Difference between revisions of "Ethical intuitionism" - New World Encyclopedia

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:''This article is about Intuitionism in mathematics and philosophical logic.  For other uses, see [[Ethical intuitionism]].''
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In the [[philosophy of mathematics]], '''intuitionism''', or '''neointuitionism''' (opposed to [[preintuitionism]]), is an approach to [[mathematics]] as the constructive mental activity of humans. That is, they are not analytic activities wherein deep properties of existence are revealed and applied. Instead, logic and mathematics are the application of internally consistent methods to realize more complex mental constructs.
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'''Ethical intuitionism''' refers to a core of related moral theories, influential in Britain already in the 1700s, but coming to especial prominence in the work of [[G.E. Moore]], [[H.A. Pritchard]] and [[W. D. Ross]] in the earlier part of the twentieth century. Somewhat confusingly, however, the label ‘ethical intuitionism’ has had at least two distinct contemporary uses. Firstly, ‘intuitionism’ between the 1860s and 1920s was another name for unranked [[pluralism]], the doctrine that there is a plurality of moral principles none of which is more basic than any other. In this respect, intuitionism is a [[Normative ethics|normative ethical theory]] contrasted with versions of [[monism]]—the view that there is only one basic moral principle—such as [[utilitarianism]], and [[Kantianism]]. Intuitionism in this sense is nowadays distinguished as methodological intuitionism.  
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Secondly, and primarily, intuitionism in ethics refers to a cluster of theories about how moral agents come to know which things are good, or which actions are right and wrong. This view may be distinguished as [[epistemology|epistemological]] intuitionism, a theory of the way in which ethical propositions come to be grasped or known. The relationship between these doctrines is primarily historical: important intuitionist thinkers such as H.A. Pritchard and W.D. Ross embraced both methodological and epistemological intuitionism.
  
== Truth and proof ==
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==Historical overview==
In classical mathematics, mathematical statements assert something about truth. Intuitionism takes the truth of a mathematical statement to be equivalent to its having been proved; what other criteria can there be for truth, an intuitionist would argue, if mathematical objects are merely mental constructions? This means that an intuitionist may not believe that a mathematical statement has the same meaning that a classical [[mathematician]] would.  
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While elements of intuitionism are present in ancient ethical philosophy, it was in the seventeenth century, in the work of the [[Cambridge Platonists]], such as [[Ralph Cudworth]] (1617-1688) and [[Henry More]] (1614-1687), and the Moral Sense Theorists such as the [[Earl of Shaftsbury]] (1671- 1713) and [[Francis Hutcheson]] (1694-1746), that it was developed into a distinctive doctrine. Notable intuitionists, in the eighteenth century, are [[Joseph Butler]] (1692 –1752), [[Thomas Reid]] (1710-1796) and [[Richard Price]]; in the nineteenth century, [[Henry Sidgwick]] (1838-1900), and in the twentieth, [[G.E. Moore]] (1873-1958), H.A. Pritchard (1871-1947) culminating in [[W.D. Ross]]’s (1877-1971) ''The Right and the Good.'' Intuitionism fell out of favor by the 1960s but has undergone some revival in the closing decades years of the twentieth century. Robert Audi, John McDowell, and Jonathan Dancy, are notable contemporary philosophers who defend versions of intuitionism.
  
For example, to claim an object with certain properties exists, is, to an intuitionist, to claim to be able to construct a certain object with those properties. Any mathematical object is considered to be a product of a construction of a [[mind]], and therefore, the existence of an object is equivalent to the possibility of its construction. This contrasts with the classical approach, which states that the existence of an entity can be proved by refuting its non-existence. For the intuitionist, this is not valid; the refutation of the non-existence does not mean that it is possible to find a ''constructive'' proof of existence. As such, intuitionism is a variety of [[mathematical constructivism]]; but it is not the only kind.
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==Two senses of intuitionism==
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In the twentieth century, the term ‘intuitionism’ has had two main uses. Firstly, from the 1860s to 1920s it was a name for an ethical theory defined by a commitment to pluralism, or more particularly, unranked [[pluralism]]. Intuitionism in this sense is usually distinguished as ''methodological'' intuitionism. Pluralism is the doctrine that there is a plurality of moral principles, and unranked pluralism adds the additional claim that none of these moral principles are more basic than any other. Methodological intuitionism stands in contrast, then, with forms of monism—the view that there is only one basic moral principle—notably [[utilitarianism]], and [[Kantianism]], and varieties of ranked pluralism, which hold that some duties are more important than others. In illustration, a Kantian would argue that duties of promise keeping, and a duty to help other people, are grounded in a more basic principle, the categorical imperative. A ranked pluralist would argue that there are several different moral duties, which are not grounded in any fundamental principle, but may add that a duty not to harm others is more important than keeping one’s promises. By contrast, methodological intuitionists would argue that there are several distinct moral principles but that none of these is more important than any other.
  
As well, to say ''A'' [[logical disjunction|or]] ''B'', to an intuitionist, is to claim that either ''A'' or ''B'' can be ''proved''. In particular, the [[law of excluded middle]], ''A'' or [[negation|not]] ''A'', is disallowed since one cannot assume that it is always possible to either prove the statement ''A'' or its negation.  
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The second and primary usage of “intuitionism” is to refer to a doctrine in moral [[epistemology]] concerning how agents come to know or justifiably believe moral judgments such as that ‘torture is wrong’ or that ‘virtue is good’. Intuitionism in this sense is a theory about how ethical beliefs acquire their justification. More specifically, it says that we can know that certain things are good or actions are right by intuition. Coming to know something by intuition is to apprehend it directly, and not on the basis of some reasoning process.
  
