L01 - Deductive Argument Flashcards
Affirming the Consequent
An invalid argument in the form ‘If P then Q (premise 1). Q (premise 2). Therefore, P (conclusion)’. This invalid form is often confused with the valid form Modus Ponens.
Antecedent
In a conditional that has the form ‘If P, then Q’ (or ‘If P, Q’), P is the antecedent.
Assertion (or Statement)
Either the act of advancing a sentence as true or the product of that act.
Conditional
A complex sentence of the form ‘If P, Q’ or ‘Q if P’. It involves two elements: P is the antecedent, and Q is the consequent.
Conjunctive Statement (Conjunction)
A complex statement consisting of two sentences (conjuncts) that are joined by a conjunction, such as ‘and’ or ‘but’.
Consequent
In a conditional that has the form ‘If P then Q’, Q is the consequent.
Constructive Dilemma
Deductively valid argument form of the following variety:
(1) P or Q
(2) If P then R
(3) If Q then S
Therefore,
(4) R or S
Disjunctive Statement (Disjunction)
A complex statement that consists in two sentences that are presented as alternatives.
Disjunctive Syllogism
Deductively valid argument form of the following variety:
(1) P or Q
(2) Not Q
Therefore,
(3) P
Hypothetical Syllogism
Deductively valid argument form of the following variety:
(1) If P then Q
(2) If Q then R
Therefore,
(3) If P then R
Modus Ponens
Deductively valid argument form of the following variety:
(1) If P, then Q
(2) P
Therefore,
(3) Q
Modus Tollens
Deductively valid argument form of the following variety:
(1) If P, then Q
(2) Not Q
Therefore
(3) Not P
Necessary Condition
A condition that must be met for a claim to be true.
Necessary Truth
A necessary truth is a claim that is true in all possible scenarios.
Soundness
For an argument to be sound is for it to be valid and for all its premises to be true. By definition, a sound argument proves its conclusion.
Truth Conditions
The truth conditions of a sentence or claim are the conditions that must be obtained in order for that sentence or claim to be true.
Validity
For an argument to be valid is for the truth of its premises to guarantee the truth of its conclusion. An argument is valid just in case there is no way for the conclusion to be false if the premises are true. A structural property of arguments.
Argument
A set of statements (i.e., premises) that purport to support a claim (i.e., the conclusion).
Assertion
The act of stating something as if it were true.
Proposition, statement, sentence, claim.
What you say in order to make an assertion.
Premise
A statement intended to provide rational support for some other statement (a conclusion), often in conjunction with other premises.
Conclusion
A statement intended to be rationally supported by a set of premises.
Law of Identity
For any proposition P: P if and only if P.
Law of Non-Contradiction
Not both P and not-P.
Law of Excluded Middle
P or not-P.
Intuitionistic Logic
Does not include Law of Excluded Middle.
Dialetheic Logic
Does not include Law of Non-Contradiction.
Modal Logics
Introduces complications such as belief, knowledge, obligation, possibility, and temporality.
Linked Arguments
Premises tie together to support a single overall conclusion.
Convergent Arguments
A range of independent grounds for a conclusion are assembled together as premises. No premise in a convergent argument requires the other premises in order to support the conclusion; rather, each premise directly supports the conclusion.
Sequential Arguments
Cases in which premises establish intermediate conclusions, which then serve as premises for some further conclusion.
