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Posterior Analytics




In the Prior Analytics , syllogistic logic is considered in its formal aspect; in the Posterior it is considered in respect of its ''matter''. The "form" of a syllogism lies in the necessary connection between the premises and the conclusion. Even where there is no fault in the form, there may be in the matter, i.e. the propositions of which it is composed, which may be true or false, probable or improbable.

When the premises are certain, and the conclusion formally follows from them, this is demonstration, and produces knowledge. Such syllogisms are called ''apodeictical'', and are dealt with in the two books of the Posterior Analytics. When they are not certain, such a syllogism is called ''dialectical'', and these are dealt with in the eight books of the Topics . A syllogism which seems to be perfect both in matter and form, but which is not, is called ''sophistical'', and these are dealt with in the book On Sophistical Refutations .

The contents of the Posterior Analytics can be summarised as follows:

  • All demonstration must be founded on principles already known. The principles on which it is founded must either themselves be demonstrable, or be so-called First Principles , which cannot be demonstrated, nor need to be, being evident in themselves (or "nota per se" in scholastic jargon).


  • We cannot demonstrate things in a circular way, supporting the conclusion by the premises, and the premises by the conclusion. Nor can there be an infinite number of middle terms between the first principle and the conclusion.


  • In all demonstration, the first principles, the conclusion, and all the intermediate propositions, must be necessary, general and Eternal Truths . Of things that happen by chance, or contingently, or which can change, or of Individual things, there is no demonstration.


  • Some demonstrations prove only that the things are a certain way, rather than why they are so. The latter are the most perfect.


  • The first figure of the syllogism (see Term Logic for an outline of syllogistic theory) is best adapted to demonstration, because it affords conclusions universally affirmative. This figure is commonly used by mathematicians.


  • The demonstration of an affirmative proposition is preferable to that of a negative; the demonstration of a universal to that of a particular; and direct demonstration to a Reductio Ad Absurdum .


  • The principles are more certain than the conclusion.


  • There cannot be both opinion and knowledge of the same thing at the same time.


In the second book, Aristotle says that the questions that may be put with regard to any thing are four

:1 Whether the thing is affected in this way.
:2 Why it is affected in this way.
:3 Whether it exists.
:4 What it is.

The last of these questions was called by Aristotle, in Greek, the "what it is" of a thing. Scholastic logicians translated this into Latin as Quiddity (''quidditas''). This quiddity cannot be demonstrated, but must be fixed by a definition. He deals with Definition , and how a correct definition should be made. As an example, he gives a definition of the number three, defining it to be the first odd number.

He deals with the four kinds of cause - efficient, material, formal, and final.

He also deals with the way in which we acquire first principles. He argues they are not innate, because we may be ignorant of them for much of our life. Nor can they be deduced from any previous knowledge, or they would not be first principles. He concludes that first principles are derived by induction, from the information of sense. From this idea comes the scholastic maxim "there is nothing in the understanding which was not before in some sense".


EXTERNAL LINKS

  • Posterior Analytics, trans. by G. R. G. Mure

  • ---http://etext.library.adelaide.edu.au/a/a8poa/