traditional logic

In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, the Peripatetics. It was revived after the third century CE by Porphyry's Isagoge.

Term logic revived in medieval times, first in Islamic logic by Alpharabius in the tenth century, and later in Christian Europe in the twelfth century with the advent of new logic, remaining dominant until the advent of predicate logic in the late nineteenth century.

However, even if eclipsed by newer logical systems, term logic still plays a significant role in the study of logic. Rather than radically breaking with term logic, modern logics typically expand it, so to understand the newer systems, one must be acquainted with the earlier one.

Aristotle's system

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 works that is about term logic. Modern work on Aristotle's logic builds on the tradition started in 1951 with the establishment by Jan Lukasiewicz of a revolutionary paradigm. Lukasiewicz's approach was reinvigorated in the early 1970s by John Corcoran and Timothy Smiley – which informs modern translations of ''Prior Analytics'' by Robin Smith in 1989 and Gisela Striker in 2009.

Basics

The fundamental assumption behind the theory is that the formal model of propositions are composed of two logical symbols called terms – hence 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, such as "man" or "mortal". As originally conceived, all terms would be drawn from one of ten ''categories'' enumerated by Aristotle in his ''Organon'', classifying all objects and qualities within the domain of logical discourse.
*The formal model of ''proposition'' consists of two terms, one of which, 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 other propositions (the "premises").

A proposition may be universal or particular, and it may be affirmative or negative. Traditionally, the four kinds of propositions are:
:* A-type: Universal and affirmative ("All philosophers are mortal")
:* I-type: Particular and affirmative ("Some philosophers are mortal")
:* E-type: Universal and negative ("All philosophers are not mortal")
:* O-type: Particular and negative ("Some philosophers are not mortal")
This was called the ''fourfold scheme'' of propositions (see types of syllogism for an explanation of the letters A, I, E, and O in the traditional square). Aristotle's ''original'' square of opposition, however, does not lack existential import.

In the Stanford Encyclopedia of Philosophy article, "The Traditional Square of Opposition", Terence Parsons explains:

Term

A term (Greek ὅρος ''horos'') is the basic component of the proposition. The original meaning of the ''horos'' (and also of 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 early modern logicians like Arnauld (whose ''Port-Royal Logic'' was the best-known text of his day), it is a psychological entity like an "idea" or "concept". Mill considers it a word. To assert "all Greeks are men" is not to say that the concept of Greeks is the concept 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.

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. 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 or another (''Posterior Analytics'' 1. 1 24a 16), so a premise is also a form of words.

However, as in modern philosophical logic, it means that which is asserted by the sentence. Writers before Frege and 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 '' logical 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 philosopher is mortal'' is affirmative, since the mortality of philosophers is affirmed universally, whereas ''no philosopher is mortal'' is negative by denying such mortality in particular.

The ''quantity'' of a proposition is whether it is universal (the predicate is affirmed or denied of all subjects or of "the whole") or particular (the predicate is affirmed or denied of some subject or a "part" thereof). In case where existential import is assumed, quantification implies the existence of at least one subject, unless disclaimed.

Singular terms

For Aristotle, the distinction between singular and universal is a fundamental metaphysical one, and not merely grammatical. A singular term for Aristotle is primary substance, which can only be predicated of itself: (this) "Callias" or (this) "Socrates" are not predicable of any other thing, thus one does not say ''every Socrates'' one says ''every human'' (''De Int.'' 7; ''Meta.'' D9, 1018a4). 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 universal (''katholou''). secondary substance, genera, with primary substance, particular (''kath' hekaston'') specimens. The formal nature of universals, in so far as they can be generalized "always, or for the most part", is the subject matter of both scientific study and formal logic.

The essential feature of the syllogism is that, of the four terms in the two premises, one must occur twice. Thus

:All Greeks are men
:All men are mortal.

The subject of one premise, must be the predicate of the other, and so it is necessary to eliminate from the logic any terms which cannot function both as subject and predicate, namely singular terms.

However, in a popular 17th-century version of the syllogism, Port-Royal Logic, singular terms were treated as universals:

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

This is clearly awkward, a weakness exploited by Frege in his devastating attack on the system.

The famous syllogism "Socrates is a man ...", is frequently quoted as though from Aristotle, but in fact, it is nowhere in the ''Organon''. Sextus Empiricus in his ''Hyp. Pyrrh'' (Outlines of Pyrronism) ii. 164 first mentions the related syllogism "Socrates is a human being, Every human being is an animal, Therefore, Socrates is an animal."

Influence on philosophy

The Aristotelian logical system had a formidable influence on the late-philosophy of the French psychoanalyst Jacques Lacan. In the early 1970s, Lacan reworked Aristotle's term logic by way of Frege and Jacques Brunschwig to produce his four formulae of sexuation. While these formulae retain the formal arrangement of the square of opposition, they seek to undermine the universals of both qualities by the 'existence without essence' of Lacan's particular negative proposition.

