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[34] [35] This means that the truth of the premises ensures the truth of the conclusion. A deductive argument is sound if it is valid and all its premises are true. [36] For example, inferring the conclusion "no cats are frogs" from the premises "all frogs are amphibians" and "no cats are amphibians" is a sound argument.
Example of an early argument map, from Richard Whately's Elements of Logic (1852 edition). Argumentation theory is the interdisciplinary study of how conclusions can be supported or undermined by premises through logical reasoning.
An argument by analogy may use a particular truth in a premise to argue towards a similar particular truth in the conclusion. For example, if A. Plato was mortal, and B. Socrates was like Plato in other respects, then asserting that C. Socrates was mortal is an example of argument by analogy because the reasoning employed in it proceeds from a ...
A priori ('from the earlier') and a posteriori ('from the later') are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on experience. A priori knowledge is independent from any experience. Examples include mathematics, [i] tautologies and deduction from pure reason.
The corresponding conditional of a valid argument is a logical truth and the negation of its corresponding conditional is a contradiction. The conclusion is a necessary consequence of its premises. An argument that is not valid is said to be "invalid". An example of a valid (and sound) argument is given by the following well-known syllogism:
Reason is the capacity of consciously applying logic by drawing valid conclusions from new or existing information, with the aim of seeking the truth. [1] It is associated with such characteristically human activities as philosophy, religion, science, language, mathematics, and art, and is normally considered to be a distinguishing ability possessed by humans.
As the study of argument is of clear importance to the reasons that we hold things to be true, logic is of essential importance to rationality. Arguments may be logical if they are "conducted or assessed according to strict principles of validity", [1] while they are rational according to the broader requirement that they are based on reason and knowledge.
The study of argument in the field of argumentation theory since Perelman and Olbrechts-Tyteca's The New Rhetoric and Stephen Toulmin's The Uses of Argument, [16] both first published in 1958, has been characterized by a recognition of the defeasible, non-monotonic nature of most ordinary everyday arguments and reasoning.