My article ‘Sidgwick's Epistemology’ presents some reflections on two themes in Bart Schultz's splendid biography Henry Sidgwick: Eye of the Universe.Footnote ¹ One theme concerns Sidgwick's conflict over his religious beliefs and how it influenced the development of his thought in The Methods of Ethics. The second concerns the neglect into which Methods fell during much of the twentieth century and what explains its having fallen into such neglect. Anthony Skelton's comment deals exclusively with my treatment of this second theme. He objects, first, to the characterizations I gave of how Methods was seen during Sidgwick's lifetime and of its fate afterwards and, second, to the explanation I offered of the neglect into which the work fell. In response, I will take up these objections in reverse order. I'll begin with a brief review of my explanation.

Schultz attributed the decline in interest in Methods that occurred after Sidgwick's death to changes in philosophical fashions and to the undue influence of the Bloomsbury literati on British intellectual culture. While not disputing that these were factors in the decline, I offered as a deeper explanation that advances in Anglo-American philosophy due to movements in the analytic tradition rendered the epistemology on which Sidgwick based his inquiries in Methods obsolete. This epistemology is the traditional epistemology of mathematics in which the truths of a branch of mathematics are either the fundamental propositions of the branch, its axioms, or propositions that follow deductively from these fundamental ones. On this epistemology – what I called ‘the traditional intuitionist epistemology’ – a proposition must, to be an axiom, not only be true but also self-evident. Knowledge of every truth in the relevant branch is therefore guaranteed since all of the axioms are self-evident and every other truth is a logical consequence of the axioms. The model for such an epistemology is Euclid's geometry, and its application to ethics in modern philosophy is characteristic of a line of thinkers that goes at least as far back as Hobbes, who declared in Leviathan that ‘Geometry . . . is the onely Science that it hath pleased God hitherto to bestow on mankind’Footnote ² and who used the model to expound ethics as ‘the science of Vertue and Vice’.Footnote ³ Sidgwick expressly sees his application of the traditional intuitionist epistemology to ethics as part of this lineage, though he identifies Clarke and Locke, rather than Hobbes, as his forbears. He characterizes Clarke as having tried more earnestly than any other thinker to go beyond rules of common-sense morality and ‘penetrate to really self-evident principles’Footnote ⁴ and attributes to Clarke and Locke the aim of showing ‘the parallelism between ethical and mathematical truth’.Footnote ⁵

Doubts about the traditional intuitionist epistemology began to arise with the development in the nineteenth century of non-Euclidean geometries. As a result of this development, the way logicians and mathematicians conceived of the axioms of a branch of mathematics gradually changed, and by the middle decades of the twentieth century mathematical propositions no longer had to be self-evident to be axioms. Indeed, absolute truth itself was no longer a condition of being an axiom – else one would have to suppose that either all of the non-Euclidean geometries were false or that Euclid's was false. Nor could these consequences be confined to geometry, though it took more than half a century before they were shown irrefutably to apply to arithmetic as well.

Initially, the development of non-Euclidean geometries undermined the received view, due to Kant, that knowledge of pure mathematics was knowledge of synthetic a priori truths. Frege and Russell, recognizing that Kant's view was no longer viable, sought to preserve the understanding of such knowledge as a priori by showing that arithmetic was founded on logic. Arithmetic could then serve as the immediate underpinning of other branches of mathematics. Logicism was their program for establishing logic as arithmetic's foundation. This program allowed Frege and Russell to remain faithful to the traditional intuitionist epistemology since the axioms of logic were self-evident. But logicism eventually collapsed as a result of Gödel's two incompleteness theorems. Gödel's second theorem, in particular, put an end to the view that all mathematical truths could be comprehended within a system in which the truths were either self-evident or logical consequences of self-evident truths. These theorems were well-known to leading analytic philosophers, and with the rise of analytic philosophy, works such as Methods that sought to present a branch of knowledge as conforming to the traditional intuitionist epistemology were bound to be regarded as obsolete. Indeed, to the extent that analytic philosophers took logicism as the most credible program for preserving the traditional intuitionist epistemology, we should expect that interest in Sidgwick's application of the epistemology in Methods would have begun to wane even before Gödel's proofs were known. For the propositions Sidgwick identified as the axioms of ethics, though very abstract, were nonetheless synthetic propositions and not logical truths.

