Prior Analytics

# Prior Analytics

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The Prior Analytics is Aristotle
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 work on deductive reasoning
Deductive reasoning
Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...

, specifically the syllogism
Syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...

. It is also part of his Organon
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...

, which is the instrument or manual of logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

al and scientific methods.

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.

Of the entire Aristotelian corpus, Aristotle gives priority to the study of his treatises on Logic. However, he never gave a general name to his treatises on Logic nor did he coin the word Logic. 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
Posterior Analytics
The Posterior Analytics is a text from Aristotle's Organon that deals with demonstration, definition, and scientific knowledge. The demonstration is distinguished as a syllogism productive of scientific knowledge, while the definition marked as the statement of a thing's nature, .....

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
Jan Lukasiewicz
Jan Łukasiewicz was a Polish logician and philosopher born in Lwów , Galicia, Austria–Hungary . His work centred on analytical philosophy and mathematical logic...

, Józef Maria Bocheński
Józef Maria Bochenski
Józef Maria Bocheński was a Polish Dominican, logician and philosopher.-Life:...

and Günther Patzig have sided with the Protasis
Protasis
In drama, a protasis is the introductory part of a play, usually its first act. The term was coined by the fourth-century Roman grammarian Aelius Donatus. He defined a play as being made up of three separate parts, the other two being epitasis and catastrophe. In modern dramatic theory the term...

-Apodosis
Apodosis
Apodosis may refer to:*In linguistics, the main clause in a conditional sentence*In logic, the apodosis corresponds to the consequent; ....

dichotomy
Dichotomy
A dichotomy is any splitting of a whole into exactly two non-overlapping parts, meaning it is a procedure in which a whole is divided into two parts...

while John Corcoran
John Corcoran (logician)
.John Corcoran is a logician, philosopher, mathematician, and historian of logic. He is best known for his philosophical work, helping us to understand such central concepts as the nature of inference, the relationship between logic and epistemology, and the place of proof theory and model theory...

prefers to consider a syllogism as simply a deduction.

In the third century AD, Alexander of Aphrodisias
Alexander of Aphrodisias
Alexander of Aphrodisias was a Peripatetic philosopher and the most celebrated of the Ancient Greek commentators on the writings of Aristotle. He was a native of Aphrodisias in Caria, and lived and taught in Athens at the beginning of the 3rd century, where he held a position as head of the...

'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, the first translation of Prior Analytics by Boethius appeared in Latin. No Westerner between Boethius and Abelard is known to have read the Prior Analytics. Anonymus Aurelianensis III from the second half of the twelfth century is the first extant Latin commentary.

## The Syllogism

The Prior Analytics represents the first formal study of logic which is the study of arguments; argument being in logic 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 consisting of three sentences: 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.

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 sentences may 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; 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
Mnemonic
A mnemonic , or mnemonic device, is any learning technique that aids memory. To improve long term memory, mnemonic systems are used to make memorization easier. Commonly encountered mnemonics are often verbal, such as a very short poem or a special word used to help a person remember something,...

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
Theophrastus
Theophrastus , a Greek native of Eresos in Lesbos, was the successor to Aristotle in the Peripatetic school. He came to Athens at a young age, and initially studied in Plato's school. After Plato's death he attached himself to Aristotle. Aristotle bequeathed to Theophrastus his writings, and...

and does not occur in Aristotle's work, although there is evidence that Aristotle knew of fourth-figure syllogisms."