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Topic: Principia Mathematica

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  Kids.net.au - Encyclopedia Principia Mathematica -   (Site not responding. Last check: 2007-10-21)
The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Bertrand Russell and Alfred North Whitehead and published in 1910-1913.
These were avoided in the Principia by building an elaborate system of types: a set has a higher type than its elements and one can not speak of the "set of all sets" and similar constructs which lead to paradoxes (see Russell's paradox).
The Principia only covered set theory, cardinal numbers, ordinal numbers and real numbers; deeper theorems from real analysis were not included, but by the end of the third volume it was clear that all known mathematics could in principle be developed in the adopted formalism.
www.kids.net.au /encyclopedia-wiki/pr/Principia_Mathematica   (258 words)

 Philosophiae Naturalis Principia Mathematica - Wikipedia, the free encyclopedia
The Philosophiae Naturalis Principia Mathematica (Latin: "mathematical principles of natural philosophy", often Principia or Principia Mathematica for short) is a three-volume work by Isaac Newton published on July 5, 1687.
Descartes' book of 1644 Principia philosophiae (Principles of philosophy) stated that bodies can act on each other only through contact: a principle that induced people, among them he himself, to conjecture an universal medium as the carrier of interactions such as light and gravity— the aether.
It was perhaps the force of the Principia, which explained so many different things about the natural world with such economy, that caused this method to become synonymous with physics, even as it is practised almost three and a half centuries after his beginning.
en.wikipedia.org /wiki/Philosophiae_Naturalis_Principia_Mathematica   (2653 words)

 Principia Mathematica   (Site not responding. Last check: 2007-10-21)
Principia Mathematica is the landmark work on mathematical logic and the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell.
Although Principia succeeded in providing detailed derivations of major theorems in set theory, finite and transfinite arithmetic, and elementary measure theory, two axioms in particular were arguably non-logical in character: the axiom of infinity and the axiom of reducibility.
Third, Principia Mathematica reaffirmed clear and interesting connections between logicism and two main branches of traditional philosophy, namely metaphysics and epistemology, thus initiating new and interesting work in both these and other areas.
www.science.uva.nl /~seop/archives/spr2002/entries/principia-mathematica   (1213 words)

 Philosophiae Naturalis Principia Mathematica - Encyclopedia.WorldSearch   (Site not responding. Last check: 2007-10-21)
In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction.
The Philosophiae Naturalis Principia Mathematica is composed of three volumes.
Newton's Principia in 1687 and 1937: A lecture given to commemorate the two hundred and fiftieth anniversary of the publication of Newton's Philosophiae naturalis principia mathematica
encyclopedia.worldsearch.com /principia.htm   (678 words)

 Principia Cybernetica and Principia Mathematica
Principia Mathematica, in which they ground the "principles of mathematical thinking" in a clear, apparently consistent and complete way.
This proved highly successful, and the Principia Mathematica stills forms the basis of the "modern" mathematics as it is taught in schools and universities.
Similar to the integrating theories of mathematics at the end of the 19th century (Cantor's set theory, formal logic,...), the integrating theories of cybernetics at the end of the 20th century (general systems theory, second-order cybernetics,...) are not integrated themselves.
pespmc1.vub.ac.be /PRMAT.html   (929 words)

 Principia Mathematica
Principia Mathematica is the landmark work on mathematical logic and the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell, and published in three volumes, in 1910, 1912 and 1913.
Principia's main goal of showing the detailed reduction of mathematics to logic proved to be controversial.
Principia itself appeared in three volumes, which together in turn are divided into six parts.
setis.library.usyd.edu.au /stanford/archives/win1997/entries/principia-mathematica   (1097 words)

 Principia Mathematica - Wikipedia, the free encyclopedia
These questions were settled by Gödel's incompleteness theorem in 1931.
Gödel's second incompleteness theorem shows that basic arithmetic cannot be used to prove its own consistency, so it certainly cannot be used to prove the consistency of anything stronger.
In other words, the statement "there are no contradictions in the Principia system" cannot be proven true or false in the Principia system unless there are contradictions in the system (in which case it can be proven both true and false).
en.wikipedia.org /wiki/Principia_Mathematica   (324 words)

 Principia Mathematica
Principia Mathematica, the landmark work written by Alfred North Whitehead and Bertrand Russell, and published in three volumes, in 1910, 1912 and 1913.
Although Principia succeeded in providing detailed derivations of many major theorems in set theory, finite and transfinite arithmetic, and elementary measure theory, two axioms in particular were arguably non-logical in character: the axiom of infinity and the axiom of reducibility.
Abridged as Principia Mathematica to *56, Cambridge: Cambridge University Press, 1962.
plato.stanford.edu /entries/principia-mathematica   (1569 words)

