Term logic
Encyclopedia
In philosophy
, term logic, also known as traditional logic or aristotelian logic, is a loose name for the way of doing logic that began with Aristotle
and that was dominant until the advent of modern predicate logic
in the late nineteenth century. This entry is an introduction to the term logic needed to understand philosophy texts written before predicate logic came to be seen as the only formal logic of interest. Readers lacking a grasp of the basic terminology and ideas of term logic can have difficulty understanding such texts, because their authors typically assumed an acquaintance with term logic.
. 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.
A proposition may be universal or particular, and it may be affirmative or negative. Thus there are just four kinds of propositions:
This was called the fourfold scheme of propositions. (See types of syllogism for the origin of the letters A, I, E, and O.) Aristotle summarised the logical relationship between four types of propositions with his square of opposition
s. The syllogistic is a formal theory explaining which combinations of true premises yield true conclusions.
For Aristotle, a term is simply a "thing", a part of a proposition. 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. 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).
However, in modern philosophical logic, it now means what is asserted as the result of uttering a sentence, and is regarded as something peculiarly mental or intentional. 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 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).
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
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
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
in his Hyp. Pyrrh. ii. 164.
, when logicians like Rodolphus Agricola
Phrisius (1444–1485) and Ramus
began to promote place logics. The logical tradition called Port-Royal Logic
, or sometimes "traditional logic", claimed that a proposition was a combination of ideas rather than terms, but otherwise followed many of the conventions of term logic and was influential, especially in England, until the 19th century. Spinoza's "way of geometry" was far more influenced by Euclid's Elements
than by Aristotelian concepts. Leibniz created a distinctive logical calculus, but nearly all of his work on logic was unpublished and unremarked until Louis Couturat
went through the Leibniz Nachlass around 1900, and published many Leibniz manuscripts and a pioneering study of Leibniz's logic.
19th century attempts to algebratize logic, such as the work of Boole
and Venn
, typically yielded systems highly influenced by the term logic tradition. The first predicate logic was that of Frege's landmark Begriffsschrift
, 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 and even more, Ernst Schröder
. It reached full fruition in the hands of Bertrand Russell
and A. N. Whitehead, whose Principia Mathematica
(1910–13) made splendid use of a variant of Peano's predicate logic.
Predicate logic was designed as a form of mathematics, and as such is capable of all sorts of mathematical reasoning beyond the powers of term logic. Predicate logic is also capable of many commonsense inferences that elude term logic. Term logic cannot, for example, explain the inference from "every car is a vehicle", to "every owner of a car is an owner of a vehicle." Syllogistic reasoning cannot explain inferences involving multiple generality
. Relations and identity
must be treated as subject-predicate relations, which make the identity
statements of mathematics difficult to handle. Term logic contains no analog of the singular term
and singular proposition, both essential features of predicate logic.
With the ascension of predicate logic
, term and syllogistic logic gradually fell into disuse except among students of ancient and medieval philosophy. Since the development of predicate logic, introductory texts on logic have ignored or disparaged term logic, except perhaps as a source of examples for beginning students. A notable exception to this generalization is the four editions of Quine's Methods of Logic (the last edition, dated 1982, is still in print), which discussed term logic (which Quine called "Boolean term schemata") and syllogism
s at some length. Quine's writings on logic contain much that is in the spirit of term logic in that they frequently invoke grammatical concepts and examples taken from natural language, even employing bits of scholastic terminology such as "syncategorematic
."
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 (1949), written for use in Catholic seminaries, made no mention of Frege or Bertrand Russell
. On Aristotle
, term logic, and Roman Catholicism, see Copleston
's A History of Philosophy
.
Even academic philosophers entirely in the mainstream, such as Gareth Evans
, have written as follows:
The writings of Fred Sommers (e.g., Sommers 1970) and his students have modified term logic so that it can address these criticisms of predicate logic and overcome the well-known weaknesses of term logic. The result is the "term functor logic" of Sommers (1982), and Sommers and Englebretsen (2000). This logic has a very Boolean appearance, in that '+' and '-' are the sole operational signs and all statements are equations. It has sufficient expressive power to handle relational terms generally, and to capture the validity of arguments that elude syllogistic reasoning. Term functor logic has similarities to Quine's predicate functor logic
, an algebraic formalism Quine devised to do first-order logic
without quantifiers.
