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'

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

Simple,atomic,complex, 'p' and 'q' also stand for atomic 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

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)

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 ?

The scholastic sense of Wittgenstein W= 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.

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

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

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

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

[(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 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

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