Enhance Your Learning with Philosophy - Formal Logic Flash Cards for quick learning
A branch of formal logic that deals with the study of logical relationships between propositions using logical operators such as 'and', 'or', and 'not'.
A formal system that extends propositional logic by introducing variables, quantifiers, and predicates to represent relationships between objects and make statements about them.
Errors in reasoning that occur when the premises of an argument are not logically connected to the conclusion, leading to invalid or unsound arguments.
A logical process in which conclusions are derived from general principles or premises through valid reasoning, leading to certain conclusions.
A logical process in which conclusions are derived from specific observations or examples, leading to probable or likely conclusions.
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.
A deductive argument consisting of two premises and a conclusion, following a specific structure and formulating valid logical reasoning.
A branch of formal logic that deals with the study of modalities such as possibility, necessity, and contingency, and their logical relationships.
Arguments presented in philosophy that involve reasoning and logical analysis to support or refute philosophical claims or theories.
A step-by-step demonstration of the validity of an argument or proposition using formal rules of inference and logical axioms.
Symbols or words used to combine or modify propositions in logic, including 'and', 'or', 'not', 'if-then', and 'if and only if'.
A property of deductive arguments in which the argument is both valid and has all true premises, ensuring the truth of the conclusion.
A property of deductive arguments in which the conclusion logically follows from the premises, regardless of the truth or falsity of the premises.
A statement or proposition that is logically inconsistent or self-contradictory, having both true and false interpretations.
A statement or proposition that is always true, regardless of the truth values of its component propositions, often represented as 'p or not p'.
A logical relationship between two conditional statements in which the antecedent and consequent are negated and swapped, resulting in an equivalent statement.
A valid form of deductive reasoning in which the antecedent of a conditional statement is affirmed, leading to the affirmation of the consequent.
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.
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'.
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'.
A rule of inference in logic that allows for the chaining of multiple conditional statements to form a longer chain of implications.
A principle in logic stating that for any proposition, either the proposition or its negation must be true, leaving no middle ground.
A principle in logic stating that a proposition cannot be both true and false at the same time, ensuring logical consistency.
A principle in logic stating that a proposition is always true when it refers to itself, asserting its own identity.
A principle in logic stating that valid reasoning follows logical rules and principles, allowing for rational inference and deduction.
A property in logic and mathematics that allows for the distribution of logical operators or mathematical operations over a set of propositions or terms.
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.
A symbol in predicate logic (∃) that indicates the existence of at least one object that satisfies a given predicate or condition.
A symbol in predicate logic (∀) that indicates that a given predicate or condition is true for all objects in a specified domain.
Two propositions that are logically contradictory, having opposite truth values, such as 'p' and 'not p'.
A set of propositions that can all be true at the same time, without any logical contradictions or inconsistencies.
A set of propositions that cannot all be true at the same time, containing logical contradictions or inconsistencies.
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'.
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'.
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'.
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'.
A condition that, if satisfied, guarantees the truth of a given proposition or statement, often represented as 'p is sufficient for q'.
A logical fallacy in which the consequent of a conditional statement is affirmed, leading to the incorrect affirmation of the antecedent.
A logical fallacy in which the antecedent of a conditional statement is denied, leading to the incorrect denial of the consequent.
A logical fallacy in which a key term or phrase is used with multiple meanings or interpretations, leading to ambiguity and invalid reasoning.
A logical fallacy in which only two options or possibilities are presented, ignoring other potential alternatives or nuances.
A logical fallacy in which a general conclusion is drawn based on insufficient or limited evidence, leading to an unwarranted generalization.
A logical fallacy in which an argument is attacked by targeting the person making the argument rather than addressing the argument itself.
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.
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.
A logical fallacy in which a causal relationship is assumed between two events or phenomena based on correlation or coincidence, without sufficient evidence.
A logical fallacy in which an argument is misrepresented or distorted in order to make it easier to attack or refute.
A logical fallacy in which an irrelevant or unrelated topic is introduced to divert attention from the main issue or argument.
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.
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.
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.
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.
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.
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.
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.
A logical fallacy in which only two options or possibilities are presented, ignoring other potential alternatives or nuances.
A logical fallacy in which a lack of evidence or knowledge is used as support for a particular claim or conclusion.