Skelton doesn't think this explanation makes sense even if one grants (which he does not) that interest in Methods among Anglo-American philosophers waned after Sidgwick's death. Skelton raises three objections to the explanation. None of them has any force. They all depend on his disregarding the differences among the several forms of intuitionism that Sidgwick distinguished. In particular, they depend on Skelton's inattention to the distinction Sidgwick made between his application to ethics of the traditional intuitionist epistemology, which he called ‘philosophical intuitionism’, and the kind of intuitionism he attributed to philosophers for whom ethical inquiry mainly consisted in expounding common-sense morality, which he called ‘dogmatic intuitionism’. For Sidgwick, the distinction not only marked a difference in method but also a difference between schools. Thus, he observed, with respect to prior attempts to find in ‘commonly received moral rules . . . genuine intuitions of the Practical Reason'’, that ‘in the history of English ethics the earlier intuitional school show a turn of thought on the whole more philosophical than that which the reaction against Hume rendered prevalent’.Footnote ⁶ And as I noted above, he took his own study of the fundamental principles of ethics, the axioms of practical reason, to be a descendant of the studies of this earlier school. Its ambition in Locke's words was to place ‘morality among the sciences capable of demonstration’.Footnote ⁷ By the same token, Sidgwick distanced his study from that of the later school. Its members in his words ‘confined themselves mainly to the definition and arrangement of the Morality of Common Sense’.Footnote ⁸ Because Skelton misses the importance of this distinction to understanding the study Sidgwick undertook in Methods, he is unable to see how the revolution in the philosophy of mathematics I described could weaken interest among philosophers in Sidgwick's Methods. Accordingly, the objections Skelton raises to my explanation merely reflect this incomprehension.

Consider Skelton's first objection. It is doubtful, Skelton argues, that Sidgwick took the traditional intuitionist epistemology to apply fully to ethics because Sidgwick ‘does not in any strict sense deduce common-sense morality or utilitarianism from [his intuitions]’.Footnote ⁹ The problem with this objection is that its premiss presupposes that Sidgwick thought common-sense morality and utilitarianism were deducible from his intuitions, which is to say, from the axioms of practical reason, and he didn't. To the contrary, Sidgwick thought that neither common-sense morality nor utilitarianism was deducible from these axioms. Consequently, the objection fails for the simple reason that if Sidgwick thought neither was deducible from these axioms, then his not so deducing them cannot be evidence against my explanation. Let us take the case of common-sense morality first.

Sidgwick's chief aim in expounding common-sense morality in book III of Methods is to show that its rules cannot be self-evident because they are inconsistent and therefore yield, when applied to particular situations, perplexity about what ought to be done. In his view, the rules present the illusion of being self-evident ‘[s]o long as they are left in the state of somewhat vague generalities as we meet them in ordinary discourse’ but that this illusion dissolves ‘as soon as we attempt to give them the definiteness which science requires’.Footnote ¹⁰ His inquiries in book III include, then, both careful statements of these rules that represent his attempt to remove the vagueness and imprecision that characterize the loose formulations of ordinary discourse and judicious assessments of them so stated for their suitability to be axioms of practical reason. In determining that they are not suitable to be axioms of practical reason, he eliminates as well the possibility that one can deduce them from such axioms. For the same reasons that, in Sidgwick's view, disqualify them from being self-evident disqualify any set of propositions from which one could deduce them from being self-evident. Hence, it is a mistake to suppose that Sidgwick thought the rules could be deduced from the axioms of practical reason.

Sidgwick's view of the rules of common-sense morality is that, while being ‘in the main sound’, they stand in need of correction and perfection.Footnote ¹¹ They are not, then, truths in the strict sense that philosophical intuitionism requires of the results of a scientific study of morality. In a passage of singular importance for the issue before us, Sidgwick, writing about these rules, distinguishes ‘between (1) the moral maxims which reflection shows not to possess ultimate validity and (2) the moral maxims which are or involve genuine ethical axioms’.Footnote ¹² The former include such rules as ‘One ought to keep one's promises’ and ‘One ought to speak the truth’ and ‘present themselves as propositions requiring rational justification of some kind’.Footnote ¹³ Plainly, though, the kind of rational justification Sidgwick thought they required is not that of deduction from the axioms of practical reason, for in that event they would involve genuine ethical axioms. The latter (i.e., the maxims in group (2)), which may include a few of the rules of common-sense morality but which also include propositions too abstract or complex to be part of this morality, represent the ethical truths whose rational justification is that of traditional intuitionist epistemology. In sum, once one grasps the implications of Sidgwick's critique of dogmatic intuitionism, one should see, pace Skelton, that Sidgwick's application of the traditional intuitionist epistemology to ethics does not imply that he regards the rules of common-sense morality as deducible from the axioms of ethics.

