Laura Takkunen

takkunen@ut.ee

Kultuurilugu

referaat

Aristotle's Logic

Aristotle, marble copy of bronze by Lysippos. Louvre Museum, France

1. Introduction

2. The definition of logic

3. Aristotle’s logic

3.1 The oragon

3.1.1 Categories (Latin: Categoriae )

3.1.2 On Interpretation (Latin: De Interpretatione )

3.1.3 Prior Analytics (Latin: Analytica Priora )

3.1.4 Posterior Analytics (Latin: Analytica Posteriora )

3.1.4 Topics (Latin: Topica )

3.1.6 On Sophistical Refutations (Latin: De Sophisticis Elenchis )

3.2 Syllogism

3.3 Definition

3.4 Demonstration

4. Conclusions

5. References

1. Introduction

Aristotle (Greek: Αριστοτέλης Aristotelēs) lived in 384 BC – March 7, 322 BC. He

was an ancient Greek philosopher, student of Plato and teacher of Alexander the

Great. He wrote many books about physics, poetry, zoology, biology, rhetoric,

government, and logic. Aristotle is one of the most important figures of the western

philosophy and science. He systemised philosophy and scientific way of thinking as a

whole and thus is considered the father of many sciences.

When Aristotle was 18 years old he joined Plato’s Academy in Athens and worked

there nearly twenty years of his life. After that he worked as the teacher of Alexander

until in 336 BC he returned to Athens to start up his own school lykeion. The most

significant of his writings are from the time after returning to Athens. Aristotle died in

332 BC in Euboia where he escaped the restless political times after the death of

Alexander the Great.

Aristotle's logic, especially his theory of the syllogism, has had an unparalleled

influence on the history of Western thought. His logical works contain the earliest

formal study of logic that we have. Together they comprise a highly developed logical

theory, one that was able to command immense respect for many centuries: Kant has

even said that nothing significant had been added to Aristotle's views in the

intervening two millennia. And Jonathan Lear has said, "Aristotle shares with modern

logicians a fundamental interest in metatheory": his primary goal is not to offer a

practical guide to argumentation but to study the properties of inferential systems

themselves.

2. The definition of Logic

Logic, from Classical Greek λόγος (logos), means originally the word, or what is

spoken, (but comes to mean thought or reason). The exact definition of logic is a

matter of controversy among philosophers, but It is often said to be the study of

arguments. However the subject is grounded, the task of the logician is the same: to

advance an account of valid and fallacious inference to allow one to distinguish good

from bad arguments.

Traditionally, logic is studied as a branch of philosophy. Since the mid-1800s logic

has been commonly studied in mathematics, and, even more recently, in computer

science. As a science, logic investigates and classifies the structure of statements and

arguments, both through the study of formal systems of inference and through the

study of arguments in natural language. The scope of logic can therefore be very

large, ranging from core topics such as study of fallacies and paradoxes, to specialist

analyses of reasoning such as probably correct reasoning and arguments involving

causality.

For Aristotle the name logic is unknown, his own name for this branch of knowledge,

or at least the study of reasoning is ‘analytics’, which primary refers to to the analysis

of reasoning into the figures of syllogism, but into it may be included the analysis of

the syllogism into propositions and of the proposition into terms. The term logic he

reserved to mean dialectics.

3. Aristotle’s logic

Aristotle divides sciences in three groups:

1. theoretical

2. practical

3. productive

He sees that the primary purpose of all of them is to know, but knowledge , conduct

and the making of beautiful or useful objects become the ultimate objects.

If one would try to enter logic into these groups, it would respectfully belong to the

group of theoretical sciences, but according to Aristotle the only theoretical sciences

are mathematics, physics and theology or metaphysics, and logic cannot belong to any

of these. Thus logic is not a substantive science but a part of general culture which

anyone should undergo before he studies any science, and which alone will enable

him to know for what sorts of proposition he should demand proof and what sorts of

proof he should demand for them.

3.1 The Organon

Aristotle failed to understand the importance of his written work for humanity. He

thus never published his books, except from his dialogues. Most of Aristotle's work is

probably not authentic, since students and later lecturers most likely edited it.

Aristotle's works on logic, are the only significant works of Aristotle that were never

"lost"; all his other books were "lost" from his death, until rediscovered in the 11th

century.

