Rules of Replacement

1. Rules of Replacement

2. Logic A very elementary introduction

3. Rules of Replacement Demorgan’s Theorems

4. 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

5. 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

6. 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.

7. Not all sentences are propositions • Sentences such as: Go outside and play ball have no truth value.

8. Sense and Reference • Sense: The meaning of a statement • Reference: The state of affairs of the universe to which my utterance points.

9. Antecedents • What goes before. In an if, then statement the antecedent would be “if” portion. For example: If it rains then wear a jacket.

10. 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.

11. 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.

12. 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.

13. 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.

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

15. Implication or Material Equivalence P implies Q is always true except when the antecedent [P] is true and the consequent is false

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

17. 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

18. Rules of Inference • Modus Ponens P -> Q P :. Q • Modus Tollens P->Q ~Q .:~P

19. Rules of Inference #2 • Hypothetical Syllogism P->Q Q->R .: P->R • Disjunctive Syllogism P v Q ~P .:Q

20. Rules of Inference • Constructive Dilemma (P->Q) & (R->S) P v R :. Q v S

21. Destructive Dilemma (p->q) & (r->s) ~q v ~s .: ~p v ~r

22. More Rules of Inference Simplification P & Q .:P Conjunction P Q .: P & Q

23. One last one Addition P .: p v q