Limits of the Aristotelian system

Greek Aristoteles;
born 384 BC , Stagira, Chalcidice, Greece, died 322 , Chalcis, Euboea
"Greek philosopher and scientist. Son of the court physician to Alexander the Great's grandfather, he became a student of Plato in Athens and taught at Plato's Academy for 20 years. He went back to Macedonia c.342 to tutor the young Alexander, then returned to Athens in 335 to found his own school, the Lyceum. Aristotle distinguished his philosophy from Plato's by declaring that the assumption of the existence of a separate realm of transcendent Ideas (see form) is unnecessary and that the world of perceived things is the real world."
The Britannica Concise

"In Western thought, systematic logic is considered to have begun with Aristotle’s collection of treatises, the Organon [tool]. Aristotle introduced the use of variables. While his contemporaries illustrated principles by the use of examples, Aristotle generalized, as in: All x are y; all y are z; therefore, all x are z. Aristotle posited three laws as basic to all valid thought: the law of identity, A is A; the law of contradiction, A cannot be both A and not A; and the law of the excluded middle, A must be either A or not A.
Aristotle believed that any logical argument could be reduced to a standard form, known as a syllogism. A syllogism is a sequence of three propositions: two premises and the conclusion."
The Columbia Encyclopedia, Sixth Edition, 2001.

a mode of argument that forms the core of the body of Western logical thought. Aristotle defined syllogistic logic, and his formulations were thought to be the final word in logic; they underwent only minor revisions in the subsequent 2,200 years. Every syllogism is a sequence of three propositions such that the first two imply the third, the conclusion. There are three basic types of syllogism: hypothetical, disjunctive, and categorical. The hypothetical syllogism, modus ponens, has as its first premise a conditional hypothesis: If p then q; it continues: p, therefore q. The disjunctive syllogism, modus tollens, has as its first premise a statement of alternatives: Either p or q; it continues: not q, therefore p. The categorical syllogism comprises three categorical propositions, which must be statements of the form all x are y, no x is y, some x is y, or some x is not y. A categorical syllogism contains precisely three terms: the major term, which is the predicate of the conclusion; the minor term, the subject of the conclusion; and the middle term, which appears in both premises but not in the conclusion. Thus: All philosophers are men (middle term); all men are mortal; therefore, All philosophers (minor term) are mortal (major term)."
The Columbia Encyclopedia, Sixth Edition, 2001.

"One implication for the modern logician is that Aristotle’s law of the excluded middle (either A or not A) is neither so simple nor so self-evident as it once seemed."
The Columbia Encyclopedia, Sixth Edition, 2001.

"Syllogisms are structures of sentences each of which can meaningfully be called true or false: assertions (apophanseis), in Aristotle’s terminology. According to Aristotle, every such sentence must have the same structure: it must contain a subject (hupokeimenon) and a predicate and must either affirm or deny the predicate of the subject. Thus, every assertion is either the affirmation (kataphasis) or the denial (apophasis) of a single predicate of a single subject."
— From Stanford University's Aristotle's Logic.
[Therefore, every logical argument can be reduced to syllogisms and every syllogism can be reduced to assertions with the subject-predicate structure]

"I know that there are many persons to whom it seems derogatory to link a body of philosophic ideas to the social life and culture of their epoch. They seem to accept a dogma of immaculate conception of philosophical systems."
— John Dewey, On Experience, Nature and Freedom.

"The language Aristotle inherited was of great antiquity, and originated in periods when knowledge was still more scanty. Being a keen observer, and scientifically and methodologically inclined, he took this language for granted and systematized the modes of speaking. This systematization was called 'logic'."
— Alfred Korzybski, Science and Sanity, p. 371, International Non-Aristotelian Publishing Company (1933)

Here are the Aristotelian-system premises:
  1. All that is, is (A is A, law of identity)
  2. Nothing can at the same time be and not be (A cannot be both A and not A, law of contradiction)
  3. All must either be or not be (A must be either A or not A, law of the excluded middle)
One can at once see the influence of the linguistic structures related to the verb 'to be', in the formulation of these premises !
We shall also show that some statements such as A is greater than B cannot be put into the syllogistic form without loss of information, a conclusion that could have been reached in Aristotle's times.
From these ' Laws of Thought' follow:

 Typical errors about the Aristotelian system 

The first usual mistake is to believe that non-Aristotelian systems, such as general semantics, are anti-Aristotelian. Non-Aristotelian systems are not anti-systems, just as non-Euclidean and non-Newtonian systems are not anti-Euclidean and anti-Newtonian. On the contrary, they include the older system as a special case. This means that every conclusion reached using the Aristotelian system is also likely to be reached using non-Aristotelian system. But the non-Aristotelian system will allow more options. Computers and their binary logic are quite 'compatible' with general semantics, as is any development based on binary Aristotelian 'logic'. But general semantics will not limit us to binary logic, allowing logics with higher numbers of possibilities, ultimately including probabilities and fuzzy logic.

A second error made by beginners is to consider "Aristotelian" as 'bad'. From the above, we know that everything that can be considered as Aristotelian is also non-Aristotelian. In science, we do not always use the newest system to reach a conclusion; we sometimes use an older one that is most easy to apply and that we know will yield a result correct enough (remember that overprecision is a failure to apply non-allness). For example, Newton's laws are applicable to predict the position of most planets, except for Mercury due to its relatively high speed.

© ESGS, 2002.