In a less formal vein, term logic has acquired a following among those advocating a return to educational methods grounded in the medieval Trivium: grammar
, logic
, and rhetoric
. Advocates of the Trivium include the Paideia Proposal
by philosopher Mortimer J. Adler, and some homeschoolers
. The Trivium views logic not as a form of mathematics, but as part of a classical education
in language. Those advocating this line see predicate logic as excessively nominalistic
, as primarily concerned with the manipulation of symbols (syntax
) and not with the whys and essences of things (ontology
and metaphysics
).
A variant of term logic, probabilistic term logic
, which assigns a probability value and a confidence value to the truth of both terms and propositions, is gaining popularity in artificial intelligence
systems. Variants include both Pei Wang's "Non-Axiomatic Reasoning System" (NARS) and Ben Goertzel's "OpenCog" system.
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
, term logic, also known as traditional logic or aristotelian logic, is a loose name for the way of doing logic that began with Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
and that was dominant until the advent of modern predicate logic
Predicate logic
In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulae contain variables which can be quantified...
in the late nineteenth century. This entry is an introduction to the term logic needed to understand philosophy texts written before predicate logic came to be seen as the only formal logic of interest. Readers lacking a grasp of the basic terminology and ideas of term logic can have difficulty understanding such texts, because their authors typically assumed an acquaintance with term logic.
Aristotle's system
Aristotle's logical work is collected in the six texts that are collectively known as the OrganonOrganon
The Organon is the name given by Aristotle's followers, the Peripatetics, to the standard collection of his six works on logic:* Categories* On Interpretation* Prior Analytics* Posterior Analytics...
. Two of these texts in particular, namely the Prior Analytics
Prior Analytics
The Prior Analytics is Aristotle's work on deductive reasoning, specifically the syllogism. It is also part of his Organon, which is the instrument or manual of logical and scientific methods....
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.
The basics
The fundamental assumption behind the theory is that propositions are composed of two 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".
- 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 truthTruthTruth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...
or falsity. - The syllogismSyllogismA syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
is an inferenceInferenceInference is the act or process of deriving logical conclusions from premises known or assumed to be true. The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic.Human inference Inference is the act or process of deriving logical conclusions...
in which one propositionPropositionIn logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...
(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 men are immortal")
- O-type: Particular and negative ("Some men are not philosophers").
This was called the fourfold scheme of propositions. (See types of syllogism for the origin of the letters A, I, E, and O.) Aristotle summarised the logical relationship between four types of propositions with his square of opposition
Square of opposition
In the system of Aristotelian logic, the square of opposition is a diagram representing the different ways in which each of the four propositions of the system are logically related to each of the others...
s. The syllogistic is a formal theory explaining which combinations of true premises yield true conclusions.
The term
A term (Greek 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 Aristotle, a term is simply a "thing", a part of a proposition. For early modern logicians like Arnauld (whose Port-Royal Logic
Port-Royal Logic
Port-Royal Logic, or Logique de Port-Royal, is the common name of La logique, ou l'art de penser, an important textbook on logic first published anonymously in 1662 by Antoine Arnauld and Pierre Nicole, two prominent members of the Jansenist movement, centered around Port-Royal. Blaise Pascal...
was the best-known text of his day), it is a psychological entity like an "idea" or "concept
Concept
The word concept is used in ordinary language as well as in almost all academic disciplines. Particularly in philosophy, psychology and cognitive sciences the term is much used and much discussed. WordNet defines concept: "conception, construct ". However, the meaning of the term concept is much...
". 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).
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. 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 (Posterior Analytics 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 peculiarly mental or intentional. Writers before Frege and Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
, such as Bradley
F. H. Bradley
Francis Herbert Bradley, OM, was a British idealist philosopher.- Life :Bradley was born at Clapham, Surrey, England . He was the child of Charles Bradley, an evangelical preacher, and Emma Linton, Charles's second wife. A. C. Bradley was his brother...
