On dictionary's definition, all syllogisms are valid the proper structure is necessary to support conclusion, but is not sufficient, then distinction between valid and invalid syllogisms is made and there are two formal aspects of syllogisms necessary to determination of validity, such as mood is determined by logical form of propositions and figure is determined by placement of middle term.
Some arguments are called syllogisms: a syllogism is in general, a deductive argument in which a conclusion is inferred from two premises. The another kind of syllogisms with which are concerned to call categorical because which are arguments based on the relations of classes or categories relations that are expressed by the categorical propositions with which are familiar.
More formally, we define a categorical syllogism is as a deductive argument consisting of three categorical propositions that together contain exactly three terms, each of which occurs in exactly two of the propositions. Syllogisms are very common, very clear and readily testable. A syllogism is in standard form, premises are arranged in a specified standard order. In a standard form syllogism, the major premise is always stated first, the minor premise is second and the conclusion is the last. It is such as major term means the predicate term of the conclusion, minor term means the subject term of the conclusion, middle term means the term that appears in both premises but not in the conclusion, major premise means containing the major term and minor premise means containing the minor term.
Categorical syllogisms mean an argument is set of premises which support some conclusion. Syllogism means an argument consisting of three statements and two premises and one conclusion. Thus, categorical syllogism means a syllogism consisting of three categorical propositions and containing three distinct terms.
I shall give an example, such as what are these three terms mentioned? Considerate the following syllogism: First point, all mammals are creatures that have hair; Second point, all dogs are mammals and therefore, third point, all dogs are creatures that have hair. I shall refer the mood of a standard form syllogism to characterize its logical form. For example, all great scientists are major term and college graduates are middle term or therefore some professional athletes are minor term and great scientists are major term. In all deduction logic, we aim to discriminate valid arguments from invalid ones; in classical logic this becomes the task of discrimination valid syllogisms for invalid ones.
Thus, it is reasonable to assume that propositions are of a syllogism are all contingent, that is no one of those propositions is necessarily true or necessary false. Under this assumption, the validity or invalidity of any syllogism depends entirely on its form. validity and invalidity are completely independent of the specific content of the argument or its subject matter.
A valid syllogism is a formally valid argument, this implies that if a given syllogism is valid, any other syllogism of the same form will also be valid. And if a syllogism is invalid, any other syllogism of the some form will also be invalid. The common recognition of this fact is attested to by the frequent use of logical analogies in argumentation and felt justifiably of its propositions, the argument is invalid. The best way to expose its character is to construct another argument that has exactly the same form but whose invalidity is immediately apparent argument may be very well have a true conclusion, that can argument is invalid simply means that its conclusion isn't logically implied or necessitated.
In conclusion, a categorical syllogism is an argument with two premises and a conclusion. The major term in a categorical syllogism is the predicate term of the conclusion. The minor term is the subject term of the conclusion. The middle term is the term that occurs in each term is the term that occurs in each premise term. Thus, a categorical syllogism is in standard form. Such as its component statements are all in standard form, its first premise contains the major term, its second premises contains the minor term and the conclusion is stated the last.