Grundgesetze, as mentioned, was to be Frege’s magnum opus. It was to provide rigorous, gapless proofs that arithmetic was just logic further. Gottlob Frege’s Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would. Gottlob Frege’s Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would finally establish his .

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We have thus reasoned that e is an element of itself if and only if it is not, showing the incoherency in Frege’s conception of an extension. This argument is not valid. A logico-mathematical enquiry into the concept of numberby J. University of Chicago Press, Therefore, no two numbers have the same successor. Gdundgesetze is one of the founders of analytic philosophywhose work on logic and language gave rise to the linguistic turn in philosophy.

Since all and only those things that have hearts have kidneys, strictly speaking, the concepts denoted by grundgesezte expressions ” has a heart”, and ” has a kidney” are one and the same.

Sheffer, edited by P. This page was last edited on 21 Decemberat Recently, Boolosdeveloped one of the more interesting suggestions for revising Basic Law V without abandoning second-order logic and its comprehension principle for concepts.

If there is one Fthen the number of F s, i. If Grundtesetze is correct, then we should be wary of taking ‘the concept F ‘ and ‘the extension of the concept F ‘ as co-referential and interchangeable.


Finally, it is important to mention that one can add the following clause to the definition of the formulas of our second-order language so as to include formulas that express identity claims:.

The reader should be able to write down instances of the comprehension principle which demonstrate these claims. Comprehension Principle for 2-place Relations: This distinguishes them from objects. Similarly, the following argument is valid. Our sole purpose in introducing such definitions is to bring about an extrinsic simplificationby stipulating an abbreviation.

Clearly, however, these expressions do not present that concept in the same way. To solve these puzzles, Frege suggested that the terms of a language have both a sense and a denotation, i.

Frege could then use mathematical induction to prove some of the basic laws of the natural numbers.

Gottlob Frege

As mentioned above, much of the material is new: Previous logic had dealt fgege the logical freg andorif The extension of a concept freg something like the set of all objects that fall under the concept, for the extension records all of the objects that the concept maps to The True.

To Frege’s mind, these statements do not deal directly with the morning star and the evening star itself. It should be kept in mind that Frege was employed as a mathematician, not a philosopher, and he published his philosophical papers in scholarly journals that often were hard to access outside of the German-speaking world. There are circumstances in which the premises are true and the conclusion false. In particular, we adopt the following conventions. Heck argues that Frege must have hit upon this principle in his proof-attempts.

Frege made extensive use of value-ranges in every proof in part II of Grundgesetzeand every non-primitive function is defined in terms of value-ranges.


The view that grundgesstze sense of a proper name such as “Aristotle” could be descriptive information as simple as the pupil of Plato and teacher of Alexander the Greathowever, has been harshly criticized by many philosophers, and perhaps most notably by Saul Kripke. Is e an element of itself?

Reading Frege’s Grundgesetze – Hardcover – Richard G. Heck, Jr. – Oxford University Press

Frege’s Life and Influences According to the curriculum vitae that the year old Frege filed in with his Habilitationsschrifthe was born on November 8, in Wismar, a town then in Mecklenburg-Schwerin but now in Mecklenburg-Vorpommern. This rapprochement between Kant and Frege is developed in some detail in MacFarlane It is an active matter of debate and discussion to what extent and how this principle coheres with Frege’s later theory of meaning, but what is clear is that it plays an important role in his own philosophy of mathematics as described in the Grundlagen.

Chapter 10 is about Frege’s incomplete development of addition, which includes a definition of cardinal addition, the uniqueness of sum if it existsbut not a proof of its existence. Enhanced bibliography for this entry at PhilPaperswith links to its database.

Heck thus argues for the controversial claim that the domain of the concept-script in Grundgesetze is restricted, while the orthodoxy is that Frege meant it to be universal. He produced very little work between and his retirement in Heck Search this author in: