Logic matters 2.5

Logic Matters Notable Thinkers Images and Quotations Prof. Dave Marans, St. Thomas University, Miami, Florida My off-campus address: davidjan43 the ‘at’ symbol aol one dot com Gottlob Frege, Chrysippus, George Boole, Jonas Salk, Marcus Aurelius, William Hamilton, Proclus Diadochus, Charlie Chan, Alfred North Whitehead, Aristotle, Alonzo Church, Averroes, Berthand Russell, Oliver Heaviside, Ludwig Wittgenstein, Moses Maimonides, Henri Poincaré, Thomas Aquinas, Francis Hutcheson, Andrew Carnegie, Roger Bacon, Michel de Montaigne, Hans Reichenbach, Tim Williamson, Emanuel Kant, Isaac Watts, Franz Kafka, Francis Bacon, Gregor Cantor, Pierre Boutroux, Blaize Pascal, Antoine Arnauld, John Locke, Saul Kripke, Gottfried Leibniz, JohnVenn, William Gladstone, Claude Bernard, Augustas De Morgan, Charles Dodgson, Ada Lovelace, John Stuart Mill, William of Ockham, Sherlock Holmes, Hermann Weyl, Alfred Tarski, John of Salisbury, Wilhelm Hegel, William Wills

In correct logic, certain things are supposed, and something else results of necessity. Aristotle 4th Century BC Greek Beyond doubt, the most influential logician and encyclopedic mind, ever. Aristotle’s Logic, the Organon, was unchallenged for over 2000 years: Categories On Interpretation Prior Analytics Posterior Analytics Topics On Sophistical Refutations Even today Aristotle is widely considered the starting point in the study of Logic. Treatises on physics, zoology, ethics, astronomy, psychology, metaphysics,,,,more. Famed ruler and conqueror Aleaxander The Great was Aristotle’s student Was at Plato’s Academy for 20 years, becoming Plato’s assumed successor. But he left Athens when Plato chose Speusippus as the next head of the Academy. http://www.linkedin.com/answers/professional-development/professional-networking/PRO_PNT/650090-8012904

To follow the scent of an animal, the hunting dog uses this logic: “The animal went either by this road, or by that, or by the other: but it did not go by this nor that, thus it went the other way.” Chrysippus 3rd Century BC Greek Head of the Stoic Academy in Athens. Wrote over 700 works, none of which survived past 200 AD. Only fragments and secondary sources remain. Work encompassed Logic, Nature, Theology, and much more. Argued that logic pervades all of Nature. His five postulates of logic: 1. If the first, then the second. The first. Therefore, the second. Modus Ponens 2. If the first, then the second. Not the second. Therefore, not the first. Modus Tolens 3. Not both the first and the second. The first. Therefore, not the second. Incompatible Argument 4. Either the first or the second. The first. Therefore, not the second. Strong Disjunctive Argument 5. Either the first or the second. Not the first. Therefore, the second. General Disjunctive Argument His logic insights stayed virtually unknown for 2,000 years, then revived and highly prized since the year 1880. In debate, would often be the only speaker and argue both sides of the question. Said to have died in a fit of laughter after drinking wine and watching a donkey eating figs. http://phoenicia.org/chrysippus.html

To fly from logic is to be a true fugitive. Marcus Aurelius 2nd Century AD Emperor of Rome His Meditations espouses kindness, charity, virtue, and moderation. His wife, however, was notoriously unfaithful and extravagant. http://www.kirjasto.sci.fi/aurelius.htm

This, therefore, is Logic: She reminds you of the invisible form of the soul; She gives light to her own discoveries; She awakens the mind and purifies the intellect; She brings light to our intrinsic ideas; She abolishes oblivion and ignorance which are ours by birth. Proclus Diadochus 5th Century AD Byzantium: Constantinople, Alexandria, Athens Scholar, mathematician, commentator. Preserved and transmitted texts from ancient Greece. Commentary on Euclid Astronomy Book of Causes Elements of Theology Elements of Physics Platonic Theology Student, teacher, and then head of the Academy founded by Plato. Composed hymns for the polytheistic religion of the time. A life-long vegetarian, and extremely self-disciplined. http://www.kheper.net/topics/Neoplatonism/Proclus.htm