, 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
Logical quality
In many philosophies of logic statements are categorized into different logical qualities based on how they go about saying what they say. Doctrines of logical quality are an attempt to answer the question: “How many qualitatively different ways are there of saying something?” Aristotle answers,...
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).
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 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
Port-Royal Logic
Port-Royal Logic, or Logique de Port-Royal, is the common name of La logique, ou l'art de penser, an important textbook on logic first published anonymously in 1662 by Antoine Arnauld and Pierre Nicole, two prominent members of the Jansenist movement, centered around Port-Royal. Blaise Pascal...
. 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
Concept and object
In the philosophy of language, the distinction between concept and object is attributable to the German philosopher Gottlob Frege.According to Frege, any sentence that expresses a singular thought consists of an expression that signifies an Object together with a predicate In the philosophy of...
.
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
A History of Philosophy (Copleston)
A History of Philosophy is an eleven-volume history of Western philosophy, written by English Jesuit priest Frederick Charles Copleston.Copleston's History provides extensive coverage of Western philosophy from the Pre-Socratics through Dewey, Russell, Moore, Sartre and Merleau-Ponty...
Vol. I., p. 277, Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
, A History of Western Philosophy London 1946 p. 218. In fact it is nowhere in the Organon
Organon
The Organon is the name given by Aristotle's followers, the Peripatetics, to the standard collection of his six works on logic:* Categories* On Interpretation* Prior Analytics* Posterior Analytics...
. It is first mentioned by Sextus Empiricus
Sextus Empiricus
Sextus Empiricus , was a physician and philosopher, and has been variously reported to have lived in Alexandria, Rome, or Athens. His philosophical work is the most complete surviving account of ancient Greek and Roman skepticism....
in his Hyp. Pyrrh. ii. 164.
Decline of term logic
Term logic began to decline in Europe during the RenaissanceRenaissance
The Renaissance was a cultural movement that spanned roughly the 14th to the 17th century, beginning in Italy in the Late Middle Ages and later spreading to the rest of Europe. The term is also used more loosely to refer to the historical era, but since the changes of the Renaissance were not...
, when logicians like Rodolphus Agricola
Rodolphus Agricola
Rodolphus Agricola was a pre-Erasmian humanist of the northern Low Countries, famous for his supple Latin and one of the first north of the Alps to know Greek well...
Phrisius (1444–1485) and Ramus
Petrus Ramus
Petrus Ramus was an influential French humanist, logician, and educational reformer. A Protestant convert, he was killed during the St. Bartholomew's Day Massacre.-Early life:...
began to promote place logics. The logical tradition called Port-Royal Logic
Port-Royal Logic
Port-Royal Logic, or Logique de Port-Royal, is the common name of La logique, ou l'art de penser, an important textbook on logic first published anonymously in 1662 by Antoine Arnauld and Pierre Nicole, two prominent members of the Jansenist movement, centered around Port-Royal. Blaise Pascal...
, or sometimes "traditional logic", claimed that a proposition was a combination of ideas rather than terms, but otherwise followed many of the conventions of term logic and was influential, especially in England, until the 19th century. Spinoza's "way of geometry" was far more influenced by Euclid's Elements
Euclid's Elements
Euclid's Elements is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria c. 300 BC. It is a collection of definitions, postulates , propositions , and mathematical proofs of the propositions...
than by Aristotelian concepts. Leibniz created a distinctive logical calculus, but nearly all of his work on logic was unpublished and unremarked until Louis Couturat
Louis Couturat
Louis Couturat was a French logician, mathematician, philosopher, and linguist.-Life:Born in Ris-Orangis, Essonne, France, he was educated in philosophy and mathematics at the École Normale Supérieure...
went through the Leibniz Nachlass around 1900, and published many Leibniz manuscripts and a pioneering study of Leibniz's logic.
19th century attempts to algebratize logic, such as the work of Boole
George Boole
George Boole was an English mathematician and philosopher.As the inventor of Boolean logic—the basis of modern digital computer logic—Boole is regarded in hindsight as a founder of the field of computer science. Boole said,...
and Venn
John Venn
Donald A. Venn FRS , was a British logician and philosopher. He is famous for introducing the Venn diagram, which is used in many fields, including set theory, probability, logic, statistics, and computer science....
