Defeasible reasoning
Encyclopedia
Defeasible reasoning is a kind of reasoning that is based on reasons that are defeasible, as opposed to the indefeasible reasons of deductive logic. Defeasible reasoning is a particular kind of non-demonstrative reasoning, where the reasoning does not produce a full, complete, or final demonstration of a claim, i.e., where fallibility and corrigibility of a conclusion are acknowledged. Other kinds of non-demonstrative reasoning are probabilistic reasoning, inductive reasoning
, statistical reasoning, abductive reasoning
, and paraconsistent reasoning. Defeasible reasoning is also a kind of ampliative
reasoning because its conclusions reach beyond the pure meanings of the premises.
The differences between these kinds of reasoning correspond to differences about the conditional that each kind of reasoning uses, and on what premise (or on what authority) the conditional is adopted:
Some have thought that defeasible reasoning could be connected to qualitative probabilistic reasoning, but such efforts have not borne great insights.
Defeasible reasoning finds its fullest expression in jurisprudence
, ethics
and moral philosophy, epistemology, pragmatics
and conversational conventions
in linguistics
, constructivist
decision theories
,
and in knowledge representation
and planning
in artificial intelligence
. It is also closely identified with prima facie
(presumptive) reasoning (i.e., reasoning on the "face" of evidence), and ceteris paribus
(default) reasoning (i.e., reasoning, all things "being equal").
differentiated the forms of reasoning that are valid for logic
and philosophy
from the more general ones that are used in everyday life (see dialectics and rhetoric
), 20th Century philosophers mainly concentrated on deductive reasoning. At the end of the 19th Century, logic texts would typically survey both demonstrative and non-demonstrative reasoning, often giving more space to the latter. However, after the blossoming of mathematical logic
at the hands of Bertrand Russell
, Alfred North Whitehead
and Willard van Orman Quine
, latter-20th Century logic texts paid little attention to the non-deductive modes of inference.
There are several notable exceptions. John Maynard Keynes
wrote his dissertation on non-demonstrative reasoning, and influenced the thinking of Ludwig Wittgenstein
on this subject. Wittgenstein, in turn, had many admirers, including the positivist legal scholar H.L.A. Hart and the speech act
linguist John L. Austin, Stephen Toulmin
in rhetoric (Chaim Perelman
too), the moral theorists W.D. Ross and C.L. Stevenson, and the vagueness
epistemologist/ontologist Friedrich Waismann
.
The etymology of defeasible usually refers to Middle English law of contracts, where a condition of defeasance is a clause that can invalidate or annul a contract or deed. Though defeat, dominate, defer, defy, deprecate and derogate are often used in the same contexts as defeasible, the verbs annul and invalidate (and nullify, overturn, rescind, vacate, repeal, debar, void, cancel, countermand, preempt, etc.) are more properly correlated with the concept of defeasibility than those words beginning with the letter d. Many dictionaries do contain the verb, to defease with past participle, defeased.
Philosophers in moral theory and rhetoric had taken defeasibility largely for granted when American epistemologists rediscovered Wittgenstein's thinking on the subject: John Ladd, Roderick Chisholm
, Roderick Firth, Ernest Sosa
, Robert Nozick
, and John L. Pollock
all began writing with new conviction about how appearance as red was only a defeasible reason for believing something to be red. More importantly Wittgenstein's orientation toward language games (and away from semantics
) emboldened these epistemologists to manage rather than to expurgate prima facie logical inconsistency.
At the same time (in the mid-1960s), two more students of Hart and Austin at Oxford, Brian Barry
and David Gauthier
, were applying defeasible reasoning to political argument and practical reasoning (of action), respectively. Joel Feinberg
and Joseph Raz
were beginning to produce equally mature works in ethics and jurisprudence informed by defeasibility.
By far the most significant works on defeasibility by the mid-1970s were in epistemology, where John Pollock
's 1974 Knowledge and Justification popularized his terminology of undercutting and rebutting (which mirrored the analysis of Toulmin). Pollock's work was significant precisely because it brought defeasibility so close to philosophical logicians. The failure of logicians to dismiss defeasibility in epistemology (as Cambridge's logicians had done to Hart decades earlier) landed defeasible reasoning in the philosophical mainstream.
