How Do We Know Something "Scientifically"? - Aristotle's Prior Analytics Bk. 1 - Ch 1-7
Prior Analytics Book I
At the beginning of the Prior Analytics Aristotle is setting out to lay the foundations of the science of logic. For Aristotle, if one properly sets up these logical parts, then one can be led with complete surety about the conclusion reached. If one starts from a first principle which is self-evident, which is comprised of clear terms, true premises, and proper formal logic, then truth is certain. This is "science" for Aristotle. He lays this out in the Prior Analytics by defining the basic parts which are needed in the use of logic, such as: premise, syllogism, demonstration, dialectic, and predication.
The science and power of logic begins with the use of terms and premises. Aristotle defines a premise as a statement which is going to either affirm or deny a predicate of a subject, which are the terms. Now, these premises can be statements of different types, such as universal, partial, or indefinite depending on the relation between the subject and predicate. A universal premise would mean that all or none of the predicate if part of the subject, for example. These premises then serve as the foundation for reasoning through the use of a syllogism. Aristotle defines the syllogism as, "... discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so." Through the syllogism, then, the mind can be brought to a new truth which was implicitly or explicitly contained in the former.
How is this possible? Well, the success of this endeavor depends on the nature of the premises involved, and this gets to the distinction Aristotle makes between demonstration and dialectic. If the premises used are first principles of a discipline, then they will be absolutely necessary and universal in nature. They must be correct and are very broad in their meaning and application. If the premise is necessary then one can absolutely come to a likewise necessary conclusion, which is demonstration. And because the premise is so universal, there may be many lesser and more specific applications of that principle that are not explicit until made so by the syllogism. Now, if the premise is not a first principle, but only suspected to be, or of a lesser nature, then one can only proceed with probability until more is learned. This is dialectic.
In part II, Aristotle makes the point again that premises are either universal, particular, or indefinite. In other words, he says, "...something either is [particular], must be [universal], or may be [indefinite]..." part of something else. What does this mean? Well, this is related to Aristotle's classification of things into genus and species. By their immaterial forms, things are related to one another. Thus, the use of logic in this way brings out the relation between things and how we can speak regarding them with certainty, or not. Given that we can speak about these three categories either affirmatively or negatively, Aristotle is laying out a system by which we one show the relation between statements and how they can or cannot be converted into one another.
Part III - VII
Part III through VII continue in this vain. They lay out the specifics of the relations between different types of premises and then how those premises relate in the formal structure of syllogisms to either properly demonstrate their conclusion or not. These rules have already been well summarized and can be understood through these figures.