The Organon was used in the school founded by Aristotle at the Lyceum, and some

parts of the works seem to be a scheme of a lecture on logic. So much so that after

Aristotle's death, his publishers (e.g. Andronicus of Rhodes in 50 BC) collected these

works. In these works we can find the first ontological category theory (relevant in

some branches of intensional logic), the first development of formal logic, the first

known serious scientific inquisitions on the theory of (formal and informal) reasoning,

the foundations of modal logic, and some antecedents of methodology of sciences.

The logical works of Aristotle were grouped into six books by he ancient

commentators at about the time of Christ. They all go under the title Organon

("Instrument"):

1. Categories

2. On Interpretation

3. Prior Analytics

4. Posterior Analytics

5. Topics

6. On Sophistical Refutations

The order of the books (or the teachings from which they are composed) is not

certain, but this list was derived from analysis of Aristotle's writings. There is one

volume of Aristotle's concerning logic not found in the Organon, namely the fourth

book of Metaphysics.

The title Organon reflects a much later controversy about whether logic is a part of

philosophy (as the Stoics maintained) or just a tool used by philosophy (as the later

Peripatetics thought); calling the logical works "The Instrument" is a way of taking

sides on this point. Aristotle never uses this term himself.

3.1.1 Categories (Latin: Categoriae)

The Categories introduces Aristotle's 10-fold classification of that which exists. The

book begins with by consideration of linguistic facts; it distinguishes ‘things said

without combination’ from *things said in combination’. I.e. words and phrases such

as ‘man’, ‘runs’, ‘in the Lyceum’ from propositions such as ‘man runs’. ‘words

uncombined’ are said to mean one or other of the following things. These categories

consist of:

Substance (e.g. man),

Quantity (e.g. three cubits long),

Quality (e.g.white),

Relation (e.g. double),

Place (e.g. in the lyceum),

Date (e.g. yesterday),

Posture(e.g. sits),

Possession (e.g. is shod),

Action (e.g. cuts),

Passion (e.g. is cut).

Subjects and predicates of assertions are terms. A term (horos) can be either

individual, e.g. Socrates, Plato or universal, e.g. human, horse, animal, white.

Subjects may be either individual or universal, but predicates can only be universals:

Socrates is human, Plato is not a horse, horses are animals, humans are not horses.

The word universal (katholou) seems to be an Aristotelian coinage. Literally, it means

"of a whole"; its opposite is therefore "of a particular" (kath’ hekaston). Universal

terms can properly serve as predicates, while particular terms cannot.

This distinction is not simply a matter of grammatical function. We can readily

enough construct a sentence with "Socrates" as its grammatical predicate: "The person

sitting down is Socrates". Aristotle, however, does not consider this a genuine

predication. He calls it instead a merely accidental, incidental (kata sumbebêkos)

predication. Such sentences are, for him, dependent for their truth values on other

genuine predications (in this case, "Socrates is sitting down").

Consequently, predication for Aristotle is as much a matter of metaphysics as a matter

of grammar. The reason that the term Socrates is an individual term and not a

universal is that the entity which it designates is an individual, not a universal. What

makes white and human universal terms is that they designate universals.

These categories appear in almost all of Aristotel’s works, but he is not very

consistent about the number of the categories, for example posture and possession

only reappear a few times and in fact it can be said that Aristotle later come to the

conclusion that posture and possession are not ultimate, unanalysable notions.

“Of things said without any combination, each signifies either substance or quantity or

quality or a relative or where or when or being-in-a-position or having or doing or

undergoing. To give a rough idea, examples of substance are man, horse; of quantity:

four-foot, five-foot; of quality: white, literate; of a relative: double, half, larger; of

where: in the Lyceum, in the market-place; of when: yesterday, last year; of being-in-

a-position: is-lying, is-sitting; of having: has-shoes-on, has-armor-on; of doing:

cutting, burning; of undergoing: being-cut, being-burned”. (Categories 4, 1b25-2a4,

tr. Ackrill, slightly modified)

3.1.2 On Interpretation (Latin: De Interpretatione)

On Interpretation introduces Aristotle's conceptions of proposition and judgement,

and treats contrarieties between them. It contains an account of simple sentences

(what later come to be called "propositions." And deals with quantifiers ("all,"

"some," "none") and their logical relations. As such, it contains Aristotle's principal

contribution to philosophy of language.

