Rules of replacement
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Rules of Replacement. Logic. A very elementary introduction. Rules of Replacement. Demorgan’s Theorems. Some basic laws of logic. The law of non-contradiction A is not ~A The law of identity A=A The law of excluded middle

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Rules of Replacement

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Rules of replacement

Rules of Replacement


Logic

Logic

A very elementary introduction


Rules of replacement1

Rules of Replacement

Demorgan’s Theorems


Some basic laws of logic

Some basic laws of logic

  • The law of non-contradiction

    A is not ~A

  • The law of identity

    A=A

  • The law of excluded middle

    statements that have a truth value are either possibly true or possibly false not half true or half false


Types of logic

Types of Logic

  • Symbolic Logic

  • Modal Logic

  • Propositional Logic

  • Propositional logic is also called propositional calculus is it includes the following A) consonants, sentential connectives such as if,then,and B) existing rules of inference


What is a proposition

What is a proposition?

  • A proposition is a statement of thought that is expressed in language. [Can be any human language] This statement has a truth value.

  • For example: Boiling water is hot. This is either true or false.


Not all sentences are propositions

Not all sentences are propositions

  • Sentences such as: Go outside and play ball have no truth value.


Sense and reference

Sense and Reference

  • Sense: The meaning of a statement

  • Reference: The state of affairs of the universe to which my utterance points.


Antecedents

Antecedents

  • What goes before. In an if, then statement the antecedent would be “if” portion.

    For example: If it rains then wear a jacket.


Consequent

Consequent

  • What follows after. The consequent is the then portion. Using our last example If it rains then wear a jacket

    Jacket here is the consequent.


Soundness vs validity

Soundness vs. Validity

  • Valid arguments contain true premises therefore the conclusion that follows must also be true. It is possible for an argument to be factually untrue but logically valid.

  • Soundness on the other hand refers to a valid argument that contains factually true premises.


Truth functional connectives

Truth Functional connectives

Truth functional connectives link propositions together. For example V or vel stands for “or” the dot . Stands for “and” these truth functional connective link together logical statements.


Causation and logical relations

Causation and Logical relations

  • Logical relations do not account for contingencies. For example if we were to look at the causal relationship between my throwing a rock and it breaking a window we would have to examine the force of my throw, the thickness of the window, the distance, the thickness of the rock, the timing of my throw, the arm I am using, etc.


Deductive nomological account

Deductive Nomological account

  • The logician Carl Hempel argued that for every antecedent cause x, the consequent y must by necessity happen.


Implication or material equivalence

Implication or Material Equivalence

P implies Q is always true except when the antecedent [P] is true and the consequent is false


A table for truth

A table for truth

  • Truth tables are logical diagrams so that every possible truth value can be examined.


Constructing truth tables

Constructing truth tables

  • 2 times the number of variables gives us the possible number of truths. 2(n)

    For example p v q contains two variable p and q so for this truth table we would construct it like this:

    p q p v q

    t t t

    t f t

    f t t

    f f f


Rules of inference

Rules of Inference

  • Modus Ponens

    P -> Q

    P

    :. Q

  • Modus Tollens

    P->Q

    ~Q

    .:~P


Rules of inference 2

Rules of Inference #2

  • Hypothetical Syllogism

    P->Q

    Q->R

    .: P->R

  • Disjunctive Syllogism

    P v Q

    ~P

    .:Q


Rules of inference1

Rules of Inference

  • Constructive Dilemma

    (P->Q) & (R->S)

    P v R

    :. Q v S


Destructive dilemma

Destructive Dilemma

(p->q) & (r->s)

~q v ~s

.: ~p v ~r


More rules of inference

More Rules of Inference

Simplification

P & Q

.:P

Conjunction

P

Q

.: P & Q


One last one

One last one

Addition

P

.: p v q


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