In
philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, language. Such quest ...
, term logic, also known as traditional logic,
syllogistic logic
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
...
or
Aristotelian logic, is a loose name for an approach to
formal logic that began with
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatet ...
and was developed further in
ancient history
Ancient history is a time period from the beginning of writing and recorded human history to as far as late antiquity. The span of recorded history is roughly 5,000 years, beginning with the Sumerian cuneiform script. Ancient history co ...
mostly by his followers, the
Peripatetics
The Peripatetic school was a school of philosophy in Ancient Greece. Its teachings derived from its founder, Aristotle (384–322 BC), and ''peripatetic'' is an adjective ascribed to his followers.
The school dates from around 335 BC when Aristo ...
. It was revived after the third century CE by
Porphyry's
Isagoge.
Term logic revived in
medieval
In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire a ...
times, first in
Islamic logic
Early Islamic law placed importance on formulating standards of argument, which gave rise to a "novel approach to logic" ( ''manṭiq'' "speech, eloquence") in Kalam (Islamic scholasticism).
However, with the rise of the Mu'tazili philosophers, wh ...
by
Alpharabius
Abu Nasr Muhammad Al-Farabi ( fa, ابونصر محمد فارابی), ( ar, أبو نصر محمد الفارابي), known in the West as Alpharabius; (c. 872 – between 14 December, 950 and 12 January, 951)PDF version was a renowned early Isla ...
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
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical Greece, Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatet ...
's logical work is collected in the six texts that are collectively known as the ''
Organon
The ''Organon'' ( grc, Ὄργανον, meaning "instrument, tool, organ") is the standard collection of Aristotle's six works on logical analysis and dialectic. The name ''Organon'' was given by Aristotle's followers, the Peripatetics.
The si ...
''. Two of these texts in particular, namely the ''
Prior Analytics
The ''Prior Analytics'' ( grc-gre, Ἀναλυτικὰ Πρότερα; la, Analytica Priora) is a work by Aristotle on reasoning, known as his syllogistic, composed around 350 BCE. Being one of the six extant Aristotelian writings on logic ...
'' and ''
De Interpretatione
''De Interpretatione'' or ''On Interpretation'' (Greek: Περὶ Ἑρμηνείας, ''Peri Hermeneias'') is the second text from Aristotle's ''Organon'' and is among the earliest surviving philosophical works in the Western tradition to deal ...
'', contain the heart of Aristotle's treatment of judgements and formal
inference
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...
, 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
Jan, JaN or JAN may refer to:
Acronyms
* Jackson, Mississippi (Amtrak station), US, Amtrak station code JAN
* Jackson-Evers International Airport, Mississippi, US, IATA code
* Jabhat al-Nusra (JaN), a Syrian militant group
* Japanese Article Numb ...
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
Formal, formality, informal or informality imply the complying with, or not complying with, some set of requirements (forms, in Ancient Greek). They may refer to:
Dress code and events
* Formal wear, attire for formal events
* Semi-formal attire ...
model of
propositions are composed of two
logical symbol
A logical symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern. Although the term "symbol" in common use refers at some times to the idea being symbolized, and at other ...
s called terms – hence the name "two-term theory" or "term logic" – and that the
reasoning
Reason is the capacity of consciously applying logic by drawing conclusions from new or existing information, with the aim of seeking the truth. It is closely associated with such characteristically human activities as philosophy, science, lang ...
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
The ''Organon'' ( grc, Ὄργανον, meaning "instrument, tool, organ") is the standard collection of Aristotle's six works on logical analysis and dialectic. The name ''Organon'' was given by Aristotle's followers, the Peripatetics.
The si ...
'', classifying all objects and qualities within the domain of logical discourse.
*The
formal
Formal, formality, informal or informality imply the complying with, or not complying with, some set of requirements (forms, in Ancient Greek). They may refer to:
Dress code and events
* Formal wear, attire for formal events
* Semi-formal attire ...
model of ''proposition'' consists of two terms, one of which, the "
predicate", is "affirmed" or "denied" of the other, the "
subject
Subject ( la, subiectus "lying beneath") may refer to:
Philosophy
*''Hypokeimenon'', or ''subiectum'', in metaphysics, the "internal", non-objective being of a thing
**Subject (philosophy), a being that has subjective experiences, subjective cons ...
", and which is capable of
truth or
falsity.
*The ''
syllogism
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
...
'' is an
inference
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in ...
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
In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions.
The origin of the square can be traced back to Aristotle's tractate ''On Interpre ...
, however, does not lack
existential import.
In the
Stanford Encyclopedia of Philosophy
The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. Eac ...
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
Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs.
They play an important role in all aspects of cognition. As such, concepts are studied by s ...
".
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
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
...
. Aristotle uses the word premise (''protasis'') as a sentence affirming or denying one thing or another (''
Posterior Analytics
The ''Posterior Analytics'' ( grc-gre, Ἀναλυτικὰ Ὕστερα; la, Analytica Posteriora) is a text from Aristotle's ''Organon'' that deals with demonstration, definition, and scientific knowledge. The demonstration is distinguished ...
