The Philosophy of Mathematics and Hilbert ’ s Proof Theory ( 1930 )

نویسنده

  • Paul Bernays
چکیده

ion than the conceptual logical ones. We therefore achieve no greater generality at all for mathematical knowledge as a result of its subsumption under logic; rather we achieve just the opposite; a specialization by logical interpretation, a kind of logical clothing. A typical example of such logical clothing is the method by which Frege P. Hertz defended the claim that logical inference contains “synthetic elements” in his essay “Über das Denken” (1923). His grounds for this claim will be explained in an essay on the nature of logic, to appear shortly; they include the point developed here but rest in addition on still other considerations.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Philosophy of Mathematics and Hilbert ’ s Proof Theory ( 1930 ) Paul Bernays

‖ When we read and hear today about the foundational crisis in mathematics or of the dispute between “formalism” and “intuitionism,” then those who are unfamiliar with the activity of mathematical science may think that this science is shaken to its very foundations. In reality, mathematics has been moving for a long time in such quiet waters, that one rather senses a lack of stronger sensation...

متن کامل

The Philosophy of Mathematics and Hilbert ’ s Proof Theory ( 1930 ) Paul

Anyone not familiar with mathematical activity may think, when reading and hearing today about the foundational crisis in mathematics or of the debate between “formalism” and “intuitionism,” that this science is shaken to its very foundations. In reality mathematics has been moving for a long time on a smooth wake, so that one senses more a lack of bigger sensations, although there is no lack o...

متن کامل

New characterizations of fusion bases and Riesz fusion bases in Hilbert spaces

In this paper we investigate a new notion of bases in Hilbert spaces and similar to fusion frame theory we introduce fusion bases theory in Hilbert spaces. We also introduce a new denition of fusion dual sequence associated with a fusion basis and show that the operators of a fusion dual sequence are continuous projections. Next we dene the fusion biorthogonal sequence, Bessel fusion basis, Hil...

متن کامل

Proof Theory in Philosophy of Mathematics

A variety of projects in proof theory of relevance to the philosophy of mathematics are surveyed, including Gödel’s incompleteness theorems, conservation results, independence results, ordinal analysis, predicativity, reverse mathematics, speed-up results, and provability logics. Proof theory is the branch of mathematical logic in which proofs are studied as formal objects in their own right. I...

متن کامل

Operator-valued bases on Hilbert spaces

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002