Exam 1 Flashcards
Argument
Has premises and conclusion
Valid argument
not possible for premises to be true and conclusion to be false
Inductive strength
indication of how well premise supports conclusion. Matter of evidence, not form
Can a valid argument have a false conclusion?
Yes.
Argument with inconsistent premises are
Valid
Simple sentence
1 subject, 1 predicate
Truth Functional compound sentence
truth value is determined by value of simple sentences that make up the compound sentence.
Biconditional Truth Table: Which are True?
TT and FF
Single Arrow Truth Table: Which are False?
T to F
Neither Nor
—| (A v B)
Both And
—| (A ^ B)
What does it mean if truth value is a model for sentence S?
If sentence is always true on that tva.
Truth functionally true sentence
always true regardless of the combination of truth values assigned to its components. True on every tva.
Truth Functionally consistent
A least 1 truth value assignment on which all members of a sentence are true (1 row on truth table)
Truth Functionally Equivalent
no tva on which their truth values differ. In other words, for two sentences P and Q, they are models of each other.
Example: For truth table A, B, A v B, B v A, always have same values
Truth functionally false
False on every truth value assignment
Truth functionally contingent
TVA of sentence depends on value of components
Truth functionally consistent
1 row for which all sentences in set are true. Note: does NOT have to be simple sentences
Sound argument
If argument is valid AND all premises are true
Counterexample
all T premises and F conclusion
Logical true/tautology
not possible to be false
Logically false
not possible for statement to be true “self contradiction”
Logically equivalent
same truth value, not possible fore them to have different truth values
Logically contradictory
only if not possible for statements to have same truth value
Logically consistent vs. inconsistent:
Is it possible fore all statements in set to be true?
X if Y
Y –> X (opposite of if then)
Whenever/Given/Assuming X, Y
X –> Y
X is SUFFICIENT for Y
X –> Y
X only if Y
X –> Y
X is NECESSARY for Y
Y –> X (opposite)
If then
Only if
Whenever/Given/Assuming
Is sufficient for
X –> Y
if
is necessary for
Y –> X
X UNLESS Y
or
X if not Y
–| Y –> X
If and only if
biconditional
if X then Y AND if Y then X
biconditional
__ just in case ___
biconditional
Truth functionally Satisfiable
sentence that is true on @ least 1 tva
truth functionally true or contingent
Truth functionally falsifiable
sentence that is false on at least 1 tva.
truth functionally false or contingent
Truth functionally contradictory
sentences always have a different truth value
Truth functionally INconsistent
no row for which all true at once
Can it be consistent and contradictory?
NO
Can it be equivalent but inconsistent?
Yes, if always False
Truth functionally valid
argument with no tva all premise true and conclusion false
Inconsistence PREMISES
at least 1 false premise
