前分析篇

The Prior Analytics (Ancient Greek: Ἀναλυτικὰ Πρότερα; Latin: Analytica Priora) is a work by Aristotle on reasoning, known as syllogistic, composed around 350 BC. Being one of the six extant Aristotelian writings on logic and scientific method, it is part of what later Peripatetics called the Organon.

The term analytics comes from the Greek words analytos (ἀναλυτός, 'solvable') and analyo (ἀναλύω, 'to solve', literally 'to loose'). However, in Aristotle's corpus, there are distinguishable differences in the meaning of ἀναλύω and its cognates. There is also the possibility that Aristotle may have borrowed his use of the word "analysis" from his teacher Plato. On the other hand, the meaning that best fits the Analytics is one derived from the study of Geometry and this meaning is very close to what Aristotle calls episteme (επιστήμη), knowing the reasoned facts. Therefore, Analysis is the process of finding the reasoned facts.

In the Analytics then, Prior Analytics is the first theoretical part dealing with the science of deduction and the Posterior Analytics is the second demonstratively practical part. Prior Analytics gives an account of deductions in general narrowed down to three basic syllogisms while Posterior Analytics deals with demonstration.

Contents

Book 1

In the first book of the Prior Analytics, Aristotle begins by defining foundational concepts:

Premiss, a statement that affirms or denies something of an object, which he divides in two different ways:

By quantity (the extension of the subject): Universal for all or none of the subject in matter "All humans are animals", particular when it is part of the subject "Some humans are male", and indefinite when it is not any the other categorizations, lacking a quantifier "Justice is good";

According to how it is obtained: Demonstrative if it is true and based on fundamental postulates, dialetical if it assumes the most plausible answer between two contradictory statements for the sake of argument. These definitions are discussed in more depth in the work Topics;

Term The components into which a premise is resolved—namely, the predicate and the subject of which it is predicated. It is crucial to understand that Aristotle's logic is categorical. It operates within his framework of categories, placing special emphasis on "substance" as the primary subject. For Aristotle, premises are fundamentally structured in the standard form "A is B" (or "B is predicated of A").

Syllogism A discourse or formal analysis in which, once certain premises are laid down, a resulting conclusion necessarily follows from them.

Following these definitions, Aristotle analyzes the various types of syllogisms. This analysis is essential for understanding his philosophy of science, which centers around a specific type of syllogism: the demonstration. Throughout the work, Aristotle extensively explores the implications of different modal premises in syllogisms—namely, the problematic (possible), assertoric (factual), and apodictic (necessary). This book also introduces the concept of the three syllogistic figures.

The three figures

In any valid syllogism, one specific term must appear in both premises to logically bridge them. Aristotle called this the middle term. Depending on the syntactic position of this middle term within the propositions (whether it serves as the subject or the predicate in the premises), the argument is classified into one of three figures. A fourth figure was later formalized by subsequent logicians, but it was not originally posited by Aristotle .

The relations between Predicate and Subject in these inferences can be:

(A) Universal Affirmative: All S is P (e.g., "All humans are mortal").

(E) Universal Negative: No S is P (e.g., "No humans are mortal").

(I) Particular Affirmative: Some S is P (e.g., "Some humans are mortal").

(O) Particular Negative: Some S is not P (e.g., "Some humans are not mortal").

Not all combinations of these relations yield a valid logical conclusion in every figure. To memorize which combinations (moods) are valid for each figure, medieval scholastic logicians developed clever mnemonic names — such as Barbara, Celarent, Darii, and Ferio. In these mnemonics, the vowels correspond exactly to the sequence of propositions (Major premise, Minor premise, Conclusion) required to form a valid syllogism.

Book 2

Book II of the Prior Analytics centers on the properties of syllogisms, the derivation of conclusions from false premises, and other related forms of argumentation. Special attention is given to two distinct types of logical demonstration:

Circular (or Reciprocal) Demonstration: This consists of proving a premise by means of the conclusion—essentially using the conclusion of a syllogism to prove one of its own original premises. Aristotle explains that such a proof is only logically valid if the subject-predicate relations can be perfectly inverted, meaning the terms must be coextensive (or conceptually equal). However, he argues that if one must assume all the converses of the original syllogism to be true, the circular demonstration becomes epistemically trivial (akin to proving that "A is A"); thus, it holds no actual demonstrative or scientific value.

Demonstration per Impossibile (Reduction to Absurdity): Analogous to modern proof by contradiction, this method aims to prove a statement by initially assuming its contradictory to be true. By combining this assumed premise with another known true premise, the per impossibile demonstration yields a conclusion that is clearly impossible or absurd, thereby proving that the initial assumption was false and the desired conclusion must be true.