Editing Term logic

{{short description|Approach to logic}}
{{Cleanup rewrite|date=January 2023}}
In [[logic]] and [[Formal semantics (natural language)|formal semantics]], '''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&nbsp;CE by [[Porphyry (philosopher)|Porphyry]]'s [[Isagoge]]. 

Term logic revived in [[Middle Ages|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.

== 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 ''[[On Interpretation]]'', 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.<ref>Degnan, M. 1994. Recent Work in Aristotle's Logic. Philosophical Books 35.2 (April, 1994): 81-89.</ref> Lukasiewicz's approach was reinvigorated in the early 1970s by [[John Corcoran (logician)|John Corcoran]] and [[Timothy Smiley]] – which informs modern translations of ''Prior Analytics'' by Robin Smith in 1989 and [[Gisela Striker]] in 2009.<ref>*Review of "Aristotle, Prior Analytics: Book I, Gisela Striker (translation and commentary), Oxford UP, 2009, 268pp., $39.95 (pbk), {{ISBN|978-0-19-925041-7}}." in the ''Notre Dame Philosophical Reviews'', [http://ndpr.nd.edu/review.cfm?id=18787 2010.02.02].</ref>

The ''Prior Analytics'' represents the first formal study of logic, where logic is understood as the study of arguments. An argument is a series of true or false statements which lead to a true or false conclusion.<ref>{{cite book |last1=Nolt |first1=John |last2=Rohatyn |first2=Dennis |title=Logic: Schaum's outline of theory and problems |page=1 |year=1988 |publisher=McGraw Hill |isbn=0-07-053628-7 }}</ref> In the ''Prior Analytics'', Aristotle identifies valid and invalid forms of arguments called [[syllogisms]]. A syllogism is an argument that consists of at least three sentences: at least two [[premise]]s and a conclusion. Although Aristotle does not call them "[[Categories (Aristotle)|categorical]] sentences", tradition does; he deals with them briefly in the ''Analytics'' and more extensively in ''[[On Interpretation]]''.<ref>{{cite book |author=Robin Smith |title=Aristotle: Prior Analytics |page=XVII }}</ref> Each proposition (statement that is a thought of the kind expressible by a declarative sentence)<ref>{{cite book |author=John Nolt/Dennis Rohatyn |title=Logic: Schaum's Outline of Theory and Problems |pages=274–275 }}</ref> of a syllogism is a categorical sentence which has a subject and a predicate connected by a verb. The usual way of connecting the subject and predicate of a categorical sentence as Aristotle does in ''On Interpretation'' is by using a linking verb e.g. P is S. However, in the Prior Analytics Aristotle rejects the usual form in favour of three of his inventions: 

*P belongs to S 
*P is predicated of S
*P is said of S 

Aristotle does not explain why he introduces these innovative expressions but scholars conjecture that the reason may have been that it facilitates the use of letters instead of terms avoiding the ambiguity that results in Greek when letters are used with the linking verb.<ref>{{cite book |last=Anagnostopoulos |first=Georgios |title=A Companion to Aristotle |page=33 |year=2009 |publisher=Wiley-Blackwell |isbn=978-1-4051-2223-8 }}</ref> In his formulation of syllogistic propositions, instead of the copula ("All/some... are/are not..."), Aristotle uses the expression, "... belongs to/does not belong to all/some..." or "... is said/is not said of all/some..."<ref>{{cite book |last=Patzig |first=Günther |title=Aristotle's theory of the syllogism |page=49 |year=1969 |publisher=Springer |isbn=978-90-277-0030-8 }}</ref> There are four different types of categorical sentences: universal affirmative (A), universal negative (E), particular affirmative (I) and particular negative (O).

*A	-	A belongs to every B
*E - A belongs to no B
*I	-	A belongs to some B
*O	-	A does not belong to some B

A method of symbolization that originated and was used in the Middle Ages greatly simplifies the study of the Prior Analytics.
Following this tradition then, let:

:a = belongs to every

:e = belongs to no

:i = belongs to some

:o = does not belong to some

Categorical sentences may then be abbreviated as follows:

:AaB = A belongs to every B (Every B is A)

:AeB = A belongs to no B (No B is A)

:AiB = A belongs to some B (Some B is A)

:AoB = A does not belong to some B (Some B is not A)

From the viewpoint of modern logic, only a few types of sentences can be represented in this way.<ref>{{cite book |title=The Cambridge Companion to Aristotle |pages=34–35 }}</ref>

