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[1] [2] The word "valid" is derived from the Latin validus, meaning strong. The validity of a measurement tool (for example, a test in education) is the degree to which the tool measures what it claims to measure. [3]
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:
Being a valid argument does not necessarily mean the conclusion will be true. It is valid because if the premises are true, then the conclusion has to be true. This can be proven for any valid argument form using a truth table which shows that there is no situation in which there are all true premises and a false conclusion. [2]
An extensional definition gives meaning to a term by specifying its extension, that is, every object that falls under the definition of the term in question.. For example, an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class.
A broadly circular definition has a larger circle of words. For example, the definition of the primary word is defined using two other words, which are defined with two other words, etc., creating a definitional chain. This can continue until the primary word is used to define one of the words used in the chain, closing the wide circle of terms.
A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). [1] [2] Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). [3]
A defining vocabulary is a list of words used by lexicographers to write dictionary definitions. The underlying principle goes back to Samuel Johnson's notion that words should be defined using 'terms less abstruse than that which is to be explained', [1] and a defining vocabulary provides the lexicographer with a restricted list of high-frequency words which can be used for producing simple ...
For example, modus ponens is a rule of inference according to which all arguments of the form "(1) p, (2) if p then q, (3) therefore q" are valid, independent of what the terms p and q stand for. [13] In this sense, formal logic can be defined as the science of valid inferences. An alternative definition sees logic as the study of logical ...