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Open archived version from archive - Logicomix: An Epic Search for Truth (with a connection in Frankfurt)

discovered the family secret that madness had taken his father s life and disabled his uncle So when he learned geometry constructed proof by proof upon common sense and reason BERTRAND embraced logic and science as tools to not only understand the world but to preserve his own sanity Bertrand Russell s Epic Search for Truth Russell studies mathematics at Cambridge University and proceeds to seek out the great minds of his time to find some articulation and validation of the basic tenets underlying mathematics Russell overcomes his shyness to engage the greatest professors of his time with his questions a thrill I remember well from studying the Sacks Theorem of recursion theory from Professor Sacks himself Russell s travels take him to Germany just 10 minutes before my Lufthansa pilot announces our imminent arrival in Frankfurt where I ll make my connection to San Francisco Russell s account of those days in Germany evokes that nation s unique capacity for both logic and madness There he meets his future best friend housemate and collaborator Alfred Whitehead who had created the first formal system for algebra He meets Gottlob Frege who had founded modern logic studies by introducing the concept of Boolean variables though eventually Frege becomes paranoid and as early as 1925 starts ranting about a Final Solution for the Jewish problem Finally RUSSELL meets Georg Cantor inventor of Set Theory who was already then losing his mind The interplay of logic and madness is a recurring theme of LogiComix as Russell struggles to stave off madness himself with only partial success as readers will learn Another recurring theme of the story is Russell s failures at love as he depends solely on logic to master courtship marriage and child rearing even as everyone around him succumbs to irrationality His memoirs humble and candid recount his nerdy fumbles followed by his inconsiderate prioritization of work over family That reminds me I ll use my layover in Frankfurt to call my family Today is the kids first day of school and they should know how proud I am As Russell strives to formalize the logic behind math he gravitates toward set theory until he himself has an epiphany now known as Russell s Paradox which can be simplified to this question Does the catalog of all books and book reviews that do NOT exhibit self reference include itself in the listing Either answer leads to a logic contradiction Russell s Paradox deflates everyone who has been working on Set Theory RUSSELL was surprised that Cantor himself takes the paradox as a sign from God As Russell embarks on his epic search for truth he continues to engage the greatest minds of the century but along the way he must navigate wars women enticing but difficult and the madness that often accompanies logical genius At one point he mentors the young Ludwig Wittgenstein the renowned philosopher and father of cognitive psychology Ultimately poor mental health ravages Wittgenstein s family and Wittgenstein

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Open archived version from archive - Is it time for Climate Change: the Comic?

showing a comics design studio at work in modern Athens while its team debate their differing views about their historical graphic novel Is it about character and emotion or the history of philosophy and mathematics Is it a tragedy about the failure of logicians to find a fundamental basis for mathematics or does it have a happy ending in the discoveries of Alan Turing and the birth of the digital era The comic s creators disagree So do readers Logicomix has a formidable and charming character at its heart Bertrand Russell who tells his own story in a speech in the US at the start of the second world war Looking back to his bizarre Victorian childhood Russell explains how he fell in love with the idea of truth a truth that must be established by reason alone and how this led him to undermine the theory of sets to attempt to remake mathematics in collaboration with AN Whitehead in their Principia Mathematica 1910 and how this in turn was demolished by Ludwig Wittgenstein and Karl Gödel The Berkeley mathematician on the Logicomix team complains in the book that there s hardly any maths in it but there is more than you would be likely to find in a literary novel about these characters It s as if having made the great populist gesture of working in the medium of comics graphic novelists feel free to bring in ideas without the timidity you see elsewhere today Comics as the last bastion of intellectual life Why not After all Logicomix is in a tradition of seriousness in this genre that goes back to Art Spiegelman s Maus So I wonder could a graphic novel do justice to the current controversy in climate science As leaked emails and errors embarrass the science

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Open archived version from archive - Holiday Wish List: Philosophy and Madness Illustrated

themselves and their debates with the authors about how say to illustrate the concept proof Such self reference is at the heart of the story from Russell s despair at the paradox that halted his effort to put mathematics on a rigorous footing to Kurt Gödel s incompleteness theorems nailing down that project s coffin Logicomix grippingly recounts the turmoil of the 20th century logical world As Russell searches for

