Russell and Leibniz: 1900-1959

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Russell and Leibniz 1900 1959David Blitz Dept of Philosophy presented to the online Annual Meeting of theBertrand Russell Society June 20 2020 The following is a slide based presentation of a survey of Russell s use of Leibniz from his monograph A Critical.
Exposition of the Philosophy of Leibniz of 1900 to the final statement of his philosophy in 1959 in MyPhilosophical Development The last several slides have audio recordings of the quotes included in the presentation extracted fromRussell s 1957 BBC talk The World and the Observer the basis for the chapter My Present View of the This is an effort in progress criticisms are welcome in fact desired and required .
Russell and Leibniz 1900 1959Russell s third book was A Critical Exposition of the Philosophy of Leibniz 1900 his first fully philosophical book and his only intensivestudy of a single philosopher Previous work were in politics German Social Democracy 1896 and mathematics An Essay on theFoundations of Geometry 1897 though of course these had significant philosophical aspects As is well known Russell wrote the volume of Leibniz due to his replacing McTaggart for a course of lectures on the German philosopher.
at Trinity College Cambridge which McTaggart was unable to give because he was on leave to travel to New Zealand to be with hisgirlfriend wife to be But despite this contingent and unplanned event it focused Russell on a philosopher who would have a significantinfluence on his own philosophy both negative in terms of critique and positive in terms of suggestion in the years to come Russell s 1900 critique of Leibniz focused on this latter s use of the old subject predicate logic as a basis for his metaphysics Note Russell s Leibniz Notebook along with G E Moore s Notes on Russell s Leibniz Lectures as well as additional contemporaneous material.
were published in Russell The Journal of Bertrand Russell Studies vol 37 no 1 Summer 2017 This previsages Russell s subsequent recognition in the year of its publication of the need to include relations as well as properties asthe referents of predicates vastly enlarging the scope of logic and changing its foundations leading on to predicate logic in the form weknow today Moreover Russell adopted a Leibnizian strategy to develop his own metaphysics of logical atomism 1910s based on thenew logic he had co invented with Whitehead Principia Mathematica 1910 1913 .
But Russell was not finished with Leibniz and he returned to this latter on a number of occasions including 1937 for a new introduction to a second printing of Critical Exposition written a decade after additional previously unpublishedmaterial of Leibniz became available through the efforts of Louis Couturat and the publication of Russell and Whitehead s PrincipiaMathematica 1st edition 1910 13 2nd edition 1925 27 1945 for a chapter in History of Western Philosophy one of the first such histories to use the term western philosophy in its title given.
Russell s 1920 visit to China where he learned that their was a distinct Chinese philosophy which he appreciated but was not in aposition to include 1954 in Human Society in Ethics and Politics where Russell explicitly borrows Leibniz s concept of compossibility a term seldom usedelsewhere or by others as the logical basis for Russell s own version of a utilitarian type of ethics and1959 in the first chapter of My Philosophical Development originally given as a BBC talk and published as an article two years previously .
where Russell in his concluding philosophical statement references Leibnizian monads for his own analysis of the relation between thepublic and the private in epistemology and metaphysics Russell s 1900 critiqueAs is well known Russell summarized some would say simplified Leibniz s system in five points arguing that one of themcontradicted the others The five points were .
Russell has proceeded to distill what he considers as thebasic premises of Leibniz s system based largely on hispublished writings presenting them as an set of axioms Note that the first principle premiss or axiom is that everyproposition has a subject just one and a predicate just.
one This is the basis for the major aspect of Russell scritique that Leibniz cannot as a result account for whatRussell will term external relations and has to resort to theartifice of pre established harmony instead The reader familiar with Leibniz will no doubt be surprised.
that Russell does not mention either God or possible worldsin his listing of premises but these apparently follow fromthe axioms or are irrelevant to the issue of determining ametaphysics based solely on logic and independent ofAs for possible worlds Russell is unimpressed with this.
concept which appears to him as an extravagance ultimatelylinked to the concept of God and ruled out by Occam s razor which always appealed to Russell based on the idea thatthe smallest possible set of premises parsimony should beadopted from which a substantial set of conclusions can be.
drawn comprehensiveness Russell on Leibniz on external relationsI will rapidly far too rapidly for an extended paper but sufficient for the purposes of this presentation look at Russell s 1900 critiqueof Leibniz with respect to external relations based on the postulate of the subject predicate nature of propositions leaving asidevarious other issues related to propositions eg unity of composition relation to truth beliefs and facts Russell notes That all sound.
philosophy should begin with an analysis of propositions is a truth too evident perhaps to demand proof p 8 This is a break withtraditional metaphysics eg that of Descartes or Hegel which begin with the idea capitalized and ultimately in its absolute form as Godfor the latter or Spinoza for whom substance ultimately God is fundamental Note the use of the term analysis a methodologicalcenter of all of Russell s philosophical variants Russell states of Leibniz s underlying logic that Every proposition is ultimately reducible to one which attributes a predicate to a subject .
In any such proposition unless existence be the predicate in question the predicate is somehow contained in the subject The subject isdefined by its predicates and would be a different subject if these were different Thus every true judgment of subject and predicate isanalytic ie the predicate forms part of the notion of the subject unless actual existence is asserted p 9 The existence of things with the exception of the existence of God are synthetic and contingent That something exists is due to the action of God in decreeingthe best of all possible worlds for whom alone the existence of that thing and every other thing is necessary .
