Premise

A premise (Latin praemissa " the advance Skillful " ) or antecedent is called in logic a requirement or acceptance. It is a statement from a logical conclusion is drawn.

Example: From " All men are mortal " and " Socrates is a man " follows " Socrates is mortal ". The first two statements are the premises, the latter statement is the implication or inference.

Premises and truth

If the premises are in a valid conclusion true, the conclusion must be true. An example of this is the above-mentioned conclusion that from the " All men are mortal " and " Socrates is a man " follows " Socrates is mortal ". However, the converse is not true: If the premises (or some of the premises ) is false, does not apply necessarily mean that the conclusion is false. For example, it follows from "All men are Greeks " and " Socrates is a man ", the sentence " Socrates is Greek". Here is a premise is false, but the conclusion is true.

Premises therefore do not need to be necessarily true. On the contrary, it is occasionally premises from which one knows that they are wrong. This is, for example, in the proof technique of indirect proof of the case in which starting from a false assumption with the aim to refute this. Perhaps the best known example of an indirect proof is the theorem of Euclid, in which it is proved that there are infinitely many prime numbers.

Symbolic representation

A conclusion is symbolically represented as follows:

Read: It follows from.

A conclusion can therefore have several premises; but instead there is usually assume that it has only one conclusion. But this is basically the Convention, there is no reason in principle why a conclusion should not have multiple conclusions.

Dependence and freedom of premises

At the conclusion presented above one says that the conclusion follows from the premises. This does not mean that the conclusion is actually true or even must always be true; Nor does it mean that the conclusion could only be true if the premises are true. Rather, it simply means that under the condition that all the premises are true, the conclusion is necessarily true.

In many logical systems, as in the classical propositional and predicate logic, the deduction theorem applies. It says that it is permissible, one of the premises in the form of the antecedent of " if-then " construction (fachsprachlich material implication or conditional called ) to move in the conclusion, so the argument:

Proceed to the argument:

This was the former premise to the antecedent, the former conclusion B to the postscript of the conditional tense (read: "If An, then B"), which forms the premise of the new argument.

On the deduction theorem is based, among other things, the calculi of natural deduction.

Another way to reduce the number of premises without affecting the validity of the argument, results, if it is possible to derive one of the premises of the other, ie if the following applies:

In this case, the premise is superfluous (fachsprachlich: dependent) and can also be deleted from the assumption set.

History of Philosophy

The term " premise " goes back to the Latin translation of the Arabic literature on Aristotle's syllogistic logic in the 12th century. " Premise " is the translation of the Greek word πρότασις ( protasis, " advance Nifty "). " Premise " are mentioned here both premisses of a syllogism.