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Open archived version from archive - Math, Philosophy, Comics and Bertrand Russell’s Search for Truth

goes beyond the comics audience to a general audience of readers Because of its dual release the book will have a significant first printing although Adams said the exact size of the printing has not been determined as yet Logicomix is a full color 336 page book 22 95 that also features a glossary of technical terms and prose annotations on all of the historical figures in the book There s a 10 city book tour that will focus on Universities in Boston Philadelphia Chicago Seattle and other towns and there s a website logicomix com that features media and background information on the writers the remarkable artist team of Papadatos and Di Donna as well as behind the scenes video on the making of the book Adams said Bloomsbury plans to make its first forays into the sometimes arcane world of comics conventions to promote the book and foreign rights have been sold to 9 countries among them France China Israel Holland and Turkey While the life of Bertrand Russell is the core narrative of Logicomix the book s focus is really on Russell s life work a passionate and ultimately futile attempt to establish a foundation for modern mathematics on clear and concretely stated logic Beginning in the early part of the 20 th century Russell and other prominent mathematicians sought to establish a set of rigorously conceived logical proofs that would eliminate the paradox and circular logic typical of mathematics of the era Logicomix is the story of that passionate search for philosophical truth and along the way documents both the efforts of Russell in particular the writing of his seminal book Principia Mathematica coauthored with Alfred North Whitehead and a long list of prominent turn of the century intellectuals who struggled with these questions in the pursuit of an unattainable intellectual dead certainty In fact Logicomix can be seen as a book about Russell s failure to achieve his goals even though his work laid the groundwork for mathematics and logic as we know them today While the book is the story of extremely smart men wrestling intellectually with profound abstractions Doxiadis Papadimitriou and the artists have managed to produce an exuberant historical yarn filled with antic portrayals of an impressive list historical figures men who either influenced Russell s thinking or argued passionately with him over their own conclusions and differences Indeed Logicomix ruminates on such figures as the ancient Greek playwright Aeschylus and offers lively portrayals of the likes of such early 20th century intellectual figures as David Hilbert Kurt Godel Alfred North Whitehead and Ludwig Wittgenstein But besides all that Logicomix is an accessible general primer on basic mathematics reason and logic that will engage ordinary readers while it skillfully shows the connections between Russell s own search for intellectual certainty and the great moral questions of our time Not a bad day s work for a comic book Although written in collaboration with Papadimitriou a professor of computer science Doxiadis is the

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Open archived version from archive - Christos at the Harvard Book Store

Harvard Book Store Wednesday 16 December 2009 09 44 See Christos s Oct 28th presentation followed by a conversation with Harry Lewis former dean of Harvard and computer scientist on iTunes U free of charge Click here to visit iTunes

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Open archived version from archive - Financial Times Review

logically rigorous good for all time foundation for mathematics Ludwig Wittgenstein the austere Austrian who argued that Russell s project was misconceived Kurt Gödel Wittgenstein s compatriot who proved that it was and assorted other pin ups of higher mathematics Cantor Poincaré Hilbert This sounds as if it could be terribly dry the quest for mathematical foundations is an abstruse one far removed from mankind s more pressing concerns But an intellectual passion is still a passion and writers Doxiadis and Papadimitriou succeed in bringing out the humanity in their story Logicomix exposes the roots of Russell s need for certainty a troubled childhood what else and tracks the collateral damage it caused in his and his loved ones lives The book is a visual treat as well thanks to Alecos Papadatos and Annie di Donna s crisp richly coloured drawings The story is told by Russell himself in the course of a lecture on the role of logic in human affairs delivered at a US university just after the outbreak of the second world war A group of demonstrators demanding that the US stay out of the conflict want Russell jailed for his pacifist beliefs in the first world war to support their stance Russell acknowledges their concern but points out that they must be guided by reason and to explain what this is he embarks on the intellectual autobiography that is the book s core It s a yarn as rich in dark family secrets forbidden love and lurking madness as a teenage vampire soap At the same time it gives due weight to the horrors of 20th century Europe and while mercifully free of equations cleaves to the essential intellectual drama Not that that tale is lacking in gothically outré details we learn for example that it

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Open archived version from archive - LOGICOMIX - About Logicomix

