- The History of Proof Methods before computers.
- Manual Methods
- Notes on MATHS Notation
- Notes on the Underlying Logic of MATHS

(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(?)... [ ../samples/syllogisms.html ]

(Descartes): Analysis,

(Liebnitz): "Let us calculate", assume little and break things down into components.

(Boole): "The Laws of Thought", Symbolic logic. [ Boolean Algebra in math_41_Two_Operators ] [ Boolean in intro_logic ]

(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, [ 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" [ intro_logic.html ]

(New Age): See

(Alternative): Deny the value of discussing things. So is not discussed here.

(Neo Aristotlean): Objects, classes, inheritance all add up to the reinvention of

(Lewis Carrol): "Game of Logic", A way to handle Aristotlean syllogisms using diagrams.

Truth Tables -- hence and/or tables in software engineering [ Example Boolean Table in notn_9_Tables ]

(Kalish and Montague): Block structured proofs.
[ logic_2_Proofs.html ]

(Hodges): Tree Diagrams analyse the possibilities. Semantic Tableau

(Algebraic): Boolean algebra -- *Boole* above.

Proofs follow a natural deduction style that start with
*assumptions* ("Let") and continue to a *consequence* ("Close Let")
and then discard the assumptions and deduce a *conclusion*. Look
here
[ Block Structure in logic_2_Proofs ]
for more on the structure and rules.

The notation also allows you to create a new *network* of variables
and constraints, and give them a name. The schema, formal system,
or an *elementary piece of documentation* starts with "Net" and finishes "End of Net".
For more, see
[ notn_13_Docn_Syntax.html ]
for these ways of defining and reusing pieces of logic and algebra
in your documents.

For a complete listing of pages by topic see [ home.html ]