Logic¶
1 Logic : relation of consequence between the premises and the conclusion of sound argument
1.1 Sound(an argument): if conclusion is a consequence of its premises ~ correct, valid
1.2 Unsound : not Sound
1.3 Argument : System of declarative sentences
1.3.1 Conclusion
1.3.2 Premises
1.3.3 Sentences : linguistic expression stating a complete thought
1.3.3.1 Declarative
1.3.3.2 Interrogative
1.3.3.3 Imperative
1.4 Criterion for the soundness of an argument : An argument is sound iff it is not possible for its premises to be true and its conclusion false
1.4.1 Necessary truth : a Sentence is necessary truth iff no conceivable circumstances of being false
1.4.2 Conditional, consequent : If (corresponding conditional) then (consequent)
1.4.3 A sentence is a necessary truth iff no unsound argument of which it is the conclusion
1.5 Parenthetical remark
1.5.1 If a sentence is known to be true, it is true,
1.5.1.1 Even if a sentence is true, it could not be known to be true.
1.5.2 Logically possible (a sentence) : the hypothesis it occurs is compatible with the laws of logic
1.5.3 Proposition, statement, thought, judgement
1.6 Logical form
1.6.1 If a sentence is necessary truth then all sentences of the same logical form are also necessarily true.
1.6.2 A truth of logic ( a sentence) iff it is a substitution-instance of a matrix all instances of which are necessary truths
1.6.2.1 Matrix : formal expressions built with logical words together with sentential, class, or individual letters
1.6.2.1.1 Logical words : and, or, if…then, not, all, is, etc
1.6.2.1.2 Sentential letters : sentence
1.6.2.1.3 Class letters : a set of elements
1.6.2.1.4 Individual letters : elements
1.7 Artificial language (Formalized language) : grammatically simpler, regular than natural language