Let us next turn to the case of utilitarianism. Sidgwick took utilitarianism to be one of the methods of ethics, specifically, the method of universalistic hedonism, and he defines such methods as ‘rational procedures for determining right conduct’.Footnote ¹⁴ On the traditional intuitionist epistemology, the deductive consequences of the axioms are further propositions. They are not rational procedures. So Skelton's objection in this case is, if we follow Sidgwick's terminology, incoherent. Presumably, though, Skelton means by ‘utilitarianism’ a system of ethical propositions whose fundamental principle is the Principle of Utility. But since this principle is identical with the axiom Sidgwick called ‘the axiom of Rational Benevolence’,Footnote ¹⁵ Skelton's objection fares no better on this reading of it. The reason should be clear: any deduction of this system from intuitions would entail a deduction of its fundamental principle from intuitions, and Sidgwick did not think axioms are deducible from intuitions.

The second objection Skelton makes to my explanation is that if it were correct, then during the period of the twentieth century when I say interest in Methods was low, there should have been a corresponding lack of interest in the works of other prominent ethical intuitionists such as Moore, Prichard and Ross, yet there was not. Skelton thinks there should have been this corresponding lack of interest, if my explanation were correct, because he sees no relevant difference between the epistemology on which these twentieth-century ethical intuitionists based their studies and the epistemology on which Sidgwick based his. All, Skelton writes, ‘subscribe to a similar epistemology’.Footnote ¹⁶ In saying this, however, he means only that they all appealed to intuitions and took the basic ethical truths to be self-evident. So it is rather like saying that Quine and Carnap subscribed to a similar semantics because they both took empirical observations to be the fundamental vehicle of linguistic meaning. Once one looks beyond the gross similarities between Sidgwick's epistemological views and those of the twentieth-century ethical intuitionists whom Skelton cites to the finer differences between them, one sees that Sidgwick alone took mathematical axioms as the standard for determining whether a proposition is self-evident. Among his reasons for rejecting dogmatic intuitionism in favor of philosophical intuitionism is his insistence that to be an ethical axiom a proposition must ‘present [itself] as self-evident; as much (e.g.) as the mathematical axiom that “if equals be added to equals the wholes are equal”.’Footnote ¹⁷ None of the twentieth-century intuitionists whom Skelton lumps together with Sidgwick comes close to applying this standard when determining whether a proposition is self-evident. None of them even remotely adheres to philosophical intuitionism. Nor could there be any mistake about this among their readers.

Indeed, Moore's ethics does not even qualify, by Sidgwick's lights, as exemplifying a method of ethics. It is, rather, a variant of what Sidgwick calls ‘aesthetic intuitionism’ in which intrinsic value replaces beauty as what ought to be the ultimate end of action.Footnote ¹⁸ Sidgwick noted that aesthetic intuitionism offered no rational procedure for determining right conduct, and the same is true of Moore's ethics. It merely tells us to attend to what has intrinsic value, something we perceive intuitively, and then to produce as much of it as we can. Plainly, then, Moore's appeal to intuition and to the self-evidence of its deliverances has no similarity to appeals to intuition in mathematics that prior to the revolution in the philosophy of mathematics I described were made to support taking mathematical axioms as self-evident. Nor would any of Moore's readers think it did. So it is hard to see how this revolution could weaken interest in it.

The views of Prichard and Ross, on the other hand, do correspond to a method of ethics. Each adheres to a form of dogmatic intuitionism. Neither, however, applies the model of an axiomatic system of mathematics to ethics. What is most telling, perhaps, is that neither is concerned with internal consistency among the propositions they identify as the fundamental principles of ethics. In any axiomatization of a branch of mathematics, such consistency is a necessary property of the set of propositions that are proposed as its axioms. Because any proposition follows deductively from an inconsistent set of propositions, deducibility from axioms ceases to be a determinant of truth if the axioms are internally inconsistent. Sidgwick, famously, insisted on consistency among the ethical axioms. Inconsistency, for him, meant that at least one of the propositions was not self-evident.Footnote ¹⁹ Ross, by contrast, expounded a system of ethics in which conflict among its fundamental principles was a given. Resolution of such conflict in the situations in which it occurred, Ross held, required judgment as to which of the conflicting principles was weightier in those situations, and such judgment was a matter of opinion only and never amounted to knowledge. This feature of his system alone shows that the system is not modeled on axiomatic systems in mathematics. And though Ross does liken the self-evidence of the principles of prima facie duty to that of mathematical axioms – ’they come to be self-evident to us just as mathematical axioms do’ – the likeness he refers to is in how we acquire our confidence in their truth and not in the abstract character of their content or in their place in a system of knowledge.Footnote ²⁰ Thus, while some philosophers might still think the abandonment of claims of self-evidence for mathematical axioms undermines Ross's claims of self-evidence for the principles of prima facie duty, the differences between those ethical principles, as Ross conceives of them, and mathematical axioms are clearly sufficient for Ross and those sympathetic to his view to continue unqualifiedly to defend his view.