, typically yielded systems highly influenced by the term logic tradition. The first predicate logic was that of Frege's landmark Begriffsschrift
Begriffsschrift
Begriffsschrift is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book...
, 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 and even more, Ernst Schröder
Ernst Schröder
Ernst Schröder was a German mathematician mainly known for his work on algebraic logic. He is a major figure in the history of mathematical logic , by virtue of summarizing and extending the work of George Boole, Augustus De Morgan, Hugh MacColl, and especially Charles Peirce...
. It reached full fruition in the hands of Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
and A. N. Whitehead, whose Principia Mathematica
Principia Mathematica
The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913...
(1910–13) made splendid use of a variant of Peano's predicate logic.
Predicate logic was designed as a form of mathematics, and as such is capable of all sorts of mathematical reasoning beyond the powers of term logic. Predicate logic is also capable of many commonsense inferences that elude term logic. Term logic cannot, for example, explain the inference from "every car is a vehicle", to "every owner of a car is an owner of a vehicle." Syllogistic reasoning cannot explain inferences involving multiple generality
Problem of multiple generality
The problem of multiple generality names a failure in traditional logic to describe certain intuitively valid inferences. For example, it is intuitively clear that if:then it follows logically that:The syntax of traditional logic permits exactly four sentence types: "All As are Bs", "No As are...
. Relations and identity
Identity (philosophy)
In philosophy, identity, from , is the relation each thing bears just to itself. According to Leibniz's law two things sharing every attribute are not only similar, but are the same thing. The concept of sameness has given rise to the general concept of identity, as in personal identity and...
must be treated as subject-predicate relations, which make the identity
Identity (mathematics)
In mathematics, the term identity has several different important meanings:*An identity is a relation which is tautologically true. This means that whatever the number or value may be, the answer stays the same. For example, algebraically, this occurs if an equation is satisfied for all values of...
statements of mathematics difficult to handle. Term logic contains no analog of the singular term
Singular term
There is no really adequate definition of singular term. Here are some definitions proposed by different writers:# A term that tells us which individual is being talked about....
and singular proposition, both essential features of predicate logic.
With the ascension of predicate logic
Predicate logic
In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulae contain variables which can be quantified...
, term and syllogistic logic gradually fell into disuse except among students of ancient and medieval philosophy. Since the development of predicate logic, introductory texts on logic have ignored or disparaged term logic, except perhaps as a source of examples for beginning students. A notable exception to this generalization is the four editions of Quine's Methods of Logic (the last edition, dated 1982, is still in print), which discussed term logic (which Quine called "Boolean term schemata") and syllogism
Syllogism
A syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
s at some length. Quine's writings on logic contain much that is in the spirit of term logic in that they frequently invoke grammatical concepts and examples taken from natural language, even employing bits of scholastic terminology such as "syncategorematic
Syncategorematic term
In scholastic logic, a syncategorematic term is a word that cannot serve as the subject or the predicate of a proposition, and thus cannot stand for any of Aristotle's categories, but can be used with other terms to form a proposition...
."
Term logic also survived to some extent in traditional Roman Catholic education, especially in seminaries
Seminary
A seminary, theological college, or divinity school is an institution of secondary or post-secondary education for educating students in theology, generally to prepare them for ordination as clergy or for other ministry...
. Medieval Catholic theology
Theology
Theology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...
, especially the writings of Thomas Aquinas
Thomas Aquinas
Thomas Aquinas, O.P. , also Thomas of Aquin or Aquino, was an Italian Dominican priest of the Catholic Church, and an immensely influential philosopher and theologian in the tradition of scholasticism, known as Doctor Angelicus, Doctor Communis, or Doctor Universalis...
, had a powerfully Aristotelean
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
cast, and thus term logic became a part of Catholic theological reasoning. For example, Joyce (1949), written for use in Catholic seminaries, made no mention of Frege or Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
. On Aristotle
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
, term logic, and Roman Catholicism, see Copleston
Frederick Copleston
Frederick Charles Copleston, SJ, CBE was a Jesuit priest and historian of philosophy.-Biography:...
