What is the logic?

1. What is the logic? • The primary concern in logic is to identify and classify valid form of inference. • The notions of 'validity' ,'form' and 'inference' are the key ones. • They can be explained in the following way.Consider these two arguments: • 'Either Tom broke the clock or Harry did.Harry did not break the clock. Therefore Tom did' • 'Either is rained on Thuesday or on Wednesday. But on Wednesday there was no rain, Therefore it rained on Tuesday'

2. Each has two premisses from wich a conclusion • The conclusion: therefore. • To drawn a conclusion from premisses is to infer it from them.;the conclusion follow from the premisses. • : 'Either Tom broke the clock or Harry did.Harry did not break the clock. Therefore Tom did' • 'Either is rained on Thuesday or on Wednesday. But on Wednesday there was no rain. Therefore it rained on Tuesday • Structure= Either p or q; not q; Therefore p. • The letters 'p' 'q' are formulae wich 'stand for' propositions

3. Simple,atomic,complex, • 'p' and 'q' also stand foratomic propositions • 'p or q' is a proposition complex made up of two simple propositions or atomic propositions • Why? Because stand for Either Tom broke the clock or Harry did • Tom broke the clock= simple=p • Harry did= simple=q

4. If the premisses are true, the truth of the conclusion are guaranteed • Why? Because the propositions are logical.Ma this must be explained. • Either p or q; not q; Therefore p. Why this is logical proposition? • Because we compute (just as in mathematics). • [(Either p or q) not q] therefore p. • In mathematical logic 'or' becomes the symbol v • In mathematical logic 'not' becomes the symbol ¬ • In mathematical logic 'therefore' becomes the symbol ⊃ • [(p v q) ¬ q] ⊃ p (Either disappears)

5. The logical calculus • You could say we just put new symbols. • It true, but these new symbols allow you to calculate the true and false. • p can be true and can be false as q • True-p-False ; True-q-False • T-p-F; T-q-F • 2 +2 = 4 but what gives true + false ?

6. The scholastic sense of WittgensteinW= true • Wittgenstein had the idea to connect the two propositions • But we can report exactly the picture of Wittgenstein's also so • p q • WF • WW • FW • FF • The first hookup of Wittgenstein is the first line, the second the second line,etc.

7. If you deny it a true statement is false, a false proposition if you deny it becomes true The negation • ¬ p • FW • WF • F- • W-p-F- • W

8. the disjunction or, v • The disjunction here is done with two propositions • p q • WF = W • WW=W • FW = W • FF = F

9. The conjuction (and) ^ (new symbol) • The conjunction is true only if the two propositions are true • pq • WF = F • WW= W • FW= F • FF= F

10. Implication (therefore ⊃) • The implication is false only if the antecedent is true and the consequent is false • pq • WF = F • WW =W • FW = W • FF = W

11. we now write p and q and calculate all possible values (true,false) ​​we see that the proposition is logical because the implication is always true. • [(p v q) ^ ¬ q] ⊃ p • W W F W W F W W • W W W F FW W W • F W W F F W W F • F F F F WF W F

12. we now write p and q and calculate all possible values (true,false) ​​we see that the proposition is logical because the implication is always true. • Calculus