In general, then, these differences between Sidgwick's intuitionism and the intuitionist views of Moore, Prichard and Ross show why the revolution in the philosophy of mathematics I described did not represent a serious threat to the latter views. Of course, no philosopher can simply declare that certain propositions are self-evident truths, especially when one can imagine the proposition's being denied by someone without that person's being suspected of being irrational or of misunderstanding the proposition. Such declarations, therefore, require reasons that justify the attributions of self-evidence the declarer is making, and consequently the question arises what reasons Moore and the other twentieth-century intuitionists gave to justify their attributing self-evidence to certain ethical propositions. The answer is that, to justify these attributions, they invoked non-natural properties, e.g., intrinsic goodness and prima facie rightness, and special intellectual faculties for discerning them. Skelton is puzzled by this answer. He cannot see how invoking non-natural ethical properties or a special moral faculty could justify taking certain ethical propositions to be self-evident. But there is no mystery here. Moore used the open question argument as a powerful tool for establishing that intrinsic goodness is a non-natural property. If there are non-natural properties and we know them, then we must know them through our intellect and not our senses. And if we know them through our intellect and not our senses, then we know them intuitively. Since what we know intuitively is self-evident, attributions of self-evidence to certain ethical propositions follow almost immediately. One could, of course, doubt that we have knowledge of goodness or right and wrong; but none of these twentieth-century ethical intuitionists did. None was a moral skeptic.

All of the intuitionists who belong to the strand of ethical intuitionism that begins with Moore and who came after him accepted Moore's open question argument and followed him in taking it to establish that ethical properties are non-natural. All were descriptivists about ethical sentences and realists about the ethical properties those sentences predicated of objects, actions, people, etc. Their intuitionism depended crucially on these semantic and metaphysical views. Sidgwick's did not. While Sidgwick took ‘ought’ and ‘right’ in their strict ethical sense to express the fundamental notion of ethics, he characterized the basic sentences in which ‘ought’ and ‘right’ were so used as precepts and imperatives. Thus, he is best interpreted as avoiding descriptivism and realism. In any case, whether he was a descriptivist about ethical sentences or a realist about ethical properties is inconsequential to his intuitionism. The difference, moreover, matters for the history of twentieth-century ethics. For what doomed the strand of ethical intuitionism that begins with Moore were not the arguments against it of critics like Strawson, as Skelton suggests, but the earlier rise of non-cognitivism in ethics. The non-cognitivists, by rejecting descriptivism, showed how one could accept Moore's open question argument without being committed to non-natural properties. Since Sidgwick's intuitionism does not depend on descriptivism, it could have withstood the non-cognitivist wave if it had not already been superseded by the strand of intuitionism that begins with Moore.Footnote ²¹ That supersession is due to the differences between the two and, in particular, to the difference between an intuitionism that takes mathematical axioms as the model of self-evidence and one that appeals instead to there being non-natural ethical properties and to our having a capacity to apprehend them directly.

Skelton's third objection is that ‘One may well accept that the [traditional intuitionist] epistemology did not work out in, e.g. geometry . . . but reject that this implies that it does not work well or plausibly in ethics.’ The problem with this objection is that it is irrelevant to the question of what explains the decline in interest in Methods during much of the twentieth century. The question is historical, whereas Skelton's point is merely philosophical. Pointing out that there is no philosophically compelling argument against applying the traditional intuitionist epistemology to ethics, given its abandonment in mathematics, tells us nothing about how likely it was that the interests of Anglo-American philosophers in Methods during the first sixty years of the twentieth century would have been affected by revolutionary changes in the philosophy of mathematics. Philosophers do not require compelling arguments against a view to lose interest in it. In this respect, they are no different from other thinkers. If a program in one branch of a discipline has a long history of drawing on analogy with a successful program in another branch, then the eventual bankruptcy of the latter is bound to cause major disinvestment of interest in the former. And one would have to be unusually ignorant of the history of philosophy, stretching back to Plato's Meno, to be unaware of the tradition among rationalist philosophers of using mathematics to buttress claims to a priori knowledge in other fields.Footnote ²²

