In this work, I will be looking at the issues raised by set-theoretic indeterminacy for a Gődelian platonist, who holds that there is a universe of independently existing math- ematical objects and that there are objective unique truth-values for any set-theoretic statement. After careful consideration of the philosophical and mathematical issues involved, I claim that Gődelian platonism is untenable. In Chapter 1, I examine dif- ferent forms of mathematical platonism and I elucidate their features. In particular, I distinguish between a substantive form (Gődel's platonism) and an operational form (anti-constructivism). I also make it clear that I will be concerned with set-theoretic Gődelian platonism. In Chapter 2, I examine the indeterminacy phenomenon in set theory through a detailed analysis of the most famous open conjecture, the Continuum Hypothesis (CH). In Chapter 3, I move on to describe the main philosophical orien- tations with regard to the indeterminacy phenomenon and I show how model-theoretic relativity is the main source of trouble for platonism. In Chapter 4, I examine the the- oretical ancestry of Gődel's conceptions (which may date back to Cantor's philosophy of the infinite) and Gődel's philosophy of indeterminacy. In Chapter 5 and Chapter 6, I deal with, respectively, Maddy's set-theoretic naturalism and plenitudinous platonism (in the form presented by Balaguer, FEP), and I raise some objections against these conceptual frameworks. In Chapter 7, I propose abandoning ontological platonism and I defend a mild form of conceptual realism resting upon the notion of non-arbitrary expansions. Finally, in Chapter 8, I tackle the problem of insolubility in contempo- rary set theory and I advise that operational platonism, qua anti-constructivism, as described in Chapter 1, is the only bit of platonism which could be upheld.

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This account of Iris Murdoch’s moral philosophy takes the form of a critique. It attempts to show the ways in which she falls foul of what she criticises. Murdoch is concerned about the influence of the romantic tradition upon our contemporary (post-war) accounts of morality. She charges contemporaries, such as Sartre and R. M. Hare with having mistakenly extended freedom in ways that make morality seem like a matter of free choice. Against this, her own most rigorous work (The Sovereignty of Good) advances three central claims: (1) an idea of moral perfection (an ideal Good) is built into our ways of thinking and speaking; (2) this idea of Good/perfection is not an unavoidable fiction but a reality principle, it helps to undermine the egocentricity that prevents us from doing justice to the reality of others; (3) this idea of a single, unitary Good pulls us towards Platonic metaphors. (We are like pilgrims, trying to move out of dark egocentricity and into the light of attention to others). My response to this is advanced in the following three parts: Part one sets out Murdoch’s position, complete with an account of the stylistic peculiarities of its exposition. (She believes that value-laden metaphors are unavoidable, and in some cases irreducible). Part Two flags up her similarity to what she attacks. Far from being a moral quietist, Murdoch is deeply critical of our everyday lack of moral ambition. (It is as if we are content to lurk about in the dark). She rejects everyday (‘bourgeois’) contentment in favour of the command ‘be ye therefore perfect’. Having flagged up this shared rejection of everyday contentment, I explore the way that Murdoch’s apparently diffuse charge of ‘romanticism’ is held together by the idea of erotic striving. Such romanticism is the general theoretical correlate of the wrong model of love, romantic love rather than the slow patient love that she wants us to emulate. On this account, avoiding romanticism requires us to meet the following conditions. Firstly, we must direct loving attention towards the contingent reality of persons without puritanically avoiding attention to messy detail. (We should not just ‘tag’ people symbolically, as one of these or one of those.) Secondly, our attention to the other should really be about them, it should not covertly redirect attention to the self. Thirdly, we should not allow our fascinating suffering to obscure the reality of death. (The realisation of our finitude is a crucial aspect of undermining egocentricity). Part Three consists of chapter-pairs which examine the central Murdochian metaphors of fallenness, eros, and the death of the self in an attempt to show that Murdoch falls foul of what she attacks.