== Basics ==
The fundamental assumption behind the theory is that the [[formal system|formal]] model of [[propositions]] are composed of two [[Symbol (formal)|logical symbol]]s 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 (Aristotle)|categories]]'' enumerated by Aristotle in his ''[[Organon]]'', classifying all objects and qualities within the domain of logical discourse.
*The [[formal system|formal]] model of ''proposition'' consists of two terms, one of which, the "[[predicate (grammar)|predicate]]", is "affirmed" or "denied" of the other, the "[[subject (grammar)|subject]]", and which is capable of [[truth]] or [[falsity]].
*The ''[[syllogism]]'' is an [[inference]] in which one [[proposition]] (the "[[Consequent|conclusion]]") follows of necessity from two other propositions (the "[[premise]]s").

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")
:* E-type: Universal and negative ("All philosophers are not mortal")
:* I-type: Particular and affirmative ("Some philosophers are mortal")
:* O-type: Particular and negative ("Some philosophers are not mortal")
This was called the ''fourfold scheme'' of propositions (see [[Syllogism#Types|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 [[Syllogism#Existential import|existential import]].

== Term ==
A [[Term (logic)|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 [[logician]]s like Arnauld (whose ''[[Port-Royal Logic]]'' was the best-known text of his day), it is a psychological entity like an "idea" or "[[concept]]". [[John Stuart Mill|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 (linguistics)|sentence]], in which the subject and [[predicate (grammar)|predicate]] are combined, so as to assert something true or false. It is not a thought, nor 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 [[Bertrand Russell|Russell]], such as [[F. H. Bradley|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, [[quantifier (linguistics)|quantification]] implies the existence of at least one subject, unless disclaimed.

== Singular terms ==
For Aristotle, the distinction between singular{{Citation needed|date=July 2022}} and universal is a fundamental [[metaphysical]] one, and not merely [[grammatical]]. A singular term for Aristotle is [[substance theory|primary substance]], which can only be [[predicate (grammar)|predicate]]d 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'')<ref name="katholouLSJ">{{LSJ|kaqo/lou|καθόλου|ref}}.</ref> secondary substance, genera, with primary substance, particular (''kath' hekaston'')<ref name="katholouLSJ"/><ref>{{LSJ|e(/kastos|καθ' ἕκαστον|shortref}}.</ref> specimens. The formal nature of [[Universal (metaphysics)|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.<ref>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.</ref>

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:<ref>Arnauld, Antoine and Nicole, Pierre; (1662) ''La logique, ou l'art de penser''. Part 2, chapter 3</ref>

: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,<ref>For example: Kapp, ''Greek Foundations of Traditional Logic'', New York 1942, p.&nbsp;17, Copleston ''[[A History of Philosophy (Copleston)|A History of Philosophy]]'' Vol. I., p.&nbsp;277, [[Bertrand Russell|Russell]], ''A History of Western Philosophy'' London 1946 p.&nbsp;218.</ref> 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."

=== The three figures ===

Depending on the position of the middle term, Aristotle divides the syllogism into three kinds: syllogism in the first, second, and third figure.<ref>{{cite book |title=The Cambridge Companion to Aristotle |page=35 |quote=At the foundation of Aristotle's syllogistic is a theory of a specific class of arguments: arguments having as premises exactly two categorical sentences with one term in common.}}</ref> If the Middle Term is subject of one premise and predicate of the other, the premises are in the First Figure. If the Middle Term is predicate of both premises, the premises are in the Second Figure. If the Middle Term is subject of both premises, the premises are in the Third Figure.<ref>{{cite book |author=Robin Smith |title=Aristotle: Prior Analytics |page=XVIII }}</ref>

Symbolically, the Three Figures may be represented as follows:<ref>{{cite book|author=Henrik Legerlund|title=Modal Syllogistics in the Middle Ages|page=4}}</ref>

{| class="wikitable"
|-
!
! First figure
! Second figure
! Third figure
|-
|
| Predicate&nbsp;— Subject
| Predicate&nbsp;— Subject
| Predicate&nbsp;— Subject
|-
| Major premise
| A ------------ B
| B ------------ A
| A ------------ B
|-
| Minor premise
| B ------------ C
| B ------------ C
| C ------------ B
|-
| Conclusion
| A ********** C
| A ********** C
| A ********** C
|}

