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In propositional logic, modus ponens (/ ˈmoʊdəs ˈpoʊnɛnz /; MP), also known as modus ponendo ponens (from Latin 'method of putting by placing'), [1] implication elimination, or affirming the antecedent, [2] is a deductive argument form and rule of inference. [3] It can be summarized as " P implies Q. P is true. Therefore, Q must also be ...
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 ...
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 logic and the philosophy of logic, specifically in deductive reasoning, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions). For example, the rule of inference called modus ponens takes two premises, one in ...
Begging the question. In classical rhetoric and logic, begging the question or assuming the conclusion (Latin: petītiō principiī) is an informal fallacy that occurs when an argument's premises assume the truth of the conclusion. Historically, begging the question refers to a fault in a dialectical argument in which the speaker assumes some ...
Argument. An argument is a series of sentences, statements, or propositions some of which are called premises and one is the conclusion. [1] The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persuasion. Arguments are intended to determine or show the degree of truth or acceptability of ...
Formal fallacy. In logic and philosophy, a formal fallacy[a] is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic. [2] It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still ...
If the premises are true, then the conclusion is necessarily true, too. Now we turn to an invalid form. All A are B. All C are B. Therefore, all C are A. To show that this form is invalid, we demonstrate how it can lead from true premises to a false conclusion. All apples are fruit. (True) All bananas are fruit. (True) Therefore, all bananas ...