Logic: Clarification of Terms and Concepts in Sentence
Logic
Tautology: a
compound sentence that is true regardless of the truth values of its component
atomic sentences. The truth table
analysis will yield all T's under the major connective.
Contradiction: a
compound sentence that is false regardless of the truth values of its component
atomic sentences. The truth table
analysis will yield all F's under the major connective.
Contingency: A
statement that is either true or false depending upon the truth values of the
component atomic sentences (or upon its own truth values if it is an atomic
sentence). The truth table analysis
will yield at least one T and one F under the major connective.
Only compound sentences can be tautologous or contradictory. All atomic sentences are contingent.
Atomic sentence:
an independent sentence with no connective.
Compound sentence:
any sentence built from shorter atomic sentences by means of sentence
connectives.
Variables: place
holders used to identify the form of any sentence or argument.
Constants:
sentence abbreviations arising either through translation or given in
statements or arguments that could be abbreviations for specific sentences.
Material Equivalence:
A contingent biconditional
Logical Implication:
A tautologous conditional
Logical Equivalence:
A tautologous biconditional
Corresponding Conditional: Every argument can be represented as a conditional
statement. An argument that is valid
and represented through a hypothetical statement will be a tautology. Thus, any valid argument that is represented
by conjoining the premises to imply the conclusion will be a logical
implication since its truth table analysis will yield a tautology and all
tautologous statements whose major connective is an implication are logical
implications.
Expansion of a Truth Table: The determination of the proper possible combinations of truth
values that hold between all the component atomic sentences. The expansion of a truth table is determined
by "2 ", where "2" is T and F and "n" is the
number of atomic sentences appearing in the statement or argument.
Major connective:
The connective yielding the final truth value of any compound sentence.
Valid: A quality
of a deductive argument in which it is impossible for all the premises to be
true while the conclusion is false. If
it can be determined that all the premises of any given argument can be true
while the conclusion is false, the argument is proven invalid.
Proof of Invalidity:
A method of assigning truth values to all sentences in an argument such
that when the argument is invalid, it will be possible to show the truth values
of each atomic sentence that will yield all true premises and a false
conclusion. If it is impossible to
assign such a combination, the argument is valid.
Argument form:
any argument type represented through the use of variables as place
markers.
Substitution instance:
Any argument represented by constants that represent atomic sentences
that is analogous in form to an argument form represented by statement
variables.
Sentence form:
any sentence type represented through the use of variables as place
markers.
Sentence: any
statement, whether atomic or compound, that is represented by constants.
Argument: any
group of statements containing at least one premise and a conclusion that is
represented by constants.