The interpretation of negation is also different. In classical logic, the negation of a statement asserts that the statement is ''false''; to an intuitionist, it means the statement is ''refutable'' (i.e., that there is a proof that there is no proof of it). The asymmetry between a positive and negative statement becomes apparent. If a statement ''P'' is provable, then it is certainly impossible to prove that there is no proof of ''P''; however, just because there is no proof that there is no proof of ''P'', we cannot conclude from this absence that there ''is'' a proof of ''P''. Thus ''P'' is a stronger statement than ''not-not-P''.
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Since intuitionism assumes that we are capable of moral knowledge, it is to be contrasted with forms of moral scepticism, such as emotivism, which deny this. It is also to be contrasted with coherentism, which denies that moral knowledge is intuitive, rather than inferred from other things already known. In illustration, an intuitionist might hold that the judgment that one ought to keep one’s promises is something that is intuitively known to be true; in contrast, an [[emotivism|emotivist]] would regard this judgment as an expression of feeling, and hence not something that could be true or false; lastly, [[epistemology|coherentists]] would argue that this principle is known by inference from other principles which are themselves not intuitively known.
  
[[Intuitionistic logic]] substitutes justification for truth in its logical calculus. The logical calculus preserves justification, rather than truth, across transformations yielding derived propositions. It has given philosophical support to several schools of philosophy, most notably the [[Anti-realism]] of [[Michael Dummett]].
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What is the relationship between methodological and epistemological intuitionism? In their historical development, the two doctrines are closely tied up with one another. Notable intuitionists such as H.A. Pritchard and W.D. Ross held both of these doctrines, endorsing unranked pluralism, and the claim that a plurality of basic principles are known through intuition. However, it is possible to deny methodological intuitionism, while sanctioning epistemological intuitionism. [[Henry Sidgwick]] is instructive in this regard. He argued that that there is one basic moral principle—[[utilitarianism|the principle of utility]]—but that this principle is grasped through intuition. So Sidgwick is an epistemological intuitionist but not a methodological intuitionist.
  
Intuitionism also rejects the [[abstraction]] of [[actual infinity]]; i.e., it does not consider as given objects [[infinite]] entities such as the [[set]] of all [[natural number]]s or an arbitrary [[sequence]] of [[rational number]]s. This requires the reconstruction of the foundations of [[set theory]] and [[calculus]] as [[Constructive_set_theory|constructivist set theory]] and [[constructivist analysis]] respectively.
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==Varieties of epistemological intuitionism==
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Within this general characterization of intuitionism as a theory of how moral beliefs are acquired and justified, a variety of different forms of intuitionism may be distinguished.  
  
== History of Intuitionism ==
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Firstly, varieties of intuitionism may be distinguished from one another in terms of differences in the content of what is intuited. The content of an intuition is roughly “what it is about.” In the case of moral intuition, moral intuitions could be about (amongst other things) values such as goodness and badness, or rightness and obligation. [[G.E. Moore]], for example, holds that goodness and badness are intuited. By contrast, [[Joseph Butler]] and H.A Pritchard hold that intuitions are about rightness and wrongness.
  
Intuitionist mathematics originated in part from (i) the strong disagreement between Cantor and his teacher [[Kronecker]] — a confirmed [[finitist]] that led to Cantor's hospitalization, and (ii) the failure of [[Frege]]'s effort to reduce all of mathematics to a logical formulation — in face of the letter from [[Bertrand Russell]] received by Frege just as his life's work was about to be published. For more on these sad events see Davis (2000) Chapters 3 and 4: ''Frege: From Breakthrough to Despair'' and ''Cantor: Detour through Infinity''. See van Heijenoort for the original works and Heijenoort's excellent commentary.  
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Secondly, various forms of intuitionism may be distinguished from one another in terms of the generality of what is intuited. This is a question as to whether intuitive moral knowledge is essentially of general principles or of particular actions and things. For instance, one might intuit the general principle that breaking promises is wrong, or that some particular action would be morally wrong. In this respect, [[Henry Sidgwick|Sidgwick]] and [[W.D. Ross]] argue that general principles are intuited; in Sidgwick’s case only one principle, the Principle of Utility; in Ross’s several basic and irreducible moral principles that cannot be ranked in terms of priority. Finally, Prichard, [[Samuel Butler|Butler]] and Dancy hold that the rightness of particular actions is intuited, such as, for example, that this action is morally wrong.
  
In the early twentieth century the battle was taken up [[Brouwer]] the intuitionist versus [[Hilbert]] the [[logicist]] — see van Heijenoort. [[Kurt Gödel]] the [[Platonist]] had his opinions (see various sources re Gödel) and even [[Alan Turing]] considers:
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Thirdly, various forms of intuitionism may be distinguished from one another in terms of the source of what is intuited. Intuitionists are here divided into two camps: rational intuitionists and perceptual intuitionists. Rational intuitionists hold that some moral judgments are known by means of reason, and are therefore [[a priori]]. They are likely to draw an analogy with the way in which mathematical principles are known by intuition. For example, in the following quotation, W.D Ross emphasizes that basic moral principles are self-evident, in a very similar way to which mathematical axioms are self-evident.
:"non-constructive systems of logic with which not all the steps in a proof are mechanical, some being intuitive" (Turing (1939)'' Systems of Logic Based on Ordinals'' in Undecidable, p. 210)
 
  
In the middle of the century [[Kleene]] brought forth a more rational consideration of intuitionism in his ''Introduction to Meta-mathematics'' (1952).
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<blockquote>
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That an act qua fulfilling a promise, or qua effecting a just distribution of good… is prima facie right, is self-evident; not in the sense that it is evident from the beginning of our lives, or as soon as we attend to the proposition for the first time, but in the sense that when we have reached sufficient mental maturity and have given sufficient attention to the proposition it is evident without any need of proof, or evidence beyond itself. It is evident just as a mathematical axiom, or the validity of a form of inference, is evident… (W.D. Ross, ''The Right and the Good,'' 1930, 29-30)</blockquote>
  
