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.