The basic claim of the school in the philosophy of mathematics known as logicism the school founded by Frege of which Bertrand Russell was one of the primary exponents was that all of mathematics can be reduced to logic or in other words that mathematics is essentially a branch of logic After the years of the foundational quest however and especially after Gödel s results logic became a well developed diversified field in the interface between philosophy and mathematics Bertrand Russell Greek Exercises March 9 1888 I read an article in the Nineteenth Century today about genius and madness I was much interested by it Some few of the characteristics mentioned as denoting genius while showing a tendency to madness I believe I can discern in myself Such are sexual passion which I have lately had great difficulty in resisting and a tinge of melancholy which I have often had lately and which makes me anxious to go to this tutor s as there I shall probably be too much occupied to indulge such thoughts Also he mentions a desire to commit suicide which though hitherto very slight has lately been present more or less with me in particular when up a tree I should say it is quite possible I may develop more or less peculiarity if I am kept at home much longer The melancholy in me is I think chiefly caused by the reserve which prompted the writing of this and which is necessary owing to my opinions Notebook Logicomix Written by Aeschylus and first performed in the theatre of Dionysus in Athens two years before the poet s death in 458 BCE it is the only extant trilogy of Greek dramas although the satirical play Proteus intended to be performed after the trilogy is missing In the trilogy s first play the Agamemnon the eponymous hero and leader of the Greek forces in Troy returns a victor to his hometown of Argos with the captive prophetess Cassandra Though his wife Clytemnestra at first appears to rejoice at his return she has other plans She and her lover Agamemnon s cousin Aegisthus murder Agamemnon and become the new sovereigns of Argos In the Libation Bearers the second play the chorus of women accompanies Agamemnon s daughter Electra to her father s tomb The forlorn Electra is hoping for revenge which she can only carry out with the help of her brother Orestes who is in exile When Orestes clandestinely returns to Argos he and Electra plan and execute the murder of Aegisthus and then in a highly dramatic scene in which Clytemnestra bares her breasts before his naked sword Orestes also kills her his own mother The third play the Eumenides or beneficent ones is one of the most unusual in the history of drama all its speaking parts apart from that of Orestes himself are taken up by gods or other supernatural entities The chorus consists of the Erinyes or Furies archaic goddesses of revenge who chase Orestes from the temple at Delphi where he has been ritually purified by the god Apollo to Athens In a totally unprecedented move for a god anyway Athena the patron god of Athens decides to let the citizens of Athens judge Orestes case thus giving a mythological origin story for the democratic innovation of a court of law with citizen jury Bertrand Russell Autobiography Routledge 2000 p 239 On the morning of August 4th I walked with Ottoline up and down the empty streets behind the British Museum where now there are University buildings We discussed the future in gloomy terms When we spoke to others of the evils we foresaw they thought us mad Yet it turned out that we were twittering optimists compared to the truth The first days of the War were to me utterly amazing My best friends such as the Whiteheads were savagely warlike I was living at the highest possible emotional tension Although I did not foresee anything like the full disaster of the War I foresaw a great deal more than most people did The prospect filled me with horror but what filled me with even more horror was the fact that the anticipation of carnage was delightful to something like ninety percent of the population I had to revise my views on human nature At that time I was wholly ignorant of psycho analysis but I arrived for myself at a view of human passions not unlike that of the psycho analysts I arrived at this view in an endeavor to understand popular feelings about the War I had supposed until that time that it was quite common for parents to love their children but the War persuaded me that it is a rare exception I had supposed that most people liked money better than almost anything else but I discovered that they liked destruction even better Thomas Kuhn The Road Since Structure Revolutionary changes involve discoveries that cannot be accommodated within the concepts in use before they were made In order to make or to assimilate such a discovery one must alter the way one thinks about and describes some range of natural phenomena The discovery in cases like these invention may be a better word of Newton s second law of motion is of this sort The concepts of force and mass deployed in that law differed from those in use before the law was introduced and the law itself was essential to their definition A second fuller but more simplistic example is provided by the transition from Ptolomaic to Copernican astronomy Before it occurred the sun and moon were planets the earth was not After it the earth was a planet like Mars and Jupiter the sun was a star and the moon was a new sort of body a satellite Changes of that sort were not simply corrections of individual mistakes embedded in the Ptolemaic system Like the transition to Newton s laws of motion they involved not only changes in laws of nature but also changes in the criteria by which some terms in those laws attached to nature These criteria furthermore were in part dependent upon the