Church, Alonzo
Publié le 16/05/2020
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Church, Alonzo (1903-95)
Alonzo Church was one of the twentieth century's leading logicians.
His work covers an extensive range of topics
in logic and in other areas of mathematics.
His most influential work relates to three areas: the general properties
of functions, as presented in his 'calculus of lambda conversion'; the theory of computability and the decision
problem, to which he made fundamental contributions, known as Church's thesis and Church's theorem; and
intensional logic, developing Frege's theory of sense and denotation.
In the last four decades of his life Church
continued working mostly in this last area.
1 Life
Alonzo Church was born in Washington, DC.
After receiving his Ph.D.
from Princeton in 1927 he spent two years
as a National Research Fellow at Harvard, Göttingen and Amsterdam.
He then held positions in mathematics and
philosophy at Princeton (1929-67) and UCLA (1967-90).
Church's work covers an extensive range of topics in mathematics and logic, including the Lorentz transformation,
differentials, recursive arithmetic, postulate theory, the law of the excluded middle, non-standard interpretations of
propositional logic, higher-order logic, a theory of weak implication and notes on the history of logic.
His most
influential work, however, relates to three areas: (1) the general properties of functions, in his 'calculus of lambda
conversion' (Lambda calculus ), first presented in 1932 and developed in 1941; (2) effective calculability - his
influential proposal that the effectively calculable functions can be identified with the recursive functions
and his negative solution to the decision problem ( 'Entscheidungsproblem ') for predicate logic
were first published in 1936; and (3) intensional logic and a
development of Frege's theory of sense and denotation.
In the last four decades of
his life Church continued working mostly in this last area.
Particularly important is his series of papers on its
'revised' formulations ( 1973 , 1974 , 1993 ).
While at Princeton Church became one of the principal founders of the Journal of Symbolic Logic , the first volume
of which appeared in 1936.
He was an editor of the journal for its first forty-four volumes.
2 A theory of functions
The notion of mathematical function dominated Church's early work.
He concentrated only on the general
properties of functions 'independently of their appearance in any particular mathematical (or other) domain' .
In his
explanation of the notion of function, Church diverged from the standard view in mathematics and logic.
Of
importance is his emphasis on the intensional aspect of functions according to which they are not identified with a
set of ordered tuples as is usual in mathematics, but are regarded as operations - items which are applied to tuples
of objects (their arguments) to yield other single objects as values.
The general properties of functions were
studied in his ¸-calculus, which presented a language permitting unambiguous denotation of functions.
The.
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