For the view that there are no paradoxes in Cantorian set theory — thus calling into question the program of intuitionist mathematics, see Alejandro Garciadiego's now-classic ''Bertrand Russell and the Origins of the Set-Theoretic Paradoxes''.
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In contrast with rational intuitionism, perceptual intuitionism holds that moral intuitions are akin to sense perceptions so that one “sees” that some particular action is wrong. Perceptual intuitionists will tend to emphasize the particularity of the knowledge that is intuited, while rational intuitionists tend to point to general moral truths known by rational insight. The moral sense theories of [[Earl of Shaftsbury|Shaftsbury]], [[Francis Hutcheson|Hutcheson]], and [[Thomas Reid|Reid]], and more recently Pritchard and Maurice Mandelbaum may be classified as perceptual intuitionists.
  
== Contributors to intuitionism ==
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Fourthly, various forms of intuitionism may be distinguished according to the degree of justification intuition confers on belief. Most classical intuitionists argue that intuition confers enough justification upon belief for it to count as knowledge. So intuiting (e.g.) a moral principle is sufficient for knowing that principle. However, there is nothing in the notion of intuition that requires that it provide certainty or knowledge and some recent thinkers have argued picked up on this, arguing that intuition provides some evidential weight insufficient for knowledge. It is also worth noticing that intuitive evidence in favor a belief does not preclude the possibility of inferential support. So intuition may provide evidence for a given moral principle, but coherence with other beliefs may add to the evidential weight in support of that belief.
* [[Luitzen Egbertus Jan Brouwer|L. E. J. Brouwer]]
 
* [[Arend Heyting]]
 
* [[Stephen Kleene]]
 
* [[Michael Dummett]]
 
  
== Branches of intuitionistic mathematics ==
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==Arguments for intuitionism==
* [[Intuitionistic logic]]
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Epistemological intuitionism is usually understood to be the outcome of a commitment to three theses: (1) moral realism, (2) the [[autonomy]] of ethics, and (3) [[epistemology|foundationalism]].
* [[Intuitionistic arithmetic]]
 
* [[Intuitionistic type theory]]
 
* [[Intuitionistic set theory]]
 
* [[Intuitionistic analysis]]
 
  
== See also ==
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Moral realism is the meta-ethical doctrine that there are objective moral facts. A moral realist may hold that it is (or could be) a fact that torture is wrong, even if everyone in the world came to believe the opposite. He or she claims that there are true and false moral propositions, and the truth of these propositions is not dependant on people’s opinions, or attitudes.
* [[Anti-realism]]
 
* [[BHK interpretation]]
 
* [[Computability logic]]
 
* [[Curry-Howard isomorphism]]
 
* [[Foundations of mathematics]]
 
* [[Game semantics]]
 
* [[Intuition (knowledge)]]
 
* [[Ultraintuitionism]]
 
  
==Further reading==
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The autonomy of ethics is the thesis that moral properties cannot be explained in terms of natural properties. Moral properties are normative (or evaluative) and include notions such as right, wrong, ought, good, bad, virtuous and vicious. Natural properties are descriptive, including such things as being pleasant, being painful, being desired (rather than desirable), or hated (rather than hateful). Normative properties provide reasons that recommend or disapprove actions or states of affairs, whereas natural properties merely report states of affairs. For example, it is one thing to say that smoking is wrong, and quite another to say that it causes lung disease. The former is an evaluation of a certain habit of action whereas the latter is a description of a causal outcome of this habit.
  
* [[Jean van Heijenoort|van Heijenoort, J.]], ''From Frege to Gödel, A Source Book in Mathematical Logic, 1879-1931'', Harvard University Press, Cambridge, MA, 1967. Reprinted with corrections, 1977.
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Intuitionists hold that ethics is autonomous, and so that it cannot be entirely explained in terms of natural properties. This makes them non-naturalists about ethics. One important argument for moral non-naturalism is [[G.E. Moore]]’s "open question argument," which says that any attempted definition of a moral property such as goodness in terms of natural properties is bound to fail. For example, suppose someone defined goodness, a normative property, in terms of “being desired,” a descriptive property. Now consider the claim that war is desired. Moore’s point is that it would make perfect sense to retort “it may be desired, but is it good?.” Since this question makes sense, ‘desired’ does not mean ‘good’. Consider that it makes no sense to ask whether Charles is unmarried upon learning that he is a bachelor because bachelor does mean unmarried man.  
  
: * Luitzen Egbertus Jan [[Brouwer]], 1923, ''On the significance of the principle of excluded middle in mathematics, especially in function theory'' [reprinted with commentary, p. 334, van Heijenoort]
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Foundationalism is an epistemological theory about the structure of justification. It says that not all beliefs rest upon other beliefs for their justification. For example, if someone’s belief that p depends on q, which in turn depends on r, the question arises as to where this relation of support comes to an end. A foundationalist thinks that if this chain of support did not come to an end somewhere, then the entire chain of belief lacks justification because one cannot know an infinite number of truths. So he concludes that there must be some beliefs that are not justified by their relationship to other beliefs, but are directly and immediately justified. These are the foundational beliefs that support the system. In the context of moral philosophy, foundationalism says that we know certain derivative moral truths only because we know basic truths. Basic moral truths are foundational and support the higher level beliefs that depend on them. They are known by intuition.
  
