kalmar arithmetic can be interpreted within the system of Russell’s Principia Mathematica with the axiom of infinity but without the axiom of reducibility. 1 Historical introduction After discovering the inconsistency in Frege’s Grundgesetze der Arithmetik, Russell proposed two changes: first, dropping the assumption that to every h...
متن کاملVirtual logic - formal arithmetic
We were well programmed long ago to do this arithmetic, and yet it is quite the most mysterious subject. A positive integer is said to be a prime if it is not equal to one, and if it has no integer factors other than itself and one. Here we see that 12 is factored into the product of the prime numbers 2 and 3. Factorization into primes is unique (a nice matter to prove and one of the first basi...
متن کاملPredicative foundations of arithmetic
Predicative mathematics in the sense originating with Poincaré and Weyl begins by taking the natural number system for granted, proceeding immediately to real analysis and related fields. On the other hand, from a logicist or set-theoretic standpoint, this appears problematic, for, as the story is usually told, impredicative principles seem to play an essential role in the foundations of arithm...
متن کاملPredicative fragments of Frege Arithmetic
Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity in...
متن کامل?Logic and Formal Ontology: Is the Final Formal Ontology Possible
Musa Akrami AbstractMany philosophers and logicians have contemplated the relationship between ontology and logic. The author of this paper, working within a Bolzanoan-Husserlian tradition of studying both ontology and logic, considers ontology as the science of the most general features of beings and the most general relations among them. He considers logic as the science concernin...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1998
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1039293018