CH#4: Necessary and Sufficient Conditions

conditional arguments: 2 main premise and conclusion

1.) one premise wil state a necessary or sufficient condition 2.) the other premise will affirm or deny on of the condiitons

sufficient condition

A is enough for B to happen, if we know A we know enough to know B, relationship can be explained in terms of cause: A is enough for B to happen knowledge: if we know A we know enough to know B truth: if A is true, B must also be true

all and only statements

ALL signals a sufficent condition for example: all basket ball players are tall ONLY signals a necessary condition for example: only women are biological mothers

counterexample

a counter example shows that the statement is false for example: counterexample to "all basketball players are tall" Michael Jordan is a famous basketball player and is not tall.

good conditional arguments

affirms the sufficient condition: modus ponen= P then Q, P, therefore Q deny's the necessary condition: modus tollens= P then Q, not Q, therefor not P P= SUFFICIENT Q=NECESSARY

deductive arguments

arguments in which if the premises are true, the conclusion must also be true, true in all possible worlds these are valid sound argument

both necessary and sufficient

conditions that are both necessary and sufficient are expressed by using if and only if, this relation holds only when we have what is basically a definition

bad conditional arguments

deny the sufficient condition and affirm the necessary condition

negations

if a then b= if not a then not b if not a then b= if not b then a if a then not b= if b then not a

if.. then statements

if= the antecedent which signals a sufficient condition then= the consequent which signal a necessary condition

only if statements

introduces a necessary condition example= elvis is still alive only if jim morrison is still alive, jim morrision being alive is necessary for elvis being alive

a condition can be....

necessary or sufficient

unless statements

not A unless B= B is necessary for A A unless B= B is necessary for not A

testing conditional arguments for validity

rule 1: affirm the sufficient rule 2: deny's the necessary

conditional statements

we often have to state that one thing is a condition for another, for example: being at least 16 years old is a condition for being a licensed driver

necessary condition

x is required for y, if x is not true y is not true