 Principia Mathematica
Principia Mathematica was first published in 1910-13; this is the ninth impression of the second edition of 1925-7.
Of course, like Newton's Philosophia Naturalis Principia Mathematica it is now, because the subjects it initiated are today tremendously advanced, mostly of historical interest, however, for the philosophers at least, Russell's introduction still holds great philosophical interest and rigourous arguments helpful in the contemporary debate.
Russell's "Principia Mathematica", although written with the wrong "motivation"(that is: to reduce the whole of mathematics into axiomatic form, finding the "universal method"), achieved unquestionable logic-mathematical results: The most valuable and original, the "theory of descriptions".
www.mountainstatestech.com /mststore/item_0052106791XP.html   (1999 words)

 Principia Mathematica to *56 (Cambridge Mathematical Library)
An abridged text of Principia Mathematica, suitable for an introductory study of logic.
Much nonsense has been said on the subject of the importance of Principia Mathematica by people ignorant of the history of mathematics and logic.
Principia Mathematica together with Frege's Grundgesetze der Arithmetik is the book which gives birth to modern logic.
www.literacyconnections.com /0_0521626064.html   (683 words)

 Newton's Principia Mathematica — Burndy Library
Newton's Philosophiae Naturalis Principia Mathematica is generally esteemed his masterpiece.
The Principia was published during Newton's lifetime in three authorized editions: London, 1687; Cambridge, 1713; and London, 1726.
This copy of the Principia is especially noteworthy because of the corrections to the text, mostly made by Halley himself.
burndy.mit.edu /Collections/Babson/Online/Principia   (842 words)

 Principia Mathematica - Metaweb   (Site not responding. Last check: 2007-10-21)
The full name of Newton's 1687 work is Philosophiae Naturalis Principia Mathematica; it should not be confused with Russell and Whitehead's Principia Mathematica, published in 1910 - 1913.
It is in the Principia that Newton expressed his famous "Hypotheses non fingo" (I feign (to assert as if true) no hypotheses).
Newton first published these laws in Philosophiae Naturalis Principia Mathematica (1687) and used them to prove many results concerning the motion of physical objects.
www.metaweb.com /wiki/wiki.phtml?title=Principia_Mathematica   (1159 words)

 SUSAN STEBBING   (Site not responding. Last check: 2007-10-21)
If this view of Principia Mathematica be correct, then it is open to a criticism which is difficult to refute, and which is independent of any such defects as the assumption of the so-called Axiom of Reducibility.
Nowhere is Principia Mathematica is there any discussion of the nature and conditions of symbolism and its relation to mathematics.
This distinction may be regarded as a distinction between the construction of a symbolic system involving arbitrarily selected rules, or postulates, and the statement of rules of significance.
www.hist-analytic.org /susan_stebbing.htm   (1679 words)

 Overview of Principia Cybernetica
The Principia Cybernetica Project (PCP) is a collaborative, computer-supported attempt to develop a complete cybernetic and evolutionary philosophy.
Similar to the metamathematical character of Whitehead and Russell's "Principia Mathematica", PCP is metacybernetical: cybernetic tools and methods are used to analyze and develop cybernetic theory (see our methodology).
Principia Cybernetica: an Introduction, a view of PCP by an outsider, Koen Van Damme, including fragments of interviews with C. Joslyn and V. Turchin (1996)
pespmc1.vub.ac.be /NUTSHELL.html   (815 words)

 Amazon.com: Books: The Principia : Mathematical Principles of Natural Philosophy   (Site not responding. Last check: 2007-10-21)
Principia explains with great detail some elements of Eucledian geometry, Calculus, Fluid mechanics, Three laws of Gravity and The Method of the Universe.
Newton's Principia CONCEPTUALLY utilizes calculus, but the proofs themselves are Euclidean with the concept of "infinitisimally small" added to the equation.
Cohen even guides us step-by-step through some of the more important proofs in the Principia-- proofs that for the most part I followed, except for certain geometric assumptions that I had to assume were true.
www.amazon.com /exec/obidos/tg/detail/-/0520088174?v=glance   (1608 words)

 BBC - h2g2 - 'Principia Mathematica' by Bertrand Russell and Alfred North Whitehead - A337303
BBC - h2g2 - 'Principia Mathematica' by Bertrand Russell and Alfred North Whitehead - A337303
Principia Mathematica was written by English academics Bertrand Russell and Alfred North Whitehead, and first published in 1910.
It was not a bestseller, and while not recommended as light reading, it is notable as a possible model for the time travellers' manual of grammar mentioned in the Hitchhiker trilogy, which, you will recall, was blank after the initial chapters.
www.bbc.co.uk /dna/h2g2/alabaster/A337303   (366 words)

 Principia Mathematica: Whitehead and Russell
Their work, Principia Mathematica, filled three volumes, almost 2,000 pages, and appeared in the years 1910-1913.
Their approach was essentially that of Frege, to define mathematical entities, like numbers, in pure logic and then derive their fundamental properties.
The main innovation of Principia Mathematica was to introduce a stratification of Frege's formulas into types, and to use this to restrict which of Frege's formulas would be permitted in their logic.
www.math.uwaterloo.ca /~snburris/htdocs/scav/principia/principia.html   (661 words)

