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A premise or premiss [a] is a proposition—a true or false declarative statement—used in an argument to prove the truth of another proposition called the conclusion. [1] Arguments consist of a set of premises and a conclusion. An argument is meaningful for its conclusion only when all of its premises are true. If one or more premises are ...
Given premises that A=B and B=C, then the conclusion follows necessarily that A=C. 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).
Premises and conclusions are normally seen as propositions. A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water is boiling." expresses a proposition since it can be true or false.
(First premise is a conditional statement). (Second premise is the negation of the consequent). (Conclusion deduced is the negation of the antecedent) The following is an example of an argument using modus tollens: If it is raining, then there are clouds in the sky. There are no clouds in the sky.
A statement or proposition that asserts both a statement and its negation, considered universally false in classical logic. contradictory Referring to a pair of statements or propositions where one is the negation of the other, such that they cannot both be true or both be false. contraposition
We begin with a famous example: All humans are mortal. All Greeks are humans. All Greeks are mortal. The reader can check that the premises and conclusion are true, but logic is concerned with inference: does the truth of the conclusion follow from that of the premises? The validity of an inference depends on the form of the inference.
From the example above, humans, mortal, and Greeks: mortal is the major term, and Greeks the minor term. The premises also have one term in common with each other, which is known as the middle term; in this example, humans. Both of the premises are universal, as is the conclusion. Major premise: All mortals die. Minor premise: All men are mortals.
The study of this ancient subject is mostly carried out today in the field of study called argumentation theory under the name of argumentation schemes. [ 1 ] [ 11 ] An example of an argumentation scheme is the scheme for argument from position to know given below.