Edward John Lemmon (1 June 1930 – 29 July 1966) was a

British British may refer to: Peoples, culture, and language * British people, nationals or natives of the United Kingdom, British Overseas Territories, and Crown Dependencies. ** Britishness, the British identity and common culture * British English, ...

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

and

philosopher A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...

born in

Sheffield Sheffield is a city in South Yorkshire, England, whose name derives from the River Sheaf which runs through it. The city serves as the administrative centre of the City of Sheffield. It is historically part of the West Riding of Yorkshire ...

England England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest and the Celtic Sea to the southwest. It is separated from continental Europe ...

. He is most well known for his work on

modal logic Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend ot ...

, particularly his joint text with

Dana Scott Dana Stewart Scott (born October 11, 1932) is an American logician who is the emeritus Hillman University Professor of Computer Science, Philosophy, and Mathematical Logic at Carnegie Mellon University; he is now retired and lives in Berkeley, Ca ...

published posthumously (Lemmon and Scott, 1977).

Biography

Lemmon attended King Edward VII SchoolSchool magazine, 1947
in Sheffield until 1947, before reading Literae humaniores at

Magdalen College, Oxford Magdalen College (, ) is a constituent college of the University of Oxford. It was founded in 1458 by William of Waynflete. Today, it is the fourth wealthiest college, with a financial endowment of £332.1 million as of 2019 and one of the ...

, as an undergraduate, and was appointed Fellow of

Trinity College, Oxford (That which you wish to be secret, tell to nobody) , named_for = The Holy Trinity , established = , sister_college = Churchill College, Cambridge , president = Dame Hilary Boulding , location = Broad Street, Oxford OX1 3BH , coordinates ...

, in 1957. In 1963, following a visiting professorship in

Texas Texas (, ; Spanish: ''Texas'', ''Tejas'') is a state in the South Central region of the United States. At 268,596 square miles (695,662 km2), and with more than 29.1 million residents in 2020, it is the second-largest U.S. state by ...

, Lemmon emigrated to the

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country Continental United States, primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., ...

to lecture at the Claremont Graduate School (now

Claremont Graduate University The Claremont Graduate University (CGU) is a private, all-graduate research university in Claremont, California. Founded in 1925, CGU is a member of the Claremont Colleges which includes five undergraduate ( Pomona College, Claremont McKenna ...

). Lemmon died from

heart failure Heart failure (HF), also known as congestive heart failure (CHF), is a syndrome, a group of signs and symptoms caused by an impairment of the heart's blood pumping function. Symptoms typically include shortness of breath, excessive fatigue, ...

while climbing.

Modal logic

John Lemmon became interested in modal logic when

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 ...

visited

Oxford University Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...

in 1956 to give the

John Locke lectures The John Locke Lectures are a series of annual lectures in philosophy given at the University of Oxford. Named for British philosopher John Locke, the Locke Lectures are the world's most prestigious lectures in philosophy, and are among the world' ...

, later published as his ''Time and Modality'' (Prior 1957). Prior returned for twelve months soon after, to lead a small group including Lemmon,

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 ...

and Ivo Thomas (Copeland 2004). John Lemmon became one of the early champions of Prior's distinctive approach to

tense logic In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time (for example, "I am ''always'' hungry", "I will ''eventually'' be hungry", or "I will be hungry ''until'' I ...

, and Lemmon's later work on alethic modality and applications of modal logic to ethics bear the mark of Prior's influence. At this time, Lemmon published a treatment of alethic and

epistemic Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics. Episte ...

modalities which introduced some systems of non-

normal modal logic In logic, a normal modal logic is a set ''L'' of modal formulas such that ''L'' contains: * All propositional tautologies; * All instances of the Kripke schema: \Box(A\to B)\to(\Box A\to\Box B) and it is closed under: * Detachment rule (''modus po ...

s that have proven to have had lasting interest, the alethic system S0.5 and the epistemic systems E1–E5 linked to the systems S0.5 and Lewis's systems S2–S5, but which lack the law of necessitation (Lemmon 1957). Lemmon was a pioneer of the modern approach to the

semantics 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 ...

of modal logic, particularly through his collaboration with

, but also became interested in the rival algebraic semantics of modal logic that follows more closely the kind of semantics found in the work of Tarski and

Jónsson Jónsson is a surname of Icelandic origin, meaning ''son of Jón''. In Icelandic names, the name is not strictly a surname, but a patronymic. The name refers to: *Arnar Jónsson (actor) (born 1943), Icelandic actor *Arnar Jónsson (basketball) (bo ...

Works

* 1957. 'New foundations for Lewis modal systems'. ''

Journal of Symbolic Logic The '' Journal of Symbolic Logic'' is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic. It was established in 1936 and covers mathematical logic. The journal is indexed by ''Mathematical Reviews'', Zentralb ...

'' 22:176-186 * With

Michael Dummett Sir Michael Anthony Eardley Dummett (27 June 1925 – 27 December 2011) was an English academic described as "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality." He ...

, 1959. 'Modal Logics between S4 and S5'. In ''Zeitschrifl für Mathematische Logik und Grundlagen der Mathematik'', 5:250-264 * 1959, "Is There Only One Correct System of Modal Logic?" ''

Proceedings of the Aristotelian Society The Aristotelian Society for the Systematic Study of Philosophy, more generally known as the Aristotelian Society, is a philosophical society in London. History Aristotelian Society was founded at a meeting on 19 April 1880, at 17 Bloomsbury Squa ...

, Supplementary Volumes'', 33:23-40 * 1962, 'Moral dilemmas'. ''

The Philosophical Review ''The Philosophical Review'' is a quarterly journal of philosophy edited by the faculty of the Sage School of Philosophy at Cornell University and published by Duke University Press (since September 2006). Overview The journal publishes original ...

'', LXXI * 1966, 'Sentences, Statements and Propositions', in B. Williams and A. Montefiore, eds., ''British Analytical Philosophy'', London: Routledge and Kegan Paul, pp.87-107 * 1967, 'If I Know, Do I Know that I Know?', in A. Stroll, ed., ''Epistemology'', New York: Harper and Rowe, pp54–83. * With

, 1977. ''An introduction to modal logic''. Oxford: Blackwell. *

References

* Ivo Thomas, 1968.
In Memoriam: Edward John Lemmon
Notre Dame Journal of Formal Logic, Vol IX(1). * Jack Copeland, 2004
Arthur Prior
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. E ...

. {{DEFAULTSORT:Lemmon, John 1930 births 1966 deaths 20th-century British non-fiction writers 20th-century British philosophers 20th-century English mathematicians Alumni of Magdalen College, Oxford British logicians British male non-fiction writers Epistemologists People educated at King Edward VII School, Sheffield Philosophers of language Philosophers of logic Philosophers of mathematics Place of death missing