Secondly what appears to be the freely chosen activity of an individual is in reality just the unrolling of the predicates packed into thesubject according to God s pre established harmony in a temporal sequence which is real only to our finite minds but alreadyconceived in advance by God Additionally though individual existents may appear to be contigent they are necessary in the sense thatGod has chosen or perhaps created them as part of the one and only best world Moreover it follows that external relations between and among things are fictitious at best creations of our minds and not part of.
Reality An apparent relation such as on as in the book is on the table is really the result of two separate properties predicates ofthe book and the table eg the book had the predicate on the table at time t The appearance of their being externally orcontingently related was predetermined by God at the beginning of time in fact each is just doing its own thing including being inmy hand at one moment on the table at another and then being returned to a bookshelf So activity and relations are all merelyappearances generated by our finite minds while what is real is the necessary existence of God and the best of all possible worlds.
created by him with a pre established harmony that mimics activity and relations along with their associated time and space All thiscontradicts the common sense empiricism which Russell shared with Moore and to a large extent derived from Hume and moreover the importance of relations which he had studied in mathematics for example in the form of functions of two and more variables Russell on Leibniz 1937 a existence and compatibilityRussell returned to Leibniz when his book was reissued in 1937 as a new edition the result of a new introduction where Russell updated.
his arguments and conclusions based on two items the publication of additional archival material by Leibniz and his own development oflogicism as a philosophy of mathematics The first is due to the work of Louis Couturat who will play an important role in another aspect ofRussell s life and work his pacifism In 1901 Couturat published his Logique de Leibniz d apr s des documents in dits Leibniz s Logic basedon unpublished documents and his further 1903 Opuscules et Fragments In dits de Leibniz Extraits des manuscrits de la Biblioth que royalede Hanovre which Russell saw as confirming to a large extent his own views .
Note Russell was in contact with Louis Couturat beginning in 1897 with Couturat writing Russell to thank him for Russell s review of his Couturat s book on mathematical infinity De L infini math matique 1897 As their correspondence continued Couturat invited Russell toa 1900 international conference on philosophy at which time Russell met Peano and became aware of Frege s work essential material thatset Russell on the path of his Principles of Mathematics 1903 and ultimately with Whitehead Principia Mathematica 1910 13 Couturatinfluenced Russell in a second way in a debate by further correspondence Couturat successfully challenged Russell s pro imperialist stance.
concerning the ongoing Boer War in South Africa 1899 1902 moving Russell to a pacifist position with some exceptions as explained inRussell s subsequent notion of non absolute pacifism and his support for WWII after opposition and jail because of his opposition toRussell in 1937 depicted Leibniz as a dual individual with a public philosophy designed for acceptance and a private one for innovation Speaking of this general duality Russell said H e had a good philosophy which after Arnauld s criticisms he kept to himself and a badphilosophy which he published with a view to fame and money p vi And I think as he grew older he forgot the good philosophy which he.
kept to himself and remembered only the vulgarized version by which he won the admiration of Princes and even more of Princesses Partof the good philosophy remains despite the inherent limitations of the subject predicate logic of propositions the fact that Leibniz based hismetaphysics on logic And in particular Russell in the newly published material found a second different view on the existence of things notdependent on the goodness of God pre established harmony or the best of all possible worlds Russell quotes translated from Leibniz s Latin I say therefore that the existent is the being which is compatible with most things or the.
most possible being so that all coexistent things are equally possible And Russell notes an important consequence of this definition nomore need for a divine being For if it was so intended there was no act of Creation the relations of essences are among eternal truths and it is a problem of pure logic to construct that world which contains the greatest number of coexisting essences This world it wouldfollow exists by definition without the need of any Divine Decree though Russell also notes that if God is to persist these essenceswould have to reside in God s mind which Russell deems a reversion to Spinoza .
Russell on Leibniz 1937 b corrections on monads andmathematicsRussell does have two corrections to make to his first edition in the new introduction one concerning monads the other concerningmathematics In the 1900 version Russell had assumed that not all monads could have organic bodies if the number of monads wasfinite since subordinate monads would eventually run out But in the Opuscules Leibniz states that the number of monads in his.
system is to be infinite and Russell comes up with an arithmetical scheme representing Leibniz s view of the world as follows Each monad is assigned a proper fraction m in lowest terms a b and at each time t the state of a monad is represented by a functionf t the same for all monads This equality is introduced to produce a correspondence at any time t between any two monads andbetween any monad and the universe as a whole Thereby each monad mirrors the world but limited by its identifying fraction m which is said to measure the intelligence of the monad presumably the closer the fraction to 1 the smarter the monad .
To satisfy the additional Leibnizian consideration of an infinity of monads Russell suggests that this could be modelled by associatingRussell and Leibniz: 1900-1959. Russell’s third book was A Critical Exposition of the Philosophy of Leibniz (1900), his first fully philosophical book, and his only intensive study of a single philosopher.Previous work were in politics (German Social Democracy, 1896) and mathematics (An Essay on the Foundations of Geometry, 1897), though of course these had significant philosophical aspects.

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