: * Andrei Nikolaevich [[Kolmogorov]], 1925, ''On the princple of excluded middle'', [reprinted with commentary, p. 414, van Heijenoort]
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Moral realism, the autonomy of ethics, and foundationalism, lead to intuitionism as follows. Moral realism says that ethical propositions are factual. The autonomy of ethics says that they cannot be entirely reduced to natural propositions. If there are indeed moral facts, then according to foundationalism they must depend on some basic moral facts. These basic beliefs must have direct justification, that is, be known directly—by intuition—and not by inference from any other moral belief. For example, we know, that lying is normally wrong. Suppose that the reason that lying is wrong is because it brings about harm. Then the wrongness of lying is justified by inferring it from a more basic moral principle. But this chain of justifications cannot go on forever (by foundationalism), and can never ultimately eliminate moral propositions (by the autonomy of ethics). Therefore, there are some moral facts known directly, that is, by intuition.
  
: * Luitzen Egbertus Jan [[Brouwer]], 1927, ''On the domains of definitons of functions'', [reprinted with commentary, p. 446, van Heijenoort]
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==Objections to intuitionism==
::Although not directly germane, in his (1923) Brouwer uses certain words defined in this paper.
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One common objection against intuitionism is that if moral principles were known directly by intuition, then there would not be so much moral disagreement. But since there is a substantial amount of disagreement, the argument goes, it follows that moral principles are not known by intuition.  
 
: * Luitzen Egbertus Jan [[Brouwer]], 1927(2), ''Intuitionistic reflections on formalism'', [reprinted with commentary, p. 490, van Heijenoort]
 
  
: * Jacques Herbrand, (1931b), "On the consistency of arithmetic", [reprinted with commentary, p. 618ff, van Heijenoort]
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Intuitionists have given two different responses to this type of argument. [[W.D. Ross]] gestures toward both responses:  
:: From van Heijenoort's commentary it is unclear whether or not Herbrand was a true "intuitionist"; Gödel (1963) asserted that indeed "...Herbrand was an intuitionist". But van Heijenoort says Herbrand's conception was "on the whole much closer to that of Hilbert's word 'finitary' ('finit') that to "intuitionistic" as applied to Brouwer's doctrine". 
 
  
*[[Arend Heyting]]: {{cite book | first=Arend | last=Heyting | title=Intuitionism: An Introduction | publisher=North-Holland Pub. Co | location=Amsterdam | origyear=1956 | year=1971 | edition=3d rev. ed. | id=ISBN 0-7204-2239-6}}
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<blockquote>
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…The diversity of opinion on moral questions is found not to rest on disagreement about fundamental moral principles, but partly on differences in the circumstances of different societies, and partly on the different views which people hold, not on moral questions but on questions of fact. (W.D. Ross, ''The Foundations of Ethics,'' 1939, 18)</blockquote>
  
*{{cite book | first=Dennis E. | last=Hesseling | title=Gnomes in the Fog. The Reception of Brouwer's Intuitionism in the 1920s | publisher=Birkhäuser | year=2003 | id=ISBN 3-7643-6536-6}}
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Ross's first point is that a good deal of moral diversity is not so much due to disagreements about moral principles, but due to differences in people's circumstances. For example, in a society in which there is no formal legal system it may be morally right for an individual to take vengeance upon a murderer. But in a society which has provisions for the state administration of justice, taking retribution by one's own hand may be morally wrong. So the rightness and wrongness of an action can depend on non-moral factors such as whether there are sophisticated mechanisms of civil justice in place.
  
* [[Paul Rosenbloom]], ''The Elements of Mathematical Logic'', Dover Publications Inc, Mineola, New York, 1950.
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Ross's second point is that diversity of moral opinion can also be explained by differences in beliefs about non-moral facts. In illustration, consider how a belief that it is wrong to eat meat could stem from a metaphysical or religious doctrine of reincarnation rather than a difference in fundamental values. A belief that one’s forebears are reincarnated into animals would seem to justify a prohibition on eating meat, but the basic value in question is one which meat-eating cultures share: respect for the life of (e.g.,) souls or persons or family members. The difference in moral belief arises as a result of a factual belief that not everyone endorses, viz. that our family members are reincarnated into animal life. So here there is no disagreement in values but only disagreement in facts.  
:In a style more of Principia Mathematica — many symbols, some antique, some from German script. Very good discussions of intuitionism in the following locations: pages 51-58 in Section 4 Many Valued Logics, Modal Logics, Intuitionism; pages 69-73 Chapter III The Logic of Propostional Functions Section 1 Informal Introduction; and p. 146-151 Section 7 the Axiom of Choice.
 
  
*[[Stephen Cole Kleene]] and [[Richard Eugene Vesley]], ''The Foundations of Intuistionistic Mathematics'', North-Holland Publishing Co. Amsterdam, 1965. The lead sentence tells it all "The constructive tendency in mathematics...". A text for specialists, but written in Kleene's wonderfully-clear style.  
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A second response, one which admits that there are some disagreements that are genuinely about values, is that propositions known by intuition need not be obvious. After all complex mathematical statements may be self evident in that that they are believed once they are understood, but need not be obvious to everyone. Similarly, intuitionists may claim that some people are morally immature or “blind,” or have not considered the matter carefully.  
  
*{{cite book | first=Stephen C. | last=[[Kleene]] | title=Introduction to Meta-Mathematics| publisher=North-Holland Pub. Co | location=Amsterdam NY| origyear=1952 | year=1991 | edition=Tenth impression 1991 | id=ISBN 0-7204-2103-9}}
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Another common objection to intuitionism is that is presupposes some mysterious faculty for apprehending moral truth. In the case of rational intuitionism, the objection is that it requires a mysterious intuitive faculty that is able to divine the moral truth. In response, intuitionists can maintain that moral principles are known a priori. If this true, the intuition requires nothing more mysterious than a capacity for a priori reasoning. In the case of perceptual intuitionism, the objection is that it requires a mysterious faculty beyond perception, a sixth sense, which somehow hones in on ethical properties. In response, some intuitionists have claimed that intuition requires only an ability to grasp reasons as considerations for actions. Jonathan Dancy suggests that moral facts “are best thought of not as facts perceived but as reasons recognized in the exercise of practical moral judgment” ("Intuitionism." in P. Singer (ed.), ''A Companion to Ethics,'' 418). These issues are the subject of considerable debate. The reader is referred to Audi (2005) for the most sophisticated contemporary treatment.
:In Chapter III ''A Critique of Mathematic Reasoning, §11. The paradoxes'', Kleene discusses Intuitionism and [[Formalism]] in depth. Throughout the rest of the book he treats, and compares, both Formalist (classical) and Intuitionist logics with an emphasis on the former. Extraordinary writing by an extraordinary mathematician.
 
