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, andsomething else

results of necessity.

Aristotle 4 Century BCth

GreekBeyond 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 studentWas 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 eitherby 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 3 Century BCrd

GreekHead 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 logicis to be a true

fugitive.

Marcus Aurelius 2 Century ADnd

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 lightto her own discoveries; She awakens the mind

and purifies the intellect; She brings light

to our intrinsic ideas; She abolishes oblivion and

ignorancewhich are ours by birth.

Proclus Diadochus 5th Century AD

Byzantium: Constantinople, Alexandria, AthensScholar, mathematician, commentator.Preserved and transmitted texts from ancient Greece.Commentary on Euclid AstronomyBook of CausesElements of TheologyElements of PhysicsPlatonic TheologyStudent, 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 wayto learn the truth

than through Logic.

Averroes 12 Centuryth

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 ReasonAlso a judge and a physician for most of his life.http://www.fordham.edu/halsall/source/arab-y67s11.html

Science can proceed only bycorrect forms of logic.

So to not embrace logicis to never find truth.

But by itself,logic is practically useless.

John of Salisbury 12 Centuryth

English, Anglo-SaxonPhilosopher, historian, churchman, diplomat, and scholar.Defender of Thomas à Becket both before and after his murder.MetalogiconFirst 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 12 Centuryth

Moorish Spanish and North AfricanPhilosopher, Historian, Logician, Jewish Theologian, Physician, RabbiGuide 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 conclusionand makes us grant the conclusion,

but does not make the conclusion certain,except through experience.

Roger Bacon 13 Centuryth

EnglishFranciscan 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 LogicComprehensive Reason and DialogueMajor WorkMinor WorkExperimented 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 isthe beginning of wisdom.

Thomas Aquinas 13 Centuryth

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 logicand then carefully studies other sciences,

will thereby developeven greater in the art of logic.

William of Ockham 14 Centuryth

EnglishA Franciscan FriarAmong 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 argumentby noise and command

show that their reason is weak.

Michel de Montaigne 16 Centuryth

FrenchStatesman, 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 17 Centuryth

EnglishEssayist, Jurist, Scientist, Statesman.The New ScienceUtopiaThe Advancement of LearningBacon 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 forall the operations of the mind,

exists for the very purpose of beingan instrument which is of service to us.

Antoine Arnauld 17 Centuryth

FrenchPort-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 childrenhttp://oregonstate.edu/instruct/phl302/philosophers/arnauld.html

The best defenseagainst logicis ignorance.

Blaise Pascal 17 Centuryth

French Mathematician, physicist, and religious philosopher.ThoughtsOn the Art of PersuasionThe Provincial LettersTreatise on the Arithmetical TriangleOn the Geometrical MindDevised an adding machineWore a death mask at his funeral.http://oregonstate.edu/instruct/phl302/philosophers/pascal.html

Logic is the anatomy of thought.

John Locke 17 Centuryth

BritishPhilosopher, 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 concernsall kinds of reasoningin which inferences

are executed by their form.

Gottfried Leibniz 17 Centuryth

GermanMathematician, rational philosopher, physicist, wide-ranging forerunner in science.Discourse on Metaphysics,A Philosopher's Creed Explanation of Binary Arithmetic ThéodicyMonadology Invented the infinitesimal calculus and binary numbers.Designed one of the earliest calculators.http://www.leibnizreview.com/

Logic is the artwhich directs the mind

in its acquisition of knowledge.

Francis Hutcheson 18 Centuryth

Scotch-IrishAuthor of Logic, Metaphysics, and the Natural Sociability of MankindA 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 offthe outward disguise of things,and to behold and judge them

in their own nature.

Isaac Watts 18 Centuryth

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 scienceof the necessary laws

of the form of thinking.-------

We cannot think or use our understanding

except by logical principles.

Immanuel Kant 18 Centuryth

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.”

LogicCritique of Pure Reason Prolegomena to any Future Metaphysics Groundwork of the Metaphysics of Morals Critique of Practical Reason Critique of Judgement On PedagogyLived 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 progressusing ideas that are free from

the coming and goingof the moment.

You develop an unsuspected powerof assimilating in rational form

all the complex branches ofknowledge.