Skelton, in pressing this objection, points to Bertrand Russell's having allowed in 1955 that ethical intuitionism is a possible view. Skelton thinks this concession of Russell's is relevant because Skelton confusedly thinks Russell's logicist program implies that Russell rejected the application of traditional intuitionist epistemology to mathematics. Thus, Skelton offers Russell as an example of a philosopher who accepts the possibility of applying traditional intuitionist epistemology to ethics even though he rejects its application to mathematics. But Russell, needless to say, did not advance logicism because he rejected the application of the traditional intuitionist epistemology to mathematics. To the contrary, as I noted, he did it to preserve its application to arithmetic. Nothing, after all, in the traditional intuitionist epistemology excludes the axioms of logic from being self-evident truths. Nor does Skelton offer any evidence that Russell was referring to the application of this epistemology to ethics when he allowed that ethical intuitionism is possible. It is far more likely that Russell was referring, instead, to the strand of ethical intuitionism that begins with Moore. Here again, because Skelton lumps the two together, he fails to produce a cogent criticism of my explanation.

Finally, let me turn to Skelton's objection to my characterizations of how Methods was seen during Sidgwick's lifetime and of its fate after Sidgwick's death. I can be brief. In saying that Methods was not seen during Sidgwick's lifetime as a major and lasting contribution to British moral philosophy, I did not mean that it was not seen as an important work. I meant that it was not regarded, as we now regard it, as one of the great works of British moral philosophy, a work to be set alongside Hobbes's Leviathan, Butler's Sermons, Hume's Second Inquiry, Smith's Theory of the Moral Sentiments, et al. That it was seen as an important work in its time is already implied by asking what explains its falling into neglect. And that Methods suffered such a fate, it seems to me, is a less remarkable fact and easier to explain if one realizes that it was not during Sidgwick's lifetime regarded as the towering work of British moral philosophy that we now see it as. After all, it is common for even the best works of thinkers who, during their lifetime, are leading figures in their field to fade in importance once their authors die and scholarly attention turns to fresher works by thinkers who have replaced them as the field's leaders.

Surely, if Methods had been regarded during Sidgwick's lifetime as one of the towering works of British moral philosophy, that opinion would have been registered in the era's most authoritative reference work, The Encyclopedia Britannica. Instead, what one finds in the edition that was published shortly after Sidgwick's death is a short, unsigned article on him, which gives a perfunctory description of his principal views and pays greater tribute to his work as an educational reformer than to his contributions to philosophy. Other leading figures in English ethics among Sidgwick's contemporaries, Herbert Spencer and T. H. Green, in particular, are honored with decidedly more robust articles. These articles are signed and substantially longer than the one on Sidgwick. In addition, they contain extensive discussion of their subjects’ philosophical theories including their ethical theories. Similarly, in the last section of the article on ethics in Britannica's 1911 edition, the title of which is ‘Ethics since 1879’, the views of Spencer and Green are discussed at length while Methods is given a couple of sentences. These sentences are preceded by the statement that it is a work ‘equal in importance’ to James Martineau's Types of Ethical Theory.Footnote ²³ There can be no question, then, that Sidgwick's contemporaries regarded the works of Spencer and Green, and not Methods, as the major and lasting contributions to British moral philosophy of their time. Readers, in any case, can easily judge for themselves, by consulting a website at which these and many other articles from the renowned 11th edition of Britannica are reprinted.Footnote ²⁴

In characterizing Methods as being largely ignored for much of the twentieth century, I did not say that references to Methods disappeared from the pages of philosophical writings during this period or that Sidgwick had no admirers during it other than Broad. Nor did I say that philosophers immediately stopped writing about Methods upon Sidgwick's death. Citations of works published within several years of Sidgwick's death show nothing more than the unsurprising facts that interest in Methods did not instantly dry up when he died and that loyal students like Constance Jones and McTaggart didn't suddenly desert him. When an important work suffers a decline in interest, the decline typically occurs over many years, and Skelton's citations are consistent with such a decline. Perhaps one must have experienced the resurgence of interest in Methods that took place in the 1970s to appreciate how neglected a work it had become by mid-century. Bernard Williams captures this well when he describes the lack of interest from which Methods suffered as ‘a period of fairly resolute neglect’.Footnote ²⁵ And Schultz, in the opening chapter of his book, masterfully conveys how the work came to appear time-bound and passé to many of the Cambridge luminaries who came after Sidgwick and who dominated British intellectual life in the first half of the twentieth century.Footnote ²⁶ My interest, in supplementing Schultz's account, has been to correct the suggestion in it that genuine advances in philosophy, as opposed to mere changes in philosophical fashions, did not significantly contribute to the neglect into which Methods fell.