Results 111 to 120 of about 3,525 (163)
Some of the next articles are maybe not open access.
The Role of the Axiomatic Method
The American Mathematical Monthly, 1967(1967). The Role of the Axiomatic Method. The American Mathematical Monthly: Vol. 74, No. 2, pp. 115-127.
openaire +1 more source
1987
This chapter discusses the verification method of Hoare, well known for proving the partial correctness of while-programs. This method is usually presented in the form of a calculus, the so-called Hoare calculus. Essentially this approach is identical with the inductive assertions method introduced in the last chapter, as may become plausible from the ...
Jacques Loeckx, Kurt Sieber
openaire +1 more source
This chapter discusses the verification method of Hoare, well known for proving the partial correctness of while-programs. This method is usually presented in the form of a calculus, the so-called Hoare calculus. Essentially this approach is identical with the inductive assertions method introduced in the last chapter, as may become plausible from the ...
Jacques Loeckx, Kurt Sieber
openaire +1 more source
*ZFC: An axiomatic * approach to nonstandard methods
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1997The author establishes a new foundation of nonstandard analysis in which it is possible to deal with external sets. To do so, a function * defined on the class \(S\) of all standard sets is introduced, namely \[ \biggl\{ \forall x,y,z\;\bigl[^* x=y\wedge {^*x}= z\to(y=z \wedge x\in S)\bigr] \biggr\} \wedge [\forall x\in S\;\exists y\;({}^*x =y ...
openaire +3 more sources
Intuition and the Axiomatic Method
2006Preface Part I Mathematical Aspects Locke and Kant on Mathematical Knowledge : Emily Carson The View from 1763: Kant on the Arithmetical Method before Intuition : Ofra Rechter The Relation of Logic and Intuition in Kant's Philosophy of Science, Particularly Geometry : Ulrich Majer Edmund Husserl on the Applicability of Formal Geometry : Rene Jagnow The
openaire +1 more source
Zermelo and the Axiomatic Method
2018This chapter intends to examine the widespread assumption, which has been uncritically accepted, that Zermelo simply adopted Hilbert’s axiomatic method in his axiomatization of set theory. What is essential in that shared axiomatic method? And, exactly when was it established?
openaire +1 more source
Euclid's Elements and the Axiomatic Method
The British Journal for the Philosophy of Science, 1969algebra, analytic geometry, real number theory, and mathematical logic. It is not possible to describe here the evolution of the idea of structure in the modern era. An important step in it is the realisation that Euclidean geometry has an interpretation in the universe of the real numbers-a realisation made possible by the existence of analytic ...
openaire +2 more sources
The Use of the Axiomatic Method in Secondary Teaching
The Mathematics Teacher, 1966The Report was prepared at the request of the Sub-committee on Instruction of the British National Committee for Mathematics. It formed the basis of the presentation of the United Kingdom point of view in a discussion on the topic at the International Congress of Mathematicians held in Moscow in August, 1966.
openaire +1 more source
The Axiomatic Method in Physics
1973The axiomatic approach has seldom been tried in physics, partly because the term ‘axiomatic’ is still widely mistaken for ‘self-evident’ or for ‘a priori’, partly because physical theories are often regarded as mere data processing devices in no need of logical organization, and partly because of a fear of rigor and clarity. As a result, between Newton’
openaire +1 more source
1992
Philosophical analysis of axiomatic methods goes back at least to Aristotle. In the large literature of many centuries a great variety of issues have been raised by those holding viewpoints that range from that of Proclus to that of Hilbert. Here I try to consider in detail only a highly selected set of ideas, but they are ones I judge important.
openaire +1 more source
Philosophical analysis of axiomatic methods goes back at least to Aristotle. In the large literature of many centuries a great variety of issues have been raised by those holding viewpoints that range from that of Proclus to that of Hilbert. Here I try to consider in detail only a highly selected set of ideas, but they are ones I judge important.
openaire +1 more source
Heuristics and the Axiomatic Method
1993Over the last 100 years a variety of arguments have been given for using the axiomatic method in mathematics and in science. There is not uniform agreement that the method is always appropriate or useful. However, there is, I think, general agreement that the use of such methods has revolutionized the presentation of mathematics and has had significant
openaire +1 more source