Crispin Wright
Encyclopedia
Crispin Wright is a British
philosopher, who has written on neo-Fregean
philosophy of mathematics
, Wittgenstein's later philosophy
, and on issues related to truth
, realism
, cognitivism
, skepticism
, knowledge
, and objectivity
.
He was born in Surrey and was educated at Birkenhead School
(1950–61) and at Trinity College, Cambridge
, graduating in Moral Sciences in 1964 and taking a PhD in 1968. He took an Oxford BPhil in 1969 and was elected Prize Fellow and then Research Fellow at All Souls College, Oxford
, where he worked until 1978. He then moved to the University of St. Andrews, where he was appointed Professor of Logic and Metaphysics and then the first Bishop Wardlaw University
Professorship in 1997. As of fall 2008, he is professor at New York University
(NYU). He has also taught at the University of Michigan
, Oxford University, Columbia University
, and Princeton University
. Crispin Wright is founder and director of Arché
, which he left in September 2009 to take up leadership of the new Northern Institute of Philosophy (NIP) at the University of Aberdeen
.
In the philosophy of mathematics, he is best-known for his book Frege's Conception of Numbers as Objects (1983), where he argues that Frege's logicist
project could be revived by removing the Principle of Unrestricted Comprehension (sometimes referred to as Basic Law V) from the formal system
. Arithmetic
is then derivable in second-order logic
from Hume's principle
. He gives informal argument
s that (i) Hume
's principle
plus second-order logic is consistent
, and (ii) from it one can produce the Dedekind–Peano axioms
. Both results were proven informally by Gottlob Frege (Frege's Theorem
), and would later be more rigorously proven by George Boolos
and Richard Heck. Wright is one of the major proponents of neo-logicism, alongside his frequent collaborator Bob Hale
. He has also written Wittgenstein and the Foundations of Mathematics (1980).
In general metaphysics, his most important work is Truth and Objectivity (Harvard University Press, 1992). He argues in this book that there need be no single, discourse-invariant thing in which truth
consists, making an analogy with identity
. There need only be some principle
s regarding how the truth predicate
can be applied to a sentence
, some 'platitudes' about true sentences. Wright also argues that in some contexts, probably including moral
contexts, superassertibility will effectively function as a truth predicate. He defines
a predicate as superassertible if and only if it is "assertible
" in some state of information and then remains so no matter how that state of information is enlarged upon or improved. Assertiveness is warrant
by whatever standards inform the discourse
in question.
Many of his most important papers in philosophy of language, epistemology, philosophical logic, meta-ethics, and the interpretation of Wittgenstein have been collected in two volumes published by Harvard University Press
.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
philosopher, who has written on neo-Fregean
Gottlob Frege
Friedrich Ludwig Gottlob Frege was a German mathematician, logician and philosopher. He is considered to be one of the founders of modern logic, and made major contributions to the foundations of mathematics. He is generally considered to be the father of analytic philosophy, for his writings on...
philosophy of mathematics
Philosophy of mathematics
The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of...
, Wittgenstein's later philosophy
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...
, and on issues related to truth
Truth
Truth 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...
, realism
Philosophical realism
Contemporary philosophical realism is the belief that our reality, or some aspect of it, is ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc....
, cognitivism
Cognitivism (ethics)
Cognitivism is the meta-ethical view that ethical sentences express propositions and can therefore be true or false , which noncognitivists deny...
, skepticism
Skepticism
Skepticism has many definitions, but generally refers to any questioning attitude towards knowledge, facts, or opinions/beliefs stated as facts, or doubt regarding claims that are taken for granted elsewhere...
, knowledge
Knowledge
Knowledge is a familiarity with someone or something unknown, which can include information, facts, descriptions, or skills acquired through experience or education. It can refer to the theoretical or practical understanding of a subject...
, and objectivity
Objectivity (philosophy)
Objectivity is a central philosophical concept which has been variously defined by sources. A proposition is generally considered to be objectively true when its truth conditions are met and are "mind-independent"—that is, not met by the judgment of a conscious entity or subject.- Objectivism...
