Mathematical Demonstration in a Mixed Science

2015 ◽  
pp. 131-142
Keyword(s):  
Mathematical Demonstration

Galileo and Mathematical Demonstration

Nature ◽  
1937 ◽  
Vol 140 (3545) ◽  
pp. 646-646 ◽  
Author(s):  
WILLIAM CUSACK FAHIE
Keyword(s):  
Mathematical Demonstration

scholarly journals V. An essay on quantity; occasioned by reading a treatise, in which simple and compound ratios are applied to virtue and merit, by the Rev. Mr. Reid ; communicated in a letter from the Rev. Henry Miles D. D. & F. R. S. To Martin Folkes Esq P. R. S

1748 ◽  
Vol 45 (489) ◽  
pp. 505-520 ◽  
Keyword(s):  
Mathematical Demonstration

Since mathematical demonstration is thought to carry a peculiar Evidence along with it, which leave no room for further dispute; it may be of some Use, or Entertainment at least, to inquire to what subject this kind of Proof may be applied.

scholarly journals Demonstration in geometry: historical and philosophical perspectives

2020 ◽  
Vol 8 (18) ◽  
pp. 540-570
Author(s):  
Saddo Ag Almouloud
Keyword(s):  
Mathematical Demonstration ◽  
Historical Origin ◽  
Evolution Of Ideas ◽  
Scientific Validation

In this article, we weave historical-philosophical reflections about demonstration in mathematics, based on works of researchers that discuss the different philosophical perspectives on the topic, more specifically on geometry. We focus first on demonstration and its relationship with intuition and figural representations. Second, we criticize Poincaré’s conception of mathematical demonstration. Third, we reflect, in a non-exhaustive way, on the philosophy of demonstration in geometry, confronting Kant’s conceptions with the axiomatizations of the non-Euclidean geometries. In this text, we do not adopt a single definition that would cover all modes of scientific validation, since we admit the possibility of an evolution of ideas about the validity of a proposition. Not to fall into the symmetrical flaws of the glorification of the Ancients or even being ungrateful to them, we must start from the naive idea that the demonstration has a historical origin and, therefore, maintains a historical character, but we should be more attentive to what characterizes, in its particularity or even its uniqueness, the productions of past and present centuries. Keywords: Philosophy of demonstration; Axiomatization; Induction; Intuition; Representation.

scholarly journals Alternative demonstration of the entropy evolution in least time

2018 ◽  
Vol 20 (2) ◽  
Author(s):  
Jhonatan Rabanal
Keyword(s):  
Open Systems ◽  
Mathematical Demonstration

Open systems evolve towards states of greater entropy, so they come into balance with their surroundings. Also, this evolution occurs in least time. This work presents a mathematical demonstration of this principle.

The Vulgate, Peshitto, Sahidic, and Bohairic Versions of Acts and the Greek Manuscripts

1928 ◽  
Vol 21 (1) ◽  
pp. 69-95
Author(s):  
James Hardy Ropes ◽  
William H. P. Hatch
Keyword(s):  
Thirteenth Century ◽  
Textual Criticism ◽  
Mathematical Demonstration ◽  
New Knowledge ◽  
Book Of Acts

The use of statistics in textual criticism is always attractive to the student, but is apt to be disappointing in application. It resembles the attempt of Raymond Lull in the thirteenth century to convert the Mohammedans by a mathematical demonstration of the truths of Christianity: in both cases the insights have been chiefly gained through other and more direct processes, and the figures can seldom do more than provide interesting illustration, or the test of an hypothesis; they seldom lead to much new knowledge. Moreover, it is very difficult to make the statistics either complete or perfectly accurate. Nevertheless, in textual criticism something can be learned from statistics both by way of verification and of suggestion; and the following study of the chief versions of the Book of Acts seems to the writers to yield some profitable fruit.

SCALING, VORONOI TESSELLATION, AND KJMA: THE DISTRIBUTION FUNCTION IN THIN SOLID FILMS

2010 ◽  
Vol 09 (01n02) ◽  
pp. 1-18 ◽  
Author(s):  
M. TOMELLINI ◽  
M. FANFONI
Keyword(s):  
Distribution Function ◽  
Film Growth ◽  
Voronoi Tessellation ◽  
Size Distribution Function ◽  
Solid Surfaces ◽  
Diffusional Growth ◽  
Scaling Properties ◽  
Solid Films ◽  
Mathematical Demonstration ◽  
Physical Observable

Among several aspects concerning the growth of thin films on solid surfaces, we focus our discussion on the physical observable known as the island size distribution function (SDF). Since this is a subject large enough to require a full review, even a whole book, we have limited our survey to the scaling properties of the distribution function and to some of its possible shapes. In particular, we discuss the fast and slow nucleation processes in diffusional growth and the KJMA (Kolmogorov–Johnson–Mehl–Avrami) distributions. Space has been given to the mathematical demonstration of the principal equations, in order to render the paper usable also to neophytes of thin film growth. Experimental particle (SDFs) are also reported and discussed.

The Deposit of Faith

1983 ◽  
Vol 36 (1) ◽  
pp. 1-28 ◽  
Author(s):  
T. F. Torrance
Keyword(s):  
Everyday Life ◽  
Scientific Inquiry ◽  
Blaise Pascal ◽  
Objective Knowledge ◽  
Michael Polanyi ◽  
Mathematical Demonstration

Blaise Pascal once pointed out in connection with mathematical demonstration that it is impossible to operate only with explicit propositions or definitions, for whenever we seek to define the meaning of something in precise terms we have to make use of other terms which for this purpose must themselves remain undefined. Michael Polanyi has shown that this applies no less to all acts of knowledge whether in everyday life or in rigorous scientific inquiry, for any formal account of what we know rests upon a base of informal undefined knowledge, from which it cannot be cut off without becoming empty and useless. This means that a complete formalisation of knowledge in explicit terms is impossible. A cognate reason for this is to be discerned in the fact that in objective knowledge the realities we seek to know inevitably break through any frame of concepts and statements which we use to describe them even though they are developed under the constraint of those realities. Concepts and statements of this kind do not have their truth in themselves but in the realities to which they refer. Hence if we are to do justice to the integrity and nature of the objects of our knowledge we must discriminate them from our knowing of them, and let them confer relativity upon our concepts and statements about them. Thus in all authentic knowledge we have to take into account an informal undefined knowledge grounded in the inherent intelligibility of what we know and must constantly find appropriate ways of letting it exercise a regulative force in all our explicit formulations of it.

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