theory with which they were introduced Notebook Logicomix The great British mathematician Alan Turing is generally considered to be the father of computer science Turing contributed to many areas of mathematics but is mostly remembered for one of his earliest results in logic His ingenious definition of an algorithm in terms of a theoretical machine with a central control and a tape for memory input and output anticipated in important ways the digital computer and has had since then an enormous influence on computational practice and thought Turing machines as they are now called share with today s computers the key property of universality in that a machine can carry out any computational task provided it is supplied with an appropriate program for it The work of Turing as well as that of the others mentioned on algorithms and methods for the general solvability of problems is an obvious outgrowth of the foundational quest and thus in a sense its culmination During World War II Turing presided over the design and construction of two series of electronic computers the Bombe and the Colossus These were used successfully and crucially for the war effort for breaking several German cryptographic codes including the notoriously hard Enigma of the German navy After the war Turing worked in the fledgling British computer industry did important work in biology and founded the field of artificial intelligence by proposing what became known as the Turing test a method for determining whether an artifact can think In 1952 he was prosecuted on account of his homosexuality then a punishable offense in Britain As an alternative to a jail sentence he agreed to undergo an experimental treatment with estrogens which probably caused the severe depression which led him to take his own life in 1954 Notebook Logicomix Often used synonymously with predicate logic and first order logic the predicate calculus is Frege s extension of the propositional logic developed by Boole In the predicate calculus elementary propositions or predicates are composite objects of the form P a b c where P is a symbol in the language and a b c etc are constants or variables For example if older is a propositional symbol Plato is a constant and x is a variable then older Plato x is a well formed proposition describing that Plato is older than x Propositions of this type can then be combined by Boole s connectives and or not and implies and prefixed by Frege s quantifiers such as for all x written and there exists y written Thus there exists x older x Plato means that there is at least one individual who is older than Plato Evidently this is a much more ambitious attempt at creating Leibniz s calculus ratiocinator than Boole s simpler formal logic By employing symbols from various fields of mathematics such as x y x y y or x y y 1 Whether a sentence in the predicate calculus first or second order is true or false depends on the model whereby the sentence is interpreted Thus for example the simple arithmetical theorem given above is true of the whole numbers in the ordinary interpretation of but becomes false if we interpret the symbol as multiplication However some sentences called valid are true independently of interpretation because they embody basic properties of Boolean connectives and quantifiers Kurt Gödel s Completeness Theorem provides a simple complete axiomatic system for proving validity in first order logic Notebook Logicomix The extremely influential but highly controversial essentially unfinished work in which Alfred North Whitehead and Bertrand Russell attempted to rescue Frege s grand project to create foundations of mathematics built on logic in the wake of the crisis brought on by Russell s Paradox The title Principia Mathematica i e Principles of Mathematics in itself provoked controversy as it is the exact same as that of Newton s greatest work many in the British mathematical community thought this choice to be in bad taste if not actually blasphemous The three volumes of the Principia published in 1910 1912 and 1913 were based on a developed version of Russell s theory of types the so called ramified which imposed a hierarchical structure on the objects of set theory This could not be made to yield the required results however without the addition of what Russell called an axiom of reducibility which eventually became one of the main reasons for negative criticism of the whole work Logicians found this axiom extremely counter intuitive a far fetched and basically artificial method to sweep the very problem it was trying to solve under the rug Despite the fact that the Principia fell short of its authors immense ambition it had a huge influence on the shaping of modern logic its greatest effect possibly being the inspiration and context it provided Kurt Gödel for his groundbreaking discovery the Incompleteness Theorem Notebook Logicomix The process of arriving at the logical verification of a mathematical or logical statement starting from a set of agreed upon first principles these could be either axioms or already proven statements deriving from these axioms and proceeding by totally unambiguous and unabridged logical steps or rules of inference The demonstrations of geometric propositions in Euclid s Elements were considered for over two millennia to set the standard of excellence to which mathematical proof should aspire Yet towards the end of the 19th century his method came under logical and philosophical scrutiny and was found to lack principally in two directions a in its sense of the logical obviousness of the axioms and b in its logical gaps where intuition which in Euclid s case was mostly visual geometric took over from strict application of a formal system of rules In a sense Frege s and Russell and