.
He was born in Surrey and was educated at Birkenhead School
Birkenhead School
Birkenhead School is an independent, selective, co-educational school located on the Wirral Peninsula in the northwest of England. It is a member of the Headmasters' and Headmistresses' Conference.-Overview:The school is subdivided into...
(1950–61) and at Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
, graduating in Moral Sciences in 1964 and taking a PhD in 1968. He took an Oxford BPhil in 1969 and was elected Prize Fellow and then Research Fellow at All Souls College, Oxford
All Souls College, Oxford
The Warden and the College of the Souls of all Faithful People deceased in the University of Oxford or All Souls College is one of the constituent colleges of the University of Oxford in England....
, where he worked until 1978. He then moved to the University of St. Andrews, where he was appointed Professor of Logic and Metaphysics and then the first Bishop Wardlaw University
Professorship in 1997. As of fall 2008, he is professor at New York University
New York University
New York University is a private, nonsectarian research university based in New York City. NYU's main campus is situated in the Greenwich Village section of Manhattan...
(NYU). He has also taught at the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...
, Oxford University, Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
, and Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
. Crispin Wright is founder and director of Arché
Arche
Arche is a Greek word with primary senses 'beginning', 'origin' or 'first cause' and 'power', 'sovereignty', 'domination' as extended meanings. This list is extended to 'ultimate underlying substance' and 'ultimate undemonstrable principle'...
, which he left in September 2009 to take up leadership of the new Northern Institute of Philosophy (NIP) at the University of Aberdeen
University of Aberdeen
The University of Aberdeen, an ancient university founded in 1495, in Aberdeen, Scotland, is a British university. It is the third oldest university in Scotland, and the fifth oldest in the United Kingdom and wider English-speaking world...
.
In the philosophy of mathematics, he is best-known for his book Frege's Conception of Numbers as Objects (1983), where he argues that Frege's logicist
Logicism
Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. Bertrand Russell and Alfred North Whitehead championed this theory fathered by Richard Dedekind...
project could be revived by removing the Principle of Unrestricted Comprehension (sometimes referred to as Basic Law V) from the formal system
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
. Arithmetic
Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...
is then derivable in second-order logic
Second-order logic
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory....
from Hume's principle
Hume's principle
Hume's Principle or HP—the terms were coined by George Boolos—says that the number of Fs is equal to the number of Gs if and only if there is a one-to-one correspondence between the Fs and the Gs. HP can be stated formally in systems of second-order logic...
. He gives informal argument
Argument
In philosophy and logic, an argument is an attempt to persuade someone of something, or give evidence or reasons for accepting a particular conclusion.Argument may also refer to:-Mathematics and computer science:...
s that (i) Hume
David Hume
David Hume was a Scottish philosopher, historian, economist, and essayist, known especially for his philosophical empiricism and skepticism. He was one of the most important figures in the history of Western philosophy and the Scottish Enlightenment...
's principle
Principle
A principle is a law or rule that has to be, or usually is to be followed, or can be desirably followed, or is an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed...
plus second-order logic is consistent
Consistency
Consistency can refer to:* Consistency , the psychological need to be consistent with prior acts and statements* "Consistency", an 1887 speech by Mark Twain...
, and (ii) from it one can produce the Dedekind–Peano axioms
Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano...
. Both results were proven informally by Gottlob Frege (Frege's Theorem
Frege's theorem
Frege's theorem states that the Peano axioms of arithmetic can be derived in second-order logic from Hume's principle. It was first proven, informally, by Gottlob Frege in his Die Grundlagen der Arithmetik , published in 1884, and proven more formally in his Grundgesetze der Arithmetik , published...
), and would later be more rigorously proven by George Boolos
George Boolos
George Stephen Boolos was a philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.- Life :...
and Richard Heck. Wright is one of the major proponents of neo-logicism, alongside his frequent collaborator Bob Hale
Bob Hale (philosopher)
Robert Hale FBA, FRSE is a British philosopher, who is well-known for his contributions to the development of the neo-Fregean philosophy of mathematics in collaboration with Crispin Wright, and for his works in modality and philosophy of language....
