Posterior Analytics
The Posterior Analytics is a text from Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...

's Organon
The Organon is the name given by Aristotle's followers, the Peripatetics, to the standard collection of his six works on logic:* Categories* On Interpretation* Prior Analytics* Posterior Analytics...

that deals with demonstration
Demonstration (teaching)
Demonstration involves showing by reason or proof, explaining or making clear by use of examples or experiments. Put more simply, demonstration means to clearly show. In teaching through demonstration, students are set up to potentially conceptualize class material more effectively as shown in a...

, definition
A definition is a passage that explains the meaning of a term , or a type of thing. The term to be defined is the definiendum. A term may have many different senses or meanings...

, and scientific knowledge. The demonstration is distinguished as a syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...

 productive of scientific knowledge
, while the definition marked as the statement of a thing's nature, ... a statement of the meaning of the name, or of an equivalent nominal formula.

In the "Prior Analytics
Prior Analytics
The Prior Analytics is Aristotle's work on deductive reasoning, specifically the syllogism. It is also part of his Organon, which is the instrument or manual of logical and scientific methods....

", 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, true, and primary, and the conclusion formally follows from them, this is demonstration, and produces scientific knowledge of a thing. Such syllogisms are called apodeictical, and are dealt with in the two books of the Posterior Analytics. When the premises are not certain, such a syllogism is called dialectical, and these are dealt with in the eight books of the Topics
Topics (Aristotle)
The Topics is the name given to one of Aristotle's six works on logic collectively known as the Organon. The other five are:*Categories*De Interpretatione*Prior Analytics*Posterior Analytics*On Sophistical Refutations...

. 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
On Sophistical Refutations
Sophistical Refutations is a text in Aristotle's Organon.Aristotle identified thirteen fallacies, as follows:Verbal fallacies* Accent or emphasis* Amphibology* Equivocation* Composition* Division...


The contents of the Posterior Analytics may 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
    First principles
    In philosophy, a first principle is a basic, foundational proposition or assumption that cannot be deduced from any other proposition or assumption. In mathematics, first principles are referred to as axioms or postulates...

    , 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
    An individual is a person or any specific object or thing in a collection. Individuality is the state or quality of being an individual; a person separate from other persons and possessing his or her own needs, goals, and desires. Being self expressive...

     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
    Term logic
    In philosophy, term logic, also known as traditional logic or aristotelian logic, is a loose name for the way of doing logic that began with Aristotle and that was dominant until the advent of modern predicate logic in the late nineteenth century...

     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
    Reductio ad absurdum
    In logic, proof by contradiction is a form of proof that establishes the truth or validity of a proposition by showing that the proposition's being false would imply a contradiction...

  • The principles are more certain than the conclusion.
  • There cannot be both opinion and knowledge of the same thing at the same time.

The second book Aristotle starts with a remarkable statement, the kinds of things determine the kinds of questions, which are four:
1 Whether the relation of a property (attribute) with a thing is a true fact.
2 What is the reason of this connection.
3 Whether a thing exists.
4 What is the nature and meaning of the thing.

The last of these questions was called by Aristotle, in Greek, the "what it is" of a thing. Scholastic logicians translated this into Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 as "quiddity
In scholastic philosophy, quiddity was another term for the essence of an object, literally its "whatness," or "what it is." The term derives from the Latin word "quidditas," which was used by the medieval scholastics as a literal translation of the equivalent term in Aristotle's Greek.It...

" (quidditas). This quiddity cannot be demonstrated, but must be fixed by a definition. He deals with definition
A definition is a passage that explains the meaning of a term , or a type of thing. The term to be defined is the definiendum. A term may have many different senses or meanings...

, 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.

Maintaining that to know a thing's nature is to know the reason why it is and we possess scientific knowledge of a thing only when we know its cause, Aristotle posited four major sorts of cause as the most sought-after, middle terms of demonstration:
the definable form; an antecedent which necessitates a consequent; the efficient cause; the final cause.

He concludes the book with the way the human mind comes to know the basic truths or primary premisses or first principles, which 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 states that first principles are derived by induction, from the sense-perception implanting the true universals in the human mind. From this idea comes the scholastic maxim "there is nothing in the understanding which was not prior in the senses".

Of all types of thinking, scientific knowing and intuition are considered as only universally true, where the latter is the originative source of scientific knowledge. The great work is closed as: science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

as a whole is...originative source to the whole body of fact
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