Sentences with phrase «philosophy of mathematics»

Turing attended Wittgenstein's lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems.

Other teachers responded immediately and confirmed their negative feelings about the statement and pointed out that we should rethink our school philosophy of mathematics teaching and learning.

Since most of these problems involve his philosophy of mathematics, and since the mathematics with «which he is concerned is primarily the calculus, it will help also, in section four, to sketch, briefly, a number of its fundamental features.

He has played the largest role in the development of the philosophy of mathematics.

That Whitehead's early attempts at a philosophy of mathematics were inadequate, does not mean that his empiricist position was wrong.

His mathematics was at most a sophisticated extension of that outlined above in An Introduction to Mathematics; his philosophy of mathematics was probably also a version only implicitly contained therein.

Murray Code has written a good introduction to Whitehead's philosophy of mathematics in his book (OO) based on Whitehead's later works.

(3) The last approach to generalization that we consider is the path not taken by Whitehead, at least not in his philosophy of mathematics.

This present article, in contrast to the older one, seeks to evaluate Whitehead's early philosophy of mathematics in terms of Whitehead's mature philosophy and contemporary mathematics.

In order to cultivate it adequately we have to examine Whitehead's mathematics and philosophy of mathematics in Universal Algebra and Principia Mathematica.

Formalism, set theory, logicism, and intuitionism are the four major recognized contemporary schools in the philosophy of mathematics.2 If Whitehead did not advocate any of these, including intuitionism (which he never engaged probably because of its Kantian roots), what was his position?

Genuine disagreement on the philosophy of mathematics / logic (of which there are more than one), and 2.

Not exact matches

In the early period, down to 1922, White - head was preoccupied with mathematics, logic, and philosophy of science.

A. N. Whitehead (1861 — 1947) retired in 1924 from an academic career in England in the fields of mathematics and education and promptly accepted an invitation to join the faculty in philosophy at Harvard University, where his work took off in a totally unexpected direction.

``... the future of Christian philosophy will therefore depend on the existence or absence of theologians equipped with scientific training, no doubt limited but genuine and, within its own limits, sufficient for them to follow with understanding such lofty dialogues not only in mathematics and physics but also in biology and wherever the knowledge of nature reaches the level of demonstration.»

The idea then current was that astronomy is a branch of mathematics devoted to calculating where and when things appear in the sky, whereas it was the job of «philosophy» (as science was then called) to explain the nature and causes of things.

During the Ottoman rule Muslim culture declined in Egypt because of the belief of the rulers that the study of philosophy, geography, mathematics, and related fields would lead to heresy.

Again, and let me be more specific, science, mathematics and philosophy give great evidence to the existence of God.

Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science.

Whereas the first approach pictures Whitehead's philosophical interests as developing in a linear manner — from mathematics, to nature philosophy, and finally to metaphysics, Mays uses the analogy of a spiral (RW 237, 259; of PW 20/15).

Just remember that «the key words [of PR] derive their meanings from his earlier studies in mathematics and the philosophy of science» (RL 284).

One thinks, for example, of Bishop Berkeley's mathematics and philosophy.

At present, however, the contemporary understanding of Whitehead's philosophy of organism involves eternal objects resting on the intuitions of logic and mathematics that contrast with concrescing actual entities united through prehension.

Whitehead's life was steeped in mathematics and philosophy, but he has insights of importance in two other areas of thought: 1.

His doctrine of eternal objects in both his earlier and later philosophy can be understood as a description of the ontological nature of pure logic and mathematics (EWP 14 - 28).

Whitehead's theme, begun in the first chapter and maintained throughout the book and, in our judgment, for the rest of his philosophy, is that mathematics begins in experience and as abstracted becomes separated from experience to become utterly general.

The justification of the rules of inference in any branch of mathematics is not properly part of mathematics; it is the business of experience or philosophy.

Trained in logic, mathematics and positive sciences, his main intention was to bring philosophy once again in touch with the sciences of his era (quantum mechanics, relativity theory, non-mechanical biology) and to elaborate a cosmological - metaphysical theory on the basis of the analysis of their presuppositions.

Most of what is known of human nature from mathematics and the physical sciences is based on reflection on those disciplines and hence is not normally thought to be part of their proper subject matter, but to belong more to the philosophy of science and mathematics.

Instead, the significance of mathematics for a philosophy of man derives from reflection on the mathematical enterprise as a type of human activity.

Indeed, according to writers and scientists such as Pierre Duhem, Stanley Jaki and Peter Hodgson, science in the modern sense of the word took root in the late Middle Ages, fuelled by a heady mix ofChristian theology and the newly rediscovered riches of Greek philosophy and mathematics.

As we made our way through the soul of the Old City to Jaffa Gate, my companion, a super-Sabra who studied mathematics and philosophy at Hebrew University, asked me the inevitable question.

Others might declare that the goal of philosophy is not the explication of science (as Russell and Whitehead once tried to explicate mathematics), and hence the question is irrelevant.

But because he developed it out of a background in mathematics and physics, it has a systematic rigor and relevance to contemporary issues that Asian philosophy usually lacks.

They were formulated in less continuity with mathematics than was true of Western philosophy.

As he was approaching retirement, after a lifetime of teaching mathematics, with publications in mathematics, the philosophy of nature, and logic, he was offered a chair in philosophy at Harvard.

Our previous editorial and Synthesis column questioned this distinction, and its concomitant «protection» of the «perennial philosophy» from the implications of the applicability of mathematics to nature.

No doubt one of his greatest heresies is to ascribe anti-rationalist views to orthodox rationalists.4 Whitehead's own thinking seems to move inexorably toward the conclusion that only good myths can engender good understandings.5 The gist of his conclusion, that mythopoesis underpins natural philosophy, does not require a renunciation of logic, mathematics, and science.

In essentials like religion, ethics, philosophy; in history, literature, art; in the concepts of all science, except perhaps mathematics, the American boy of 1854 stood nearer the year 1 than to the year 1900.2

Whether it be Thomas Bradwardine's (c.1290 - 1349) assumptions that mathematics and philosophy belong together or William of Conches» (c. 1090 -?)

If you know your philosophy, you are probably familiar with the efforts of the 20th century analytics to provide logical «foundations» for all of knowledge, including mathematics.

Earlier works on mathematics, science and philosophy of science have 7 — Introduction to Mathematics (the first reference noted); «First Physical Synthesis,» CN, R have one each; «Uniformity and Contingency;» has 2.

Philosophy, after all, needs precision of statement, more even than mathematics and natural science do.

Descartes (1596 - 1650) contributed to mathematics and especially to philosophy — to the latter with his basic questioning and his principle of cogito, ergo sum («I think, therefore I am»).

The marriage of form and content at the abovementioned colleges, which neither specialize nor departmentalize nor ignore mathematics and science any more than literature and philosophy, is a promising alternative to the research university.

This analysis of mathematics seems to be the reason for Whitehead to attach e attribute of a «particular individuality» (SMW 229) to eternal objects in his later philosophy.

Philosophy of science, epistemology, ontology, logic, and mathematics, along with broad humanistic concerns, dominated his thought.

Herodotus claimed that the Greeks learned to worship Dionysus from the Egyptians, and Aristotle said that Egypt was the source of all philosophy and mathematics.

Without a doubt it does so in regard to culture, history and developments in philosophy, politics, medicine, mathematics or almost any discipline for that matter if it comes to laying the foundations of Western civilization.

«Since we are likely to draw more votes than the other minor party candidates, the spotlight will shine on our philosophy of maximum liberty, minimal government, and greater privacy,» added Boman, a physics, mathematics and astronomy instructor at two Detroit - area community colleges.