There is no other way to learn the truth than through Logic. Averroes 12 th Century Cordoba and the Mediterranean A prolific scholar. Largely credited with transmitting the wisdom of ancient Greece to Western Europe. Incoherence of the Incoherence – an important step in the revival of leaning. Major commentaries on Aristotle’s Logic, Physics, Zoology, Ethics, Astronomy, Pyschology, Meteorology, Intellect, and more. A devout Islam theologian, dedicated to reconciling Faith and Reason Also a judge and a physician for most of his life. http://www.fordham.edu/halsall/source/arab-y67s11.html

Science can proceed only by correct forms of logic. So to not embrace logic is to never find truth. But by itself, logic is practically useless. John of Salisbury 12th Century English, Anglo-Saxon Philosopher, historian, churchman, diplomat, and scholar. Defender of Thomas à Becket both before and after his murder. Metalogicon First complete presentation of Aristotle’s Organon in Western Europe. An eloquent statement of Logic’s place in learning. His large personal library provides an illuminating depiction of the medieval culture. http://www.bartleby.com/211/1002.html

Consequently one who wishes to attain to human perfection must thus first study Logic. Moses Maimonides 12th Century Moorish Spanish and North African Philosopher, Historian, Logician, Jewish Theologian, Physician, Rabbi Guide to the Perplexed seeks to reconcile science, philosophy, and religion and urges a rational approach to Judaism. Lived mostly in Egypt and was physician/advisor to Moslem royal families. http://plato.stanford.edu/entries/maimonides/

Logic draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, except through experience. Roger Bacon 13th Century English Franciscan friar and lecturer at Oxford and Paris. Ostracized by university and church hierarchy. Forced into life as an independent scholar. Then given full permission to write and publish by Pope Clement IV. Produced enormous volumes. Comprehensive Logic Comprehensive Reason and Dialogue Major Work Minor Work Experimented in Optics and other sciences. Stressed that all the sciences depend on mathematics. Accused of and imprisoned for promoting demonic ideas. Released only to die in obscurity. http://plato.stanford.edu/entries/roger-bacon/

Logic is the beginning of wisdom. Thomas Aquinas 13th Century Italian Summa Theologica Summa Contra Gentiles Greatest Catholic Theologian, Canonized the “The Angelic Doctor” His family was appalled at the prospect of his becoming a Dominican monk. So they sent an impure woman to tempt him. She was unsuccessful, so we are told. http://plato.stanford.edu/entries/aquinas/

One who is learns the principles of logic and then carefully studies other sciences, will thereby develop even greater in the art of logic. William of Ockham 14th Century English A Franciscan Friar Among the most highly regarded scholars of the late middle ages. Best known for Ockham’s Razor: “For explanation, use no more hypotheses than necessary.” Argues that Logical Forms are simply human abstraction and have no reality in themselves. His theological views were considered heretical. Papal authority confined him in a monastary. Spent much of his adult life in France and Germany, seeking freedom to think and write. Often forced to live in hiding. Was then excommunicated and forced to live in hiding. http://www.bbc.co.uk/programmes/b007m0w4

Those who establish argument by noise and command show that their reason is weak. Michel de Montaigne 16th Century French Statesman, advisor, and writer. Essays: remarkable observations and comments on human nature still reads well today. For example, “The best marriage is a blind woman and a deaf man.” http://plato.stanford.edu/entries/montaigne/

With logic, judgment, and invention, a person may do great matters. Francis Bacon 17th Century English Essayist, Jurist, Scientist, Statesman. The New Science Utopia The Advancement of Learning Bacon argues that empirical knowledge requires more logic than just Aristotle. Died of pneumonia after trying to freeze a chicken. http://oregonstate.edu/instruct/phl302/philosophers/bacon.html

Logic, being the rules for all the operations of the mind, exists for the very purpose of being an instrument which is of service to us. Antoine Arnauld 17th Century French Port-Royal Logic, The Art of Thinking (with Pierre Nicole) The recognized model statement of Aristotle's logic for more than two centuries. But accepted the new “scientific” materialism in opposition to both Aristotle and Aquinas. Entire life embroiled the religious and social turmoil of the times. Removed from the University of Paris because of his theology. First condemned, then restored, re-condemned, and re-restored by successive Popes. His works total 40 large volumes. Was the youngest of twenty children http://oregonstate.edu/instruct/phl302/philosophers/arnauld.html