=== The fourth figure ===
<blockquote>In Aristotelian syllogistic (''Prior Analytics'', Bk I Caps 4-7), syllogisms are divided into three figures according to the position of the middle term in the two premises. The fourth figure, in which the middle term is the predicate in the major premise and the subject in the minor, was added by Aristotle's pupil [[Theophrastus]] and does not occur in Aristotle's work, although there is evidence that Aristotle knew of fourth-figure syllogisms.<ref>{{cite book|last1=Russell|first1=Bertrand|title=Cambridge essays, 1888-99|last2=Blackwell|first2=Kenneth|publisher=Routledge|year=1983|isbn=978-0-04-920067-8|page=411}}</ref></blockquote>

== Syllogism in the first figure ==

In the ''Prior Analytics'' translated by A. J. Jenkins as it appears in volume 8 of the Great Books of the Western World, Aristotle says of the First Figure: "... If A is predicated of all B, and B of all C, A must be predicated of all C."<ref>{{cite book |title=Great Books of the Western World |volume=8 |page=40 }}</ref> In the ''Prior Analytics'' translated by Robin Smith, Aristotle says of the first figure: "... For if A is predicated of every B and B of every C, it is necessary for A to be predicated of every C."<ref>{{cite book |author=Robin Smith |title=Aristotle: ''Prior Analytics'' |page=4 }}</ref>

Taking ''a'' = ''is predicated of all'' = ''is predicated of every'', and using the symbolical method used in the Middle Ages, then the first figure is simplified to:<ref>{{cite book|title=The Cambridge Companion to Aristotle|page=41}}</ref>

:If AaB
:
:and BaC
:
:then AaC.

Or what amounts to the same thing:

:AaB, BaC; therefore AaC

When the four syllogistic propositions, a, e, i, o are placed in the first figure, Aristotle comes up with the following valid forms of deduction for the first figure:

:AaB, BaC; therefore, AaC

:AeB, BaC; therefore, AeC

:AaB, BiC; therefore, AiC

:BeC, AiC; therefore, AoC

In the Middle Ages, for [[mnemonic]] reasons they were called "Barbara", "Celarent", "Darii" and "Ferio" respectively.<ref>{{cite book |title=The Cambridge Companion to Aristotle |page=41 }}</ref>

The difference between the first figure and the other two figures is that the syllogism of the first figure is complete while that of the second and third is not. This is important in Aristotle's theory of the syllogism for the first figure is axiomatic while the second and third require proof. The proof of the second and third figure always leads back to the first figure.<ref>{{cite book |author=Henrik Legerlund |title=Modal Syllogistics in the Middle Ages |page=6}}</ref>

== Syllogism in the second figure ==

This is what Robin Smith says in English that Aristotle said in Ancient Greek: "... If M belongs to every N but to no X, then neither will N belong to any X. For if M belongs to no X, neither does X belong to any M; but M belonged to every N; therefore, X will belong to no N (for the first figure has again come about)."<ref>{{cite book |author=Robin Smith |title=Aristotle: Prior Analytics |page=7}}</ref>

The above statement can be simplified by using the symbolical method used in the Middle Ages:

:If MaN
:
:but MeX
:
:then NeX.
:
:For if MeX
:
:then XeM
:
:but MaN
:
:therefore XeN.

When the four syllogistic propositions, a, e, i, o are placed in the second figure, Aristotle comes up with the following valid forms of deduction for the second figure:

:MaN, MeX; therefore NeX

:MeN, MaX; therefore NeX

:MeN, MiX; therefore NoX

:MaN, MoX; therefore NoX

In the Middle Ages, for mnemonic reasons they were called respectively "Camestres", "Cesare", "Festino" and "Baroco".<ref>{{cite book |title=The Cambridge Companion to Aristotle |page=41}}</ref>

== Syllogism in the third figure ==

Aristotle says in the Prior Analytics, "... If one term belongs to all and another to none of the same thing, or if they both belong to all or none of it, I call such figure the third." Referring to universal terms, "... then when both P and R belongs to every S, it results of necessity that P will belong to some R."<ref>{{cite book |author=Robin Smith |title=Aristotle: Prior Analytics |page=9 }}</ref>

Simplifying:

:If PaS
:
:and RaS
:
:then PiR.

