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(?)...
[ ../samples/syllogisms.html ]
(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.
(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,
(Lewis Carrol): "Game of Logic", A way to handle Aristotlean syllogisms
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.
Notes on MATHS Notation
Special characters are defined in
[ intro_characters.html ]
that also outlines the syntax of expressions and a document.
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
[ 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.
Notes on the Underlying Logic of MATHS
The notation used here is a formal language with syntax
and a semantics described using traditional formal logic
[ logic_0_Intro.html ]
plus sets, functions, relations, and other mathematical extensions.
For a complete listing of pages by topic see
[ home.html ]