The best defense against logic is ignorance. Blaise Pascal 17th Century French Mathematician, physicist, and religious philosopher. Thoughts On the Art of Persuasion The Provincial Letters Treatise on the Arithmetical Triangle On the Geometrical Mind Devised an adding machine Wore a death mask at his funeral. http://oregonstate.edu/instruct/phl302/philosophers/pascal.html

Logic is the anatomy of thought. John Locke 17th Century British Philosopher, physician, and defender of free government. Two Treatises of Government An Essay Concerning Human Understanding Performed life-saving liver surgery. http://oregonstate.edu/instruct/phl302/philosophers/locke.html

This art of logic concerns all kinds of reasoning in which inferences are executed by their form. Gottfried Leibniz 17 th Century German Mathematician, rational philosopher, physicist, wide-ranging forerunner in science. Discourse on Metaphysics, A Philosopher's Creed Explanation of Binary Arithmetic Théodicy Monadology Invented the infinitesimal calculus and binary numbers. Designed one of the earliest calculators. http://www.leibnizreview.com/

Logic is the art which directs the mind in its acquisition of knowledge. Francis Hutcheson 18 th Century Scotch-Irish Author of Logic, Metaphysics, and the Natural Sociability of Mankind A significant figure in the Period Of Enlightenment . Proponent of liberty and freedom of ideas. Highly influential mentor of the great economist Adam Smith. http://plato.stanford.edu/entries/scottish-18th/

Logic helps us to strip off the outward disguise of things, and to behold and judge them in their own nature. Isaac Watts 18th Century British Logic, or, The Right Use of Reason in the Inquiry After Truth. The standard textbook in much the English-speaking world for 100 years Best known then and now for prodigious and marvelous hymns, one of which concludes: Where reason fails, With all her powers, There faith prevails And love adores. http://www.victorshepherd.on.ca/Sermons/isaac.htm

Logic is the science of the necessary laws of the form of thinking. ------- We cannot think or use our understanding except by logical principles. Immanuel Kant 18th Century German. Arguably the greatest philosopher since Aristotle. But even Kant held fast to Aristotle’s Logic: “Logic has not gained much since Aristotle’s time, indeed it cannot. Logic is in a permanent state from which it cannot undergo any change.” Logic Critique of Pure Reason Prolegomena to any Future Metaphysics Groundwork of the Metaphysics of Morals Critique of Practical Reason Critique of Judgement On Pedagogy Lived his entire life in Konigsberg. Famous for self-discipline and extreme punctuality. http://www.hkbu.edu.hk/~ppp/Kant.html

By studying logic, your mind acquires self-reliance and independence. You become at home in abstractions and you can progress using ideas that are free from the coming and going of the moment. You develop an unsuspected power of assimilating in rational form all the complex branches of knowledge. By studying logic you begin to grasp and retain the essential character of all the sciences, stripping them of their external features and in this way extracting the logical element Friedrich Wilhelm Hegel 19th Century they hold in common. German A prominent figure in the history of philosophy. Eminent Professor at Jena, Heidelberg, and Berlin. Science of Logic Phenomenology of Spirit Encyclopaedia of the Philosophical Sciences Elements of the Philosophy of Right Writing are highly complex, difficult, and rather murky. Denied that a logical form has no content in itself. Argued instead that logical form is its own content (“being” and “becoming”) so central to the metaphysics of Reality. As for politics, supported peaceful progress toward freedom and equality. Witnessed and was impressed by Napoleon's triumphal march though Jena. Died in the cholera epidemic of the 1830's. Hegel’s last words: “They didn’t understand me.” http://www.sparknotes.com/philosophy/hegel/section4.rhtml http://www.gwfhegel.org/

The heated mind resents the chill touch and relentless scrutiny of logic. William Gladstone 19th Century British Liberal Party statesman and four times Prime Minister of the United Kingdom. http://www.spartacus.schoolnet.co.uk/PRdisraeli.htm

The question of logic is: Does the conclusion certainly follow if the premises be true? Augustus De Morgan 19 th Century British (born in India) Professor of Mathematics and Logic (and occasional) Lawyer. Anticipated and provided impetus for subsequent developments in logic and mathematics. First Notions of Logic Formal Logic or The Calculus of Inference Syllabus of a Proposed System of Logic An Essay on Probabilities The Elements of Arithmetic He never felt comfortable anywhere outside of London. http://www.nndb.com/people/437/000097146/

