Term logic

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Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century.

It can sometimes be difficult to understand philosophy before the period of Frege and Russell without an elementary grasp of the terminology and ideas that were assumed by all philosophers until then. This article provides a basic introduction to the traditional system, with suggestions for further reading.

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Aristotle's system

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Aristotle's logical work is collected in the six texts that are collectively known as the Organon. Two of these texts in particular, namely the Prior Analytics and De Interpretatione contain the heart of Aristotle's treatment of judgements and formal inference, and it is principally this part of Aristotle's work that term logic is about.

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The basics

The fundamental assumption behind the theory is that propositions are composed of two terms - whence the name "two-term theory" or "term logic" – and that the reasoning process is in turn built from propositions:

  • The term is a part of speech representing something, but which is not true or false in its own right, as "man" or "mortal".
  • The proposition consists of two terms, in which one term (the "predicate") is "affirmed" or "denied" of the other (the "subject"), and which is capable of truth or falsity.
  • The syllogism is an inference in which one proposition (the "conclusion") follows of necessity from two others (the "premises").

A proposition may be universal or particular, and it may be affirmative or negative. Thus there are just four kinds of propositions:

  • A-type: universal and affirmative or ("All men are mortal")
  • I-type: Particular and affirmative ("Some men are philosophers")
  • E-type: Universal and negative ("No philosophers are rich")
  • O-type: Particular and negative ("Some men are not philosophers").

This was called the fourfold scheme of propositions. (The origin of the letters A, I, E, and O are explained below in the section on syllogistic maxims.) Aristotle summarised the logical relationship between four types of propositions with his square of oppositions. The syllogistic is a formal theory explaining which combinations of true premises yield true conclusions.

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The term

A term (Greek horos) is the basic component of the proposition. The original meaning of the horos and also the Latin terminus is "extreme" or "boundary". The two terms lie on the outside of the proposition, joined by the act of affirmation or denial.

For Aristotle, a term is simply a "thing", a part of a proposition. For early modern logicians like Arnauld (whose Port-Royal Logic is the most well-known textbook of the period) it is a psychological entity like an "idea" or "concept". Mill considers it a word. None of these interpretations are quite satisfactory. In asserting that something is a unicorn, we are not asserting anything of anything. Nor does "all Greeks are men" say that the ideas of Greeks are ideas of men, or that word "Greeks" is the word "men". A proposition cannot be built from real things or ideas, but it is not just meaningless words either. This is a problem about the meaning of language that is still not entirely resolved. (See the book by Prior below for an excellent discussion of the problem).

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The proposition

In term logic, a "proposition" is simply a form of language: a particular kind of sentence, in which the subject and predicate are combined, so as to assert something true or false. It is not a thought, or an abstract entity or anything. The word "propositio" is from the Latin, meaning the first premise of a syllogism. Aristotle uses the word premise (protasis) as a sentence affirming or denying one thing of another (AP 1. 1 24a 16), so a premise is also a form of words.

However, in modern philosophical logic, it now means what is asserted as the result of uttering a sentence, and is regarded as something peculiar mental or intentional. Writers before Frege-Russell, such as Bradley, sometimes spoke of the "judgment" as something distinct from a sentence, but this is not quite the same. As a further confusion the word "sentence" derives from the Latin, meaning an opinion or judgment, and so is equivalent to "proposition".

The quality of a proposition is whether it is affirmative (the predicate is affirmed of the subject) or negative(the predicate is denied of the subject). Thus "every man is a mortal" is affirmative, since "mortal" is affirmed of "man". "No men are immortals" is negative, since "immortal" is denied of "man".

The quantity of a proposition is whether it is universal (the predicate is affirmed or denied of "the whole" of the subject) or particular (the predicate is affirmed or denied of only "part of" the subject).

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Singular terms

The distinction between singular and universal is fundamental to Aristotle's metaphysics, and not merely grammatical. A singular term for Aristotle is that which is of such a nature as to be predicated of only one thing, thus "Callias". (De Int 7). It is not predicable of more than one thing: "Socrates is not predicable of more than one subject, and therefore we do not say every Socrates as we say every man". (Metaphysics D 9, 1018 a4). It may feature as a grammatical predicate, as in the sentence "the person coming this way is Callias". But it is still a logical subject.

He contrasts it with "universal" (katholou - "of a whole"). Universal terms are the basic materials of Aristotle's logic, propositions containing singular terms do not form part of it at all. They are mentioned briefly in the De Interpretatione. Afterwards, in the chapters of the Prior Analytics where Aristotle methodically sets out his theory of the syllogism, they are entirely ignored.

The reason for this omission is clear. The essential feature of term logic is that, of the four terms in the two premises, one must occur twice. Thus

All greeks are men
All men are mortal.

What is subject in one premise, must be predicate in the other, and so it is necessary to eliminate from the logic any terms which cannot function both as subject and predicate. Singular terms do not function this way, so they are omitted from Aristotle's syllogistic.

In later versions of the syllogistic, singular terms were treated as universals. See for example (where it is clearly stated as received opinion) Part 2, chapter 3, of the Port-Royal Logic. Thus

All men are mortals
All Socrates are men
All Socrates are mortals

This is clearly awkward, and is a weakness exploited by Frege in his devastating attack on the system (from which, ultimately, it never recovered). See concept and object.

