Logic test 1 Flashcards
Argument
A group pf statements in which the conclusion is claimed to follow the premises
Statement
A sentence that is either true or false
Expressing a statement
show why something is the case
Asserting a statement
forwardly approaching the main point
Premise
the information intended to provide support for a conclusion
Conclusion
The statement is claimed to follow from the premises of an argument; the main point of the argument
Conclusion indicators
Words and phrases that indicate the presence of a conclusion (the statement claimed to follow from the premises)
Necessary Conditions (consequent/end)
Whenever one thing is essential, mandatory, or required in order for another thing to be realized. In other words falsity of the consequent ensures that falsity of the antecedent
Induction (inductive argument)
An argument in which the inferential claim is that the conclusion is probably true if the premises are true. In other words, under the assumption that the premises are true it is improbable for the conclusion to be false.
Sufficient Conditions (antecedent/ beginning)
Whenever one event ensures that another event is realized. In other words, the truth of the antecedent gauruntees the truth of the consequent
Deduction (deductive arguments)
An argument in which the inferential claim is that the conclusion follows necessarily from the premises. In other words, under the assumption that the premises are true it is impossible for the conclusion to be false.
Arguments based on mathematics
An argument in which the conclusion depends on some purely arrhythmic, geometric computation or measurement
Argument from definition
Argument in which the conclusion is claimed to depend merely on the definition of some word or phrase used in the premise or conclusion
Categorical Syllogism
A syllogism constructed entirely of categorical propositions (all cats are mammals/ all c are m) (start with all, no or some)
hypothetical syllogism
A syllogism having a conditional statement for 1 or both of its premises (deductive) (ex: If it snows, school will be canceled. If school is canceled, we will fall behind our schedule. Therefore, if it snows, we will fall behind our schedule) (3 types: conjunctive, disjunctive, conditional)
Disjunctive Syllogism
A rule of inference (implication rule) (P or Q not P therefore Q) (ex: either the vikings win or the eagles will play in the superbowl. The vikings did not win. Therefore, the eagles will play in the superbowl (WEDGE F when F/F)
Conditonal
the antecedent follow the IF and the consequent follows the THEN (horse shoe >) (only F when T/F)
Biconditional
A compound statement consisting of 2 condtionals- one indicated by the word “if” and the other indicated by the phrase “only if”. The triple bar symbol is used to translate a biconditional statement
- conditional is true if and only if the other is true as well.
unless
means wedge V or tilde ~
only if
horseshoe > (if…then, only if) (only F when T/F) (conditional)
if and only if
triple bar
if
horseshoe>
Negation Truth Table
Negation flips truth value (~P ,opposite)
Conjunction Truth Table
Only true when both parts are true( P . Q) only T when T/T ( Dot .)
Disjunction Truth Table
Inclusive (both can be True) or Exclusive (only 1 can be true) ,V wedge, only F when F/F (either or, unless, OR)
Conditional Truth Table
> horseshoe ,If…Then ,(if P then Q) ,Only F when T/F
Biconditional Truth Table
Triple Bar =, (if, only if), only T when T/T or F/F
Premise Indicators
Words and Phrases that help us recognize arguments by indicating the presence of premises (statements being offered in support of a conclusion)
Proposition
The information content imparted by a statement, or simply put, its meaning
Nonarguments
if they merely give information, with no intent to persuade and without conclusion keywords (warnings, pieces of advice, statements of belief or opinion, narratives, illustrations, explanations)
Explandum
the statement that describes the event or phenomenon to be explained
Explanans
the statement or group of statements that purports to do the explaining
Conditional statements
Horseshoe > , If…Then statements, only F when T/F
Validity
DEDUCTIVE, An argument in which assuming the premises are true, it is impossible for the conclusion to be false
Soundness
If we determine a deductive argument to be valid (true premises true conclusion), we are saying the premises support the conclusion- there is no way the premises can be true and the conclusion false (sound+deductive+valid= all true premises and conclusion)
cogency
An inductive argument is COGENT when both requirements are met
1. argument is strong (logical analysis)
2. All premises are True (truth value analysis)
Negation
The word “not” and the phrase “it is not the case that” are used to deny the statement that follows them
Conjunction
DOT ( . ), only T when T/T
Disjunction
WEDGE ( V ), only F when F/F (either, unless, or)
Inclusive “or”
Disjunction V, both are True
Exclusive “or”
Disjunction V, only one is True
Tautology
A statement that is necessarily True (all True under main operator)
Self- Contradiction
A statement that is necessarily False (all False under main operator)
Contingency
Statements that are neither true nor false (sometimes true sometimes false under main operator)
Logically Equivalent Statements
2 truth functional statements that have identical truth tables under the main operator
Contradictory statements
2 statements that have OPPOSITE truth values under the main operator on every line of their respective truth tables
Consistent statements
2 or more statements that have AT LEAST 1 LINE on their respective truth tables where the main operators are BOTH TRUE)
