Prior Analytics

The Prior Analytics or Analytica Priora is Aristotle's work on deductive reasoning, which is known as his syllogistic. Being one of the six extant Aristotelian writings on logic and scientific method, it is part of what later Peripatetics called the Organon.

Analytics comes from the Greek word "analutos" meaning "solvable" and the Greek verb "analuein" meaning "to solve". However, in Aristotle's corpus, there are distinguishable differences in the meaning of "analuein" 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 έπιστήμη "episteme", knowing the reasoned facts. Therefore, Analysis is the process of finding the reasoned facts.

Aristotle's Prior Analytics represents the first time in history when Logic is scientifically investigated. On those grounds alone, Aristotle could be considered the Father of Logic for as he himself says in Sophistical Refutations, "... When it comes to this subject, it is not the case that part had been worked out before in advance and part had not; instead, nothing existed at all."

A problem in meaning arises in the study of Prior Analytics for the word "syllogism" as used by Aristotle in general does not carry the same narrow connotation as it does at present; Aristotle defines this term in a way that would apply to a wide range of valid arguments. Some scholars prefer to use the word "deduction" instead as the meaning given by Aristotle to the Greek word συλλογισμός "sullogismos". At present, "syllogism" is used exclusively as the method used to reach a conclusion which is really the narrow sense in which it is used in the Prior Analytics dealing as it does with a much narrower class of arguments closely resembling the "syllogisms" of traditional logic texts: two premises followed by a conclusion each of which is a categorial sentence containing all together three terms, two extremes which appear in the conclusion and one middle term which appears in both premises but not in the conclusion. 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.

In the Prior Analytics, Aristotle defines syllogism as "... A deduction in a discourse in which, certain things being supposed, something different from the things supposed results of necessity because these things are so." In modern times, this definition has led to a debate as to how the word "syllogism" should be interpreted. Scholars Jan Lukasiewicz, Józef Maria Bocheński and Günther Patzig have sided with the Protasis-Apodosis dichotomy while John Corcoran prefers to consider a syllogism as simply a deduction.

In the third century AD, Alexander of Aphrodisias's commentary on the Prior Analytics is the oldest extant and one of the best of the ancient tradition and is presently available in the English language.

In the sixth century, Boethius composed the first — known — Latin translation of the Prior Analytics. No Westerner between Boethius and Abelard is known to have read the Prior Analytics. The so-called Anonymus Aurelianensis III from the second half of the twelfth century is the first extant Latin commentary, or rather fragment of a commentary.

The Syllogism

The Prior Analytics represents the first formal study of logic, where logic is understood as the study of arguments. An argument is a series of true or false statements which lead to a true or false conclusion. In the Prior Analytics, Aristotle identifies valid and invalid forms of arguments called syllogisms. A syllogism is an argument that consists of at least three sentences: at least two premises and a conclusion. Although Aristotles does not call them "categorical sentences," tradition does; he deals with them briefly in the Analytics and more extensively in On Interpretation. Each proposition (statement that is a thought of the kind expressible by a declarative sentence) of a syllogism is a categorical sentence which has a subject and a predicate connected by a verb. The usual way of connecting the subject and predicate of a categorical sentence as Aristotle does in On Interpretation is by using a linking verb e.g. P is S. However, in the Prior Analytics Aristotle rejects the usual form in favor of three of his inventions: 1) P belongs to S, 2) P is predicated of S and 3) P is said of S. Aristotle does not explain why he introduces these innovative expressions but scholars conjecture that the reason may have been that it facilitates the use of letters instead of terms avoiding the ambiguity that results in Greek when letters are used with the linking verb. In his formulation of syllogistic propositions, instead of the copula ("All/some... are/are not..."), Aristotle uses the expression, "... belongs to/does not belong to all/some..." or "... is said/is not said of all/some..." There are four different types of categorical sentences: universal affirmative (A), particular affirmative (I), universal negative (E) and particular negative (O).

• A - A belongs to every B
• E - A belongs to no B
• I - A belongs to some B
• O - A does not belong to some B

A method of symbolization that originated and was used in the Middle Ages greatly simplifies the study of the Prior Analytics. Following this tradition then, let:

a = belongs to every

e = belongs to no

i = belongs to some

o = does not belong to some

Categorical sentences may then be abbreviated as follows:

AaB = A belongs to every B (Every B is A)

AeB = A belongs to no B (No B is A)

AiB = A belongs to some B (Some B is A)

AoB = A does not belong to some B (Some B is not A)

From the viewpoint of modern logic, only a few types of sentences can be represented in this way.

The Three Figures

Depending on the position of the middle term, Aristotle divides the syllogism into three kinds: Syllogism in the first, second and third figure. If the Middle Term is subject of one premise and predicate of the other, the premises are in the First Figure. If the Middle Term is predicate of both premises, the premises are in the Second Figure. If the Middle Term is subject of both premises, the premises are in the Third Figure.