  
*"analysis." ''Encyclopædia Britannica''. 2006. Encyclopædia Britannica 2006 Ultimate Reference Suite DVD 15 June 2006, "[[Constructive analysis]]" ([[Ian Stewart]], author)
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== Bibliography ==
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*Audi, R. (1996) "‘Intuitionism, pluralism, and the foundations of ethics," in W. Sinnott Armstrong and M. Timmons (eds) ''Moral Knowledge?: New Readings in Moral Epistemology.'' Oxford: Oxford University Press, 101-136. ISBN 0195089898
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*Audi, R. (2005) ''The Good in the Right: A Theory of Intuition and Intrinsic Value.'' Princeton: Princeton University Press. ISBN 069111434X
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*Dancy, J. (1983) "Ethical particularism and morally relevant properties." ''Mind'' 92: 530-547.
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*Dancy, J. (1991) "Intuitionism." in P. Singer (ed.), ''A Companion to Ethics.'' Oxford: Blackwell. ISBN 9780631162117
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*Huemer, M. (2005) ''Ethical Intuitionism.'' Palgrave: Macmillan. ISBN 1403989680
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*Moore, G.E. (1903) ''Principia Ethica.'' Cambridge: Cambridge University Press, esp. chaps 5, 6.
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*Prichard, H.A. (1949) ''Moral Obligation.'' Oxford: Oxford University Press.
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*Ross, W.D. (1930) ''The Right and the Good.'' Oxford: Clarendon Press, esp. ch. 2.
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*Ross, W.D. (1939) ''The Foundations of Ethics.'' Oxford: Clarendon Press, esp. 79-86 and ch. 8.
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*Schneewind, J.B. (1990) ''Moral Philosophy from Montaigne to Kant.'' Cambridge: Cambridge University Press, 2 vols. ISBN 0521802598
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*Sidgwick, H., ''The Methods of Ethics,'' 7th edn. London: Macmillan, [1907] 1967); and in ''The Works of Henry Sidgwick.'' ed., J. Slater, Bristol, UK: Thoemmes, 1996. ISBN 1855064731
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*Sinnott-Armstrong, W. "Intuitionism" in L.C. Becker (ed.), ''The Encyclopedia of Ethics.'' Vol. I  New York: Garland, 1992). ISBN 081530403X
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*Stratton-Lake, P. (2006) ''Ethical Intuitionism: Re-evaluations.'' New York: Oxford University Press. ISBN 0198250991
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*Strawson, P.F., "Ethical Intuitionism." ''Philosophy'' 24 (1949): 23-33.
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*Williams, B., "What does Intuitionism Imply?" in Dancy (e.g.), ''Human Agency.'' Stanford: Stanford University Press, 1988.
  
*[[W. S. Anglin]], ''Mathematics: A Concise history and Philosophy'', Springer-Verlag, New York, 1994.
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== External links ==
:In ''Chapter 39 Foundations'', with respect to the 20th century Anglin gives very precise, short descriptions of  [[Platonism]] (with respect to Godel), [[Formalism]] (with respet to Hilbert), and Intuitionism (with respect to Brouwer).
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All links retrieved March 22, 2024.
 
 
*[[Constance Reid]], ''Hilbert'', Copernicus - Springer-Verlag, 1st edition 1970, 2nd edition 1996.
 
:Definitive biography of Hilbert places his "Program" in historical context together with the subsequent fighting, sometimes rancorous, between the Intuitionists and the Formalists.
 
 
 
*[[John W. Dawson]] Jr., ''Logical Dilemmas: The Life and Work of [[Kurt Gödel]]'', A. K. Peters, Wellesley, MA, 1997.
 
:Less readable than Goldstein but, in ''Chapter III Excursis'', Dawson gives an excellent "A Capsule History of the Development of Logic to 1928".
 
 
 
*[[Rebecca Goldstein]], ''Incompleteness: The Proof and Paradox of Kurt Godel'', Atlas Books, W.W. Norton, New York, 2005.
 
:In ''Chapter II Hilbert and the Formalists'' Goldstein gives further historical context. As a Platonist [[Gödel]] was reticent in the presence of the [[logical positivism]] of the Vienna Circle. She discusses [[Wittgenstein]]'s impact and the impact of the formalists. Goldstein notes that the intuitionists were even more opposed to [[Platonism]] than [[Formalism]].
 
  
=== Secondary References ===
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*[http://plato.stanford.edu/entries/sidgwick/ Henry Sidgwick], Stanford Encyclopedia of Philosophy.
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*[http://plato.stanford.edu/entries/moral-non-naturalism/ Moral Non-Naturalism], Stanford Encyclopedia of Philosophy.
  