Defeasibility had always been closely related to argument, rhetoric, and law, except in epistemology, where the chains of reasons, and the origin of reasons, were not often discussed. Nicholas Rescher
's Dialectics is an example of how difficult it was for philosophers to contemplate more complex systems of defeasible reasoning. This was in part because proponents of informal logic
became the keepers of argument and rhetoric while insisting that formalism was anathema to argument.
About this time, researchers in artificial intelligence
became interested in non-monotonic reasoning and its semantics
. With philosophers such as Pollock and Donald Nute (e.g., defeasible logic
), dozens of computer scientists and logicians produced complex systems of defeasible reasoning between 1980 and 2000. No single system of defeasible reasoning would emerge in the same way that Quine's system of logic became a de facto standard. Nevertheless, the 100-year head start on non-demonstrative logical calculi, due to George Boole
, Charles Sanders Peirce, and Gottlob Frege
was being closed: both demonstrative and non-demonstrative reasoning now have formal calculi.
There are related (and slightly competing) systems of reasoning that are newer than systems of defeasible reasoning, e.g., belief revision
and dynamic logic
. The dialogue logics of Charles Hamblin and Jim Mackenzie (logician), and their colleagues, can also be tied closely to defeasible reasoning. Belief revision is a non-constructive specification of the desiderata with which, or constraints according to which, epistemic change takes place. Dynamic logic is related mainly because, like paraconsistent logic, the reordering of premises can change the set of justified conclusions. Dialogue logics introduce an adversary, but are like belief revision theories in their adherence to deductively consistent states of belief.
, "community hath an indubitable, inalienable, and indefeasible right to reform, alter or abolish government..." (also attributed to James Madison
); and John Adams
, "The people have a right, an indisputable, unalienable, indefeasible, divine right to that most dreaded and envied kind of knowledge - I mean of the character and conduct of their rulers."
Also, Lord Aberdeen: "indefeasible right inherent in the British Crown" and Gouverneur Morris
: "the Basis of our own Constitution is the indefeasible Right of the People." Scholarship about Abraham Lincoln
often cites these passages in the justification of secession. Philosophers who use the word defeasible have historically had different world views from those who use the word indefeasible (and this distinction has often been mirrored by Oxford and Cambridge zeitgeist); hence it is rare to find authors who use both words.
In judicial opinions, the use of defeasible is commonplace. There is however disagreement among legal logicians whether defeasible reasoning is central, e.g., in the consideration of open texture, precedent
, exceptions, and rationales, or whether it applies only to explicit defeasance clauses. H.L.A. Hart in The Concept of Law
gives two famous examples of defeasibility: "No vehicles in the park" (except during parades); and "Offer, acceptance, and memorandum produce a contract" (except when the contract is illegal, the parties are minors, inebriated, or incapacitated, etc.).
preempting class inheritance:
(R1) if p then (defeasibly) q e.g., if penguin then not-flies
(R2) if r then (defeasibly) not-q e.g., if bird then flies
(O1) if p then (deductively) r e.g., if penguin then bird
(M1) arguably, p e.g., arguably, penguin
(M2) R1 is a more specific reason than R2 e.g., R1 is better than R2
(M3) therefore, arguably, q e.g., therefore, arguably, not-flies
Approximately half of the systems of defeasible reasoning discussed today adopt a rule of specificity, while half expect that such preference rules be written explicitly by whomever provides the defeasible reasons. For example, Rescher's dialectical system uses specificity, as do early systems of multiple inheritance (e.g., David Touretzky) and the early argument systems of Donald Nute and of Guillermo Simari
and Ronald Loui
. Defeasible reasoning accounts of precedent (stare decisis
and case-based reasoning
) also make use of specificity (e.g., Joseph Raz
and the work of Kevin D. Ashley and Edwina Rissland). Meanwhile, the argument systems of Henry Prakken and Giovanni Sartor, of Bart Verheij and Jaap Hage, and the system of Phan Minh Dung do not adopt such a rule.
), and those who theorize about defeasibility as if it were the result of further (non-empirical) investigation. There are at least three kinds of further non-empirical investigation: progress in a lexical/syntactic process, progress in a computational process, and progress in an adversary or legal proceeding.
Defeasibility as corrigibility: Here, a person learns something new that annuls a prior inference. In this case, defeasible reasoning provides a constructive mechanism for belief revision, like a truth maintenance system
as envisioned by Jon Doyle.