“Contrariwise,”continued Tweedledee, “if it was so, it might be; and if it were so, it would be: but as it isn’t it ain’t. That’s logic.” Charles Dodgson 19 th Century British Mathematics Lecturer at Christ Church college, Oxford. Wrote advanced logic texts and books of logic puzzles. Best known then and now as Lewis Carroll. Author of Alice's Adventures in Wonderland and Through the Looking-Glass. Excellent at charades and an accomplished photographer. http://www.kirjasto.sci.fi/lcarroll.htm

Logic is the necessary conditions of thought itself. William Hamilton 19th Century Scotch Scientist, logician, historian, philosopher. Formulated ground-breaking ideas concerning Logical Form. Championed the use of psychology in education. Discussions on Philosophy and Literature, Education and University Reform Notes and Dissertations. Lectures on Metaphysics and Logic His salary, as professor at Edinburgh University, came from a local tax on beer. http://plato.stanford.edu/entries/scottish-19th/#SirWilHam178185

In every enterprise logic directs the mind. Only we are not aware of it. Claude Bernard 19th Century French Physiologist and historian of science. An Introduction to the Study of Experimental Medicine Formulated the method of a “Blind Experiment”. http://www.cerebromente.org.br/n06/historia/bernard_i.htm

Nothing in modern education tends so much to form exact thinkers as logic. John Stuart Mill 19th Century British Home schooled and never attended college (except an aborted attempt at Law). Yet a philosopher of unmatched overall impact in the last 200 years. System of Logic A persuasive (though flawed) rejection of Aristotelian logic. Insists on a new Logic of uncertainty and verification. Lays out Logical Methods for advancing knowledge. Principles of Political Economy On Liberty—Individual freedom, democratic but limited government. Utilitarianism— Ethics based on consequences and happiness. Argued, wrote and worked for equality: economic, racial, sexual, religious–the lot. As a respected Member of Parliament proposed Proportional Representation and Universal Suffrage. Godfather to Bertrand Russell. http://plato.stanford.edu/entries/mill/

Logic has its own peculiar truth and value. Augusta Ada King 19th Century British Countess of Lovelace Exceptional mathematician and world’s first computer programer. Collaborated with Charles Babbage who designed the first computer. Daughter of poet Lord Byron. http://www.well.com/~adatoole/bio.htm

John Venn 19th Century Logic is not concerned with what we do believe, but what we ought to believe, if we are to believe correctly. British Mathematician, ordained Deacon, Logician, Lecturer in Moral Science. The Logic of Chance Symbolic Logic The Principles of Empirical Logic Best remember for Venn Diagrams used ever since in logic, mathematics and computer science. For 70 years, graduate and then Fellow of Gonville and Caius College, Cambridge Compiled a 500 year Biographical History of the college, requiring vast research and listing over 130,000 students! In Venn’s honor and memory there is a unique stained glass at the college chapel. A skilled mountain climber and a keen botanist. Built a cricket machine capable of a clean bowl against top strikers. http://www.newworldencyclopedia.org/entry/John_Venn

The rules of logic hold good of any symbols, written, spoken, or thought. __________ I define logic therefore as the science of the conditions which enable symbols in general to refer to objects. Charles Sanders Peirce 19 th Century American Perhaps the greatest intellect in the United States of America, ever. What Is Logic? Harvard Logic Lecture #1. Little known but remarkably important and original: http://www.cspeirce.com/menu/library/bycsp/earlymss/ms94harvard1.pdf Questions Concerning Certain Faculties Claimed For Man Some Consequences of Four Incapacities The Fixation of Belief How to Make Our Ideas Clear Philosopher, logician, mathematician, scentist (in several 10 areas) inventor; psychologist, historian, economist, critic, playwright, stage performer, fiction author. Fundamentally opposed to the psychologization of logic so prevalent in his time, and still today. Largely unrecognized in his lifetime, except by a few notable figures. Publish several important papers in newsstand magazines Only really steady job was with the government's Coast and Geodetic Survey Was excluded from academe because he lived with a woman out of wedlock. Died destitute and (were it not for his wife) nearly alone. http://www.peirce.org/

