Among the various theses in the philosophy of mathematics, intuitionism is the thesis that numbers are constructs of the human mind. In this thesis, a historical account of intuitionism will be exposited- - from its beginnings in Kant's classic work, Critique of Pure Reason, to contemporary treatments by Brouwer and other intuitionists who have developed his position further. In chapter II, I examine the ontology of Kant's philosophy of arithmetic. The issue at hand is to explore how Kant, using intuition and time, argues for numbers as mental constructs. In chapter III, I examine how mathematics for Kant yields synthetic a priori truth, which is to say an informative statement about the world whose truth can be known independently of observation. In chapter IV, I examine how intuitionism developed under the care of Brouwer and others (e.g. Dummett) and how Hilbert sought to address issues in Kantian philosophy of mathematics with his finitist approach. In conclusion, I examine briefly what intuitionism resolves and what it leaves to be desired.

Among the various theses in the philosophy of mathematics, intuitionism is the thesis that numbers are constructs of the human mind. In this thesis, a historical account of intuitionism will be exposited- - from its beginnings in Kant's classic work, Critique of Pure Reason, to contemporary treatments by Brouwer and other intuitionists who have developed his position further. In chapter II, I examine the ontology of Kant's philosophy of arithmetic. The issue at hand is to explore how Kant, using intuition and time, argues for numbers as mental constructs. In chapter III, I examine how mathematics for Kant yields synthetic a priori truth, which is to say an informative statement about the world whose truth can be known independently of observation. In chapter IV, I examine how intuitionism developed under the care of Brouwer and others (e.g. Dummett) and how Hilbert sought to address issues in Kantian philosophy of mathematics with his finitist approach. In conclusion, I examine briefly what intuitionism resolves and what it leaves to be desired.

In his paper “Framing Moral Intuitions” (Sinnott-Armstrong 2008), Sinnott-Armstrong argues that three studies which he cites provide evidence of unreliability in all moral intuitions in all circumstances. Therefore, he argues that all of one’s moral intuitions require inferential confirmation for justification. I argue that the studies do not strike me as evidence for this conclusion. Thus, anyone who reads the studies and is not struck that they are evidence for this conclusion can have justified moral intuitions without inferential confirmation. Further, arguments are given for why Sinnott-Armstrong’s arguments fail to show that all moral intuitions are unreliable in all circumstances. Finally an argument is given which shows that even if one accepts the master argument, it need not lead to moral scepticism.

In his paper “Framing Moral Intuitions” (Sinnott-Armstrong 2008), Sinnott-Armstrong argues that three studies which he cites provide evidence of unreliability in all moral intuitions in all circumstances. Therefore, he argues that all of one’s moral intuitions require inferential confirmation for justification. I argue that the studies do not strike me as evidence for this conclusion. Thus, anyone who reads the studies and is not struck that they are evidence for this conclusion can have justified moral intuitions without inferential confirmation. Further, arguments are given for why Sinnott-Armstrong’s arguments fail to show that all moral intuitions are unreliable in all circumstances. Finally an argument is given which shows that even if one accepts the master argument, it need not lead to moral scepticism.

Stephen Read has done significant work towards clarifying the concepts of harmony, consistency, and conservative extensions as introduced by Prior, Belnap, and Dummett. Read argues that the conservative extension requirement is too stringent. Nonetheless, he develops a formal system in which the negation, though classical, is a conservative extension of the positive fragment, by strengthening the theory of the conditional and allowing multiple conclusions. In this thesis, I will closely examine this system to determine how he achieves this. Read concludes that this result indicates that the true debate between the classicist and the intuitionist is over bivalence. My project is to critically investigate Read’s work on intuitionistic terms, noting the non-intuitionistic moves made to reach this result. If Read’s conclusion is correct, and bivalence is the true source of disagreement between the classicist and intuitionist, then it follows that any disagreement along the way should stem from bivalence. Ultimately I conclude that Read correctly identifies the source of disagreement. With this in mind, I return to Dummett’s philosophy and attempt to show why this conclusion is perfectly in line with the intuitionist’s stance.

A pesquisa investiga os desenvolvimentos iniciais da filosofia de Husserl, tendo por foco a análise da evolução de sua teoria do simbolismo e a explicitação dos diversos sentidos que assume a problemática intuicionista que lhe é essencial. O período abordado compreende os anos 1890-1901, e os textos aos quais se dedica exposição e comentário são Filosofia da Aritmética (1891), Sobre a Lógica dos Signos - Semiótica (1890/91), Estudos Psicológicos para a Lógica Elementar (1894) e Investigações Lógicas (1900/91). Pretende-se apresentar o que conduz Husserl ao abandono de seu intento original - aquele de oferecer uma fundamentação filosófica do cálculo simbólico - em favor de uma filosofia que se centra na analítica da consciência intencional. / This research investigates the initial developments of Husserl's philosophy, focusing on the analysis of the evolution of his theory of symbolism and the explanation of the different senses that the intuitionist problem essential to it assumes. The period covered comprises the years 1890-1901, and the texts to which exposure and commentary have been devoted are Philosophy of Arithmetic (1891), On the Logic of Signs - Semiotics (1890/91), Psychological Studies for Elementary Logic (1894) and Logical Investigations (1900/91). It is intended to present what leads Husserl to the abandonment of his original program - that of offering a philosophical foundation for symbolic calculation - in favor of a philosophy that focuses on the analytic of intentional consciousness.