When the four syllogistic propositions, a, e, i, o are placed in the third figure, Aristotle develops six more valid forms of deduction:

:PaS, RaS; therefore PiR

:PeS, RaS; therefore PoR

:PiS, RaS; therefore PiR

:PaS, RiS; therefore PiR

:PoS, RaS; therefore PoR

:PeS, RiS; therefore PoR

In the Middle Ages, for mnemonic reasons, these six forms were called respectively: "Darapti", "Felapton", "Disamis", "Datisi", "Bocardo" and "Ferison".<ref>{{cite book |title=The Cambridge Companion to Aristotle |page=41 }}</ref>

== Table of syllogisms ==

{| class="wikitable"
|+Table of syllogisms<ref>{{cite book|title=The Cambridge Companion to Aristotle|page=41}}</ref>
|-
! Figure
! Major premise
! Minor premise
! Conclusion
! Mnemonic name
|-
! rowspan="4" | First Figure
| AaB
| BaC
| AaC
| Barbara
|-
| AeB
| BaC
| AeC
| Celarent
|-
| AaB
| BiC
| AiC
| Darii
|-
| BeC
| AiC
| AoC
| Ferio
|-
! rowspan="4" | Second Figure
| MaN
| MeX
| NeX
| Camestres
|-
| MeN
| MaX
| NeX
| Cesare
|-
| MeN
| MiX
| NoX
| Festino
|-
| MaN
| MoX
| NoX
| [[Baroco]]
|-
! rowspan="6" | Third Figure
| PaS
| RaS
| PiR
| Darapti
|-
| PeS
| RaS
| PoR
| Felapton
|-
| PiS
| RaS
| PiR
| Disamis
|-
| PaS
| RiS
| PiR
| Datisi
|-
| PoS
| RaS
| PoR
| Bocardo
|-
| PeS
| RiS
| PoR
| Ferison
|}

== Decline of term logic ==
Term logic began to decline in [[Europe]] during the [[Renaissance]], when logicians like [[Rodolphus Agricola]] Phrisius (1444–1485) and [[Petrus Ramus|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. [[Gottfried Wilhelm Leibniz|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 [[George Boole|Boole]] (1815–1864) and [[John Venn|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 (mathematician)|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 [[seminary|seminaries]]. Medieval Catholic [[theology]], especially the writings of [[Thomas Aquinas]], had a powerfully [[Aristotle|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]].<ref>[[Frederick Copleston|Copleston]]'s ''[[A History of Philosophy (Copleston)|A History of Philosophy]]''</ref>{{page number needed|date=August 2023}}{{quotation needed|date=August 2023}}

== 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 [[Willard Van Orman Quine|Quine]] acknowledged, "[[Procrustean]]," employing an [[artificial language]] of [[function (mathematics)|function]] and [[Logical argument|argument]], [[Quantifier (logic)|quantifier]], and [[bound variable]].
* Suffers from theoretical problems, probably the most serious being [[empty name]]s and identity statements.

Even academic philosophers entirely in the mainstream, such as [[Gareth Evans (philosopher)|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 [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)

==Boole’s acceptance of Aristotle==
[[File:Alexander - Commentaria in Analytica priora Aristotelis, 1549 - 4725692.tif |thumb|''Commentaria in Analytica priora Aristotelis'', 1549]]
[[George Boole]]'s unwavering acceptance of Aristotle's logic is emphasized by the historian of logic [[John Corcoran (logician)|John Corcoran]] in an accessible introduction to ''Laws of Thought''<ref>[[George Boole]]. 1854/2003. The Laws of Thought, facsimile of 1854 edition, with an introduction by J. Corcoran. Buffalo: Prometheus Books (2003). Reviewed by James van Evra in Philosophy in Review.24 (2004) 167–169.</ref> Corcoran also wrote a point-by-point comparison of ''Prior Analytics'' and ''Laws of Thought''.<ref>John Corcoran, Aristotle's Prior Analytics and Boole's Laws of Thought, History and Philosophy of Logic, vol. 24 (2003), pp. 261–288.</ref> According to Corcoran, Boole fully accepted and endorsed Aristotle's logic. Boole's goals were “to go under, over, and beyond” Aristotle's logic by:

# providing it with mathematical foundations involving equations;
# extending the class of problems it could treat– from assessing validity to solving equations; and
# expanding the range of applications it could handle– e.g. from propositions having only two terms to those having arbitrarily many.

