Statement that contains another statement as a component
Ex: The lights are on, the lights are off
In order to have a complex statement, you must be able to replace it with something that makes sense.
Common compound propositions:
Their parts are called:
Conjunctions
Conjuncts
Conjuncts are connected together with the word:
And
Yet
But
Never the less
Ex: Andrew went swimming and Susan went hiking
Disjunction:
Or
Unless
Propositional variables=
p, q, r, s.....
Truth Functional Component
Any component of a compound statement whose replacement by another statement having the same truth value would notchange the truth value of the compound statement
Exclusive Sense of Disjunction:
It is either one or the other, BUT not both are true
Inclusive sense of disjunction
One or the other or both may be true
Ex: Getting a 3.8 gpa will get you on the deans list, or having a 3.9 will...
Disjunctions "v" will only be false when:
both p and q are false
Conditional statements:
a compound statement with the form, "if p, then q"
Antecedent in a conditional statement:
the component that immediately follows the "if"
Consequent in a conditional statement:
component that immediately follows the "then"
Implication:
the relation that holds between the antecedent and the consequent of a conditional state.
Whenever you have a true antecedent:
the whole thing will be true
If Combes was a rockstar he'd be famous
Combes isnt a rockstar
Therefore Combes isnt famous
C (horseshoe) F
- C
- F
This is nota good argument...
refutation by counter example:
If obama were a rockstar hed be famous
Obama isnt a rockstar
Therefore obama is famous
Valid argument=
When youhave true premises and true conclusions
True premises and False conclusion=
invalidity
Material implication:
Symbolized by the horseshoe
p materially implies q
is true when either p is false, or q is trueq
Refutation by logical analogy:
exhibiting the fault of an argument by presenting another argument with the same form whose premises are known to be true and whose conclusion is known to be false
The obama and combes example of being a rockstar
Statement variable:
A letter (lower case) for which a statement may be substituted
Invalid argument form:
argument form that has at least one substitution instance with true premises and a false conclusion
Valid argument form
argument form that has no substitution instances with true premises and a false con.
Disjunctive Syllogism:
a valid argument where one premise is a disjunction, another premise is is the denial of one of the two disjuncts, and the conclusion is the truth of the other disjunct.
p v q
-p
q
Modus Ponens:
A valid argument that relies on a conditional premise, and another premise affirms the antecedent of that conditional, and the conclusion affirms its consequent
p (horseshoe) q
p
q
Modus Tollens:
Valid argument that relies on a conditional premise and another premise denies the consequent of that conditional, and the conclusion denies its antecedent
p (horseshoe) q
-q
-p
Hypothetical Syllogism:
Valid argument containing only conditional propositions.
p (horseshoe) q
q (horseshoe) r
p (horseshoe) r
Common invalid forms
1. Fallacy of affirming the consequent
2. Fallacy of denying the antecedent
Fallacy of affirming the consequent:
Fallacy in which the second premise of an argument affirms the consequent of a conditional premise and the conclusion of its argument affirms its antecedent.
p (horseshoe) q
q
p
Fallacy of denying the antecedent:
Fallacy in which the second premise of an argument denies the antecedent of a conditional premise and the conclusion of the argument denies its consequent
p (horseshoe) q
-p
-q
Tautologous Statement form:
A statement form that has only true substitution instances, a "tautology"
Self-contradictory statement form:
A statement form that has only false substituion instances, a "contradiction"
Contingent Statement form:
A statement form that has both true and false substitution instances