Defeasibility as shorthand for preconditions: Here, the author of a set of rules or legislative code is writing rules with exceptions. Sometimes a set of defeasible rules can be rewritten, with more cogency, with explicit (local) pre-conditions instead of (non-local) competing rules. Many non-monotonic systems with fixed-point or preferential semantics fit this view. However, sometimes the rules govern a process of argument (the last view on this list), so that they cannot be re-compiled into a set of deductive rules lest they lose their force in situations with incomplete knowledge or incomplete derivation of preconditions.
Defeasibility as an anytime algorithm
: Here, it is assumed that calculating arguments takes time, and at any given time, based on a subset of the potentially constructible arguments, a conclusion is defeasibly justified. Isaac Levi
has protested against this kind of defeasibility, but it is well-suited to the heuristic projects of, for example, Herbert Simon
. On this view, the best move so far in a chess-playing program's analysis at a particular depth is a defeasibly justified conclusion. This interpretation works with either the prior or the next semantical view.
Defeasibility as a means of controlling an investigative or social process: Here, justification is the result of the right kind of procedure (e.g., a fair and efficient hearing), and defeasible reasoning provides impetus for pro and con responses to each other. Defeasibility has to do with the alternation of verdict as locutions are made and cases presented, not the changing of a mind with respect to new (empirical) discovery. Under this view, defeasible reasoning and defeasible argumentation refer to the same phenomenon.
Inductive reasoning
Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...
, statistical reasoning, abductive reasoning
Abductive reasoning
Abduction is a kind of logical inference described by Charles Sanders Peirce as "guessing". The term refers to the process of arriving at an explanatory hypothesis. Peirce said that to abduce a hypothetical explanation a from an observed surprising circumstance b is to surmise that a may be true...
, and paraconsistent reasoning. Defeasible reasoning is also a kind of ampliative
Ampliative
Ampliative , a term used mainly in logic, meaning "extending" or "adding to that which is already known."In Norman law, an "ampliation" was a postponement of a sentence in order to obtain further evidence....
reasoning because its conclusions reach beyond the pure meanings of the premises.
The differences between these kinds of reasoning correspond to differences about the conditional that each kind of reasoning uses, and on what premise (or on what authority) the conditional is adopted:
- DeductiveDeductive reasoningDeductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...
(from meaning postulate, axiom, or contingent assertion): if p then q (i.e., q or not-p) - Defeasible (from authority): if p then (defeasibly) q
- ProbabilisticProbabilistic logicThe aim of a probabilistic logic is to combine the capacity of probability theory to handle uncertainty with the capacity of deductive logic to exploit structure. The result is a richer and more expressive formalism with a broad range of possible application areas...
(from combinatorics and indifference): if p then (probably) q - StatisticalStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
(from data and presumption): the frequency of qs among ps is high (or inference from a model fit to data); hence, (in the right context) if p then (probably) q - InductiveInductive reasoningInductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...
(theory formation; from data, coherence, simplicity, and confirmation): (inducibly) "if p then q"; hence, if p then (deducibly-but-revisably) q - AbductiveAbductive reasoningAbduction is a kind of logical inference described by Charles Sanders Peirce as "guessing". The term refers to the process of arriving at an explanatory hypothesis. Peirce said that to abduce a hypothetical explanation a from an observed surprising circumstance b is to surmise that a may be true...
(from data and theory): p and q are correlated, and q is sufficient for p; hence, if p then (abducibly) q as cause
Some have thought that defeasible reasoning could be connected to qualitative probabilistic reasoning, but such efforts have not borne great insights.
Defeasible reasoning finds its fullest expression in jurisprudence
Jurisprudence
Jurisprudence is the theory and philosophy of law. Scholars of jurisprudence, or legal theorists , hope to obtain a deeper understanding of the nature of law, of legal reasoning, legal systems and of legal institutions...
, ethics
Ethics
Ethics, also known as moral philosophy, is a branch of philosophy that addresses questions about morality—that is, concepts such as good and evil, right and wrong, virtue and vice, justice and crime, etc.Major branches of ethics include:...
and moral philosophy, epistemology, pragmatics
Pragmatics
Pragmatics is a subfield of linguistics which studies the ways in which context contributes to meaning. Pragmatics encompasses speech act theory, conversational implicature, talk in interaction and other approaches to language behavior in philosophy, sociology, and linguistics. It studies how the...
and conversational conventions
Convention (norm)
A convention is a set of agreed, stipulated or generally accepted standards, norms, social norms or criteria, often taking the form of a custom....
in linguistics
Linguistics
Linguistics is the scientific study of human language. Linguistics can be broadly broken into three categories or subfields of study: language form, language meaning, and language in context....