And these symbols of Logic are in their use subject to definite laws. George Boole 19th Century British Had minimal formal education, so studied and worked privately. At age 34, appointed lecturer, Queen’s College, Cork, Ireland. An Investigation of the Laws of Thought Mathematical Analysis of Logic Developed Logico-Mathematics based on a yes/no, on/off, zero/one model– “Boolean Algebra”. This evolved into and continues as the underlying architecture of all digital science and technology. His contemporary, Augustus De Morgan wrote (prophetically): “Boole's system of logic is but one of many proofs of genius and patience combined that the symbolic processes of algebra, invented as tools of numerical calculation, should be competent to express every act of thought, and to furnish the grammar and dictionary of an all-containing system of logic.” Sadly, at age 49 Boole died of pneumonia after a long walk to class through the rain and then lecturing in wet clothes. http://www.gutenberg.org/etext/15114

Carefully study the Art of Reasoning. It is what most people are deficient in. William John Wills 19th Century British-Australian Scientist, explorer, and physician. Died at age 27 on expedition to cross Australia from south to north. http://www.win.tue.nl/~engels/discovery/burke.html

We are not sure of the logical soundness of our methods and results until we make everything about them quite definite. Gregor Cantor 19th Century German (born in Russia) Professor at University of Halle, Wittenberg Regarded as one of the greatest of all mathematicians. Almost singlehandedly created set theory and transfinite mathematics. Argued that for every infinite set, there a larger infinite set, and thus infinitely many infinite sets! Foundations of a General Theory of Aggregates Contributions to the Founding of the Theory of Transfinite Numbers Believed his theory of transfinite numbers had been communicated to him by God. Published papers attempting to show that Francis Bacon wrote all of "Shakespeare’s" works. Argued that transfinite numbers and multiple infinities disprove fatalism and materialism. Beset by academic, theological, and social criticism, Cantor even wrote letters to Pope Leo XIII. “Transfinite numbers are at the disposal of the intentions of the Creator and His absolute boundless will.” http://www.iep.utm.edu/par-log/

Crime is common. Logic is rare. Therefore it is upon the logic rather than upon the crime that you should dwell. Sherlock Holmes 19th Century Arthur Conan Doyle's fictional detective, famous for his power logical deduction. http://sites.google.com/site/martinhickes/home

What really pertains to logic lies not in truth but in the asserting force by which truth is spoken. Gottlob Frege 19th Century German Scholar of profound insight who virtually redefined logic Concept Script On Sense and Reference Foundations of Arithmetic Though modest and reserved, Frege was politically conservative, even xenophobic. He left numerous private and unpublished papers, many of which were destroyed in the carnage of the Second World War, 20 years after Frege’s death. http://www.ocf.berkeley.edu/~brianwc/frege/

Logic can be patient, for it is eternal. Oliver Heaviside 19th Century British Physicist and mathematician Electromagnetic Theory. First to theorize the import of the earth’s ionosphere layer. Large craters on both the moon and Mars are named for him. Earned no university degree. Studied and published as a private citizen. Heaviside played the Aeolian harp and the ocarina. http://www.oliverheaviside.com/

Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us which is the road that leads to the desired end. Henri Poicaré 19th Century French Multifaceted mathematician and scientist Had absolute photographic memory his entire life. Was a mine inspector from age 22 until his death. University of Paris, primary lecturer in mathematics and science from age 27. Could work out complete solutions without paper. Ground breaking discoveries in topology, algebra, celestial mechanics, relativity, and Chaos Theory. On the Foundations of Geometry Intuition and Logic in Mathematics Mathematics and Logic Science and Hypothesis The Value of Science Science and Method Stressed that mathematics in not simply an extension of logic. His brother, Raymond, was President of France during the Great War. Contributed much toward the acquittal in the Dreyfus affair. http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Poincare.html

Logic is invincible because in order to combat logic it is necessary to use logic. Pierre Léon Boutroux 20 th Century French Highly respected mathematician and historian. The Principles of Mathematical Analysis Ideas of Science and Mathematics from Ancient to Modern Times Also a spiritual philosopher insisting on freedom and spontaneity of the spirit. Argued that of modern science requires indeterminancy. Both the form and the content of the above quote echos Aristotle’s own: “If we ought to philosophize, then we ought to philosophize. And if we ought not to philosophize, then we ought to philosophize. [to prove that we ought not] Thus, we ought to philosophize.” http://query.nytimes.com/mem/archive-free/pdf?_r=1&res=9800EFDF1F39E633A25757C2A9639C946596D6CF