By studying logicyou begin to grasp and retain

the essential characterof all the sciences, stripping them

of their external featuresand in this way

extracting the logical element Friedrich Wilhelm Hegel 19 Centuryth

they hold in common.

GermanA prominent figure in the history of philosophy.Eminent Professor at Jena, Heidelberg, and Berlin.Science of LogicPhenomenology of Spirit Encyclopaedia of the Philosophical SciencesElements of the Philosophy of RightWriting 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.rhtmlhttp://www.gwfhegel.org/

The heated mind resentsthe chill touch

and relentless scrutinyof logic.

William Gladstone 19 Centuryth

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 thepremises be true?

Augustus De Morgan 19 Centuryth

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 Centuryth

BritishMathematics 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 19 Centuryth

ScotchScientist, 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 ReformNotes and Dissertations.Lectures on Metaphysics and LogicHis salary, as professor at Edinburgh University, came from a local tax on beer.http://plato.stanford.edu/entries/scottish-19th/#SirWilHam178185

In every enterpriselogic directs the mind.

Only we are not aware of it.

Claude Bernard 19 Centuryth

FrenchPhysiologist and historian of science.An Introduction to the Study of Experimental MedicineFormulated the method of a “Blind Experiment”.http://www.cerebromente.org.br/n06/historia/bernard_i.htm

Nothing in modern educationtends so much to form exact thinkers

as logic.

John Stuart Mill 19 Centuryth

BritishHome 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 EconomyOn 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 19 Centuryth

BritishCountess of LovelaceExceptional 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 Venn19 Centuryth

Logic is not concerned with what we do believe,but what we ought to believe, if we are to believe correctly.

BritishMathematician, ordained Deacon, Logician, Lecturer in Moral Science.The Logic of ChanceSymbolic Logic The Principles of Empirical LogicBest 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, CambridgeCompiled a 500 year Biographical History of the college, requiring vast research and listing over130,000 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 holdgood of any symbols,

written, spoken, or thought. __________

I define logic thereforeas the science of the conditions

which enable symbols in generalto refer to objects.

Charles Sanders Peirce 19 Centuryth

AmericanPerhaps 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.pdfQuestions Concerning Certain Faculties Claimed For Man Some Consequences of Four Incapacities The Fixation of BeliefHow to Make Our Ideas ClearPhilosopher, 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 magazinesOnly really steady job was with the government's Coast and Geodetic SurveyWas 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 19 Centuryth

BritishHad minimal formal education, so studied and worked privately.At age 34, appointed lecturer, Queen’s College, Cork, Ireland.An Investigation of the Laws of ThoughtMathematical Analysis of LogicDeveloped 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 logicis but one of many proofs of genius and patience combinedthat 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 dictionaryof 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 studythe Art of Reasoning.It is what most people

are deficient in.

William John Wills 19 Centuryth

British-AustralianScientist, 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 sureof the logical soundness

of our methods and resultsuntil we make everything about them

quite definite.

Gregor Cantor 19 Centuryth

German (born in Russia)Professor at University of Halle, WittenbergRegarded 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 AggregatesContributions to the Founding of the Theory of Transfinite NumbersBelieved 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 crimethat you should dwell.

Sherlock Holmes 19 Centuryth

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 whichtruth is spoken.

Gottlob Frege 19 Centuryth

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 bepatient,

for it is eternal.

Oliver Heaviside 19th Century

BritishPhysicist and mathematicianElectromagnetic 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 usthat on such and such a road

we are sure of not meeting an obstacle;

it does not tell us which is the roadthat leads to the desired end.

Henri Poicaré 19 Centuryth

FrenchMultifaceted mathematician and scientistHad 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 GeometryIntuition and Logic in MathematicsMathematics and LogicScience and HypothesisThe Value of ScienceScience and MethodStressed 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 Centuryth

FrenchHighly respected mathematician and historian.The Principles of Mathematical Analysis Ideas of Science and Mathematics from Ancient to Modern TimesAlso 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 Centuryth

GermanA 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 MatterOn generalized Riemann MatricesPhilosophy of Mathematics and Natural ScienceRepulsed 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 collaboratedwith 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 20 Centuryth

CzechoslovakianArguably the quintessential author of the 20th century.Profoundly depicts life's terror since the automobile, radio, dynamite, and photography.The TrialMetamorphosisThe CastleAmerikaThe Penal ColonySuffered 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

PrincipiaMathematica

Hailed as the most significantwork in Logic since Aristotle

20 Centuryth

Bertrand Russell Alfred North Whitehead

Knowledge of logical formsis something quite different from

knowledge of existing things.

