Welcome this website accompanies our new translation of gottlob freges basic laws of arithmetic. Grundgesetze, as mentioned, was to be freges magnum opus. Other articles where the foundations of arithmetic is discussed. Freges intention in section 31 of grundgesetze is to show that every. Reading freges grundgesetze the philosophical quarterly. You can find out more about the team behind the translation project. Logic is an old subject, and since 1879 it has been a great one. Band 1 richard heck journal of symbolic logic 58 2.
Frege on referentiality and julius caesar in grundgesetze section 10. Department of philosophy harvard university published in w. It was to provide rigorous, gapless proofs that arithmetic was just logic further. In this paper, we show that the above fragment augmented with the axiom. Freges theorem and foundations for arithmetic stanford. In metalogic and metamathematics, freges theorem is a metatheorem that states that the peano axioms of arithmetic can be derived in secondorder logic from humes principle. Verschiedene digitalisate des originalbuchs bei archive. Frege on referentiality and julius caesar in grundgesetze. You can find out more about freges original work here. This idea was formulated in nonsymbolic terms in his the foundations of arithmetic he is understood by many to be the father of analytic.
This system is, except for minor differences, secondorder logic together with an abstraction operator governed by freges axiom v. An illustration of a computer application window wayback machine an illustration of an open book. Freges goal was to show that mathematics grows out of logicand in so doing, he devised techniques that took him far beyond the aristotelian syllogistic and stoic. The grundlagen was a work that must on any count stand as a masterpiece of philosophical writing. A few years ago, richard heck showed that the ramified predicative secondorder fragment of the grundgesetze is consistent. Reduction and tarskis definition of logical consequence edwards, jim, notre dame journal of formal logic, 2003. Friedrich ludwig gottlob frege was a german philosopher, logician, and mathematician. There are arguably two main reasons for this, both addressed by hecks book. Pdf russells paradox in consistent fragments of freges. The main work of the paper consists in grundgeeetze a new understanding of the semantics frege offers for the quantifiers.
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