The great three-volume Principia Mathematica is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premisses and primitive ideas, and so to prove that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students (...) will wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part 1 (in which the logical properties of propositions, propositional functions, classes and relations are established); section 6 of Part 2 (dealing with unit classes and couples); and Appendices A and B (which give further developments of the argument on the theory of deduction and truth functions). (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This volume of Bertrand Russell's Collected Papers finds Russell focused on writing Principia Mathematica during 1905-08. The volume's 80-page introduction covers the evolution of his logic from 1896 until 1909, when volume I of Principia went to the printer.

Motus quidem veros corporum singulorum cognofcere , & ab apparentibus actu diícriminare, difficillimum est ; propterca quod partes ípatij illius immobilis in quo corpora vere moventur, non incurrunt in sensus.

Originally published in 1910, Principia Mathematica led to the development of mathematical logic and computers and thus to information sciences. It became a model for modern analytic philosophy and remains an important work. In the late 1960s the Bertrand Russell Archives at McMaster University in Canada obtained Russell's papers, letters and library. These archives contained the manuscripts for the new Introduction and three Appendices that Russell added to the second edition in 1925. Also included was another manuscript, 'The (...) Hierarchy of Propositions and Functions', which was divided up and re-used to create the final changes for the second edition. These documents provide fascinating insight, including Russell's attempts to work out the theorems in the flawed Appendix B, 'On Induction'. An extensive introduction describes the stages of the manuscript material on the way to print and analyzes the proposed changes in the context of the development of symbolic logic after 1910. (shrink)

This paper has the aim to provide a general view of the so called Jesuit Edition (hereafter JE) of Newton’s Philosophiae Naturalis Principia Mathematica (1739–1742). This edition was conceived to explain all Newton’s methods through an apparatus of notes and commentaries. Every Newton’s proposition is annotated. Because of this, the text – in four volumes – is one of the most important documents to understand Newton’s way of reasoning. This edition is well known, but systematic works on it (...) are still missing. We are going to fill this gap by means of a project exposed in the final remarks of this paper. In this paper we will: A) expound the way in which the notes and the additions to the JE were conceived by the commentators; B) provide some pieces of information about the commentators; C) summarize the most important of their notes; D) examine closely their notes as to a particularly important question: the so called "inverse problem of the central forces". (shrink)

Early in Principia Mathematica Russell presents an argument that "‘the author of Waverley’ means nothing", an argument that he calls a "definite proof". He generalizes it to claim that definite descriptions are incomplete symbols having meaning only in sentential context. This Principia "proof" went largely unnoticed until Russell reaffirmed a near-identical "proof" in his philosophical autobiography nearly 50 years later. The "proof" is important, not only because it grounds our understanding of incomplete symbols in the Principia (...) programme, but also because failure to understand it fully has been a source of much unjustified criticism of Russell to the effect that he was wedded to a naive theory of meaning and prone to carelessness and confusion in his philosophy of logic and language generally. In my paper, I (1) defend Russell’s "proof" against attacks from several sources over the last half century, (2) examine the implications of the "proof" for understanding Russell’s treatment of class symbols in Principia, and (3) see how the Principia notion of incomplete symbol was carried forward into Russell’s conception of philosophical analysis as it developed in his logical atomist period after 1910. (shrink)

First English translation of revolutionary paper that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.

On the occasion of the centenary of the publication of the first volume of Principia Mathematica, this article aims to shed some light on Whitehead’s philosophy of mathematics, to differentiate Whitehead’s version of logicism from Russell’s, and to show the unity of Whitehead’s thought. These aims rely on Whitehead’s basic insight that mathematics is the study of pattern.

Attempts have recently been made (Blackwell, 2011; Berumen, 2014) to catalogue the humour in Principia Mathematica, but so far overlooked has been a joke in the symbolism of PM itself.