*[[A. A. Markov]] (1954) ''Theory of algorithms''. [Translated by Jacques J. Schorr-Kon and PST staff] Imprint Moscow, Academy of Sciences of the USSR, 1954 [i.e. Jerusalem, Israel Program for Scientific Translations, 1961; available from the Office of Technical Services, U.S. Dept. of Commerce, Washington] Description 444 p. 28 cm. Added t.p. in Russian Translation of Works of the Mathematical Institute, Academy of Sciences of the USSR, v. 42. Original title: Teoriya algerifmov. [QA248.M2943 Dartmouth College library. U.S. Dept. of Commerce, Office of Technical Services, number OTS 60-51085.]
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===General Philosophy Sources===
:A secondary reference for specialists: Markov opined that "The entire significance for mathematics of rendering more precise the concept of algorithm emerges, however, in connection with the problem of ''a constructive foundation for mathematics''....[p. 3, italics added.] Markov believed that further applications of his work "merit a special book, which the author hopes to write in the future" (p. 3). Sadly, said work apparently never appeared.
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*[http://plato.stanford.edu/ Stanford Encyclopedia of Philosophy].  
 
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*[http://www.iep.utm.edu/ The Internet Encyclopedia of Philosophy].  
== External links ==
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*[http://www.bu.edu/wcp/PaidArch.html Paideia Project Online].  
* [http://www.intuitionism.org/ Ten Questions about Intuitionism]
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*[http://www.gutenberg.org/ Project Gutenberg].
  
[[Category:Epistemology]]
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[[Category:Mathematical constructivism]]
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Ethical intuitionism refers to a core of related moral theories, influential in Britain already in the 1700s, but coming to especial prominence in the work of G.E. Moore, H.A. Pritchard and W. D. Ross in the earlier part of the twentieth century. Somewhat confusingly, however, the label ‘ethical intuitionism’ has had at least two distinct contemporary uses. Firstly, ‘intuitionism’ between the 1860s and 1920s was another name for unranked pluralism, the doctrine that there is a plurality of moral principles none of which is more basic than any other. In this respect, intuitionism is a normative ethical theory contrasted with versions of monism—the view that there is only one basic moral principle—such as utilitarianism, and Kantianism. Intuitionism in this sense is nowadays distinguished as methodological intuitionism.

Secondly, and primarily, intuitionism in ethics refers to a cluster of theories about how moral agents come to know which things are good, or which actions are right and wrong. This view may be distinguished as epistemological intuitionism, a theory of the way in which ethical propositions come to be grasped or known. The relationship between these doctrines is primarily historical: important intuitionist thinkers such as H.A. Pritchard and W.D. Ross embraced both methodological and epistemological intuitionism.

Historical overview

While elements of intuitionism are present in ancient ethical philosophy, it was in the seventeenth century, in the work of the Cambridge Platonists, such as Ralph Cudworth (1617-1688) and Henry More (1614-1687), and the Moral Sense Theorists such as the Earl of Shaftsbury (1671- 1713) and Francis Hutcheson (1694-1746), that it was developed into a distinctive doctrine. Notable intuitionists, in the eighteenth century, are Joseph Butler (1692 –1752), Thomas Reid (1710-1796) and Richard Price; in the nineteenth century, Henry Sidgwick (1838-1900), and in the twentieth, G.E. Moore (1873-1958), H.A. Pritchard (1871-1947) culminating in W.D. Ross’s (1877-1971) The Right and the Good. Intuitionism fell out of favor by the 1960s but has undergone some revival in the closing decades years of the twentieth century. Robert Audi, John McDowell, and Jonathan Dancy, are notable contemporary philosophers who defend versions of intuitionism.

Two senses of intuitionism

In the twentieth century, the term ‘intuitionism’ has had two main uses. Firstly, from the 1860s to 1920s it was a name for an ethical theory defined by a commitment to pluralism, or more particularly, unranked pluralism. Intuitionism in this sense is usually distinguished as methodological intuitionism. Pluralism is the doctrine that there is a plurality of moral principles, and unranked pluralism adds the additional claim that none of these moral principles are more basic than any other. Methodological intuitionism stands in contrast, then, with forms of monism—the view that there is only one basic moral principle—notably utilitarianism, and Kantianism, and varieties of ranked pluralism, which hold that some duties are more important than others. In illustration, a Kantian would argue that duties of promise keeping, and a duty to help other people, are grounded in a more basic principle, the categorical imperative. A ranked pluralist would argue that there are several different moral duties, which are not grounded in any fundamental principle, but may add that a duty not to harm others is more important than keeping one’s promises. By contrast, methodological intuitionists would argue that there are several distinct moral principles but that none of these is more important than any other.

The second and primary usage of “intuitionism” is to refer to a doctrine in moral epistemology concerning how agents come to know or justifiably believe moral judgments such as that ‘torture is wrong’ or that ‘virtue is good’. Intuitionism in this sense is a theory about how ethical beliefs acquire their justification. More specifically, it says that we can know that certain things are good or actions are right by intuition. Coming to know something by intuition is to apprehend it directly, and not on the basis of some reasoning process.

Since intuitionism assumes that we are capable of moral knowledge, it is to be contrasted with forms of moral scepticism, such as emotivism, which deny this. It is also to be contrasted with coherentism, which denies that moral knowledge is intuitive, rather than inferred from other things already known. In illustration, an intuitionist might hold that the judgment that one ought to keep one’s promises is something that is intuitively known to be true; in contrast, an emotivist would regard this judgment as an expression of feeling, and hence not something that could be true or false; lastly, coherentists would argue that this principle is known by inference from other principles which are themselves not intuitively known.

What is the relationship between methodological and epistemological intuitionism? In their historical development, the two doctrines are closely tied up with one another. Notable intuitionists such as H.A. Pritchard and W.D. Ross held both of these doctrines, endorsing unranked pluralism, and the claim that a plurality of basic principles are known through intuition. However, it is possible to deny methodological intuitionism, while sanctioning epistemological intuitionism. Henry Sidgwick is instructive in this regard. He argued that that there is one basic moral principle—the principle of utility—but that this principle is grasped through intuition. So Sidgwick is an epistemological intuitionist but not a methodological intuitionist.