BritishBegan as Whitehead’s studentLogician, philosopher, mathematicianIntroduction to Mathematical PhilosophyOn DenotingThe Analysis of MindThe Problems of PhilosophyA History of Western PhilosophyAn Outline of PhilosophyLife-long peace activist.Imprisoned for WWI pacifismFree-Love advocate One day when out peddling his bicycle,Russell realized he no longer loved his wife.

Without deductive logicscience would be entirely useless.

BritishProfessor:

Trinity College, Cambridge,Imperial College, London,Harvard University, Boston

Science and the Modern WorldThe Concept of NaturePrecess and RealityThe Aims of EducationAdventures in IdeasHosted open-house every weekend.Ordered all his papers destroyed at death.There was no funeral.

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 20 Centuryth

AmericanHigh priest of Self-improvement.How to Win Friends and Influence PeopleDynamic lecturerA large and loyal public followingBorn in poverty, worked as a traveling salesman, and began speaking at local YMCA’s.http://www.westegg.com/unmaintained/carnegie/carnegie.html

Logic is priorto all truth and falsehood.

Ludwig Wittgenstein 20 Centuryth

AustrianPhilosopher. Considered a seminal philosophical genius of the 20 century.th

Studied with Bertrand Russell.Few publications, but highly influentialTractatusPhilosophical InvestigationsServed 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 experiencedin his own mind

the great clarification processwhich logical analysis

accomplishes,will know what logic can achieve.

Hans Reichenbach 20 Centuryth

GermanNaturalized American citizen late in life.Prodigious output in Logic, Mathematics, Physics, and History of Science.Elements of Symbolic LogicThe Rise of Scientific PhilosophyFrom Copernicus to EinsteinPhilosophic Foundations of Quantum MechanicsA 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 UCLAhttp://plato.stanford.edu/entries/reichenbach/

Logic is concerned with the analysisof 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

AmericanMathematician and LogicianCredited 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 logicallyvalid. The Calculi of Lambda-Conversion A Note on the Decision-ProblemAn Unsolvable Problem in Elementary Number Theory On the Concept of a Random Sequence Introduction to Mathematical LogicPrinceton 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 novelsBefore 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 andevenly distributed, and the cereal never has a chance to get soggy.

http://www-gap.dcs.st-and.ac.uk/~history/Biographies/Church.html

Conclusionoften like toy balloon.

easy blow-up, easy pop.

Charlie Chan 20 century th

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 epistemologicalattitude.-----------

Objective concepts of mathematicsare fundamental to my work in logic.

Kurt Godel 20 Centuryth

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 century, if not ever.th

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 meaningof concepts common to all scienceand establishes the general laws

governing those concepts.

Alfred Tarski 20 Century th

Polish-AmericanLeading figure in advancing Logic far, far, far beyond Aristotle.On the Concept of Logical ConsequenceIntroduction to Logic and to the Methodology of Deductive SciencesOn the calculus of Relations The Semantical Concept of Truth and the Foundations of SemanticsFor 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 taughtthat toxoid immunization

is impossible.I didn't doubt it.I just questioned

the logic of it.

Jonas Salk 20 Centuryth

AmericanResearch 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 20 Centuryth

Any necessary truth, whether logical or empirical,could not have turned out otherwise.

AmericanA most remarkable genius in Logical analysis.Highly eccentric and quite baffling to all but a few.Naming and NecessityWittgenstein 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 honorarydegrees, 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 allanyway, just reading on my own."http://www.nytimes.com/2006/01/28/books/28krip.html?_r=1

Logic resembles goodpoetry: precise, radical,

imaginative, elegant,powerful, orderly, subtle, reflective, and accurate.

Tim Williamson 21 Centuryst

British, born in SwedenThe Philosophy of PhilosophyKnowledge and Its LimitsVaguenessIdentity 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’tattempt to do philosophy.”

http://sciencestage.com/v/6808/timothy-williamson-on-truth-and-certainty.html