The famous syllogism "Socrates is a man ...", is frequently quoted as though from Aristotle. See for example Kapp, Greek Foundations of Traditional Logic, New York 1942, p.17, Copleston A history of Philosophy Vol. I. P. 277, Russell, A History of Western Philosophy London 1946 p. 218. In fact it is nowhere in the Organon. It is first mentioned by Sextus Empiricus (Hyp. Pyrrh. ii. 164).

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Decline of term logic

Term logic dominated logic throughout most of its history until the advent of modern or predicate logic a century ago, in the late nineteenth and early twentieth century, which led to its eclipse.

The decline was ultimately due to the superiority of the new logic in the mathematical reasoning for which it was designed. Term logic cannot, for example, explain the inference from "every car is a vehicle", to "every owner of a car is an owner of an vehicle ", which is elementary in predicate logic. It is confined to syllogistic arguments, and cannot explain inferences involving multiple generality. Relations and identity must be treated as subject-predicate relations, which makes the identity statements of mathematics difficult to handle, and of course the singular term and singular proposition, which is essential to modern predicate logic, does not properly feature at all.

Note, however, that the decline was a protracted affair. It is simply not true that there was a brief "Frege Russell" period 1890-1910 in which the old logic vanished overnight. The process took more like 70 years. Even Quine's Methods of Logic devotes considerable space to the syllogistic, and Joyce's manual, whose final edition was in 1949, does not mention Frege or Russell at all.


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Revisionist logic

The innovation of predicate logic led to an almost complete abandonment of the traditional system. It is customary to revile or disparage it in standard textbook introductions. However, it is not entirely in disuse. Term logic was still part of the curriculum in many Catholic schools until the late part of the twentieth century, and taught in places even today. More recently, some philosophers have begun work on a revisionist programme to reinstate some of the fundamental ideas of term logic. Their main complaint about modern logic is

  • that Predicate Logic is in a sense unnatural, in that its syntax does not follow the syntax of the sentences that figure in our everyday reasoning. It is, as Quine acknowledges, "Procrustean" employing an artificial language of function and argument, quantifier and bound variable.
  • that there are still embarrassing theoretical problems faced by Predicate Logic. Possibly the most serious are of empty names, and of identity statements.

Even orthodox and entirely mainstream philosophers such as Gareth Evans have voiced discontent:

"I come to semantic investigations with a preference for homophonic theories; theories which try to take serious account of the syntactic and semantic devices which actually exist in the language ...I would prefer [such] a theory ... over a theory which is only able to deal with [sentences of the form "all A's are B's"] by "discovering" hidden logical constants ... The objection would not be that such [Fregean] truth conditions are not correct, but that, in a sense which we would all dearly love to have more exactly explained, the syntactic shape of the sentence is treated as so much misleading surface structure" (Evans 1977)

Heeding the Paideia proposal from philosopher Mortimer J. Adler, advocates of the homeschooling movement in recent years have been trying to revive the traditional curriculum of the Trivium – grammar, logic, and rhetoric – and have argued that logic properly belongs in the language arts of a classical education, not in mathematics. The problem, as they see it, is the excessive nominalism in modern formal logic, which concerns itself with the manipulation of symbols and not with the whys and essences of things. Predicate logic is too difficult to be taught generally in school and is merely introduced in college. School children a hundred years ago were taught a usable form of formal logic; today – in the information age – they are taught nothing.

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References

  • I. M. Bocheński, I. M., 1951. Ancient Formal Logic. North-Holland, Amsterdam.
  • Louis Couturat, 1961. La Logique de Leibniz. Georg Olms Verlagsbuchhandlung, Hildesheim.
  • Gareth Evans, 1977. 'Pronouns, Quantifiers and Relative Clauses'. Canadian Journal of Philosophy.
  • Peter Geach, 1976. Reason and Argument. University of California Press.
  • Hammond and Scullard, 1992. The Oxford Classical Dictionary. Oxford University Press, ISBN 0198691173.
  • Joyce, G.H., 1949. [http://uk.geocities.com/frege@btinternet.com/joyce/principlesoflogic.htm Principles of Logic. London, 3rd edition. A manual written for Catholic schools, probably in the early 1910s. It is spendidly out of date, there being no hint even of the existence of modern logic, yet it is completely authoritative within its own subject area. There are also many useful references to medieval and ancient sources.
  • Jan Lukasiewicz, 1951. Aristotle's Syllogistic, from the Standpoint of Modern Formal Logic. Clarendon Press, Oxford.
  • John Stuart Mill, 1904. A System of Logic. London, 8th edition.
  • Parry and Hacker, 1991. Aristotelian Logic. State University of New York Press, Albany.
  • Terence Parsons, 1999. 'Traditional Square of Opposition'. Article at the Stanford Encyclopedia of Philosophy.
  • Arthur Prior, 1976. The Doctrine of Propositions & Terms. London.
  • Lynn E. Rose, 1968. Aristotle's Syllogistic. Clarence C. Thomas, Springfield.
  • Robin Smith, 2004. 'Aristotle's Logic'. Article at the Stanford Encyclopedia of Philosophy.
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See also

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External references

zh:传统逻辑

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