, constructivist
Constructivist epistemology
Constructivist epistemology is an epistemological perspective in philosophy about the nature of scientific knowledge. Constructivists maintain that scientific knowledge is constructed by scientists and not discovered from the world. Constructivists claim that the concepts of science are mental...
decision theories
Decision theory
Decision theory in economics, psychology, philosophy, mathematics, and statistics is concerned with identifying the values, uncertainties and other issues relevant in a given decision, its rationality, and the resulting optimal decision...
,
and in knowledge representation
Knowledge representation
Knowledge representation is an area of artificial intelligence research aimed at representing knowledge in symbols to facilitate inferencing from those knowledge elements, creating new elements of knowledge...
and planning
Planning
Planning in organizations and public policy is both the organizational process of creating and maintaining a plan; and the psychological process of thinking about the activities required to create a desired goal on some scale. As such, it is a fundamental property of intelligent behavior...
in artificial intelligence
Artificial intelligence
Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...
. It is also closely identified with prima facie
Prima facie
Prima facie is a Latin expression meaning on its first encounter, first blush, or at first sight. The literal translation would be "at first face", from the feminine form of primus and facies , both in the ablative case. It is used in modern legal English to signify that on first examination, a...
(presumptive) reasoning (i.e., reasoning on the "face" of evidence), and ceteris paribus
Ceteris paribus
or is a Latin phrase, literally translated as "with other things the same," or "all other things being equal or held constant." It is an example of an ablative absolute and is commonly rendered in English as "all other things being equal." A prediction, or a statement about causal or logical...
(default) reasoning (i.e., reasoning, all things "being equal").
History
Though AristotleAristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
differentiated the forms of reasoning that are valid for logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
and 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...
from the more general ones that are used in everyday life (see dialectics and rhetoric
Rhetoric
Rhetoric is the art of discourse, an art that aims to improve the facility of speakers or writers who attempt to inform, persuade, or motivate particular audiences in specific situations. As a subject of formal study and a productive civic practice, rhetoric has played a central role in the Western...
), 20th Century philosophers mainly concentrated on deductive reasoning. At the end of the 19th Century, logic texts would typically survey both demonstrative and non-demonstrative reasoning, often giving more space to the latter. However, after the blossoming of mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
at the hands of Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
, Alfred North Whitehead
Alfred North Whitehead
Alfred North Whitehead, OM FRS was an English mathematician who became a philosopher. He wrote on algebra, logic, foundations of mathematics, philosophy of science, physics, metaphysics, and education...
and Willard van Orman Quine
Willard Van Orman Quine
Willard Van Orman Quine was an American philosopher and logician in the analytic tradition...
, latter-20th Century logic texts paid little attention to the non-deductive modes of inference.
There are several notable exceptions. John Maynard Keynes
John Maynard Keynes
John Maynard Keynes, Baron Keynes of Tilton, CB FBA , was a British economist whose ideas have profoundly affected the theory and practice of modern macroeconomics, as well as the economic policies of governments...
wrote his dissertation on non-demonstrative reasoning, and influenced the thinking of Ludwig Wittgenstein
Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...
on this subject. Wittgenstein, in turn, had many admirers, including the positivist legal scholar H.L.A. Hart and the speech act
Speech act
Speech Act is a technical term in linguistics and the philosophy of language. The contemporary use of the term goes back to John L. Austin's doctrine of locutionary, illocutionary, and perlocutionary acts...
linguist John L. Austin, Stephen Toulmin
Stephen Toulmin
Stephen Edelston Toulmin was a British philosopher, author, and educator. Influenced by Ludwig Wittgenstein, Toulmin devoted his works to the analysis of moral reasoning. Throughout his writings, he sought to develop practical arguments which can be used effectively in evaluating the ethics behind...
in rhetoric (Chaim Perelman
Chaim Perelman
Chaïm Perelman was a Polish-born philosopher of law, who studied, taught, and lived most of his life in Brussels. He was among the most important argumentation theorists of the twentieth century...
too), the moral theorists W.D. Ross and C.L. Stevenson, and the vagueness
Vagueness
The term vagueness denotes a property of concepts . A concept is vague:* if the concept's extension is unclear;* if there are objects which one cannot say with certainty whether belong to a group of objects which are identified with this concept or which exhibit characteristics that have this...
epistemologist/ontologist Friedrich Waismann
Friedrich Waismann
Friedrich Waismann was an Austrian mathematician, physicist, and philosopher. He is best known for being a member of the Vienna Circle and one of the key theorists in logical positivism.-Birth & Early Interest in Philosophy:...