Varieties of epistemological intuitionism

Within this general characterization of intuitionism as a theory of how moral beliefs are acquired and justified, a variety of different forms of intuitionism may be distinguished.

Firstly, varieties of intuitionism may be distinguished from one another in terms of differences in the content of what is intuited. The content of an intuition is roughly “what it is about.” In the case of moral intuition, moral intuitions could be about (amongst other things) values such as goodness and badness, or rightness and obligation. G.E. Moore, for example, holds that goodness and badness are intuited. By contrast, Joseph Butler and H.A Pritchard hold that intuitions are about rightness and wrongness.

Secondly, various forms of intuitionism may be distinguished from one another in terms of the generality of what is intuited. This is a question as to whether intuitive moral knowledge is essentially of general principles or of particular actions and things. For instance, one might intuit the general principle that breaking promises is wrong, or that some particular action would be morally wrong. In this respect, Sidgwick and W.D. Ross argue that general principles are intuited; in Sidgwick’s case only one principle, the Principle of Utility; in Ross’s several basic and irreducible moral principles that cannot be ranked in terms of priority. Finally, Prichard, Butler and Dancy hold that the rightness of particular actions is intuited, such as, for example, that this action is morally wrong.

Thirdly, various forms of intuitionism may be distinguished from one another in terms of the source of what is intuited. Intuitionists are here divided into two camps: rational intuitionists and perceptual intuitionists. Rational intuitionists hold that some moral judgments are known by means of reason, and are therefore a priori. They are likely to draw an analogy with the way in which mathematical principles are known by intuition. For example, in the following quotation, W.D Ross emphasizes that basic moral principles are self-evident, in a very similar way to which mathematical axioms are self-evident.

That an act qua fulfilling a promise, or qua effecting a just distribution of good… is prima facie right, is self-evident; not in the sense that it is evident from the beginning of our lives, or as soon as we attend to the proposition for the first time, but in the sense that when we have reached sufficient mental maturity and have given sufficient attention to the proposition it is evident without any need of proof, or evidence beyond itself. It is evident just as a mathematical axiom, or the validity of a form of inference, is evident… (W.D. Ross, The Right and the Good, 1930, 29-30)

In contrast with rational intuitionism, perceptual intuitionism holds that moral intuitions are akin to sense perceptions so that one “sees” that some particular action is wrong. Perceptual intuitionists will tend to emphasize the particularity of the knowledge that is intuited, while rational intuitionists tend to point to general moral truths known by rational insight. The moral sense theories of Shaftsbury, Hutcheson, and Reid, and more recently Pritchard and Maurice Mandelbaum may be classified as perceptual intuitionists.

Fourthly, various forms of intuitionism may be distinguished according to the degree of justification intuition confers on belief. Most classical intuitionists argue that intuition confers enough justification upon belief for it to count as knowledge. So intuiting (e.g.) a moral principle is sufficient for knowing that principle. However, there is nothing in the notion of intuition that requires that it provide certainty or knowledge and some recent thinkers have argued picked up on this, arguing that intuition provides some evidential weight insufficient for knowledge. It is also worth noticing that intuitive evidence in favor a belief does not preclude the possibility of inferential support. So intuition may provide evidence for a given moral principle, but coherence with other beliefs may add to the evidential weight in support of that belief.

Arguments for intuitionism

Epistemological intuitionism is usually understood to be the outcome of a commitment to three theses: (1) moral realism, (2) the autonomy of ethics, and (3) foundationalism.

Moral realism is the meta-ethical doctrine that there are objective moral facts. A moral realist may hold that it is (or could be) a fact that torture is wrong, even if everyone in the world came to believe the opposite. He or she claims that there are true and false moral propositions, and the truth of these propositions is not dependant on people’s opinions, or attitudes.

The autonomy of ethics is the thesis that moral properties cannot be explained in terms of natural properties. Moral properties are normative (or evaluative) and include notions such as right, wrong, ought, good, bad, virtuous and vicious. Natural properties are descriptive, including such things as being pleasant, being painful, being desired (rather than desirable), or hated (rather than hateful). Normative properties provide reasons that recommend or disapprove actions or states of affairs, whereas natural properties merely report states of affairs. For example, it is one thing to say that smoking is wrong, and quite another to say that it causes lung disease. The former is an evaluation of a certain habit of action whereas the latter is a description of a causal outcome of this habit.

Intuitionists hold that ethics is autonomous, and so that it cannot be entirely explained in terms of natural properties. This makes them non-naturalists about ethics. One important argument for moral non-naturalism is G.E. Moore’s "open question argument," which says that any attempted definition of a moral property such as goodness in terms of natural properties is bound to fail. For example, suppose someone defined goodness, a normative property, in terms of “being desired,” a descriptive property. Now consider the claim that war is desired. Moore’s point is that it would make perfect sense to retort “it may be desired, but is it good?.” Since this question makes sense, ‘desired’ does not mean ‘good’. Consider that it makes no sense to ask whether Charles is unmarried upon learning that he is a bachelor because bachelor does mean unmarried man.

Foundationalism is an epistemological theory about the structure of justification. It says that not all beliefs rest upon other beliefs for their justification. For example, if someone’s belief that p depends on q, which in turn depends on r, the question arises as to where this relation of support comes to an end. A foundationalist thinks that if this chain of support did not come to an end somewhere, then the entire chain of belief lacks justification because one cannot know an infinite number of truths. So he concludes that there must be some beliefs that are not justified by their relationship to other beliefs, but are directly and immediately justified. These are the foundational beliefs that support the system. In the context of moral philosophy, foundationalism says that we know certain derivative moral truths only because we know basic truths. Basic moral truths are foundational and support the higher level beliefs that depend on them. They are known by intuition.