 Malaspina Great Books - Isaac Newton (1642)
Sir Isaac Newton, (December 25, 1642 - March 20, 1727), was an English philosopher, mathematician, and physician who published the Philosophiae Naturalis Principia Mathematica, more commonly referred to as the Principia, where he described the laws of gravity and, via his laws of motion, laid the ground work for the field of Classical Mechanics.
The Philosophiae naturalis principia mathematica (The Mathematical Principles of Natural Philosophy), also referred to as the Principia Mathematica or Principia, is a three-volume work on the foundations of classical mechanics, written by Isaac Newton and published in 1687.
Newton first gave his laws in the first volume of his Philosophiae Naturalis Principia Mathematica in 1687 and, using the mathematical tools of his newly developed calculus, proved many results concerning the motion of idealised particles.
www.malaspina.org /home.asp?topic=./search/details&lastpage=./search/results&ID=165   (1000 words)

 Citations: Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme - Godel (ResearchIndex)   (Site not responding. Last check: 2007-10-21)
In the face of an open conjecture we can try to prove it or try to refute it, but Godel has brought to our awareness a third possibility it may sometimes be the case that, in the framework of what we consider as acceptable....
From a more application oriented 4 Note that Q need not be well typed in context Gamma if some x i occurs free in Q. 8 view, meta level architectures have been used extensively in the realm of mechanical theorem proving [3, 2, 18, 20] since in many cases it is quite straightforward to....
While the purpose of these studies was merely to define the effectively computable functions by establishing what could possibly be computed in a mechanical way, the formulation still ended up having a profound influence on what was to be known as high level programming languages since few....
citeseer.ist.psu.edu /context/104647/0   (2210 words)

 [No title]
In connection with a recent discussion in sci.crypt, I obtained some seemingly radically different opinions or facts on the readability of Whitehead and Russell's Principia Mathematica, a book which I till the present have only heard talking about but never even actually seen.
To provide a comparison, it was not until proposition *110.643, on page 83 of the second volume of Principia Mathematica that Whitehead and Russell were able to prove that 1 + 1 = 2, let alone that 2 + 2 = 4.
Sales of Principia Mathematica have soared recently after it was voted one (number 23 to be exact) of the 100 greatest nonfiction books of the 20th century.
www.math.niu.edu /~rusin/known-math/01_incoming/PM   (848 words)

 Philosophiae Naturalis Principia Mathematica, page 2
Isaac Newton (1642-1727) is considered to be one of the most influential scientists to have ever lived.
The Principia combined the ideas of Copernicus, Galileo and Kepler into a single theory which explained the underlying universal laws of the cosmos in mathematical terms.
The Principia was first published in London in 1687.
www.slv.vic.gov.au /collections/treasures/newtonprincipia2.html   (247 words)

 Philosophiae Naturalis Principia Mathematica, a treasure of the State Library of Victoria
Commonly known as the Principia, it is considered to be one of the most important single works in the history of modern science.
In Principia, Sir Isaac Newton formulated the three laws of motion and the law of universal gravitation.
These laws enabled him to explain a range of phenomena, including the motion of planets, moons and comets within the solar system, the behaviour of Earth's tides, the precession of the equinoxes and the irregularities in the moon's orbit.
www.slv.vic.gov.au /collections/treasures/newtonprincipia1.html   (126 words)

 sciforums.com - Humanity as the Principia Mathematica-Inspired by Godel   (Site not responding. Last check: 2007-10-21)
The “Principia Mathematica’s” claims: that at no point do the meaningless symbols within its formalized system used to talk about mathematics either reference themselves or gain meaning.
However, some believe its in the treating of ethics as consistent the way the Principia Mathematica was treated as consistent before Godel mauled it that is responsible for our inventions of god or spirit or in the resorting to dogma to explain away the inconsistencies in order to keep functioning.
As Russell also noted of the Principia Mathematica, the chief problem was the construction of entities used in the definition or construction of themselves, what he referred to as a "vicious circle".
www.sciforums.com /showthread.php?t=43398   (12288 words)

 Newton, Descartes and the Role of Experiments in Principia Mathematica: Mechanics and Cosmology: IMSS   (Site not responding. Last check: 2007-10-21)
Traditionally, Principia Mathematica has been considered as a mathematical masterpiece, whereas Newtonian scholars interested in experiment have looked at the Opticks.
Some of the experiments in the Principia, such as the rotating bucket experiment or the one proving that gravitational and inertial mass are proportional, have been discussed in different contexts, but surprisingly we still lack an overall study of the role experiments play in Newton's masterpiece as a whole.
An overall look at the experiments in the Principia shows that Newton did not rely on them at the beginning of his investigations, but rather at a later stage in the midst of his extraordinary creative effort.
galileo.imss.firenze.it /news/mechcos/ebertoloni.html   (373 words)

 Principia Mathematica III
By a nice irony, that intellectual space was bought by the millions he made out of Mathematica, a computer program that makes complicated mathematics doable for ordinary mortals.
It turned out that the very fact that I could figure out how to build all the complexity of Mathematica from quite simple "primitives" was an important inspiration.
It could be as simple as a few lines of Mathematica code.
www.pivot.net /~jpierce/principia_mathematica_III.htm   (1793 words)

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