Philosophy Formal Logic Study Cards

Enhance Your Learning with Philosophy - Formal Logic Flash Cards for quick learning



Propositional Logic

A branch of formal logic that deals with the study of logical relationships between propositions using logical operators such as 'and', 'or', and 'not'.

Predicate Logic

A formal system that extends propositional logic by introducing variables, quantifiers, and predicates to represent relationships between objects and make statements about them.

Logical Fallacies

Errors in reasoning that occur when the premises of an argument are not logically connected to the conclusion, leading to invalid or unsound arguments.

Deductive Reasoning

A logical process in which conclusions are derived from general principles or premises through valid reasoning, leading to certain conclusions.

Inductive Reasoning

A logical process in which conclusions are derived from specific observations or examples, leading to probable or likely conclusions.

Truth Tables

Tables used in logic to determine the truth values of complex propositions by systematically evaluating all possible combinations of truth values for the component propositions.

Syllogisms

A deductive argument consisting of two premises and a conclusion, following a specific structure and formulating valid logical reasoning.

Modal Logic

A branch of formal logic that deals with the study of modalities such as possibility, necessity, and contingency, and their logical relationships.

Philosophical Arguments

Arguments presented in philosophy that involve reasoning and logical analysis to support or refute philosophical claims or theories.

Formal Proofs

A step-by-step demonstration of the validity of an argument or proposition using formal rules of inference and logical axioms.

Logical Connectives

Symbols or words used to combine or modify propositions in logic, including 'and', 'or', 'not', 'if-then', and 'if and only if'.

Soundness

A property of deductive arguments in which the argument is both valid and has all true premises, ensuring the truth of the conclusion.

Validity

A property of deductive arguments in which the conclusion logically follows from the premises, regardless of the truth or falsity of the premises.

Contradiction

A statement or proposition that is logically inconsistent or self-contradictory, having both true and false interpretations.

Tautology

A statement or proposition that is always true, regardless of the truth values of its component propositions, often represented as 'p or not p'.

Contrapositive

A logical relationship between two conditional statements in which the antecedent and consequent are negated and swapped, resulting in an equivalent statement.

Modus Ponens

A valid form of deductive reasoning in which the antecedent of a conditional statement is affirmed, leading to the affirmation of the consequent.

Modus Tollens

A valid form of deductive reasoning in which the negation of the consequent of a conditional statement is affirmed, leading to the negation of the antecedent.

Hypothetical Syllogism

A valid form of deductive reasoning in which two conditional statements are combined to form a conclusion, following the structure 'if p then q, and if q then r, then if p then r'.

Disjunctive Syllogism

A valid form of deductive reasoning in which a disjunction is used to derive a conclusion, following the structure 'either p or q, not p, therefore q'.

Chain Rule

A rule of inference in logic that allows for the chaining of multiple conditional statements to form a longer chain of implications.

Law of Excluded Middle

A principle in logic stating that for any proposition, either the proposition or its negation must be true, leaving no middle ground.

Law of Non-Contradiction

A principle in logic stating that a proposition cannot be both true and false at the same time, ensuring logical consistency.

Law of Identity

A principle in logic stating that a proposition is always true when it refers to itself, asserting its own identity.

Law of Rational Inference

A principle in logic stating that valid reasoning follows logical rules and principles, allowing for rational inference and deduction.

Distributive Property

A property in logic and mathematics that allows for the distribution of logical operators or mathematical operations over a set of propositions or terms.

De Morgan's Laws

Two laws in logic that describe the negation of logical conjunction and disjunction, stating that the negation of a conjunction is the disjunction of the negations, and the negation of a disjunction is the conjunction of the negations.

Existential Quantifier

A symbol in predicate logic (∃) that indicates the existence of at least one object that satisfies a given predicate or condition.

Universal Quantifier

A symbol in predicate logic (∀) that indicates that a given predicate or condition is true for all objects in a specified domain.

