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Moral philosophy during the period under review was marked by the dominance in England of a form of ethical intuitionism that arose in response to G. E. Moore's Principia Ethica (1903). By the mid-1930s this began to be challenged, both in England and in the United States, by various forms of emotivism. In some isolation from this debate, Dewey continued to write extensively on ethics. Intuitionism The intuitionist school consisted of H. A. Prichard, W.D. Ross, H.W. B. Joseph, and E. F. Carritt in Oxford and C. D. Broad and A. C. Ewing in Cambridge. Prichard should probably be considered the leader of the school, though he published the least; Broad called Prichard ‘a man of immense ability whom I have always regarded as the Oxford Moore’ (1971: 14). The intuitionists believed that rightness and goodness were distinct qualities, qualities that such things as people, actions, emotions, motives, intentions, and consequences could have. They were interested in the nature of and relation between these two qualities and in the distinction between intrinsic and extrinsic forms of them, and in which things in fact have these properties. Ross, for instance, argued that there was no such thing as instrumental goodness, that is, value as a means (1930: 133, 1939: 257); but he insisted that there was such a thing as intrinsic value, and that it was distinct from intrinsic rightness. Further, nothing was capable of being both intrinsically good and intrinsically right (Prichard 1912: 5–6). [ABSTRACT FROM AUTHOR]

Introduction The first-order logic that is commonly taught and used today did not exist at the beginning of the twentieth century. A series of investigations in ‘foundations of mathematics’ by a variety of researchers led to its treatment as the core element of. These investigations searched for a detailed account of how our finite reasoning capacity could lead to knowledge of the infinite quantities involved in mathematics. This issue took on an acute form in the late 1800s when Georg Cantor (1845–1918) showed that mathematics could not be understood without accepting the existence of infinite sets of entities, in particular the complete set of counting (or natural) numbers. He also showed that the existence of such a denumerably infinite set entails the existence of ever larger infinite sets, each having a larger infinite ‘cardinal number’. The methods developed in the studies of mathematical logic were taken over to formulate alternatives to first-order logic. The most important of these were modal logic and intuitionistic logic. This chapter tells the story of these changes. First-order logic A first-order logic is a set of logical axioms and formal inference rules for a first-order language. Such a language will contain one-place predicate symbols and multiple-place relation symbols. The language may also have symbols for individual objects and functions. For logical symbols, it typically has the sentential connectives ˜, &, →, ∨, ↔, and the two quantifiers, ∀, ∃. The language is ‘first-order’ because quantifiers apply only to variables which range over the individual objects of the domain. Second-order or higher-order languages have variables that range over sets of objects or of n-tuples drawn from the domain. [ABSTRACT FROM AUTHOR]

In the period from 1870 to 1914 there was a shift within moral philosophy towards meta-ethical concerns. Metaethics and its guiding idea that the first task in moral philosophy is an enquiry into the semantics of moral discourse and into its ontological foundations, though by no means an invention of twentieth-century philosophy, has become its most characteristic feature. The history of twentieth-century ethics starts in Cambridge, where in 1903 G. E. Moore published Principia Ethica. It rarely happens, as it did with Principia Ethica, that one book accounts for so many of the later developments in a field. It was Moore's declared intention to break sharply with the philosophical tradition. According to him, even the most prominent figures in the history of moral philosophy, for example, Aristotle, Kant, and Mill, have misunderstood the foundations of ethics. Too late to be of any influence on Principia Ethica, Moore thinks he has discovered a soul-mate. In the Preface to the first edition of Principia Ethica Moore writes: ‘When this book had been completed, I found, in Brentano's Origins of the Knowledge of Right and Wrong opinions far more resembling my own, than those of any other ethical writer with whom I am acquainted’ (Moore 1903 [1993a: 36]). Brentano and Moore both try to provide a philosophical foundation of ethical knowledge that can withstand the undermining efforts of relativism and subjectivism. In this sense they are both realists. They also share the methodological conviction that only meta-ethical investigations can provide solid foundations for morality. [ABSTRACT FROM AUTHOR]