Symbolically, the Three Figures may be represented as follows:

	First Figure	Second Figure	Third Figure
	Predicate — Subject	Predicate — Subject	Predicate — Subject
Major Premise	A ------------ B	B ------------ A	A ------------ B
Minor Premise	B ------------ C	B ------------ C	C ------------ B
Conclusion	A ********** C	A ********** C	A ********** C

Syllogism in the first figure

In the Prior Analytics translated by A. J. Jenkins as it appears in volume 8 of the Great Books of the Western World, Aristotle says of the First Figure: "... If A is predicated of all B, and B of all C, A must be predicated of all C." In the Prior Analytics translated by Robin Smith, Aristotle says of the first figure: "... For if A is predicated of every B and B of every C, it is necessary for A to be predicated of every C."

Taking a = is predicated of all = is predicated of every, and using the symbolical method used in the Middle Ages, then the first figure is simplified to:

If AaB

and BaC

then AaC.

Or what amounts to the same thing:

AaB, BaC; therefore AaC

When the four syllogistic propositions, a, e, i, o are placed in the first figure, Aristotle comes up with the following valid forms of deduction for the first figure:

AaB, BaC; therefore, AaC

AeB, BaC; therefore, AeC

AaB, BiC; therefore, AiC

AeB, BiC; therefore, AoC

In the Middle Ages, for mnemonic reasons they were called respectively "Barbara", "Celarent", "Darii" and "Ferio".

The difference between the first figure and the other two figures is that the syllogism of the first figure is complete while that of the second and fourth is not. This is important in Aristotle's theory of the syllogism for the first figure is axiomatic while the second and third require proof. The proof of the second and third figure always leads back to the first figure.

Syllogism in the second figure

This is what Robin Smith says in English that Aristotle said in Ancient Greek: "... If M belongs to every N but to no X, then neither will N belong to any X. For if M belongs to no X, neither does X belong to any M; but M belonged to every N; therefore, X will belong to no N (for the first figure has again come about)."

The above statement can be simplified by using the symbolical method used in the Middle Ages:

If MaN

but MeX

then NeX.

For if MeX

then XeM

but MaN

therefore XeN.

When the four syllogistic propositions, a, e, i, o are placed in the second figure, Aristotle comes up with the following valid forms of deduction for the second figure:

MaN, MeX; therefore NeX

MeN, MaX; therefore NeX

MeN, MiX; therefore NoX

MaN, MoX; therefore NoX

In the Middle Ages, for mnemonic resons they were called respectively "Camestres", "Cesare", "Festino" and "Baroco".

Syllogism in the third figure

Aristotle says in the Prior Analytics, "... If one term belongs to all and another to none of the same thing, or if they both belong to all or none of it, I call such figure the third." Referring to universal terms, "... then when both P and R belongs to every S, it results of necessity that P will belong to some R."

Simplifying:

If PaS

and RaS

then PiR.

When the four syllogistic propositions, a, e, i, o are placed in the third figure, Aristotle develops six more valid forms of deduction:

PaS, RaS; therefore PiR

PeS, RaS; therefore PoR

PiS, RaS; therefore PiR

PaS, RiS; therefore PiR

PoS, RaS; therefore PoR

PeS, RiS; therefore PoR

In the Middle Ages, for mnemonic reasons, these six forms were called respectively: "Darapti", "Felapton", "Disamis", "Datisi", "Bocardo"and "Ferison".

Table of syllogisms

Figure	Major Premise	Minor Premise	Conclusion	Mnemonic Name
First Figure	AaB	BaC	AaC	Barbara
	AeB	BaC	AeC	Celarent
	AaB	BiC	AiC	Darii
	AeB	BiC	AoC	Ferio
Second Figure	MaN	MeX	NeX	Camestres
	MeN	MaX	NeX	Cesare
	MeN	MiX	NoX	Festino
	MaN	MoX	NoX	Baroco
Third Figure	PaS	RaS	PiR	Darapti
	PeS	RaS	PoR	Felapton
	PiS	RaS	PiR	Disamis
	PaS	RiS	PiR	Datisi
	PoS	RaS	PoR	Bocardo
	PeS	RiS	PoR	Ferison

The Fourth Figure

"In Aristotelian syllogistic (Prior Analytics, Bk I Caps 4-7), syllogisms are divided into three figures according to the position of the middle term in the two premisses. The fourth figure, in which the middle term is the predicate in the major premiss and the subject in the minor, was added by Aristotle's pupil Theophrastus and does not occur in Aristotle's work, although there is evidence that Aristotle knew of fourth-figure syllogisms."

External links

• The text of the Prior Analytics is available from the MIT classics archive.
• Prior Analytics, trans. by A. J. Jenkinson
• Template:Librivox
• Robin Smith. "Aristotle's Logic". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
• Aristotle's Prior Analytics: the Theory of Categorical Syllogism an annotated bibliography on Aristotle's syllogistic