Decline of term logic

Term logic began to decline in Europe during the Renaissance, when logicians like Rodolphus Agricola Phrisius (1444–1485) and Ramus (1515–1572) began to promote place logics. The logical tradition called Port-Royal Logic, or sometimes "traditional logic", saw propositions as combinations of ideas rather than of terms, but otherwise followed many of the conventions of term logic. It remained influential, especially in England, until the 19th century. Leibniz created a distinctive logical calculus, but nearly all of his work on logic remained unpublished and unremarked until Louis Couturat went through the Leibniz ''Nachlass'' around 1900, publishing his pioneering studies in logic.

19th-century attempts to algebraize logic, such as the work of Boole (1815–1864) and Venn (1834–1923), typically yielded systems highly influenced by the term-logic tradition. The first predicate logic was that of Frege's landmark ''Begriffsschrift'' (1879), little read before 1950, in part because of its eccentric notation. Modern predicate logic as we know it began in the 1880s with the writings of Charles Sanders Peirce, who influenced Peano (1858–1932) and even more, Ernst Schröder (1841–1902). It reached fruition in the hands of Bertrand Russell and A. N. Whitehead, whose ''Principia Mathematica'' (1910–13) made use of a variant of Peano's predicate logic.

Term logic also survived to some extent in traditional Roman Catholic education, especially in seminaries. Medieval Catholic theology, especially the writings of Thomas Aquinas, had a powerfully Aristotelean cast, and thus term logic became a part of Catholic theological reasoning. For example, Joyce's ''Principles of Logic'' (1908; 3rd edition 1949), written for use in Catholic seminaries, made no mention of Frege or of Bertrand Russell. Copleston's ''A History of Philosophy''

Revival

Some philosophers have complained that predicate logic:
* Is unnatural in a sense, in that its syntax does not follow the syntax of the sentences that figure in our everyday reasoning. It is, as Quine acknowledged, " Procrustean," employing an artificial language of function and argument, quantifier, and bound variable.
* Suffers from theoretical problems, probably the most serious being empty names and identity statements.

Even academic philosophers entirely in the mainstream, such as Gareth Evans, have written as follows:
:"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 ucha theory ... over a theory which is only able to deal with entences of the form "all A's are B's"by "discovering" hidden logical constants ... The objection would not be that such regeantruth 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)

See also

*Converse (logic)
*Obversion
*Port-Royal Logic
*Propositional calculus
*Stoic logic
*Transposition (logic)

Notes

References

* Bochenski, I. M., 1951. ''Ancient Formal Logic''. North-Holland.
* Louis Couturat, 1961 (1901). ''La Logique de Leibniz''. Hildesheim: Georg Olms Verlagsbuchhandlung.
* 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, .
* Joyce, George Hayward, 1949 (1908).
Principles of Logic
', 3rd ed. Longmans. A manual written for use in Catholic seminaries. Authoritative on traditional logic, with many references to medieval and ancient sources. Contains no hint of modern formal logic. The author lived 1864–1943.
* Jan Lukasiewicz, 1951. ''Aristotle's Syllogistic, from the Standpoint of Modern Formal Logic''. Oxford Univ. Press.
* John Stuart Mill, 1904. ''A System of Logic'', 8th ed. London.
* Parry and Hacker, 1991. ''Aristotelian Logic''. State University of New York Press.
* Arthur Prior
*: 1962: ''Formal Logic'', 2nd ed. Oxford Univ. Press. While primarily devoted to modern formal logic, contains much on term and medieval logic.
*: 1976: ''The Doctrine of Propositions and Terms''. Peter Geach and A. J. P. Kenny, eds. London: Duckworth.
* Willard Quine, 1986. ''Philosophy of Logic'' 2nd ed. Harvard Univ. Press.
* Rose, Lynn E., 1968. ''Aristotle's Syllogistic''. Springfield: Clarence C. Thomas.
* Sommers, Fred
*: 1970: "The Calculus of Terms," ''Mind 79'': 1-39. Reprinted in Englebretsen, G., ed., 1987. ''The new syllogistic'' New York: Peter Lang.
*: 1982: ''The logic of natural language''. Oxford University Press.
*: 1990:
Predication in the Logic of Terms
" ''Notre Dame Journal of Formal Logic 31'': 106–26.
*: and Englebretsen, George, 2000: ''An invitation to formal reasoning. The logic of terms''. Aldershot UK: Ashgate. .
* Szabolcsi Lorne, 2008. ''Numerical Term Logic''. Lewiston: Edwin Mellen Press.

External links

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Aristotle's term logic online
This online program provides a platform for experimentation and research on Aristotelian logic.
* Annotated bibliographies:




*PlanetMath
Aristotelian Logic

Interactive Syllogistic Machine for Term Logic
A web based syllogistic machine for exploring fallacies, figures, terms, and modes of syllogisms.

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