. 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.