Contradictory Pairs

Two propositions that are logically contradictory, having opposite truth values, such as 'p' and 'not p'.

Consistent Set

A set of propositions that can all be true at the same time, without any logical contradictions or inconsistencies.

Inconsistent Set

A set of propositions that cannot all be true at the same time, containing logical contradictions or inconsistencies.

Logical Equivalence

A relationship between two propositions in which they have the same truth values in all possible cases, often represented as 'p if and only if q'.

Material Implication

A logical relationship between two propositions in which the truth of one proposition implies the truth of another, often represented as 'if p then q'.

Material Equivalence

A logical relationship between two propositions in which they have the same truth values in all possible cases, often represented as 'p is equivalent to q'.

Necessary Condition

A condition that must be satisfied in order for a given proposition or statement to be true, often represented as 'p is necessary for q'.

Sufficient Condition

A condition that, if satisfied, guarantees the truth of a given proposition or statement, often represented as 'p is sufficient for q'.

Fallacy of Affirming the Consequent

A logical fallacy in which the consequent of a conditional statement is affirmed, leading to the incorrect affirmation of the antecedent.

Fallacy of Denying the Antecedent

A logical fallacy in which the antecedent of a conditional statement is denied, leading to the incorrect denial of the consequent.

Fallacy of Equivocation

A logical fallacy in which a key term or phrase is used with multiple meanings or interpretations, leading to ambiguity and invalid reasoning.

Fallacy of False Dilemma

A logical fallacy in which only two options or possibilities are presented, ignoring other potential alternatives or nuances.

Fallacy of Hasty Generalization

A logical fallacy in which a general conclusion is drawn based on insufficient or limited evidence, leading to an unwarranted generalization.

Fallacy of Ad Hominem

A logical fallacy in which an argument is attacked by targeting the person making the argument rather than addressing the argument itself.

Fallacy of Appeal to Authority

A logical fallacy in which an argument is supported solely by the endorsement or authority of a person or source, without sufficient evidence or reasoning.

Fallacy of Circular Reasoning

A logical fallacy in which the conclusion of an argument is assumed or restated in one of the premises, resulting in a circular or tautological argument.

Fallacy of False Cause

A logical fallacy in which a causal relationship is assumed between two events or phenomena based on correlation or coincidence, without sufficient evidence.

Fallacy of Straw Man

A logical fallacy in which an argument is misrepresented or distorted in order to make it easier to attack or refute.

Fallacy of Red Herring

A logical fallacy in which an irrelevant or unrelated topic is introduced to divert attention from the main issue or argument.

Fallacy of Slippery Slope

A logical fallacy in which it is claimed that a particular action or event will inevitably lead to a series of increasingly negative or extreme consequences.

Fallacy of Begging the Question

A logical fallacy in which the conclusion of an argument is assumed or presupposed in one of the premises, resulting in a circular or tautological argument.

Fallacy of False Analogy

A logical fallacy in which an analogy is drawn between two or more things that are not sufficiently similar, leading to invalid or misleading reasoning.

Fallacy of Composition

A logical fallacy in which it is assumed that what is true for the parts of a whole is also true for the whole itself, leading to invalid reasoning.

Fallacy of Division

A logical fallacy in which it is assumed that what is true for the whole is also true for its individual parts, leading to invalid reasoning.

Fallacy of Loaded Question

A logical fallacy in which a question is asked in a way that assumes a controversial or unproven premise, making it difficult to answer without accepting the premise.

Fallacy of Post Hoc

A logical fallacy in which it is assumed that because one event follows another, the first event must have caused the second event, without sufficient evidence.

Fallacy of False Dichotomy

A logical fallacy in which only two options or possibilities are presented, ignoring other potential alternatives or nuances.

Fallacy of Appeal to Ignorance

A logical fallacy in which a lack of evidence or knowledge is used as support for a particular claim or conclusion.