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An example of this is the use of the rules of inference found within symbolic logic. Aristotle held that any logical argument could be reduced to two premises and a conclusion. [2] Premises are sometimes left unstated, in which case, they are called missing premises, for example: Socrates is mortal because all men are mortal.
Historically, begging the question refers to a fault in a dialectical argument in which the speaker assumes some premise that has not been demonstrated to be true. In modern usage, it has come to refer to an argument in which the premises assume the conclusion without supporting it. This makes it an example of circular reasoning. [1] [2]
Deductive reasoning offers the strongest support: the premises ensure the conclusion, meaning that it is impossible for the conclusion to be false if all the premises are true. Such an argument is called a valid argument, for example: all men are mortal; Socrates is a man; therefore, Socrates is mortal. For valid arguments, it is not important ...
See also List of Ship of Theseus examples Sorites paradox (also known as the paradox of the heap ): If one removes a single grain of sand from a heap, they still have a heap. If they keep removing single grains, the heap will disappear.
Deductive arguments are sometimes referred to as "truth-preserving" arguments. For example, consider the argument that because bats can fly (premise=true), and all flying creatures are birds (premise=false), therefore bats are birds (conclusion=false). If we assume the premises are true, the conclusion follows necessarily, and it is a valid ...
A definition of a function, set, or other mathematical object that is defined in terms of itself, using a base case and a rule for generating subsequent elements. recursive function A function that can be computed by a procedure that calls itself, directly or indirectly, with a base case to prevent infinite recursion. recursive function theory
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 are apples. (False) A valid argument with a false premise may lead to a false conclusion, (this and the following examples do not follow the Greek syllogism):
An argument map or argument diagram is a visual representation of the structure of an argument.An argument map typically includes all the key components of the argument, traditionally called the conclusion and the premises, also called contention and reasons. [1]