I begin by asking whether there was a Fregean revolution in logic, and, if so, in what did it consist. I then ask whether, and if so, to what extent, Russell played a decisive role in carrying through the Fregean revolution, and, if so, how. A subsidiary question is whether it was primarily the influence of _The Principles of Mathematics_ or _Principia Mathematica_, or perhaps both, that stimulated and helped consummate the Fregean revolution. Finally, I examine cases in which logicians (...) sought, in the years immediately following publication of the _Principles_ and _Principia_, to integrate traditional logic into the Fregean paradigm, focusing on the case of Henry Bradford Smith. My proposed conclusion is that there were different means adopted for rewriting the syllogism, in terms of the logic of relations, in terms of the propositional calculus, or as formulas of the monadic predicate calculus. This suggests that the changes implemented as a result of the adoption of the Russello-Fregean conception of logic could more accurately be called by Grattan-Guinness’s term _convolution_, rather than _revolution_. (shrink)

As Alasdair Urquhart has noted, Bertrand Russell asserted that developing the theory of definite descriptions from 1905 was the first step towards solving the paradoxes that were finally resolved after 1908 in Principia Mathematica with the theory of types. I extend Urquhart’s suggestion that Russell was referring to the use of the notion of incomplete symbol in his solution to the paradoxes in his doomed theory “substitutional theory” of “Russellian propositions” in 1906. The Introduction to PM states that (...) expressions for propositions are incomplete symbols. This paper assesses the status of propositions in PM and connects the theory of types with the theory of descriptions. (shrink)

Bernard Linsky, The Evolution of Principia Mathematica; Bertrand Russell's Manuscripts and Notes for the Second Edition. Cambridge: Cambridge University Press. 2011. 407 pp. + two plates. $150.00/£...

To mark the centenary of the 1910 to 1913 publication of the monumental Principia Mathematica by Alfred N. Whitehead and Bertrand Russell, this collection of fifteen new essays by distinguished scholars considers the influence and history of PM over the last hundred years.

In an article in "mind," 1971, pp. 282-283, the authors raised objections to a certain definition in "principia mathematica." in this paper we demonstrate that (a) their argument is faulty, (b) their suggested remedies are unsatisfactory, and (c) there is nothing wrong with the original definition.

La decouverte par le Dr. E. A. Fellmann de l'exemplaire des Principia Mathematica de Newton ayant appartenu a Leibniz et contenant des notes marginales manuscrites (datant vraisemblablement de 1689), apporte un temoignage direct de la premiere reaction de Leibniz devant l'oeuvre du savant anglais. La presente edition met le document original entre les mains du lecteur, en l'accompagnant des notes et commentaires objectifs indispensables (en allemand et en francais). Le rapport de Leibniz a Newton a souvent ete envisage (...) dans le cadre de la facheuse querelle de priorite dans l'invention du calcul differentiel et integral. Or Leibniz, prenant connaissance des Principia, n'y voit pas un traite purement mathematique: refusant d'enteriner la scission entre la mecanique et les lois de la pensee, il se soucie avant tout d'etablir une fondation metaphysique pour la dynamique. Les Marginalia ont l'originalite de nous presenter, non pas un Leibniz adversaire ou rival, mais un Leibniz lecteur de Newton, dispose a tirer le meilleur parti d'un systeme qui aurait pu, a bien des egards, lui sembler etranger, comme le confirmera la systemisation ulterieure du concept de vis visa. (shrink)

Bertrand Russell presented three systems of propositional logic, one first in Principles of Mathematics, University Press, Cambridge, 1903 then in “The Theory of Implication”, Routledge, New York, London, pp. 14–61, 1906) and culminating with Principia Mathematica, Cambridge University Press, Cambridge, 1910. They are each based on different primitive connectives and axioms. This paper follows “Peirce’s Law” through those systems with the aim of understanding some of the notorious peculiarities of the 1910 system and so revealing some of the (...) early history of classical propositional logic. “Peirce’s Law” is a valid formula of elementary propositional logic: [ ⊃ p] ⊃ p This sentence is not even a theorem in the 1910 system although it is one of the axioms in 1903 and is proved as a theorem in 1906. Although it is not proved in 1910, the two lemmas from the proof in 1906 occur as theorems, and Peirce’s Law could have been derived from them in a two step proof. The history of Peirce’s Law in Russell’s systems helps to reconstruct some of the history of axiomatic systems of classical propositional logic. (shrink)

Here the concern is with the logic underlying Whitehead and Russell's Principia Mathematica and with the relation of that logic to Russell's underlying metaphysics. The author emphasizes the fact that work is, strictly speaking, a theory of propositional functions, not of classes; sentences containing symbols for classes are defined by means of propositional functions. It is terms of the latter sort of entity that Russell's Paradox must be solved; the theory of types is, strictly speaking, a theory of (...) the stratification of propositional functions. (shrink)