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Contraposition. In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent inverted and flipped.
In propositional logic, affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "if the lamp was broken, then the room would be dark") under certain assumptions (there are no other lights in the room, it is ...
In logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. More specifically, given a conditional sentence of the form , the inverse refers to the sentence . Since an inverse is the contrapositive of the converse, inverse and converse are logically equivalent to each other.
Modus tollens is a mixed hypothetical syllogism that takes the form of "If P, then Q. Not Q. Therefore, not P." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from P implies Q to the negation of Q implies the negation of P is a valid argument.
Logical reasoning is a mental activity that aims to arrive at a conclusion in a rigorous way. It happens in the form of inferences or arguments by starting from a set of premises and reasoning to a conclusion supported by these premises. The premises and the conclusion are propositions, i.e. true or false claims about what is the case.
In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions. The origin of the square can be traced back to Aristotle 's tractate On Interpretation and its distinction between two oppositions: contradiction and contrariety.
Deductive reasoning. Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and " Socrates is a man" to ...
The fallacy of four terms is a syllogistic fallacy. Types of syllogism to which it applies include statistical syllogism, hypothetical syllogism, and categorical syllogism, all of which must have exactly three terms. Because it applies to the argument's form, as opposed to the argument's content, it is classified as a formal fallacy.