New beginnings The 1870s was a decade of new beginnings in British moral philosophy. This was partly in reaction to the work of J. S. Mill, who had dominated the previous decade and whose Utilitarianism had appeared in book form in 1863. First, in 1870, John Grote's Examination of the Utilitarian Philosophy was posthumously published (Grote had been professor at Cambridge when Mill's work appeared). Then in 1874, also from Cambridge, came what has justly been called the first work of modern professional moral philosophy, Henry Sidgwick's Methods of Ethics. Meanwhile an idealist response to Mill (and to empiricist thinking more generally) had been brewing in Oxford, particularly in the lectures of T. H. Green. Its first significant ethical work was F. H. Bradley's Ethical Studies, published two years after Sidgwick's in 1876 (whereupon Bradley and Sidgwick promptly fell on each other in critical reviews and pamphlets). At the end of this decade, in 1879, came Herbert Spencer's Data of Ethics. Although Spencer was more favourable to empirical methods than Sidgwick, Green, or Bradley, and although like Mill and unlike them he worked outside the established universities, he was nevertheless another critic of Mill. Mill stood for empirical, observational, methods and held that the central ethical issue was between results based on observation of actual human behaviour (which he thought led to his own utilitarianism) and results based upon supposed direct intuitions of moral truths (as believed in by his Cambridge opponent, Whewell). In 1870 the conflict between empiricist utilitarianism and intuitionism seemed to be the central issue, or problem, in ethics. For example W. Lecky's History of European Morals of 1869 frames its study round the ‘great controversy, springing from the rival claims of intuition and utility’ (Lecky 1869: 1). [ABSTRACT FROM AUTHOR]

Hume drew more radical, skeptical conclusions from an empirical naturalist conception of reason than did Hutcheson (his theory of justice to one side). If reason is, as both agreed, exclusively theoretical, concerned only with “the discovery of truth and falsehood” (THN. 458; IMS. I; R.307), then, since no action can be literally true or false, neither, strictly, can any be reasonable or unreasonable. It is not “contrary to reason,” Hume famously concluded, “to prefer even my own acknowledg'd lesser good to my greater” (THN. 416). This conflicts with a calm reflective deliberation view as articulated by Hutcheson and Cumberland. A person acts “reasonably,” Hutcheson claimed, when, upon considering the “various Actions in his Power” in light of “true Opinions of their Tendencies” he “chuses to do that which will obtain the highest Degree of that, to which the Instincts of his Nature incline him” (IMS. I). Because calm, informed reflection leads beings with our psychological makeup to desires for their own greatest good and for the greatest good of all, self-love and universal benevolence are the “two grand determinations” of human will, structuring rational human deliberation. Hume accepted that the pursuit of lesser goods may result from a failure of theoretical reason, but he thought that reason is violated only when there is false judgment, and “even then 'tis not the passion [or action], properly speaking, which is unreasonable, but the judgment” (THN. 416; see also 413–18, 458–60). Nor does the pursuit of a lesser good entail that the agent has judged falsely. [ABSTRACT FROM AUTHOR]

Butler and Hutcheson provide radically different vantage points on the role of autonomy and reason in action and the moral life. Hutcheson carries forward an empiricist tradition – one including Hobbes, Cumberland, and Locke – that holds agency to be entirely instrumental. Every motive is a desire for some naturally good effect of action, usually some pleasurable state of the agent or of someone else. Reason's task is exclusively theoretical: to inform the agent of means to these desired end states or of natural goods of which she may have been insufficiently aware, giving rise to new desires or new levels of desire. What human agents learn from this use of reason (contingently) presents itself, within the deliberative context, as a kind of directive or dictate to take necessary means or to desire new natural goods. But there is nothing more to normativity than this appearance under these conditions, or, perhaps, than the contingent fact that human agents are motivated in these ways. This might be thought to have the effect of explaining normativity away, at least as a fundamental ethical concept. For all these writers, practical ethics can proceed entirely in terms of natural good and evil: the valuable and disvaluable states action can bring about. No further normative practical notion (of a reason for acting, for example) is required by deliberating agents or by any ethics addressed to them. This is most obvious in Cumberland and Hutcheson. [ABSTRACT FROM AUTHOR]