Moral realism, the autonomy of ethics, and foundationalism, lead to intuitionism as follows. Moral realism says that ethical propositions are factual. The autonomy of ethics says that they cannot be entirely reduced to natural propositions. If there are indeed moral facts, then according to foundationalism they must depend on some basic moral facts. These basic beliefs must have direct justification, that is, be known directly—by intuition—and not by inference from any other moral belief. For example, we know, that lying is normally wrong. Suppose that the reason that lying is wrong is because it brings about harm. Then the wrongness of lying is justified by inferring it from a more basic moral principle. But this chain of justifications cannot go on forever (by foundationalism), and can never ultimately eliminate moral propositions (by the autonomy of ethics). Therefore, there are some moral facts known directly, that is, by intuition.

Objections to intuitionism

One common objection against intuitionism is that if moral principles were known directly by intuition, then there would not be so much moral disagreement. But since there is a substantial amount of disagreement, the argument goes, it follows that moral principles are not known by intuition.

Intuitionists have given two different responses to this type of argument. W.D. Ross gestures toward both responses:

…The diversity of opinion on moral questions is found not to rest on disagreement about fundamental moral principles, but partly on differences in the circumstances of different societies, and partly on the different views which people hold, not on moral questions but on questions of fact. (W.D. Ross, The Foundations of Ethics, 1939, 18)

Ross's first point is that a good deal of moral diversity is not so much due to disagreements about moral principles, but due to differences in people's circumstances. For example, in a society in which there is no formal legal system it may be morally right for an individual to take vengeance upon a murderer. But in a society which has provisions for the state administration of justice, taking retribution by one's own hand may be morally wrong. So the rightness and wrongness of an action can depend on non-moral factors such as whether there are sophisticated mechanisms of civil justice in place.

Ross's second point is that diversity of moral opinion can also be explained by differences in beliefs about non-moral facts. In illustration, consider how a belief that it is wrong to eat meat could stem from a metaphysical or religious doctrine of reincarnation rather than a difference in fundamental values. A belief that one’s forebears are reincarnated into animals would seem to justify a prohibition on eating meat, but the basic value in question is one which meat-eating cultures share: respect for the life of (e.g.,) souls or persons or family members. The difference in moral belief arises as a result of a factual belief that not everyone endorses, viz. that our family members are reincarnated into animal life. So here there is no disagreement in values but only disagreement in facts.

A second response, one which admits that there are some disagreements that are genuinely about values, is that propositions known by intuition need not be obvious. After all complex mathematical statements may be self evident in that that they are believed once they are understood, but need not be obvious to everyone. Similarly, intuitionists may claim that some people are morally immature or “blind,” or have not considered the matter carefully.

Another common objection to intuitionism is that is presupposes some mysterious faculty for apprehending moral truth. In the case of rational intuitionism, the objection is that it requires a mysterious intuitive faculty that is able to divine the moral truth. In response, intuitionists can maintain that moral principles are known a priori. If this true, the intuition requires nothing more mysterious than a capacity for a priori reasoning. In the case of perceptual intuitionism, the objection is that it requires a mysterious faculty beyond perception, a sixth sense, which somehow hones in on ethical properties. In response, some intuitionists have claimed that intuition requires only an ability to grasp reasons as considerations for actions. Jonathan Dancy suggests that moral facts “are best thought of not as facts perceived but as reasons recognized in the exercise of practical moral judgment” ("Intuitionism." in P. Singer (ed.), A Companion to Ethics, 418). These issues are the subject of considerable debate. The reader is referred to Audi (2005) for the most sophisticated contemporary treatment.

Bibliography

  • Audi, R. (1996) "‘Intuitionism, pluralism, and the foundations of ethics," in W. Sinnott Armstrong and M. Timmons (eds) Moral Knowledge?: New Readings in Moral Epistemology. Oxford: Oxford University Press, 101-136. ISBN 0195089898
  • Audi, R. (2005) The Good in the Right: A Theory of Intuition and Intrinsic Value. Princeton: Princeton University Press. ISBN 069111434X
  • Dancy, J. (1983) "Ethical particularism and morally relevant properties." Mind 92: 530-547.
  • Dancy, J. (1991) "Intuitionism." in P. Singer (ed.), A Companion to Ethics. Oxford: Blackwell. ISBN 9780631162117
  • Huemer, M. (2005) Ethical Intuitionism. Palgrave: Macmillan. ISBN 1403989680
  • Moore, G.E. (1903) Principia Ethica. Cambridge: Cambridge University Press, esp. chaps 5, 6.
  • Prichard, H.A. (1949) Moral Obligation. Oxford: Oxford University Press.
  • Ross, W.D. (1930) The Right and the Good. Oxford: Clarendon Press, esp. ch. 2.
  • Ross, W.D. (1939) The Foundations of Ethics. Oxford: Clarendon Press, esp. 79-86 and ch. 8.
  • Schneewind, J.B. (1990) Moral Philosophy from Montaigne to Kant. Cambridge: Cambridge University Press, 2 vols. ISBN 0521802598
  • Sidgwick, H., The Methods of Ethics, 7th edn. London: Macmillan, [1907] 1967); and in The Works of Henry Sidgwick. ed., J. Slater, Bristol, UK: Thoemmes, 1996. ISBN 1855064731
  • Sinnott-Armstrong, W. "Intuitionism" in L.C. Becker (ed.), The Encyclopedia of Ethics. Vol. I New York: Garland, 1992). ISBN 081530403X
  • Stratton-Lake, P. (2006) Ethical Intuitionism: Re-evaluations. New York: Oxford University Press. ISBN 0198250991
  • Strawson, P.F., "Ethical Intuitionism." Philosophy 24 (1949): 23-33.
  • Williams, B., "What does Intuitionism Imply?" in Dancy (e.g.), Human Agency. Stanford: Stanford University Press, 1988.

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