Midterm Flashcards
What is critical thinking
Critical thinking is the ability to think clearly and rationally about what to do or what to believe
What is an argument?
A set of statements (a conclusion supported by premises)
What are the types of statements?
Statements: sentences that are used to make an assertion - “spot is a good dog”
Interrogative sentences: sentences that ask a question - “is spot a good dog?”
Imperative sentences: sentences that issue a command - “be a good dog, spot”
If it is grammatical to add _____ to the beginning of a statement, then it is a statement
“it is true that…”
What is standard form of argument?
Number and display each premise on a separate line.
Display the conclusion on the last line.
Remove all premise indicators.
Remove all conclusion indicators or replace with a simple conclusion indicator like “therefore”.
Rewrite premises and conclusion so that they are complete, explicit, and clear.
Validity
an argument is valid if and only if it is logically impossible for the premises to be true while the conclusion is false
Soundness
valid + all the premises are true
What are invalidating counterexamples
a logically possible scenario in which the premises are true, and the conclusion is false
Modus Ponens (mode that affirms)
If P, then Q.
P.
Therefore Q.
P and Q are variables that stand for statements, any argument with this argument form is valid, no matter which statements “P” and “Q” are.
Note: the order of the premises does not matter
Modus Tollens (mode that denies)
If P, then Q.
Not Q.
Therefore, not P.
Hypothetical syllogism
If P, then Q.
If Q, then R.
Therefore, if P, then R.
Disjunctive syllogism
P or Q.
Not P
Therefore Q.
Dilemma
P or Q.
If P, then R.
If Q, then S.
Therefore, R or S
P or Q.
If P, then R.
If Q, then R.
Therefore, R.
Reductio ad absurdum
Aim: to show that some statement S is true
Assume that not S is true
Show that not S leads to a contradiction or other absurd (clearly false) claim
Conclude that S is true
True or false: Denying the antecedent is a valid argument form, what is it?
False
If P, then Q.
Not P
Therefore, not Q
True or False - Circular arguments are valid
True, A circular argument is an argument where the conclusion is also a premise
Tautologies
statements that are true no matter what - “Therefore, either it is raining here now, or it is not raining here now”
True or False Tautologies are not valid
false
True or False - Arguments with inconsistent premises are valid
True, Its valid because there will never be a situation where all the premises are true, and the conclusion is false
There must be a way for all the premises to be true and the conclusion false for argument for be invalid
What are inconsistent premises
premises that can’t all be true at the same time “it’s raining here now” “it’s not raining here now”
Necessary conditions
X is a necessary condition for Y just in case X is required for Y
- The first thing is required for the second thing
- No second thing without first thing
how to have counterexamples to claims about necessary conditions
Prove that a necessary condition is false
Y obtains but not X
(EXAMPLE)
completing all the exercises is necessary in order to pass the course
Counterexample: Becca missed an exercise and passed with a B.
Sufficient conditions
X is a sufficient condition for Y just in case X guarantees Y
- If X obtains, Y obtains too
Counterexamples to claims about sufficient conditions
show that X is not a sufficient condition for Y, find a case where X obtains but not Y
