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    Symbolic Logic

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    Janet Tal-udan
    The document discusses symbolic logic and logical operators. It explains that classical logic deals with the relation of terms in arguments and whether reasoning is valid depends on the proper arrangement of terms. Modern logic identifies fundamental logical connectives like negation, conjunction, disjunction, conditional, and biconditional. Negation is represented by the tilde symbol "~" and reverses the truth value of a statement. Logical validity can be tested by considering argument forms and finding a counterargument with the same form but true premises and a false conclusion.

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    Symbolic Logic

    Uploaded by

    Janet Tal-udan
    632 views24 pages
    The document discusses symbolic logic and logical operators. It explains that classical logic deals with the relation of terms in arguments and whether reasoning is valid depends on the proper arrangement of terms. Modern logic identifies fundamental logical connectives like negation, conjunction, disjunction, conditional, and biconditional. Negation is represented by the tilde symbol "~" and reverses the truth value of a statement. Logical validity can be tested by considering argument forms and finding a counterargument with the same form but true premises and a false conclusion.

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    The document discusses symbolic logic and logical operators. It explains that classical logic deals with the relation of terms in arguments and whether reasoning is valid depends on the proper arrangement of terms. Modern logic identifies fundamental logical connectives like negation, conjunction, disjunction, conditional, and biconditional. Negation is represented by the tilde symbol "~" and reverses the truth value of a statement. Logical validity can be tested by considering argument forms and finding a counterargument with the same form but true premises and a false conclusion.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    632 views24 pages

    Symbolic Logic

    Uploaded by

    Janet Tal-udan
    The document discusses symbolic logic and logical operators. It explains that classical logic deals with the relation of terms in arguments and whether reasoning is valid depends on the proper arrangement of terms. Modern logic identifies fundamental logical connectives like negation, conjunction, disjunction, conditional, and biconditional. Negation is represented by the tilde symbol "~" and reverses the truth value of a statement. Logical validity can be tested by considering argument forms and finding a counterargument with the same form but true premises and a false conclusion.

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    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
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    At a glance
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    The document discusses the differences between classical/traditional logic and modern logic. It also covers topics like simple and compound statements, logical operators like negation, and argument forms.

    The document discusses simple statements, which do not contain other statements, and compound statements, which contain at least one simple statement and a connective.

    The document discusses the logical operator of negation ('~') and how it reverses the truth value of a statement. It also covers De Morgan's laws.

    Chapter 8

    Symbolic Logic

    Classical or Traditional
    logic
    deals

    primarily (but not exclusively)


    with the relation of terms in an
    argument.

    Whether

    the reasoning is valid


    depends on the proper arrangement
    of these terms in an argument.

    The

    relation of classes of things are


    central concern.

    Classic example of a simple


    syllogism
    All men are mortal
    Socrates is a man
    Therefore, Socrates is mortal

    Modern logic
    Modern

    Logic begins by first


    identifying the fundamental logical
    connectives on which deductive
    arguments depends. Using these
    connectives, a general account of
    such arguments is given, and
    methods for testing the validity of
    arguments are developed.

    These

    newer logical languages are often


    called "symbolic logic," since they
    employ special symbols to represent
    clearly even highly complex logical
    relationships.

    There

    are five connectives: negation,


    conjunction, disjunction, conditional, and
    biconditional. In the notation of symbolic
    logic, these connectives are represented
    byoperators.

    Statement
    We

    must distinguish Simple


    statements from Compound
    statements to understand the
    symbolic representation used in
    propositional logic.

    Simplestatement

    Does not contain another statement as a


    component.

    Contains

    a subject and a predicate.

    e.g.
    Charlie is neat
    S

    James Joyce wrote Ulysses.


    S
    P

    Compoundstatement
    It

    contains at least one simple


    statement as a component along
    with aconnective.
    e.g.
    Either Charlie is neat or Charlie is
    sweet.
    1
    2
    Paris is the capital of France and
    Rome is
    1
    2

    Compound

    statements can be
    formed by inserting the word NOT, or
    joining two or more statements with
    connective words such as AND, OR,
    IFTHEN, ONLY IF, IF AND ONLY IF.
    (Will be discussed on the later part)

    Logical operators:
    Negation (~)
    The ~ signifies logical negation;
    it simply reverses the truth value of
    any statement (simple or compound)
    in front of which it appears.
    If the original is true, the ~
    statement is false, and if the original
    is false, the ~ statement is true. Thus,
    its meaning can be represented by
    the truth-table:

    Negation (~) truth


    table
    P
    T

    ~P
    F

    The tilde ~ symbol is used to


    translate any negated simple or
    compound statements.
    Simple :
    Rolex does not make computers.
    It is false that Rolex makes computers
    It is not the case that Rolex make

    computers.
    Can be presented as :

    ~(R )

    Compound:
    It is not the case that Rolex makes
    computer nor
    1
    Honda makes computer.
    2
    Presented as: ~ (R H)

    De Morgans law
    The rules allow the expression of
    conjunctions and disjunctions purely
    in
    terms of each other via negation.
    ~ (R H)
    ~ (R) v ~ (H)

    More examples:

    ~ (P v Q)
    ~P~Q

    ~ [ (R H) v ~ A]
    ~[ ( R H ) A]
    ~ (R v ~ A) A

    ~ [~(R v H) v A]
    (R v H) ~ A

    As these example shows, the tilde


    is always placed in front or before
    the proposition it negate.
    All of the other operators are
    placed between two propositions.
    Also unlike other propositions, the
    tilde cannot be used to connect two
    propositions.

    Argument Forms and refutation


    by Logical Analogy
    This

    method of refutation by
    logical analogy points the way to
    an excellent general technique for
    testing arguments. To prove the
    invalidity of an argument, it suffices
    to formulate another argument that:
    (1) Has exactly the same form as
    the first.
    (2) Has true premises and false

    This informal account of validity


    must now be made more precise. To
    do this, we introduce the concept of
    an argument form. Consider the
    following two arguments:

    Modus ponens: affirms an antecedent.

    Valid argument

    If it rained last night,


    then the ground is wet
    If P then
    Q
    It rained last night__________
    P_______
    Therefore, the ground is wet Q

    VALID: affirms an
    antecedent.
    If P is true, then Q is true
    P is true
    Therefore, Q is true

    Fallacy of affirming the consequent

    Not valid

    If it rained last night,


    then the ground is wet
    If P then
    Q
    The ground is wet_______
    Q_________
    Therefore, It rained last night
    P

    Not valid: affirms the


    consequent
    If P then Q
    Q
    Therefore, P is true

    Nothing follows.

    -EndThanks.

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