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Fri Jul 29 08:39:53 PDT 2005

Contents


    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 ]
    (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.
    (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 [ 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 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.

    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 ]

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