Symbolic Logic Flashcards
Simple Statement
A statement that does not contain any other statement as a component.
Compound Statement
A statement that contains two or more statements as components.
Component
A part of a compound statement that is itself a statement, and is of such a nature that, if replaced in the larger statement by any other statement, the result will be meaningful.
Conjunction
A truth-functional connective meaning “and,” symbolized by the dot, •.
A statement of the form p•q is true if and only if p is true and q is true.
Conjunct
Each one of the component statements connected in a conjunctive statement.
Truth-functional component
Any component of a compound statement whose replacement there by any other statement having the same truth value would leave the truth value of the compound statement unchanged.
Truth-functional compound statement
A compound statement whose truth value is determined wholly by the truth value of its components.
Truth-functional connective
Any logical connective (e.g. conjunction, disjunction, material implication and material equivalence) between the components of a truth-functionally compound statement.
Truth table
An array on which all possible truth values of compound statements are displayed, through the display of all possible combinations of the truth values of their simple components.
A truth table may be used to define truth-functional connectives; it may also be used to test the validity of many deductive arguments.
Negation
Denial
Symbolised by the tilde or curl.
~p simply means “it is not the case that p”, and may be read as “not-p”.
Disjunction
A truth-functional connective meaning “or”; components so connected are call disjuncts.
There are two types of disjunction: inclusive and exclusive.
Inclusive disjunction
A truth-functional connective between two components called disjuncts.
A compound statement asserting inclusive disjunction is true when at least one of the disjuncts (that is, one or both) is true.
Normally called simply “disjunction”, it is also called “weak disjunction” and is symbolized by the wedge, V.
Exclusive disjunction
A logical relation meaning “or” that may connect two component statements.
A compound statement asserting exclusive disjunction says that at least one of the disjuncts is true and that at least one of the disjuncts is false.
It is contracted with an “inclusive” (or “weak”) disjunction, which says that at least one of the disjuncts is true and that they may both be true.
Punctuation
The parentheses, brackets and braces used in mathematics and logic to eliminate ambiguity.
Conditional Statement
A hypothetical statement; a compound proposition or statement of the form “if p then q”.
Antecedent
In a conditional statement (“if … then …”), the component that immediately follows the “if”.
Sometimes called the implicans or the protasis.
Consequent
In a conditional statement (“if … then …”), the component that immediately follows the “then”.
Sometimes called the implicate or the apodosis.
Implication
The relation that holds between the antecedent and the consequent of a true conditional or hypothetical statement.
Horseshoe
The symbol for material implication, ⊃.
Material implication
A truth-functional relation (symbolized by the horeshoe, ⊃) that may connect two statements.
The statement “p materially implies q” is true when either p is false, or q is true.
Refutation by logical analogy
A method that shows the invalidity of an argument by presenting another argument that has the same form, but whose premises are known to be true and whose conclusion is known to be false.
Variable
or Statement Variable
A place-holder.
A letter for which a statement may be substituted.
By convention, any of the lowercase letters beginning with p, q, etc. are used.