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Rules of Replacement - PowerPoint PPT Presentation

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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Logic

A very elementary introduction

Demorgan’s Theorems

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

• 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

• 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.

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

• Sense: The meaning of a statement

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

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

For example: If it rains then wear a jacket.

• 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.

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

• 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.

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

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

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

• 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

• Modus Ponens

P -> Q

P

:. Q

• Modus Tollens

P->Q

~Q

.:~P

• Hypothetical Syllogism

P->Q

Q->R

.: P->R

• Disjunctive Syllogism

P v Q

~P

.:Q

• Constructive Dilemma

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

P v R

:. Q v S

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

~q v ~s

.: ~p v ~r

Simplification

P & Q

.:P

Conjunction

P

Q

.: P & Q