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# Logic 1 - LOGIC Handout#1 N Apostol STATEMENTS/PROPOSITIONS...

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#1 - N. Apostol **** STATEMENTS/PROPOSITIONS Truth or falsity are features of (apply to) declarative statements (sentences, propositions, etc.). Questions, commands, conterfactuals, are not declarative statements, thus are outside the scope of the system of logic under investigation in this class (no rigorous assessment of their truth of falsity can be offered). This definition of truth is derived from a correspondence theory of truth . There are competing theories of truth (coherence theories of truth, semantic theories of truth, etc.), they are the domain of metaphysics and philosophy of logic, thus besides the scope of this class. The correspondence theory of truth is the basis of the system of logic we will study in this class. According to this conception of truth, we assess truth/falsity by reference to actual world scenarios. Truth/falsity is a problem of content . If a statement corresponds to (mirrors ) the actual world scenario, it is assessed as a true statement. If it fails to do so, it is said to be false (think about a photograph). Think of truth as a relation between that which exists in the 'real' world and that which exists in our head as a reflection of that 'reality' outside. Beware of the distinction between truth and truthfullness !! (to be discussed later). Statements are sentences that can be either true or false (called truth-values) and not both or neither. This is correct according to the system of logic we study in this class. There are several other systems of logic which accept more truth values (multi-valued logic, for example) but they are studied in higher level logic classes. This system of logic we study is intuitively and historically the most wide-spread, which does not mean that is necessarily the best one - but we shall leave this discusssion aside for now. (A) . Given the logical possibility of truth, statements can be consistent or inconsistent (not consistent). i. consistency: it is logically possible for the statement to be true ii. inconsistency: it is logically impossible for the statement to be true (B) . Given the logical possibility of truth and falsity , statements are classified in three categories: contingent, tautogolous or self contradictory. i. contingency : it is logically possible for such statement to be either true or false; in fact it will be one of the two but both possibilities must be analyzed; Ex. of contingent statements: Today is Tuesday. Chicago is in Illinois.

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Logic 1 - LOGIC Handout#1 N Apostol STATEMENTS/PROPOSITIONS...

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