's A History of Philosophy
A History of Philosophy (Copleston)
A History of Philosophy is an eleven-volume history of Western philosophy, written by English Jesuit priest Frederick Charles Copleston.Copleston's History provides extensive coverage of Western philosophy from the Pre-Socratics through Dewey, Russell, Moore, Sartre and Merleau-Ponty...
.
A 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 functionFunction (mathematics)In mathematics, a function associates one quantity, the argument of the function, also known as the input, with another quantity, the value of the function, also known as the output. A function assigns exactly one output to each input. The argument and the value may be real numbers, but they can...
and argument, quantifier and bound variable. - Suffers from theoretical problems, probably the most serious being empty nameEmpty nameIn the philosophy of language, an empty name is a proper name that has no referent.The problem of empty names is that empty names have a meaning that it seems they shouldn't have. The name "Pegasus" is empty; there is nothing to which it refers. Yet though there is no Pegasus, we know what the...
s and identity statements.
Even academic philosophers entirely in the mainstream, such as Gareth Evans
Gareth Evans (philosopher)
Gareth Evans was a British philosopher.-Life:Gareth Evans studied Philosophy, Politics and Economics at University College, Oxford . His philosophy tutor was Peter Strawson...
, 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 [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)
The writings of Fred Sommers (e.g., Sommers 1970) and his students have modified term logic so that it can address these criticisms of predicate logic and overcome the well-known weaknesses of term logic. The result is the "term functor logic" of Sommers (1982), and Sommers and Englebretsen (2000). This logic has a very Boolean appearance, in that '+' and '-' are the sole operational signs and all statements are equations. It has sufficient expressive power to handle relational terms generally, and to capture the validity of arguments that elude syllogistic reasoning. Term functor logic has similarities to Quine's predicate functor logic
Predicate functor logic
In mathematical logic, predicate functor logic is one of several ways to express first-order logic by purely algebraic means, i.e., without quantified variables. PFL employs a small number of algebraic devices called predicate functors that operate on terms to yield terms...
, an algebraic formalism Quine devised to do first-order logic
First-order logic
First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...
without quantifiers.
In a less formal vein, term logic has acquired a following among those advocating a return to educational methods grounded in the medieval Trivium: grammar
Grammar
In linguistics, grammar is the set of structural rules that govern the composition of clauses, phrases, and words in any given natural language. The term refers also to the study of such rules, and this field includes morphology, syntax, and phonology, often complemented by phonetics, semantics,...
, logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, and rhetoric
Rhetoric
Rhetoric is the art of discourse, an art that aims to improve the facility of speakers or writers who attempt to inform, persuade, or motivate particular audiences in specific situations. As a subject of formal study and a productive civic practice, rhetoric has played a central role in the Western...
. Advocates of the Trivium include the Paideia Proposal
Paideia Proposal
The Paideia Proposal was a K-12 educational reform plan proposed by Mortimer Adler. Adler was a prolific author, and references to the Paideia plan for educational reform can be found in a number of his books listed in the references below.-The Proposal:...
by philosopher Mortimer J. Adler, and some homeschoolers
Homeschooling
Homeschooling or homeschool is the education of children at home, typically by parents but sometimes by tutors, rather than in other formal settings of public or private school...
. The Trivium views logic not as a form of mathematics, but as part of a classical education
Classics
Classics is the branch of the Humanities comprising the languages, literature, philosophy, history, art, archaeology and other culture of the ancient Mediterranean world ; especially Ancient Greece and Ancient Rome during Classical Antiquity Classics (sometimes encompassing Classical Studies or...
in language. Those advocating this line see predicate logic as excessively nominalistic
Nominalism
Nominalism is a metaphysical view in philosophy according to which general or abstract terms and predicates exist, while universals or abstract objects, which are sometimes thought to correspond to these terms, do not exist. Thus, there are at least two main versions of nominalism...
, as primarily concerned with the manipulation of symbols (syntax
Syntax
In linguistics, syntax is the study of the principles and rules for constructing phrases and sentences in natural languages....