Logic is the hygiene that keeps ideas healthy and strong. Hermann Weyl 20 th Century German A major figure in contemporary mathematics and physics. The Continuum : A Critical Examination of the Foundation of Analysis. Group Theoretic Method in Quantum Physics. Space, Time, and Matter On generalized Riemann Matrices Philosophy of Mathematics and Natural Science Repulsed by the rise of Nazism, in 1933 Weyl and his Jewish wife went to the United States and Princeton University, staying until several years after the war. There he collaborated with the likes of Albert Einstein. http://faculty.evansville.edu/ck6/bstud/weyl.html

Logic is doubtless unshakable, but it cannot withstand those who want to go on living. Franz Kafka 20th Century Czechoslovakian Arguably the quintessential author of the 20th century. Profoundly depicts life's terror since the automobile, radio, dynamite, and photography. The Trial Metamorphosis The Castle Amerika The Penal Colony Suffered Tuberculosis and Migraines; and died at age forty from starvation in a sanatarium. Wanted all his work (mostly unpublished) destroyed, but his best friend preserved it. http://www.levity.com/corduroy/kafka.htm

Principia Mathematica Hailed as the most significant work in Logic since Aristotle 20th Century Bertrand Russell Alfred North Whitehead Knowledge of logical forms Without deductive logic is something quite different from science would be knowledge of existing things. entirely useless. British British Professor: Began as Whitehead’s student Trinity College, Cambridge, Logician, philosopher, mathematician Imperial College, London, Introduction to Mathematical Philosophy Harvard University, Boston On Denoting Science and the Modern World The Analysis of Mind The Concept of Nature The Problems of Philosophy Precess and Reality A History of Western Philosophy The Aims of Education An Outline of Philosophy Adventures in Ideas Life-long peace activist. Hosted open-house every weekend. Imprisoned for WWI pacifism Ordered all his papers destroyed at death. Free-Love advocate There was no funeral. One day when out peddling his bicycle, Russell realized he no longer loved his wife. http://plato.stanford.edu/entries/principia-mathematica/

When dealing with people, remember you are not dealing with creatures of logic, but creatures of emotion. Dale Carnegie 20th Century American High priest of Self-improvement. How to Win Friends and Influence People Dynamic lecturer A large and loyal public following Born in poverty, worked as a traveling salesman, and began speaking at local YMCA’s. http://www.westegg.com/unmaintained/carnegie/carnegie.html

Logic is prior to all truth and falsehood. Ludwig Wittgenstein 20th Century Austrian Philosopher. Considered a seminal philosophical genius of the 20th century. Studied with Bertrand Russell. Few publications, but highly influential Tractatus Philosophical Investigations Served loyally in the army of Austria (against Britain) throughout the Great War. Ten years later, he returned to Britain permanently. Wittgenstein loved American B-grade Western movies. http://www.editor.net/BWS/wittgenstein.html

Whoever has experienced in his own mind the great clarification process which logical analysis accomplishes, will know what logic can achieve. Hans Reichenbach 20th Century German Naturalized American citizen late in life. Prodigious output in Logic, Mathematics, Physics, and History of Science. Elements of Symbolic Logic The Rise of Scientific Philosophy From Copernicus to Einstein Philosophic Foundations of Quantum Mechanics A loyal German soldier in The Great War. Having Jewish grandparents, was dismissed from Professorship at University of Berlin in 1933. Being vocally anti-Nazi, moved to Turkey and then to the USA. Distinguished professor at UCLA http://plato.stanford.edu/entries/reichenbach/

Logic is concerned with the analysis of sentences and proofs, with attention to form in abstraction from matter. ------------ If error is corrected whenever it is recognized as such, the path of error is the path of truth. Alonzo Church American Mathematician and Logician Credited for much of the original theoretical bases of computer science. Regarded by many as the greatest America-born logician-mathematician. Proved there's no possible algorithm for determining whether an arbitrary argument is logically valid. The Calculi of Lambda-Conversion A Note on the Decision-Problem An Unsolvable Problem in Elementary Number Theory On the Concept of a Random Sequence Introduction to Mathematical Logic Princeton University: from freshman (1920) to professor until 1967. then at UCLA until 1990. Church looked like a “cross between a panda and a large owl.” Enjoyed and collected science-fiction novels Before beginning lecture Church methodically erased the blackboard spotlessly in even rows. Church even had a logical way of eating breakfast: First pour the milk into the empty bowl. Next pour in the proper amount of sugar. Stir the mixture with the breakfast spoon. Then pour in a spoonful or two of cereal. Eat that. Then pour in another spoonful or two, eat that, and so on. The sugar is dissolved and evenly distributed, and the cereal never has a chance to get soggy. http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Church.html

