. The History of Proof Methods before computers. (Chinese literature): - analogies, imposition of order symbolized by geometry, binary as oracle(The Oracle of change. (Homer): - the book as a source of analogies, The hero gets up and argues the case and other reply. Argumentative ability has a value. Logic as dependent on language: Logos vs Barbarian (Ionia): Rhetoric - how to win a case without being right. Lawyers get a bad name: sophists. (Plato/Socrates): Question and answer Dialogues, and so dialectic. (Euclid): System=assumptions + rules give theorems, applied to geometry (Aristotle): Inheritance Hierarchy(genus, species, accidents) & Syllogism, Formal Logic. (The Islamic scholars): Algebra, (Medieval): disputations and syllogisms, Barbara Celarent Daptista(?)... .See ../samples/syllogisms.html (Descartes):Analysis, (Liebnitz):"Let us calculate", assume little and break things down into components. (Boole):"The Laws of Thought", Symbolic logic. .See http://www/dick/maths/math_41_Two_Operators.html#Boolean Algebra .See http://www/dick/maths/intro_logic.html#Boolean (Mathematicians): Discovery of multiple geometries and so multiple logics, As a rule mathematicians do not use formal logic. Only some mathematicians in any age have been interested in logic, .See http://www/dick/maths/math_10_Intro.html (Lewis Carrol): Formulates medieval logic as a game -- not a very exciting game, invents a kind of Karnot Map for reasoning about syllogisms,... (Frege): Formalism, Can mathematics be derived from logic? (Jentzen): Natural deduction, Proof by assumption and reduction to absurdity. (Russell and Whitehead): Three volume attempt to construct math from logic, Relationship between reason and scientific methods? (Church): Logistic Systems (Goedel): the logic of Logics, completeness of boring logics,incompleteness of interesting logics, "Goedel Escher Bach" (Gardner):"Logic Machines and Diagrams" .See http://www/dick/maths/intro_logic.html (New Age): See \$Alternative. (Alternative): Deny the value of discussing things. So is not discussed here. (Neo Aristotlean): Objects, classes, inheritance all add up to the reinvention of \$Aristotle's individuals, genus, species, differentia, etc.. . Manual Methods (Lewis Carrol):"Game of Logic", A way to handle Aristotlean syllogisms using diagrams. Truth Tables -- hence and/or tables in software engineering .See http://www/dick/maths/notn_9_Tables.html#Example Boolean Table (Kalish and Montague): Block structured proofs. .See http://www/dick/maths/logic_2_Proofs.html (Hodges):Tree Diagrams analyse the possibilities. Semantic Tableau (Algebraic): Boolean algebra -- \$Boole above.