.
The etymology of defeasible usually refers to Middle English law of contracts, where a condition of defeasance is a clause that can invalidate or annul a contract or deed. Though defeat, dominate, defer, defy, deprecate and derogate are often used in the same contexts as defeasible, the verbs annul and invalidate (and nullify, overturn, rescind, vacate, repeal, debar, void, cancel, countermand, preempt, etc.) are more properly correlated with the concept of defeasibility than those words beginning with the letter d. Many dictionaries do contain the verb, to defease with past participle, defeased.
Philosophers in moral theory and rhetoric had taken defeasibility largely for granted when American epistemologists rediscovered Wittgenstein's thinking on the subject: John Ladd, Roderick Chisholm
Roderick Chisholm
Roderick M. Chisholm was an American philosopher known for his work on epistemology, metaphysics, free will, and the philosophy of perception. He received his Ph.D. at Harvard University under Clarence Irving Lewis and Donald C. Williams, and taught at Brown University...
, Roderick Firth, Ernest Sosa
Ernest Sosa
Ernest Sosa is an American philosopher primarily interested in epistemology. He is currently Board of Governors Professor of Philosophy at Rutgers University. He has been at Rutgers full-time since January, 2007; previously, he had been at Brown University since 1964...
, Robert Nozick
Robert Nozick
Robert Nozick was an American political philosopher, most prominent in the 1970s and 1980s. He was a professor at Harvard University. He is best known for his book Anarchy, State, and Utopia , a right-libertarian answer to John Rawls's A Theory of Justice...
, and John L. Pollock
John L. Pollock
John L. Pollock was an American philosopher known for influential work in epistemology, philosophical logic, cognitive science, and artificial intelligence....
all began writing with new conviction about how appearance as red was only a defeasible reason for believing something to be red. More importantly Wittgenstein's orientation toward language games (and away from semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
) emboldened these epistemologists to manage rather than to expurgate prima facie logical inconsistency.
At the same time (in the mid-1960s), two more students of Hart and Austin at Oxford, Brian Barry
Brian Barry
Brian Barry FBA was a moral and political philosopher. He was educated at the Queen's College, Oxford, obtaining the degrees of B.A. and D.Phil under the direction of H. L. A. Hart....
and David Gauthier
David Gauthier
David Gauthier is a Canadian-American philosopher best known for his neo-Hobbesian social contract theory of morality, as laid out in his book Morals by Agreement.-Biography:...
, were applying defeasible reasoning to political argument and practical reasoning (of action), respectively. Joel Feinberg
Joel Feinberg
Joel Feinberg was an American political and social philosopher. He is known for his work in the fields of ethics, action theory, philosophy of law, and political philosophy as well as individual rights and the authority of the state...
and Joseph Raz
Joseph Raz
Joseph Raz is a legal, moral and political philosopher. He is one of the most prominent advocates of legal positivism. He has spent most of his career as professor of philosophy of law and a fellow of Balliol College, Oxford, and simultaneously as professor of law at Columbia University Law...
were beginning to produce equally mature works in ethics and jurisprudence informed by defeasibility.
By far the most significant works on defeasibility by the mid-1970s were in epistemology, where John Pollock
John L. Pollock
John L. Pollock was an American philosopher known for influential work in epistemology, philosophical logic, cognitive science, and artificial intelligence....
's 1974 Knowledge and Justification popularized his terminology of undercutting and rebutting (which mirrored the analysis of Toulmin). Pollock's work was significant precisely because it brought defeasibility so close to philosophical logicians. The failure of logicians to dismiss defeasibility in epistemology (as Cambridge's logicians had done to Hart decades earlier) landed defeasible reasoning in the philosophical mainstream.
Defeasibility had always been closely related to argument, rhetoric, and law, except in epistemology, where the chains of reasons, and the origin of reasons, were not often discussed. Nicholas Rescher
Nicholas Rescher
Nicholas Rescher is an American philosopher at the University of Pittsburgh. In a productive research career extending over six decades, Rescher has established himself as a systematic philosopher of the old style and author of a system of pragmatic idealism which weaves together threads of...