For Hobbes and Cumberland, the rationale for the internal turn was philosophical naturalism. If ethics is simply the study of “consequences from the passions of men,” and if “the Whole of moral Philosophy” is to be “resolv'd into … conclusions of true Natural Philosophy” then there may seem nothing plausible for morality's normative grip to be other than its motive power, viewed from the perspective of a rational human agent. From an agent's point of view, empirical truths to which an observer is indifferent can present themselves as demands – as matters of practical, rather than merely natural, necessity. To the agent for whom self-preservation is an inescapable end, for example, facts about the natural necessities of survival have an unavoidable practical force; they present themselves as what ought to or must be done. Empirical naturalist internalism of this sort exercised a continuing attraction throughout the early modern period, as it has, indeed, to the present day. At the same time, a second, quite different, internalist line of thought developed alongside it: an autonomist internalism or internalism of practical reason. We encountered elements of this line, in early form, in Culverwell's notion that only a being capable of “moral government” can be subject to obligation. We shall return to it again in Locke's Essay thesis that moral government must involve self-government. Neither Culverwell nor Locke (at least in his earlier writings) proposed, however, that obligation itself be understood to consist in the motives of a self-determining agent, and so neither was an autonomist internalist. [ABSTRACT FROM AUTHOR]

As we have seen, Hobbes would not have said that an agent is obligated to do something simply by virtue of the fact that action is necessary to achieve an inescapable end. He was prepared to say that the laws of nature oblige on these grounds, or that this is how obligation binds, but he reserved ‘obligation’ for the state a person enters by laying down a right. By the turn of the century, however, many British moralists would come to find this way of thinking and speaking both sensible and familiar. They frequently posed the question Why be moral? by asking whether there is an obligation to be virtuous. And they often sought the answer to this question in whether or not the virtuous life conduces most to an agent's interest, taking for granted that this is an end all rational human beings seek. His diction notwithstanding, Hobbes was firmly behind this phenomenon. But another, insufficiently appreciated, source was Richard Cumberland. Hobbes aimed to understand morality's normative grip in entirely naturalistic terms. The laws of nature are dictates of reason, but this does not mean that they structure an independent, irreducible normative order grasped by an intuitive faculty. Right reason is right reasoning – the correct use of calculative, theoretical reason. And it dictates not by discovering norms but through the practical force of its discoveries from an agent's deliberative point of view, indicating unavoidable means to an inescapable end. The practicality of its dictates is carried, we might say, not in the content of what it discovers, but by the unavoidable relevance that content has from a human agent's perspective in deliberating about what to do. [ABSTRACT FROM AUTHOR]

In intuitionistic logic system, constructive negation operator complies with the law of contradiction but not the law of excluded middle in intuitionistic logic system.In da Costa΄s paraconsistent logic system , paraconsistent negation operator complies with the law of excluded middle but not the law of contradiction. Putting aside classical negation operator, both intuitionistic logic and da Costa΄s paraconsistent logic establish logic systems by directly introducing new negation operators basing on the positive proposition logic. This paper attempts to make constructive negation operator and paraconsistent negation operator satisfying the conditions mentioned above in classical logical system. Oppositional logic is an extended system of classical propositional logic. It can be obtained from the classical propositional logic by adding an unary connective * and introducing the definitions of two unary connectives ∆ and ∇. In oppositional logic system, there are four kinds of negation: the classical negation ¬ complying with both law of contradiction and law of excluded middle, the constructive negation ∇ complying with law of contradiction but not law of excluded middle, the paraconsistent negation ∆ complying with law of excluded middle but not law of contradiction, as well as the dialectical negation * complying with neither law of contradiction nor law of excluded middle. This paper gives the proof of the soundness and completenesstheorem of oppositional logic. It also gives the following conclusions: [1] Oppositonal logic can be a kind of tools for paraconsistent theory and intuitionistic theory; the famous Duns Scotus law does not hold according to the paraconsistent negation and the dialectical negation; [2] In oppositonal logic, according to the unary connective ¬, * , ∇ and ∆, A is in contradictory opposition with ¬A; A is in subaltern opposition with *A; A is in contrary opposition with ∇ A; A is in subcontrary opposition with ∆ A. In this sense, we call the logical system mentioned above oppositional logic. [ABSTRACT FROM AUTHOR]