'' 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
Russell may refer to:
People
* Russell (given name)
* Russell (surname)
* Lady Russell (disambiguation)
* Lord Russell (disambiguation)
Places Australia
*Russell, Australian Capital Territory
*Russell Island, Queensland (disambiguation)
**Ru ...
, 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
An opinion is a judgment, viewpoint, or statement that is not conclusive, rather than facts, which are true statements.
Definition
A given opinion may deal with subjective matters in which there is no conclusive finding, or it may deal with f ...
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
In linguistics, grammaticality is determined by the conformity to language usage as derived by the grammar of a particular variety (linguistics), speech variety. The notion of grammaticality rose alongside the theory of generative grammar, the go ...
. 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
A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
...
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
The ''Organon'' ( grc, Ὄργανον, meaning "instrument, tool, organ") is the standard collection of Aristotle's six works on logical analysis and dialectic. The name ''Organon'' was given by Aristotle's followers, the Peripatetics.
The si ...
''.
Sextus Empiricus
Sextus Empiricus ( grc-gre, Σέξτος Ἐμπειρικός, ; ) was a Ancient Greece, Greek Pyrrhonism, Pyrrhonist philosopher and Empiric school physician. His philosophical works are the most complete surviving account of ancient Greek and ...
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
Jacques Marie Émile Lacan (, , ; 13 April 1901 – 9 September 1981) was a French psychoanalyst and psychiatrist. Described as "the most controversial psycho-analyst since Freud", Lacan gave yearly seminars in Paris from 1953 to 1981, and pu ...
. 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
Europe is a large peninsula conventionally considered a continent in its own right because of its great physical size and the weight of its history and traditions. Europe is also considered a subcontinent of Eurasia and it is located enti ...
during the
Renaissance, when logicians like
Rodolphus Agricola Phrisius (1444–1485) and
Ramus Ramus can refer to:
* A branch (botany)
* A portion of a bone (from Latin ''ramus'', "branch"), as in the Ramus of the mandible or Superior pubic ramus
* A nerve ramus such as the Dorsal ramus of spinal nerve
* A taxonomic rank ("branch" in English ...
(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
George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Irel ...
(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
Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism".
Educated as a chemist and employed as a scientist for ...
, who influenced
Peano (1858–1932) and even more,
Ernst Schröder (1841–1902). It reached fruition in the hands of
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...
and
A. N. Whitehead
Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He is best known as the defining figure of the philosophical school known as process philosophy, which today has found applicat ...
, 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
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...
.
[ Copleston's '']A History of Philosophy
''A History of Philosophy'' is a history of Western philosophy written by the English Jesuit priest Frederick Charles Copleston originally published in nine volumes between 1946 and 1975. As is noted by '' The Encyclopedia Britannica,'' the work ...
''
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
Quine may refer to:
* Quine (surname), people with the surname ''Quine''
* Willard Van Orman Quine, the philosopher, or things named after him:
** Quine (computing), a program that produces its source code as output
** Quine–McCluskey algorithm, ...
acknowledged, "
Procrustean
In Greek mythology, Procrustes (; Greek: Προκρούστης ''Prokroustes'', "the stretcher ho hammers out the metal), also known as Prokoptas, Damastes (Δαμαστής, "subduer") or Polypemon, was a rogue smith and bandit from Attica ...
," 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
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy, linguistics and comput ...
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 In logic, a logical constant of a language \mathcal is a symbol that has the same semantic value under every interpretation of \mathcal. Two important types of logical constants are logical connectives and quantifiers. The equality predicate (us ...
... 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
Peter Thomas Geach (29 March 1916 – 21 December 2013) was a British philosopher who was Professor of Logic at the University of Leeds. His areas of interest were philosophical logic, ethics, history of philosophy, philosophy of religion and t ...
, 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
Jan, JaN or JAN may refer to:
Acronyms
* Jackson, Mississippi (Amtrak station), US, Amtrak station code JAN
* Jackson-Evers International Airport, Mississippi, US, IATA code
* Jabhat al-Nusra (JaN), a Syrian militant group
* Japanese Article Numb ...
, 1951. ''Aristotle's Syllogistic, from the Standpoint of Modern Formal Logic''. Oxford Univ. Press.
*
John Stuart Mill
John Stuart Mill (20 May 1806 – 7 May 1873) was an English philosopher, political economist, Member of Parliament (MP) and civil servant. One of the most influential thinkers in the history of classical liberalism, he contributed widely ...
, 1904. ''A System of Logic'', 8th ed. London.
* Parry and Hacker, 1991. ''Aristotelian Logic''. State University of New York Press.
*
Arthur Prior
Arthur Norman Prior (4 December 1914 – 6 October 1969), usually cited as A. N. Prior, was a New Zealand–born logician and philosopher. Prior (1957) founded tense logic, now also known as temporal logic, and made important contributi ...
*: 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
Peter Thomas Geach (29 March 1916 – 21 December 2013) was a British philosopher who was Professor of Logic at the University of Leeds. His areas of interest were philosophical logic, ethics, history of philosophy, philosophy of religion and t ...
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
*
*
*
Aristotle's term logic onlineThis online program provides a platform for experimentation and research on Aristotelian logic.
* Annotated bibliographies:
*
PlanetMathAristotelian Logic Interactive Syllogistic Machine for Term LogicA web based syllogistic machine for exploring fallacies, figures, terms, and modes of syllogisms.
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