More specifically, Boole agreed with what [[Aristotle]] said; Boole's ‘disagreements’, if they might be called that, concern what Aristotle did not say. First, in the realm of foundations, Boole reduced the four propositional forms of [[Aristotle's logic]] to formulas in the form of equations– by itself a revolutionary idea. Second, in the realm of logic's problems, Boole's addition of equation solving to logic– another revolutionary idea –involved Boole's doctrine that Aristotle's rules of inference (the “perfect syllogisms”) must be supplemented by rules for equation solving. Third, in the realm of applications, Boole's system could handle multi-term propositions and arguments whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, Aristotle's system could not deduce “No quadrangle that is a square is a rectangle that is a rhombus” from “No square that is a quadrangle is a rhombus that is a rectangle” or from “No rhombus that is a rectangle is a square that is a quadrangle”.

== See also ==
{{Portal|Philosophy}}
{{div col|colwidth=22em}}
*[[Converse (logic)]]
*[[Obversion]]
*[[Propositional calculus]]
*[[Stoic logic]]
*[[Syntax–semantics interface]]
*[[Traditional grammar]]
*[[Transposition (logic)]]
{{div col end}}

== Notes ==
{{reflist|25em}}

== References ==
* Bochenski, I. M., 1951. ''Ancient Formal Logic''. North-Holland.
* [[Louis Couturat]], 1961 (1901). ''La Logique de Leibniz''. Hildesheim: Georg Olms Verlagsbuchhandlung.
* [[Gareth Evans (philosopher)|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|0-19-869117-3}}.
* Joyce, George Hayward, 1949 (1908). ''[https://web.archive.org/web/20060227234924/http://uk.geocities.com/frege@btinternet.com/joyce/principlesoflogic.htm  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 Łukasiewicz]], 1951. ''Aristotle's Syllogistic, from the Standpoint of Modern Formal Logic''. Oxford Univ. Press.
* [[William Calvert Kneale]] and [[Martha Kneale]], 1962. ''The Development of Logic''. Oxford [England] Clarendon Press. Reviews Aristotelean logic and its influences up to modern times.
* {{Cite book |last=Pratt-Hartmann |first=Ian |url=https://academic.oup.com/book/46400 |title=Fragments of First-Order Logic |date=2023-03-30 |publisher=Oxford University Press |isbn=978-0-19-196006-2 |language=en}}. Chapter 2 presents a modern overview, with a bibliography.
* [[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.
* [[Frederic Tamler Sommers|Sommers, Fred]]
*: 1970: "The Calculus of Terms," ''Mind 79'': 1-39. Reprinted in Englebretsen, G., ed., 1987. ''The new syllogistic'' New York: Peter Lang. {{ISBN|0-8204-0448-9}}
*: 1982: ''The logic of natural language''. Oxford University Press.
*: 1990: "[http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.ndjfl/1093635336 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. {{ISBN|0-7546-1366-6}}.
* Szabolcsi Lorne, 2008. ''Numerical Term Logic''. Lewiston: Edwin Mellen Press.

==External links==
{{Commons category}}
*{{PhilPapers|category|aristotelian-logic}}
*{{cite SEP |url-id=aristotle-logic |title=Aristotle's Logic |last=Smith |first=Robin}}
*{{cite IEP |url-id=aris-log |title=Term logic}}
*[http://aristotelianlogic.glashoff.eu Aristotle's term logic online]-This online program provides a platform for experimentation and research on Aristotelian logic.
* Annotated bibliographies:
*:[http://www.ontology.co/sommersf.htm Fred Sommers.]
*:[http://www.ontology.co/biblio/englebretseng.htm George Englebretsen.]
*[[PlanetMath]]: [http://planetmath.org/AristotelianLogic Aristotelian Logic].
*[http://thefirstscience.org/syllogistic-machine/  Interactive Syllogistic Machine for Term Logic] A web based syllogistic machine for exploring fallacies, figures, terms, and modes of syllogisms.

{{Formal semantics}}
{{Aristotelianism}}
{{Mathematical logic}}
{{Authority control}}

[[Category:Term logic| ]]
[[Category:Philosophy of Aristotle| Logic]]
[[Category:Logic| ]]
[[Category:Concepts in epistemology]]
[[Category:Philosophy of language]]
[[Category:Concepts in logic]]
[[Category:Semantics]]
[[Category:Concepts in metaphysics]]
[[Category:History of logic]]
[[Category:Mathematical logic]]
[[Category:Formal semantics (natural language)]]
[[Category:Philosophical logic]]
[[Category:Philosophy of logic]]