Unit 1 - Logic and Critical Thinking Basic Concepts Critical Thinking ● In academic philosophy, ‘critical thinking’ is the field that concerns logic and norms of rationality applied to everyday contexts. ● It is not the same as the critical tradition in politics, though critical thinking can help one be more properly politically engaged. Propositions and Sentences ● A proposition is a statement that can be true or false. ● Propositions are expressed by declarative sentences and some rhetorical questions. ● Other types of sentences are interrogative questions and imperatives (commands). Examples ● Declarative sentences: ○ The Earth revolves around the sun. ○ Cats are mammals. ○ 1+1=2. ○ All good things must come to an end. ● Rhetorical questions that express propositions: ○ Do you have no shame?? (Expresses: you have no shame.) ○ Could you walk any slower? (Expresses: you are walking very slowly.) Examples ● Interrogative questions: ○ Where were you born? ○ How much does one of these cost? ● Imperatives: ○ Close the door. ○ Go away. Types of Propositions ● Propositions can be atomic or propositional formulae. ● Propositional formulae contain atomic propositions connected by logical connectives. ● Logical connectives include: ‘not’, ‘or’, ‘and’, and ‘if-then’. Conditionals ● ‘If-then’ statements are called conditionals. They have the form ‘if p then q’. ● Here p is the antecedent and q is the consequent. ● The antecedent is a sufficient condition for the consequent, and the consequent is a necessary condition for the antecedent. Examples ● Propositional formulae that are not conditionals: ○ My cat is furry and my cat is cute. ○ Either it will rain tomorrow or it will hail tomorrow. ○ It is not the case that the Earth is flat. ● Conditionals: ○ If you’re old enough to vote, then you’re old enough to drive. ○ If you got an A in PHIL 203, then you were enrolled in PHIL 203. More on Conditionals ● Not all conditionals are expressed in the ‘if p, then q’ format. ● Sometimes they are expressed using ‘only if’, sometimes other ways. ● For example: ○ Something is a mammal only if it is an animal. ○ This is a true conditional. ○ How would you put this in the standard format? Biconditionals ● Biconditionals are ‘if and only if’ statements, where both the antecedent and the consequent are necessary and sufficient for each other. ● In biconditionals the antecedent is whichever proposition comes first, and the consequent whichever comes second. ● In semi-formal notation it is: p iff q. ● Here p is the antecedent and q the consequent. Examples ● Something is a triangle if and only if it is a polygon with exactly three sides. ● You get an A in PHIL 203 if and only if you fulfill all the course requirements to a high standard. ● Tomorrow is Friday if and only if today is Thursday.