Definitions
An uppercase letter that represents a single, given proposition.
What is a propositional constant?
The disjunction truth table.
What is:
T T T
T F T
F T T
F F T
If Caesar had been a benevolent king (B), then all Romans would have received their full rights under the law (R). The Roman Christians were persecuted for their faith (P). If all Romans had received their full rights, then the Roman Christians would not have been persecuted. Therefore Caesar was not a benevolent king.
What is valid?
B>R P R>~P :. ~B
We assume this when building truth tables for equivalence.
What is not equivalent?
A constructive dilemma is similar to this other type of hypothetical argument.
What is a modus ponens?
The conditional truth table.
What is:
T T T
T F F
F T T
F F T
If composition has both meter (M) and rhyme (R), then it is a poem (P). It is not the case that this composition has meter or rhyme. Therefore this composition is not a poem.
What is invalid?
(M*R)>P ~(MvR) :. ~P
When no contradiction occurs in an equivalence truth table, this is assumed about the argument.
What is not equivalent?
When you find a way to charge a dilemma with an either/or fallacy.
What is "going between the horns?"
The biconditional truth table.
What is:
T T T
T F F
F T F
F F T
If a truth table is completed without contradiction, this is what is assumed about the argument.
What is invalid?
We assume this when building truth tables for consistency.
What is consistency?
A valid argument from which can be used to justify steps in a proof.
What is a rule of inference?
Words that modify or combine simple propositions to make compound propositions.
What is a logical operator?
The translation of "p unless q" in a truth table.
Hint: Conditional Translations
What is ~q>p?
What is invalid?
When no contradiction occurs in a consistency truth table, this is assumed about the argument.
What is consistency?
A step-by-step deduction of a conclusion from a set of premises, each step being justified by an appropriate basic rule.
What is a formal proof of validity?
A valid argument which presents a choice between two conditionals.
What is a dilemma?
These truth tables are solved by assuming the premises to be true and the conclusion to be false.
What is a truth table for validity?
If a number is rational then its digits repeat. A number is rational or its digits do not repeat. Thus, a number is rational if and only if its digits repeat. (R, D)
What is valid?
R > D R v ~D :. R = D
Use the shorter truth table in determining the consistency of the following statements: If you do not have your own business then if you want to make money then you must be an employee. You must be an employee. You have your own business and you want to make money.
What is consistent?
~B > (M > E) E B * M
FT T T T T T T T T
Three hindrances for recognizing the rules of inference in formal proofs.
What is:
1. Single variable can represent very complicated compound propositions
2. Variables can represent propositions which are similar to those represented by other variables
3. Variables can change value from one step to the next within the same proof