In On Interpretation Aristotel traces the possible oppositions between propositions. He

takes the existential judgment as the primary kind and argues that to every affirmation

there corresponds exactly one denial such that that denial denies exactly what that

affirmation affirms. The pair consisting of an affirmation and its corresponding denial

is a contradiction (antiphasis). In general, Aristotle holds, exactly one member of any

contradiction is true and one false: they cannot both be true, and they cannot both be

false. An example of possible varieties:

A (i.e. some) man exists.

A man does not exist.

A not-man exists.

A not-man does not exist.

3.1.3 Prior Analytics (Latin: Analytica Priora)

The Prior Analytics introduces his syllogistic method, argues for its correctness, and

discusses inductive inference.

Aristotle's anaylsis of the simplest form of argument: the three-term

Syllogism. The standard example in philosophy has always been:

o All men are mortal. [Premise1 in the form: All B's are

C's.]

o Socrates is a man. [Premise 2 in the form: (All) A is B.]

o Therefore, Socrates is mortal. [Conclusion in the form:

All A's are C's.]

This example is somewhat misleading, despite the fact that it is the standard

one, since it treats a proper name ("Socrates") as a term (or class name.) One

of the fundamental departures of modern (19th & 20th Century C.E.) symbolic

logic is that it treats sentences about individuals differently from the way it

treats sentences about classes. But with this first figure form of the syllogism

Aristotle arrives at a clear and explicit distinction between truth and validity,

where the latter is a property of argument forms. (If the premises of a valid

argument are true, the conclusion must be true.)

Syllogism will be discussed more in the later parts.

3.1.4 Posterior Analytics (Latin: Analytica Posteriora)

The Posterior Analytics discusses correct reasoning in general. The book is for the

most part occupied with demonstration, which presupposes the knowledge of first

premises not themselves known by demonstration.

Here Aristotle identifies the valid forms of the syllogism. He identifies the

formal key to valid syllogistic forms in the middle term (identified in the form

above by "B.") The middle term must be "distributed" (quantified) if an

argument form is to be valid. (Of course this is a necessary but not sufficient

condition. Not every argument form with a distributed middle term is valid.)

For a syllogism to achieve the status of a demonstration the argument form

must be valid and the premises must be true, and must be known to be true

unconditionally. The premises must, therefore, either be themselves derivable

as conclusions of other demonstrations following necessarily from necessarily

true premises or they must be known by "intuition".

At the end Aristotle talks about the question how these are known. What is the faculty

by which we know them: and is the knowledge acquired, or is it latent in us from the

beginning of our lives? It would be hard to imagine, that knowledge would be there

from the beginning on without us knowing it but just as hard is to imagine, that it

would be acquired without any pre-existing knowledge. Aristotle sees that these two

problems can be passed by assuming that some humble faculty of knowledge is a

starting point from which on we can further develop our knowledge. Such faculty is

perception, the discriminative power that is inborn in all animals. From perception to

knowledge the first stage is memory, the remaining of the percept when the

perception is over. And the second stage is experience or framing, on the bases of

repeated memories of the perceived things.

Later he raises the question whether defining and demonstrating can be alternative

ways of acquiring the same knowledge. His reply is complex:

1. Not everything demonstrable can be known by finding definitions, since all

definitions are universal and affirmative whereas some demonstrable

propositions are negative.

2. If a thing is demonstrable, then to know it just is to possess its demonstration;

therefore, it cannot be known just by definition.

3. Nevertheless, some definitions can be understood as demonstrations

differently arranged.

As an example of case 3, Aristotle considers the definition "Thunder is the extinction

of fire in the clouds". He sees this as a compressed and rearranged form of this

demonstration:

Sound accompanies the extinguishing of fire.

Fire is extinguished in the clouds.

Therefore, a sound occurs in the clouds.

We can see the connection by considering the answers to two questions: "What is

thunder?" "The extinction of fire in the clouds" (definition). "Why does it thunder?"

"Because fire is extinguished in the clouds" (demonstration).

Definition and demonstration will be discussed more later.

3.1.5 Topics (Latin: Topica)

The Topics treats issues in constructing valid arguments, and inference that is

probable, rather than certain. It is in this treatise that Aristotle mentions the idea of the

Predicables, which was further developed by Porphyry and the scholastic logicians.

