Basic Logic

Logic, both traditional and modern (mathematical) is about sound reasoning and the rules that govern it. Formally established by Aristotle, logic has crept into all fields of human knowledge with impartiality. Aristotle drew from many individuals (Socrates, Zeno of Elea, Parmenides, and Plato) the principles of what would be known as the Organon (five treatises on logic). In the Organon, Aristotle holds that a proposition is a complex involving two terms, a subject and a predicate, each of which is represented by a noun.

Though a series of proposition, an individual would then be able to analyze its logical form though converting them into a syllogistic form. The syllogistic method is sometimes called the logic of terms. Every proposition is said to contain two elements: an element which names or refers to something (the subject) and an element which expresses what is said about it (the predicate). Traditional logic is concerned with four forms of propositions which are often stated as:

All S is P

No S is P

Some S is P

Some S is not P

‘All S is P’ is called a universal affirmative or A. ‘No S is P’ is called the ‘universal negative’ or E. ‘Some S is P’ is called the ‘particular affirmative’ or I while ‘Some S is not P’ is called the ‘particular negative’ or O. Note that ‘All S is P’ can be substituted by ‘Every S is P’ to accommodate certain grammatical complications.

A syllogism consists of three propositions. The first two, the premises, share exactly one term, and they logically entail the third proposition, the conclusion, which contains the two non-shared terms of the premises. The logical form of a proposition would then be determined by its quantity (universal or particular) and by its quality (affirmative or negative). When put together, these propositions form the core of the study of deductive inference. Syllogism can be properly defined as a discourse in which certain things having been stated would entail a necessary following statement. This would then lead to deductively valid arguments in the form of:

All as are b,

All bs are c,

All as are c.

All as are b,

No bs are c,

No a is c.

Some as are b,

All bs are c,

Some as are c.

Some as are b,

No bs are c,

Not all as are c.

As we can see from the four basic forms of syllogism, any deductively valid argument can be expressed in one of the four obvious perfect syllogisms through simplification and conversion. The conclusion of every syllogism must be a conclusion that obviously follows out of necessity.

Comments
One Response to “Basic Logic”
  1. henrypoong says:

    haha..back to basic huh

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