# Carew Arthur Meredith

Carew Arthur Meredith (July 28, 1904 – March 31, 1976), usually cited as C. A. Meredith, was an influential Irish logician, appointed to Trinity College, Dublin in 1947. His work on condensed detachment (inspired by the work of Łukasiewicz) was under-appreciated in his own time, but is influential in modern research.[citation needed]

## Biography

Born July 28, 1904 into a distinguished Dublin family, he was the son of barrister Arthur Francis Carew Meredith K.C. (1862 – May 16, 1938),[1] whose opinions were sought by Éamon de Valera in drafting the constitution of the Irish Republic (1919–22). Educated in England at Winchester College, he went on to read mathematics at Trinity College, Cambridge, in 1922 becoming the first mathematical student to take a double first and 'B star' in two years.

Łukasiewicz was appointed professor at the Royal Irish Academy, where he lectured on mathematical logic. Meredith attended these lectures from 1947 on, and became keenly interested in the Lukasiewicz's detachment operation, for which—as he himself once phrased it—he "seemed to have some aptitude."

Meredith was related to another mathematician, Thomas Meredith. He was a nephew of Richard Edmund Meredith and a cousin of Monk Gibbon, Judge James Creed Meredith and Ralph Creed Meredith. His old school friend from Winchester, William Empson, described him as "a small, gnomelike figure with a grin like a Cheshire cat and a pronounced Dublin accent (good for reading aloud from Joyce)".

He did logic whenever time and opportunity presented themselves, and he did it on whatever materials came to hand: in a pub, his favored pint of porter within reach, he would use the inside of cigarette packs to write proofs for logical colleagues.[2]

## Work

He proved the shortest known axiomatic bases for a number of logic systems, such as this one-axiom basis for propositional calculus:[3]

${\displaystyle (((((\phi \to \psi )\to (\neg \chi \to \neg \theta ))\to \chi )\to \tau )\to ((\tau \to \phi )\to (\theta \to \phi )))}$

His achievements in that area were unsurpassed until automated theorem provers in the last few years, which build on his work, proved some shorter ones for some systems and proved his shortest for others. Notably, Stephen Wolfram, William McCune and others built on Meredith's work to produce the shortest known single axiom equivalent to the axioms of propositional calculus.[4][5]

## Selected publications

• C.A. Meredith (1953). "Single axioms for the systems (C,N), (C,0), and (A,N) of the two-valued propositional calculus". Journal of Computing Systems. 1: 155–164.
• E.J. Lemmon and C.A. Meredith and D. Meredith and A.N. Prior and I. Thomas (1957). Calculi of pure strict implication (Technical Report). Canterbury University College, Christchurch. (Reprinted in Philosophical Logic, Reidel, 1970 doi:10.1007/978-94-010-9614-0_17)
• C. Meredith and A. Prior (1963). "Notes on the axiomatics of the propositional calculus". Notre Dame Journal of Formal Logic. 4 (3): 171–187.
• C.A. Meredith and A.N. Prior (1968). "Equational logic". Notre Dame Journal of Formal Logic. 9 (3): 212–226.

## References

1. ^ Arthur Francis Carew Meredith at findagrave.com
2. ^ Meredith, David (October 1977). "In memoriam: Carew Arthur Meredith (1904--1976)". Notre Dame Journal of Formal Logic. 18 (4): 513–516. doi:10.1305/ndjfl/1093888116. ISSN 0029-4527.
3. ^ "meredith - Metamath Proof Explorer". us.metamath.org. Retrieved 2019-05-22.
4. ^ History of logic axioms Stephen Wolfram, A New Kind of Science, 2002, p. 1175.
5. ^ McCune, William; Veroff, Robert; Fitelson, Branden; Harris, Kenneth; Feist, Andrew; Wos, Larry (2002), "Short single axioms for Boolean algebra", Journal of Automated Reasoning, 29 (1): 1–16, doi:10.1023/A:1020542009983, MR 1940227