The "Topics" identify strategies and techniques Aristotle identified for

constructing valid arguments. The general name for this kind of reasoning is

dialectic. Dialectic begins with a opinion or belief, examines, criticizes, and

revises that opinion/belief in the light of reason and other things known or

believed to be true, in order to establish scientifically known premises which

can then be used in demonstrations to generate syllogistically the truth of

conclusions derived. Aristotle's account of dialectic owes much to the "method

of hypotheses" in Plato's Phaedo.

“We should distinguish the kinds of predication (ta genê tôn katêgoriôn) in which the

four predications mentioned are found. These are ten in number: what-it-is, quantity,

quality, relative, where, when, being-in-a-position, having, doing, undergoing. An

accident, a genus, a peculiar property and a definition will always be in one of these

categories”. (Topics I.9, 103b20-25)

3.1.6 On Sophistical Refutations (Latin:De Sophisticis Elenchis)

On Sophistical Refutations deals with a variety of bad or invalid argument forms:

"fallacies" and gives a treatment of logical fallacies, and provides a key link to

Aristotle's work on rhetoric.

3.2 Syllogism

The most famous achievement of Aristotle as logician is his theory of inference,

traditionally called the syllogistic (though not by Aristotle). That theory is in fact the

theory of inferences of a very specific sort: inferences with two premises, each of

which is a categorical sentence, having exactly one term in common, and having as

conclusion a categorical sentence the terms of which are just those two terms not

shared by the premises. Aristotle calls the term shared by the premises the middle

term (meson) and each of the other two terms in the premises an extreme (akron). The

middle term must be either subject or predicate of each premise, and this can occur in

three ways: the middle term can be the subject of one premise and the predicate of the

other, the predicate of both premises, or the subject of both premises. Aristotle refers

to these term arrangements as figures (schêmata): Syllogism is defined by Aristotle as

a 'discourse in which, certain things being stated, something other than what is stated

follows of necessity from their being so'.

The propostions of a categorical syllogism must between them employ exactly three

terms, each term appearing twice as, for example, in

1.) All men are mortal

2.) No gods are mortal

Therefore

3.) no men are gods.

or

1.) Everybody likes Fridays

2.) Today is Friday

Therefore

3.) Everybody likes today,

or

All B's are A's.

All C's are B's.

All C's are A's.

The syllogism has two premises and a conclusion. Each premise is a proposition with

a subject term and a predicate term. In the conclusion, the subject term is C and the

predicate term is A. There is also a "middle term" B, which is the term linking the C's

and the A's. Hence Aristotle regards the middle term as what provides the explanation

(i.e., B explains why all C's are A's.)

Aristotle recogniced four tipes of categorical sentences, which all include a subject (S)

and a predicat (P):

A,B,C.... Terms

a universal affirmation: belongs to everybody

i particular afformation: belongs to some

e universal negation: doesn’t belong to anybody

o particular negation: doesn’t belong to some

These sentences can form syllogisms in many ways, both non-logical and logical. In

the Middle age students of Aristotelian logic categorised all logical possibilities and

named them:

(www.wikipedia.com)

3.3 Definition

For Aristotle, a definition is "an account which signifies what it is to be for

something" (logos ho to ti ên einai sêmainei). The phrase "what it is to be" and its

variants are crucial: giving a definition is saying, of some existent thing, what it is, not

simply specifying the meaning of a word (Aristotle does recognize definitions of the

latter sort, but he has little interest in them).

In the second book Aristotle considers demonstration as the instrument than with what

definition is reached. The four great problem types, the ‘That’, the ‘Why’, the ‘If’, the

‘¨What’ are all concerned with the middle term. These terms are in all five objects of

knowledge:

1. What a name means

2. That the corresponding thing is

3. What it is

4, That it has certain properties

5. Why it has certain properties

An example of using a syllogism in demonstrating something could be:

Question: What is an eclipse?

Answer: a blocking of the moon's light by the earth.

Let A=eclipse, B=blocking by the earth, and C=moon.

B is A.

C is B.

C is A.

In this example, asking whether the moon is eclipsed = asking whether B is or is not.

We have the "account" of eclipse (namely, B, the middle term), so we learn both the

fact (that there is eclipse) and the reasoned fact (why) at the same time.

Alternatively we might only know the fact, not the reason.

Let A=eclipse, B=inability of moon to cast shadows, C=moon.

If it's clear that A belongs to C, then to inquire why it belongs is to inquire into what

B is (blocking? rotating? extinguishing?). B is an "account" or explanation of one of

the other two "extreme" terms, A (eclipse).

