RULES OF LOGIC Flashcards
“Perhaps truth is a non-concrete construct. It could be relative.”
Aristotle’s Law of the Middle states that there is no middle-ground of truth, either something is true or it is not. If it is not false, then it is true.
In order for a statement to be a statement, it must have…
A truth statement
What is a negation? What is the negation of “the hat is red”
A version of the original statement which has the opposite truth value of the original statement. “The hat is not red,”
What is the negation of “all men are mortal.”
Some men are not mortal.
What is an implication? What is its converse?
An if-then statement.
If P, then Q
P is called the antecedent, and Q is called the consequent
If it is a bird (P), then it flies (Q)
A converse switches the antecedent and the consequent
If Q, then P
“If it flies, then it is a bird”
Are converses logically equivalent to an implication?
No
What is the inverse of an implication? Are they logically equivalent to implications?
The negation of BOTH the antecedent and the consequent.
Original implication: If P, then Q
Inverse: If not P, then not Q
No, they are not logically equivalent with implications
What is the contrapositive to an implication? Is it logically equivalent to the implication?
Negate both antecedent and the consequent, AND swap the antecedent with the consequent
Original implication: If P, then Q
Contrapositive: If NOT Q, then NOT P
Yes, it is logically equivalent to the implication, and if true, it proves the original implication
What are the inverse, converse, and contrapositive of the statement: “If the money is not spent, the program fails.”
CONVERSE: If the program fails, then the money is not spent
INVERSE: if the money is spent, the program does not fail
CONTRAPOSITIVE: If the program does not fail, then the money is spent.
What is Modus Ponens? What is the Fallacy of Denying the Antecedent?
Affirming the Antecedent
Statements:
If it is a man, then it is mortal
Socrates is a man, therefore Socrates is mortal
Thusly the fallacy of denying the antecedent is…
Flipper is not a man, therefore flipper is not mortal.
What is Modus Tollens? What is the Fallacy of Affirming the Consequent?
Denying the Consequent. It is related to the contrapositive.
If it rains then I will take my umbrella.
I did not take my umbrella, therefore it did not rain.
Fallacy of the Consequent
I took my umbrella, therefore it rained.
What is Reductio Ad Absurdum?
A proof by contradiction. “Reduction to Absurdity.”
Proof of an implication to be true by proving the negation of the implication must be false
What is the negation of an implication?
If P then Q
NEGATION:
P = true
Q is either not true, or the negation of Q is true
What two fallacies can easily come from misuse of reduction ad absurdum?
Strawman fallacy & Slippery slope fallacy
