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Logic
50 flashcards
A cogent argument is an inductive argument with true premises that make the conclusion probable or likely.
Logic is the study of principles and criteria for valid reasoning and argument structure.
The two main branches of logic are deductive logic and inductive logic.
Deductive logic is a form of reasoning where conclusions necessarily follow from the premises, if the premises are true and the reasoning is valid.
An example deductive argument: All humans are mortal. Socrates is a human. Therefore, Socrates is mortal.
Inductive logic is a form of reasoning that moves from specific observations or premises to a general conclusion.
Example inductive argument: The sun has risen every day for billions of years. Therefore, the sun will rise tomorrow.
A valid argument is one where the conclusion necessarily follows from the premises, assuming the premises are true.
A sound argument is a valid argument with true premises.
A tautology is a statement that is always true by its logical form alone, regardless of the truth values assigned to its components.
A contradiction is a statement that is always false by its logical form alone.
The law of non-contradiction states that contradictory statements cannot both be true in the same sense at the same time.
Propositions are statements that can be either true or false, but not both.
A compound proposition is a proposition formed by combining two or more simpler propositions using logical connectives.
Examples of logical connectives include and, or, not, if...then, if and only if.
A truth table is a table that shows the truth values of a compound proposition for all possible combinations of truth values for its component propositions.
A fallacy is a defect or flaw in an argument that causes the stated conclusion to not necessarily follow from the premises.
Deductive reasoning derives necessarily true conclusions from true premises, while inductive reasoning derives probable conclusions from observations.
An example of a formal deductive system is propositional logic.
Modus ponens is a rule of inference stating that if P implies Q, and P is true, then Q must also be true.
Validity refers to the logical form of an argument, while truth refers to whether the premises and conclusion of an argument accurately describe reality.
Affirming the consequent is an informal fallacy of taking the form: If P, then Q. Q is true. Therefore, P is true.
Denying the antecedent is an informal fallacy of taking the form: If P, then Q. P is false. Therefore, Q is false.
Necessary conditions must be true for something else to be true. Sufficient conditions guarantee that something else is true if they are true.
A syllogism is a deductive argument with two premises and a conclusion, following a valid logical form.
Aristotelian logic, developed by Aristotle, was one of the earliest formal deductive logical systems and included syllogistic logic.
Symbolic logic is the study of formal logical systems using variables and symbolic notation rather than natural language.
Boolean logic is a symbolic logical system dealing with only two truth values - true and false.
A logical proof is a sequence of statements, with each statement being inductively derived from previous statements using valid rules of inference.
Categorical logic deals with categorical propositions that relate two classes or categories of objects.
The inverse of a conditional 'If P then Q' is 'If not-Q then not-P'.
The converse of a conditional 'If P then Q' is 'If Q then P'.
The contrapositive of 'If P then Q' is 'If not-Q then not-P', which is logically equivalent.
Disjunctive syllogism is a valid form of argument: P or Q, not P, therefore Q.
A hypothetical syllogism is a valid argument form combining two conditional premises.
The law of excluded middle states that for any proposition P, either P is true or its negation not-P is true.
Quantification deals with quantifiers like 'all' and 'some' to reason about groups or sets.
Universal quantification uses the quantifier 'all' or 'every' to state that something is true for every instance.
Existential quantification uses 'some' or 'there exists' to state that something is true for at least one instance.
The Law of Double Negation states that not(not-P) is logically equivalent to P.
De Morgan's Laws describe the relationship between negation and conjunction/disjunction: not(P and Q) = (not-P) or (not-Q), and not(P or Q) = (not-P) and (not-Q).
Logical equivalence means two statements have the same truth value under all possible assignments of truth values to their components.
A conditional proof shows that if certain premises are true, then some conclusion necessarily follows from those premises.
A reductio ad absurdum proof shows a statement is true by demonstrating that its negation leads to a logical contradiction.
A premise is a statement taken to be true in an argument. An assumption is something taken for granted in reasoning.
Analytic statements are true by definition or meaning alone. Synthetic statements make claims about the world based on evidence.
The Principle of Explosion states that from a contradiction (false statement), any proposition whatsoever can be validly derived.
Fuzzy logic is a form of reasoning that admits degrees of truth, rather than just true or false.
Examples of inductive reasoning include generalizing from observations, using statistical syllogisms, and arguments from analogy.
Hume pointed out that inductive reasoning assumes the future will resemble the past, but this itself cannot be deductively proven.