If 'p' then 'q' : Asserts that something is true based on a certain condition
The "p" in the conditional statement formula - where "q" is claimed to be true
The "q" in the conditional statement formula - what is claimed to follow if 'p' is true
Claims that the premises provide logically conclusive support for the conclusion
VALID or INVALID
Claims that the premises provide probably support for the conclusion
STRONG or WEAK
A deductive argument that succeeds in providing conclusive support for its conclusion
A deductive argument that fails to provide conclusive support for its conclusion
Deductively valid argument with true premises
Defining characteristics of valid deductive argument: their structure guarantees that if the premises are true so also are the conclusions
Inductive argument that provides highly probable support for its conclusion
Inductive argument that fails to provide strong support for its conclusion
a strong, inductive argument with all premises true
Must be combined with one or more other premises to support the conclusion
Provides support for the conclusion on its own
Deductive argument consisting of two premises and one conclusion
Common valid deductive forms
1. Affirming the antecedent 2. Denying the consequent 3. Disjunctive syllogism 4. Hypothetical syllogism
Affirming the antecedent
if 'p' then 'q', 'p'; therefore 'q' If Spot barks, a burglar is in the house. Spot is barking. Therefore, a burglar is in the house.
Denying the consequent
If 'p' then 'q', not 'q'; therefore not 'p' If it rains, the sidewalk gets wet. But the sidewalk's not wet. So, it must not have rained
Either 'p' or 'q', not 'p'; therefore 'q' The number 3 is either even or odd. However, it is not even. Therefore, it is odd
If 'p' then 'q', if 'q' then 'r'; therefore if 'p' then 'r' If Guy steals the money, he will go to jail. If Guy goes to jail, his family will suffer. Therefore, if Guy steals the money, his family will suffer.
Common invalid deductive forms
1. Affirming the consequent 2. Denying the antecedent
Affirming the consequent
Invalid deductive form If 'p' then 'q', 'q'; therefore 'p'
Denying the antecedent
Invalid deductive form If 'p' then 'q', not 'p'; therefore not 'q' “If today is Tuesday we have logic class. Today's not Tuesday. Hence, we don't have logic today.”
What do good arguments do?
Appeal to reason - they show that it is reasonable to accept the conclusions given the premises
Two forms of agrument
1. Deductive argument 2. Inductive argument
Example of deductive arguments
"Im taller than Aimee. Aimee is taller than Melissa. So I'm taller than Melissa.' -> If the premises offered really are true, then the conclusion must also be true
A rule in invalid arguments?
It is a deductive argument that fails to provide conclusive support for its conclusion. ALTHOUGH - It is still possible for the premises to be true and yet the conclusion to be false.
How to evaluate soundness of an argument
1. Are the premises true? 2. Do those premises lead to the conclusion?
Example of false premises that still support the given conclusion.
Pigs have wings (P). Any animal with wings can fly (P). So, pigs can fly (C). This argument is VALID but UNSOUND.
Example of true premises that don't support the conclusion
Birds have wings (P). Bats have wings (P). Therefore, birds are bats (C).