's Dialectics is an example of how difficult it was for philosophers to contemplate more complex systems of defeasible reasoning. This was in part because proponents of informal logic
Informal logic
Informal logic, intuitively, refers to the principles of logic and logical thought outside of a formal setting. However, perhaps because of the informal in the title, the precise definition of informal logic is matters of some dispute. Ralph H. Johnson and J...
became the keepers of argument and rhetoric while insisting that formalism was anathema to argument.
About this time, researchers in artificial intelligence
Artificial intelligence
Artificial intelligence is the intelligence of machines and the branch of computer science that aims to create it. AI textbooks define the field as "the study and design of intelligent agents" where an intelligent agent is a system that perceives its environment and takes actions that maximize its...
became interested in non-monotonic reasoning and its semantics
Semantics
Semantics is the study of meaning. It focuses on the relation between signifiers, such as words, phrases, signs and symbols, and what they stand for, their denotata....
. With philosophers such as Pollock and Donald Nute (e.g., defeasible logic
Defeasible logic
Defeasible logic is a non-monotonic logic proposed by Donald Nute to formalize defeasible reasoning. In defeasible logic, there are three different types of propositions:strict rules : specify that a fact is always a consequence of another;...
), dozens of computer scientists and logicians produced complex systems of defeasible reasoning between 1980 and 2000. No single system of defeasible reasoning would emerge in the same way that Quine's system of logic became a de facto standard. Nevertheless, the 100-year head start on non-demonstrative logical calculi, due to George Boole
George Boole
George Boole was an English mathematician and philosopher.As the inventor of Boolean logic—the basis of modern digital computer logic—Boole is regarded in hindsight as a founder of the field of computer science. Boole said,...
, Charles Sanders Peirce, and Gottlob Frege
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...
was being closed: both demonstrative and non-demonstrative reasoning now have formal calculi.
There are related (and slightly competing) systems of reasoning that are newer than systems of defeasible reasoning, e.g., belief revision
Belief revision
Belief revision is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents....
and dynamic logic
Dynamic logic
Dynamic logic may mean:* In theoretical computer science, dynamic logic is a modal logic for reasoning about dynamic behaviour* In digital electronics, dynamic logic is a technique used for combinatorial circuit design* A different concept proposed by Leonid Perlovsky...
. The dialogue logics of Charles Hamblin and Jim Mackenzie (logician), and their colleagues, can also be tied closely to defeasible reasoning. Belief revision is a non-constructive specification of the desiderata with which, or constraints according to which, epistemic change takes place. Dynamic logic is related mainly because, like paraconsistent logic, the reordering of premises can change the set of justified conclusions. Dialogue logics introduce an adversary, but are like belief revision theories in their adherence to deductively consistent states of belief.
Political and judicial use
Many political philosophers have been fond of the word indefeasible when referring to rights, e.g., that were inalienable, divine, or indubitable. For example, in the 1776 Virginia Declaration of RightsVirginia Declaration of Rights
The Virginia Declaration of Rights is a document drafted in 1776 to proclaim the inherent rights of men, including the right to rebel against "inadequate" government...
, "community hath an indubitable, inalienable, and indefeasible right to reform, alter or abolish government..." (also attributed to James Madison
James Madison
James Madison, Jr. was an American statesman and political theorist. He was the fourth President of the United States and is hailed as the “Father of the Constitution” for being the primary author of the United States Constitution and at first an opponent of, and then a key author of the United...
); and John Adams
John Adams
John Adams was an American lawyer, statesman, diplomat and political theorist. A leading champion of independence in 1776, he was the second President of the United States...
, "The people have a right, an indisputable, unalienable, indefeasible, divine right to that most dreaded and envied kind of knowledge - I mean of the character and conduct of their rulers."
Also, Lord Aberdeen: "indefeasible right inherent in the British Crown" and Gouverneur Morris
Gouverneur Morris
Gouverneur Morris , was an American statesman, a Founding Father of the United States, and a native of New York City who represented Pennsylvania in the Constitutional Convention of 1787. He was a signatory to the Articles of Confederation. Morris was also an author of large sections of the...