Conclusion often like toy balloon. easy blow-up, easy pop. Charlie Chan 20 th century Fictional Chinese-American detective created by Earl Derr Biggers in 1923. Portrayed in a series on movies between 1935 and 1948. (actor Warner Oland above). http://www.charliechan.net/mainmenu.html

The blindness of past logicians was the widespread lack of the required epistemological attitude. ----------- Objective concepts of mathematics are fundamental to my work in logic. Kurt Godel 20 th Century With Albert Einstein German At the start of the Second World War, fled from Germany to America. Considered the most brilliant logician of the 20 th century, if not ever. On Formally Undecidable Propositions of Principia Mathematica and Related Systems...... The Completeness of the Axioms of the Functional Calculus of Logic Some Metamathematical Results on Completeness and Consistency On Completeness and Consistency Astoundingly demonstrated that simple arithmetic contains true statements that can never be proved! http://users.ox.ac.uk/~jrlucas/simplex.html Was a convinced theist and rejected his friend Albert Einstein’s view that God was impersonal. Believed firmly in immortality, stating: "If the world is rationally constructed, there must be an afterlife." At his swearing-in for American citizenship, he told the judge that there is a logical inconsistency in the Constitution that would allow for a dictatorship. But as Gödel’s best friend Albert Einstein standing next to him, the judge hastily silenced Gödel and granted citizenship! http://plato.stanford.edu/entries/goedel/

Logic analyzes the meaning of concepts common to all science and establishes the general laws governing those concepts. Alfred Tarski 20th Century Polish-American Leading figure in advancing Logic far, far, far beyond Aristotle. On the Concept of Logical Consequence Introduction to Logic and to the Methodology of Deductive Sciences On the calculus of Relations The Semantical Concept of Truth and the Foundations of Semantics For a symposium in Boston, he was on the last ship from Poland to the USA before WWII. http://plato.stanford.edu/entries/tarski/

Medical Science taught that toxoid immunization is impossible. I didn't doubt it. I just questioned the logic of it. Jonas Salk 20th Century American Research physician who developed the first safe and effective Polio Vaccine. Used a Waring Blender with an Aseptic Dispersal Container attachment to develop the vaccine. http://www.achievement.org/autodoc/page/sal0bio-1

Teenage Sensation Senior Icon Saul Kripke 20th Century Any necessary truth, whether logical or empirical, could not have turned out otherwise. American A most remarkable genius in Logical analysis. Highly eccentric and quite baffling to all but a few. Naming and Necessity Wittgenstein on Rules and Private Language. Many, many important papers still unpublished. When his first essay arrived at Harvard, the philosophy department was so stunned it invited him to join the faculty. But Saul wrote back that his mother wanted him to first finish high school. While a sophomore at Harvard, was named University Fellow for high level math and logic. Graduated B.A. Summa Cum Laude Yet that was Kripke’s ONLY earned degree, even though he has been handed many honorary degrees, international awards, and distinguished Professorships at leading universities. There is even a SAUL KRIPKE CENTER in Manhattan the mission of which is: “To promote the study of the intellectual achievements of Saul Kripke.” At age 65 Kripke remarked, "I wish I could have skipped college...I got to know some interesting people, but I can't say I learned anything. I probably would have learned it all anyway, just reading on my own." http://www.nytimes.com/2006/01/28/books/28krip.html?_r=1

Logic resembles good poetry: precise, radical, imaginative, elegant, powerful, orderly, subtle, reflective, and accurate. Tim Williamson 21 st Century British, born in Sweden The Philosophy of Philosophy Knowledge and Its Limits Vagueness Identity and Discrimination In his own words: "My central theme in the gap between what is true and what can be known." Williamson’s advice to everyone: “To be precise is to make it as easy as possible for others to prove one wrong. That is what requires courage.” For fiction, Williamson likes Jane Austen, Dashiell Hammett and authors “who are as clever and clear-eyed as good philosophers, and as exact in their use of words, but who don’t attempt to do philosophy.” http://sciencestage.com/v/6808/timothy-williamson-on-truth-and-certainty.html

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