Against moral intuitionism, which holds that moral intuitions can be non-inferentially justified, Walter Sinnott-Armstrong argues that moral intuitions are unreliable and must be confirmed to be justified (i.e. must be justified inferentially) because they are subject to cognitive biases. However, I suggest this is merely a renewed version of the argument from disagreement against intuitionism. As such, I attempt to show that the renewed argument is subject to an analogous objection as the old one; many cognitive biases of moral intuitions result from biases of non-moral judgments. Thus, the unreliability of moral intuitions due to biases (and the reason inferential justification was required) can be removed by clearing up the non-moral biases. Accordingly, biases of moral intuitions do not threaten a slightly qualified version intuitionism which posits non-inferential justification of intuitions when non-moral biases are not present. I also present an empirical study that lends initial support to my argument.

In Moral Realism and the Foundations of Ethics, David Brink defends a version of moral realism that makes use of a coherentist epistemology. I argue that we have good reasons to prefer a coherentist epistemology in ethics, and that common arguments in favor of foundationalism and against coherentism fail. I conclude that only the multiple coherent systems (MCS) objection poses a serious threat to coherentism, and that there is a way of meeting this objection as it is traditionally construed. Doing so requires adding an explanatory requirement to coherentism: a coherent system must not only be coherent, but explain why it is coherent. Though I argue that the MCS objection fails as traditionally construed, I propose variants of the objection which apply specifically to coherentist moral realism. Based on the social intuitionist model of moral decision-making, I point to evidence which indicates that intuitive moral judgments are the cause of reasoned moral judgments. This raises two problems: "the problem of intransigence" and the "limited problem of intransigence." These two problems constitute MCS objections to coherentist moral realism. The first problem claims that coherentism itself might not be possible for actual human beings, and that even if people are capable of forming coherent systems of belief, these systems are necessarily radically divergent as a result of various cultural and sociological factors. The second problem is that the coherentist moral realist should not expect a single moral system to result from moral reasoning (even ideally), because all such systems will include intuitions which are immune to reasoning. I argue that these MCS objections must be overcome if coherentist moral realism is to be a viable option.

Title from title page of PDF (University of Missouri--St. Louis, viewed March 2, 2010). Includes bibliographical references (p. 55).

This thesis sets out an argument in defence of moral objectivism. It takes Mackie as the critic of objectivism and it ends by proposing that the best defence of objectivism may be found in what I shall call Kantian intuitionism, which brings together elements of the intuitionism of Ross and a Kantian epistemology. The argument is fundamentally transcendental in form and it proceeds by first setting out what we intuitively believe, rejecting the sceptical attacks on those beliefs, and by then proposing a theory that can legitimize what we already do believe. Chapter One sets out our intuitive understanding of morality: (1) that morality is cognitive, moral beliefs can be true or false; (2) that morality is real, we do not construct it; (3) that morality is rational, we can learn about it by rational investigation; and (4) that morality places us under an absolute constraint. The chapter ends by clarifying the nature of that absolute demand and by arguing that the critical idea within morality is the idea of duty. In Chapter Two Mackie’s sceptical attack on objectivism is examined. Four key arguments are identified: (1) that moral beliefs are relative to bfferent agents; (2) that morality is based upon on non-rational causes; (3) that the idea of moral properties or entities is too queer to be sustainable; and (4) that moral objectivism involves queer epistemological commitments. Essentially all of these arguments are shown to be ambiguous; however it is proposed that Mackie has an underlying epistemological and metaphysical theory, scientific empiricism, which is (a) hostile to objectivism and (b) a theory that many find attractive for reasons that are independent of morality. Chapter Three explores the nature of moral rationality and whether scientific empiricism can use the idea of reflective equilibrium to offer a reasonable account of moral rationality. It concludes that, while reflective equilibrium is a useful account of moral rationality, it cannot be effectively reconciled with scientific empiricism. In order to function effectively as a rational process, reflective equilibrium must be rationally constrained by our moral judgements and our moral principles. Chapter Four begins the process of exploring some alternative epistemologies and argues that the only account that remains true to objectivism and the needs of reflective equilibrium is the account of intuitionism proposed by Ross. However this account can be developed further by drawing upon number of Kantian ideas and using them to supplement Ross ’ s intuitionism. So Chapter Five draws upon a number of Kant's ideas, most notably some key notions from the Critique of Judgement. These ideas are: (1) that we possess a rational will that is subject to the Moral law and determined by practical reason; (2) that we possess a faculty of judgement which enables us to become aware of moral properties and (3) that these two faculties together with the third faculty of thought can function to constitute the moral understanding. Using these ideas the thesis explores whether they can serve to explain how intuitions can be rational and how objectivism can be justified.