: "the Basis of our own Constitution is the indefeasible Right of the People." Scholarship about Abraham Lincoln
Abraham Lincoln
Abraham Lincoln was the 16th President of the United States, serving from March 1861 until his assassination in April 1865. He successfully led his country through a great constitutional, military and moral crisis – the American Civil War – preserving the Union, while ending slavery, and...
often cites these passages in the justification of secession. Philosophers who use the word defeasible have historically had different world views from those who use the word indefeasible (and this distinction has often been mirrored by Oxford and Cambridge zeitgeist); hence it is rare to find authors who use both words.
In judicial opinions, the use of defeasible is commonplace. There is however disagreement among legal logicians whether defeasible reasoning is central, e.g., in the consideration of open texture, precedent
Precedent
In common law legal systems, a precedent or authority is a principle or rule established in a legal case that a court or other judicial body may apply when deciding subsequent cases with similar issues or facts...
, exceptions, and rationales, or whether it applies only to explicit defeasance clauses. H.L.A. Hart in The Concept of Law
The Concept of Law
The Concept of Law is the most famous work of the legal philosopher H. L. A. Hart. It was first published in 1961 and develops Hart's theory of legal positivism within the framework of analytic philosophy...
gives two famous examples of defeasibility: "No vehicles in the park" (except during parades); and "Offer, acceptance, and memorandum produce a contract" (except when the contract is illegal, the parties are minors, inebriated, or incapacitated, etc.).
Specificity
One of the main disputes among those who produce systems of defeasible reasoning is the status of a rule of specificity. In its simplest form, it is the same rule as subclass inheritanceInheritance (computer science)
In object-oriented programming , inheritance is a way to reuse code of existing objects, establish a subtype from an existing object, or both, depending upon programming language support...
preempting class inheritance:
(R1) if p then (defeasibly) q e.g., if penguin then not-flies
(R2) if r then (defeasibly) not-q e.g., if bird then flies
(O1) if p then (deductively) r e.g., if penguin then bird
(M1) arguably, p e.g., arguably, penguin
(M2) R1 is a more specific reason than R2 e.g., R1 is better than R2
(M3) therefore, arguably, q e.g., therefore, arguably, not-flies
Approximately half of the systems of defeasible reasoning discussed today adopt a rule of specificity, while half expect that such preference rules be written explicitly by whomever provides the defeasible reasons. For example, Rescher's dialectical system uses specificity, as do early systems of multiple inheritance (e.g., David Touretzky) and the early argument systems of Donald Nute and of Guillermo Simari
Guillermo Simari
Guillermo Ricardo Simari is an Argentinian computer scientist. He is an international leader in defeasible reasoning and argument , a national leader in logic programming in Argentina, and one of the leaders of artificial intelligence in South America...
and Ronald Loui
Ronald Loui
Ronald Prescott Loui is an American computer scientist and philosopher identified as "Frederick" in U.S. President Barack Obama's Dreams From My Father memoir, the first student the ten year-old Obama meets at Punahou School...
. Defeasible reasoning accounts of precedent (stare decisis
Stare decisis
Stare decisis is a legal principle by which judges are obliged to respect the precedents established by prior decisions...
and case-based reasoning
Case-based reasoning
Case-based reasoning , broadly construed, is the process of solving new problems based on the solutions of similar past problems. An auto mechanic who fixes an engine by recalling another car that exhibited similar symptoms is using case-based reasoning...
) also make use of specificity (e.g., Joseph Raz
Joseph Raz
Joseph Raz is a legal, moral and political philosopher. He is one of the most prominent advocates of legal positivism. He has spent most of his career as professor of philosophy of law and a fellow of Balliol College, Oxford, and simultaneously as professor of law at Columbia University Law...
and the work of Kevin D. Ashley and Edwina Rissland). Meanwhile, the argument systems of Henry Prakken and Giovanni Sartor, of Bart Verheij and Jaap Hage, and the system of Phan Minh Dung do not adopt such a rule.
Nature of defeasibility
There is a distinct difference between those who theorize about defeasible reasoning as if it were a system of confirmational revision (with affinities to belief revisionBelief revision
Belief revision is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents....
), and those who theorize about defeasibility as if it were the result of further (non-empirical) investigation. There are at least three kinds of further non-empirical investigation: progress in a lexical/syntactic process, progress in a computational process, and progress in an adversary or legal proceeding.
Defeasibility as corrigibility: Here, a person learns something new that annuls a prior inference. In this case, defeasible reasoning provides a constructive mechanism for belief revision, like a truth maintenance system
Truth maintenance system
Reason maintenance is a knowledge representation approach to efficient handling of inferred information that is explicitly stored. Reason maintenance distinguishes between base facts, which can be defeated, and derived facts. As such it differs from belief revision which, in its basic form,...
as envisioned by Jon Doyle.