) and not with the whys and essences of things (ontology
Ontology
Ontology is the philosophical study of the nature of being, existence or reality as such, as well as the basic categories of being and their relations...
and metaphysics
Metaphysics
Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...
).
A variant of term logic, probabilistic term logic
Probabilistic logic
The aim of a probabilistic logic is to combine the capacity of probability theory to handle uncertainty with the capacity of deductive logic to exploit structure. The result is a richer and more expressive formalism with a broad range of possible application areas...
, which assigns a probability value and a confidence value to the truth of both terms and propositions, is gaining popularity in artificial intelligence
Artificial intelligence
Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...
systems. Variants include both Pei Wang's "Non-Axiomatic Reasoning System" (NARS) and Ben Goertzel's "OpenCog" system.
See also
- AristotleAristotleAristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
- ContrapositionContrapositionIn traditional logic, contraposition is a form of immediate inference in which from a given proposition another is inferred having for its subject the contradictory of the original predicate, and in some cases involving a change of quality . For its symbolic expression in modern logic see the rule...
- Contraposition (traditional logic)
- Conversion (logic)
- De Interpretatione
- ObversionObversionIn traditional logic, obversion is a "type of immediate inference in which from a given proposition another proposition is inferred whose subject is the same as the original subject, whose predicate is the contradictory of the original predicate, and whose quality is affirmative if the original...
- OrganonOrganonThe Organon is the name given by Aristotle's followers, the Peripatetics, to the standard collection of his six works on logic:* Categories* On Interpretation* Prior Analytics* Posterior Analytics...
- Port-Royal LogicPort-Royal LogicPort-Royal Logic, or Logique de Port-Royal, is the common name of La logique, ou l'art de penser, an important textbook on logic first published anonymously in 1662 by Antoine Arnauld and Pierre Nicole, two prominent members of the Jansenist movement, centered around Port-Royal. Blaise Pascal...
- Prior AnalyticsPrior AnalyticsThe Prior Analytics is Aristotle's work on deductive reasoning, specifically the syllogism. It is also part of his Organon, which is the instrument or manual of logical and scientific methods....
- Propositional calculusPropositional calculusIn mathematical logic, a propositional calculus or logic is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules and axioms allows certain formulas to be derived, called theorems; which may be interpreted as true...
- SyllogismSyllogismA syllogism is a kind of logical argument in which one proposition is inferred from two or more others of a certain form...
- Transposition (logic)Transposition (logic)In the methods of deductive reasoning in classical logic, transposition is the rule of inference that permits one to infer from the truth of "A implies B" the truth of "Not-B implies not-A", and conversely. Its symbolic expression is:...
External links
- Stanford Encyclopedia of PhilosophyStanford Encyclopedia of PhilosophyThe Stanford Encyclopedia of Philosophy is a freely-accessible online encyclopedia of philosophy maintained by Stanford University. Each entry is written and maintained by an expert in the field, including professors from over 65 academic institutions worldwide...
:- Aristotle's Logic -- by Robin Smith.
- Traditional Square of Opposition -- by Terence ParsonsTerence ParsonsTerence Parsons is an American contemporary philosopher of the analytic tradition. Parsons is also a Professor at UCLA in its Department of Philosophy....
.
- Internet Encyclopedia of PhilosophyInternet Encyclopedia of PhilosophyThe Internet Encyclopedia of Philosophy is a free online encyclopedia on philosophical topics and philosophers founded by James Fieser in 1995. The current general editors are James Fieser and Bradley Dowden...
: "Aristotle." Discusses how Aristotle's logic was viewed by his many successors. - Aristotle's term logic online -- This online program provides a platform for experimentation and research on Aristotelian logic.
- Annotated bibliographies of writings by:
- PlanetMathPlanetMathPlanetMath is a free, collaborative, online mathematics encyclopedia. The emphasis is on rigour, openness, pedagogy, real-time content, interlinked content, and also community of about 24,000 people with various maths interests. Intended to be comprehensive, the project is hosted by the Digital...
: Aristotelian Logic.