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2 kinds of symbolic logic:
- 1. Simple (atomic)
- 2. Compound (complex)
- has no other part to it.
- Ex: Columbia is the capital of S.C.
- 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:
Conjuncts are connected together with the word:
- Never the less
- Ex: Andrew went swimming and Susan went hiking
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
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"
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
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
When youhave true premises and true conclusions
True premises and False conclusion=
- 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
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.
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.
A valid argument that relies on a conditional premise, and another premise affirms the antecedent of that conditional, and the conclusion affirms its consequent
Valid argument that relies on a conditional premise and another premise denies the consequent of that conditional, and the conclusion denies its antecedent
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.
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
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
- A tautological statement of the form:
- [(p horseshoe q) horseshoe p] horseshoe p
A truth funcvtional relation asserting that two statements connected by the three bar sign have the same truth values
A compound statement that asserts that its two component statements imply one another and therefore are materially equivalent.
two statements for which the statement of their material equivalence is a tautology; they are equivalent in meaning and can replace one another.
An expression of logical equivalence between a symbol and the negation of the negation of that symbol.
De Morgan's Theorems
- 1. the negation of the disjunction of two statements is logically equivalent to the conjunction ofthe negations of the two disjuncts
- 2. The negation of the conjunction of two statements is logically equivalent to the disjunction of the negations of the two conjuncts
p (horseshoe) q is logically equivalent to:
- p v q
The three laws of thought:
- 1. principle of identity
- 2. principle of noncontradiction
- 3. principle of excluded middle
Principle of identity:
if any statement is true, it is true
Principle of Noncontradiction:
- No statement can be both true and false
- Every state. of the form p dot -p must be false. that every such state. is self contradictory
Principle of excluded middle:
- Every state. is either true or false
- Every state. of the form p v -p must be true
- That every such state. is a tautology