Defeasibility as shorthand for preconditions: Here, the author of a set of rules or legislative code is writing rules with exceptions. Sometimes a set of defeasible rules can be rewritten, with more cogency, with explicit (local) pre-conditions instead of (non-local) competing rules. Many non-monotonic systems with fixed-point or preferential semantics fit this view. However, sometimes the rules govern a process of argument (the last view on this list), so that they cannot be re-compiled into a set of deductive rules lest they lose their force in situations with incomplete knowledge or incomplete derivation of preconditions.
Defeasibility as an anytime algorithm
Anytime algorithm
In computer science an anytime algorithm is an algorithm that can return a valid solution to a problem even if it's interrupted at any time before it ends. The algorithm is expected to find better and better solutions the more time it keeps running....
: Here, it is assumed that calculating arguments takes time, and at any given time, based on a subset of the potentially constructible arguments, a conclusion is defeasibly justified. Isaac Levi
Isaac Levi
Isaac Levi is the John Dewey Professor of Philosophy Emeritus at Columbia University. Levi came onto the philosophic scene with his groundbreaking first book, Gambling with Truth. In the text Levi offers a decision theoretic reconstruction of epistemology with a close-eye towards the classical...
has protested against this kind of defeasibility, but it is well-suited to the heuristic projects of, for example, Herbert Simon
Herbert Simon
Herbert Alexander Simon was an American political scientist, economist, sociologist, and psychologist, and professor—most notably at Carnegie Mellon University—whose research ranged across the fields of cognitive psychology, cognitive science, computer science, public administration, economics,...
. On this view, the best move so far in a chess-playing program's analysis at a particular depth is a defeasibly justified conclusion. This interpretation works with either the prior or the next semantical view.
Defeasibility as a means of controlling an investigative or social process: Here, justification is the result of the right kind of procedure (e.g., a fair and efficient hearing), and defeasible reasoning provides impetus for pro and con responses to each other. Defeasibility has to do with the alternation of verdict as locutions are made and cases presented, not the changing of a mind with respect to new (empirical) discovery. Under this view, defeasible reasoning and defeasible argumentation refer to the same phenomenon.
See also
- defeasible estateDefeasible estateA defeasible estate is created when a grantor transfers land conditionally. Upon the happening of the event or condition stated by the grantor, the transfer may be void or at least subject to annulment...
- indefeasible rights of useIndefeasible rights of useIndefeasible right of use is a contractual agreement between the operators of a communications cable, such as submarine communications cable or a fiber optic network and a client.The IRU:...
- Argument (logic)
- prima faciePrima faciePrima facie is a Latin expression meaning on its first encounter, first blush, or at first sight. The literal translation would be "at first face", from the feminine form of primus and facies , both in the ablative case. It is used in modern legal English to signify that on first examination, a...
- ceteris paribusCeteris paribusor is a Latin phrase, literally translated as "with other things the same," or "all other things being equal or held constant." It is an example of an ablative absolute and is commonly rendered in English as "all other things being equal." A prediction, or a statement about causal or logical...
- ethicsEthicsEthics, also known as moral philosophy, is a branch of philosophy that addresses questions about morality—that is, concepts such as good and evil, right and wrong, virtue and vice, justice and crime, etc.Major branches of ethics include:...
- practical reasoning
- epistemology
- jurisprudenceJurisprudenceJurisprudence is the theory and philosophy of law. Scholars of jurisprudence, or legal theorists , hope to obtain a deeper understanding of the nature of law, of legal reasoning, legal systems and of legal institutions...
- pragmaticsPragmaticsPragmatics is a subfield of linguistics which studies the ways in which context contributes to meaning. Pragmatics encompasses speech act theory, conversational implicature, talk in interaction and other approaches to language behavior in philosophy, sociology, and linguistics. It studies how the...
- non-monotonic reasoning
External links
- Article on Defeasible Reasoning in the Stanford Encyclopedia of PhilosophyStanford Encyclopedia of PhilosophyThe Stanford Encyclopedia of Philosophy is a freely-accessible online encyclopedia of philosophy maintained by Stanford University. Each entry is written and maintained by an expert in the field, including professors from over 65 academic institutions worldwide...
- An example of defeasible reasoning in action