Another example: A=thunder, B=extinguishing of fire, C=cloud. Then we get an

account of thunder as "extinguishing of fire in the cloud."

Since a thing's definition says what it is, definitions are essentially predicated.

en predicate X is an essential predicate of Y but also of other things, then X is a genus

(genos) of Y. A definition of X must not only be essentially predicated of it but must

also be predicated only of it: to use a term from Aristotle's Topics, a definition and

what it defines must "counterpredicate" (antikatêgoreisthai) with one another. X

counterpredicates with Y if X applies to what Y applies to and conversely. Though

X's definition must counterpredicate with X, not everything that counterpredicates

with X is its definition. "Capable to cry", for example, counterpredicates with

"human" but fails to be its definition. Such a predicate (non-essential but

counterpredicating) is a peculiar property or proprium (idion).

Finally, if X is predicated of Y but is neither essential nor counterpredicates, then X is

an accident (sumbebêkos) of Y.

3.4 Demonstration

1. Whatever is scientifically known must be demonstrated.

2. The premises of a demonstration must be scientifically known.

Aristotle says all teaching and all learning start from pre-existing knowledge. The

knowledge thus presupposed is of two types of fact; it is knowledge ‘that so-and-so is’

(which is a question also in the centre of many of Plato’s dialogues), or knowledge of

‘what the word used mean’. With regard to some things, the meaning of the words

being quite clear, all that needs to be explicitly assumed is that the thing is so; this is

true, for example of the law that everything may with truth either be affirmed or be

denied. With regard to others it is enough if we know explicitly the meaning of the

name; it is then sufficiently obvious that the thing exists, and this need not be

explicitly stated. With regard to other things we must explicitly know both what the

name means and that the thing is.

Demonstration is scientific syllogism, i.e. a syllogism which is through and through

knowledge and not opinion. A demonstration (apodeixis) is "a deduction that

produces knowledge". Aristotle's Posterior Analytics contains his account of

demonstrations and their role in knowledge. From a modern perspective, we might

think that this subject moves outside of logic to epistemology. From Aristotle's

perspective, however, the connection of the theory of sullogismoi with the theory of

knowledge is especially close.

Aristotle says that a demonstration is a deduction in which the premises are:

1. true

2. primary (prota)

3. immediate (amesa, "without a middle")

4. better known or more familiar (gnôrimôtera) than the conclusion

5. prior to the conclusion

6. causes (aitia) of the conclusion

4. Conclusions

It is difficult to write a shortly on Aristotle, there is just too much ‘stuff’ in his

writings. A Finnish philosopher Eero Ojanen writes about this in his book ‘Mitä

Aristoteles on opettanut minulle’ (Eero Ojanen ja Kirjastudio, Helsinki 2005). He also

talks about his experiences in reading Aristotle, how he feels like this is what he’s

always been reading. I had very much the same experience with reading his logical

writings and the articles people have written about them. Aristotle is so much inside

our culture, that even when we are not directly reading him, we come in touch with

his ideas everywhere. As Ojanen puts it (translation is by me, since the book is so far

only published in Finnish): “Aristotle is not a target of knowledge, he is the tool, the

method we have for knowing and sharing what we know”(p.19). This is of course

very much true when one talks about his logical works, they certainly are a tool. His

logical works have been criticised very harshly, for example by Bertrand Russel in the

History of western philosophy, where he in the end of his introduction to Aristotle’s

logic, states that he concludes that all the Aristotle’s teachings he presents in the

introduction are completely wrong, except syllogism. But even he has to admit the

talent of the writings and the role of Aristotle in history. “The historical importance of

Aristotle is true”, as Ojanen puts it (p.115, syllabus mine).

References:

- Ojanen Eero, Mitä Aristoteles on minulle opettanut, Eero Ojanen ja Kirjastudio,

Helsinki 2005

- Oliver, Martyn, Filosofian Historia (orig, The Hamlyn History of Philosophy),

Gummerus kirjapaino oy, China 1997

- Russel, Bertrand, Länsimaisen filosofian historia (orig. The History of Western

Philosophy), WSOY, Porvoo 1992

- Sir David Ross, Aristotle, London 1995

- Smith Robin, Aristotle’s logic, http://plato.stanford.edu

- www.wikipedia.com