Whitehead s logicist project was developed as a reaction to the imperfections found in Euclid s proofs as well as all those developed in his wake The logicists as well as the formalists working on the foundations of mathematics aimed at a fully developed theory and practice of rigorous proof by which arithmetic as the basis of all mathematics would begin from a small number of consistent axioms and eventually lead via proof to the full range of truth Notebook Logicomix Discovered in 1901 as Russell was working on his first book on the foundations of mathematics the Principles of Mathematics published in 1903 the Paradox in the form originally expressed shows an essential flaw in Cantor s set theory developed from Bolzano s simple concept of a collection of elements with a common property By the generality of this definition which Frege extended to the realm of logic one can speak of a sets of sets and thus eventually of the set of all sets Of the elements of this all encompassing set one defines the property of self inclusiveness i e of a set containing itself as an element Thus for example the set of all sets is a set and thus contained in itself as is the set of all entries in a list it can appear as an entry in a list but the set of all numbers is not a number and thus not contained in itself By virtue of this property we can define the set of all sets which don t contain themselves and ask with the young Russell the question Does this set contain itself or not See what happens if it does contain itself it follows that it is one of the sets which don t contain themselves as this is the property that characterizes elements of this set and thus cannot contain itself But if it doesn t contain itself then it does not have the property of not containing itself and thus does contain itself This situation in which assuming something implies its negation and vice versa is called a paradox When a paradox such as Russell s arises in a theory it is a sign that one of its basic premises definitions or axioms is faulty Notebook Logicomix Literally the quality of a statement of referring to itself However it is also used more generally in logic to characterize statements which include themselves within their scope of reference as in the barber story used to explain Russell s Paradox The barber lives in a town wherein a law decrees that all residents of the town must either shave themselves or be shaved by the barber This law is self referential as the barber apart from being the barber referred to is also one of the residents of the town Self reference has played a seminal role in logic and mathematics already from the time of the Greeks From Euboulides self referential statements to Gödel In fact Gödel proved his Incompleteness Theorem by creating in the context of modern logic a statement that is quite similar in spirit to that of Euboulides with one crucial difference while Euboulides states this statement is false Gödel s ingenious variant essentially says in the language of arithmetic this statement is unprovable Any consistent axiomatic theory in which one can formulate such a statement must be necessarily incomplete for either this statement is false in which case it is both false and provable contradicting the consistency of the axiomatic system or true in which case it is both true and unprovable establishing its incompleteness Notebook Logicomix The study of collections of objects united by a common property in some cases this property can be nothing more than the fact that they are defined to be members of the same set as for example in the arbitrarily defined set whose elements are the numbers 2 3 8 134 579 Sets were first studied by the Czech mathematician Bernard Bolzano 1781 1848 who also introduced the term Menge set and defined the notion of a set s cardinality i e of its size in a way not directly involving measurement The advanced mathematical discipline of set theory was arguably born on December 7 1873 when Georg Cantor wrote to his teacher Richard Dedekind describing his proof of the non denumerability of the real numbers the set of the whole numbers decimals zero and the negative numbers as opposed to the denumerability of the rationals all fractions which Cantor also proved denumerability is defined as a one to one correspondence with the natural numbers 1 2 3 etc The concept of a set is almost too primitive to merit a mathematical definition and is practically impossible to define informally without the use of some synonym here we used the word collection It is precisely this naturalness of the concept in Bolzano s and Cantor s work that led to Russell s Paradox To overcome it and to rule out the flawed concept of the set of all sets it allowed for one has to come up with bottom up constructions and axioms for sets as in the Principia Mathematica and later the system called ZFC from the names of its two creators Ernst Zermelo and Abraham Fraenkel and the Axiom of Choice a necessary additional axiom that allows the theory to deal with infinite sets Set theory is considered by some the most basic branch of mathematics as all others can be defined in terms of it This was the gist of an over ambitious project undertaken from the 1930s onwards by the group of brilliant French mathematicians writing under the pen name of Nicolas Bourbaki Notebook Logicomix Ludwig Wittgenstein wrote his seminal philosophical work during WWI building on his pre war notebooks and ideas on logic It contains his solution of in his own words all the problems of philosophy dealing with the world representation and language Originally called Logische Philosophische Abhandlung Logical Philosophical Treatise it was renamed for

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Open archived version from archive