. He has also written Wittgenstein and the Foundations of Mathematics (1980).
In general metaphysics, his most important work is Truth and Objectivity (Harvard University Press, 1992). He argues in this book that there need be no single, discourse-invariant thing in which truth
Truth
Truth 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...
consists, making an analogy with identity
Identity (social science)
Identity is a term used to describe a person's conception and expression of their individuality or group affiliations . The term is used more specifically in psychology and sociology, and is given a great deal of attention in social psychology...
. There need only be some principle
Principle
A principle is a law or rule that has to be, or usually is to be followed, or can be desirably followed, or is an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed...
s regarding how the truth predicate
Predicate (grammar)
There are two competing notions of the predicate in theories of grammar. Traditional grammar tends to view a predicate as one of two main parts of a sentence, the other being the subject, which the predicate modifies. The other understanding of predicates is inspired from work in predicate calculus...
can be applied to a sentence
Sentence (linguistics)
In the field of linguistics, a sentence is an expression in natural language, and often defined to indicate a grammatical unit consisting of one or more words that generally bear minimal syntactic relation to the words that precede or follow it...
, some 'platitudes' about true sentences. Wright also argues that in some contexts, probably including moral
Morality
Morality is the differentiation among intentions, decisions, and actions between those that are good and bad . A moral code is a system of morality and a moral is any one practice or teaching within a moral code...
contexts, superassertibility will effectively function as a truth predicate. He defines
Stipulative definition
A stipulative definition is a type of definition in which a new or currently-existing term is given a specific meaning for the purposes of argument or discussion in a given context. When the term already exists, this definition may, but does not necessarily, contradict the dictionary definition of...
a predicate as superassertible if and only if it is "assertible
Assertiveness
Assertiveness is a particular mode of communication. Dorland's Medical Dictionary defines assertiveness as:During the second half of the 20th century, assertiveness was increasingly singled out as a behavioral skill taught by many personal development experts, behavior therapists, and cognitive...
" in some state of information and then remains so no matter how that state of information is enlarged upon or improved. Assertiveness is warrant
Theory of justification
Theory of justification is a part of epistemology that attempts to understand the justification of propositions and beliefs. Epistemologists are concerned with various epistemic features of belief, which include the ideas of justification, warrant, rationality, and probability...
by whatever standards inform the discourse
Discourse
Discourse generally refers to "written or spoken communication". The following are three more specific definitions:...
in question.
Many of his most important papers in philosophy of language, epistemology, philosophical logic, meta-ethics, and the interpretation of Wittgenstein have been collected in two volumes published by Harvard University Press
Harvard University Press
Harvard University Press is a publishing house established on January 13, 1913, as a division of Harvard University, and focused on academic publishing. In 2005, it published 220 new titles. It is a member of the Association of American University Presses. Its current director is William P...
.
Awards
- FBA: Fellow of the British Academy, 1992
- FRSE: Fellow of the Royal Society of Edinburgh, 1996
- Fulbright scholar at Princeton UniversityPrinceton UniversityPrinceton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
, 1985-6 - Leverhulme TrustLeverhulme TrustThe Leverhulme Trust was established in 1925 under the will of the First Viscount Leverhulme, William Hesketh Lever, with the instruction that its resources should be used to support "scholarships for the purposes of research and education."...
Personal Research Professor, 1998–2003 - British AcademyBritish AcademyThe British Academy is the United Kingdom's national body for the humanities and the social sciences. Its purpose is to inspire, recognise and support excellence in the humanities and social sciences, throughout the UK and internationally, and to champion their role and value.It receives an annual...
Research Reader, 1990-2 - Prize Fellow, All Souls College, OxfordOxfordThe city of Oxford is the county town of Oxfordshire, England. The city, made prominent by its medieval university, has a population of just under 165,000, with 153,900 living within the district boundary. It lies about 50 miles north-west of London. The rivers Cherwell and Thames run through...
, 1969–71