The following is a transcript of the interview I (Yasuko Kitano) conducted with Neil Levy (The Centre for Applied Philosophy and Public Ethics, CAPPE) on the 23rd in July 2009, while he was in Tokyo to give a series of lectures on neuroethics at The University of Tokyo Center for Philosophy. I edited his words for publication with his approval.

The verses have constituted a living document upon which our various forebears, seeking to discover and revitalize for themselves identities in the world, have left behind a succession of exegetical imprints.

A number of concerns have been raised about the possible future use of pharmaceuticals designed to enhance cognitive, affective, and motivational processes, particularly where the aim is to produce morally better decisions or behavior. In this article, we draw attention to what is arguably a more worrying possibility: that pharmaceuticals currently in widespread therapeutic use are already having unintended effects on these processes, and thus on moral decision making and morally significant behavior. We review current evidence on the moral effects (...) of three widely used drugs or drug types: propranolol, selective serotonin reuptake inhibitors, and drugs that effect oxytocin physiology. This evidence suggests that the alterations to moral decision making and behavior caused by these agents may have important and difficult-to-evaluate consequences, at least at the population level. We argue that the moral effects of these and other widely used pharmaceuticals warrant further empirical research and ethical analysis. (shrink)

The rightness and wrongness of actions fits on a continuous scale. This fits the way we evaluate actions chosen among a diverse range of options, even though English speakers don’t use the words “righter” and “wronger”. I outline and defend a version of scalar consequentialism, according to which rightness is a matter of degree, determined by how good the consequences are. Linguistic resources are available to let us truly describe actions simply as right. Some deontological theories face problems in accounting (...) for degrees of rightness, as they don't invoke continuous parameters among the right-making features of action. (shrink)

This essay defends a strong version of the Humean theory of motivation on which desire is necessary both for motivation and for reasoning that changes our desires. Those who hold that moral judgments are beliefs with intrinsic motivational force need to oppose this view, and many of them have proposed counterexamples to it. Using a novel account of desire, this essay handles the proposed counterexamples in a way that shows the superiority of the Humean theory. The essay addresses the classic (...) objection that the Humean theory cannot explain the feeling of obligation, Stephen Darwall's example of motivationally potent reasoning that is not based on preexisting desires, Thomas Scanlon's criticism that the Humean theory fails to account for the structure and phenomenology of deliberation, and the phenomenon of akrasia as discussed by John Searle. In each case a Humean account explains the data at least as thoroughly as opposing views can, while fitting within a simpler total account of how we deliberate and act. (shrink)

We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.

Recent work in neuroimaging suggests that some patients diagnosed as being in the persistent vegetative state are actually conscious. In this paper, we critically examine this new evidence. We argue that though it remains open to alternative interpretations, it strongly suggests the presence of consciousness in some patients. However, we argue that its ethical significance is less than many people seem to think. There are several different kinds of consciousness, and though all kinds of consciousness have some ethical significance, different (...) kinds underwrite different kinds of moral value. Demonstrating that patients have phenomenal consciousness — conscious states with some kind of qualitative feel to them — shows that they are moral patients, whose welfare must be taken into consideration. But only if they are subjects of a sophisticated kind of access consciousness — where access consciousness entails global availability of information to cognitive systems — are they persons, in the technical sense of the word employed by philosophers. In this sense, being a person is having the full moral status of ordinary human beings. We call for further research which might settle whether patients who manifest signs of consciousness possess the sophisticated kind of access consciousness required for personhood. (shrink)

Propositionalism is the view that the contents of intentional attitudes have a propositional structure. Objectualism opposes propositionalism in allowing the contents of these attitudes to be ordinary objects or properties. Philosophers including Talbot Brewer, Paul Thagard, Michelle Montague, and Alex Grzankowski attack propositionalism about such attitudes as desire, liking, and fearing. This article defends propositionalism, mainly on grounds that it better supports psychological explanations.

Many people who have achieved a certain age, live in a certain sense of bewilderment. How can people, companies, and countries do the things they do? How can our neighbors, our co-workers, our bosses, our employees, and our family members do the things that they do? How can the opposing political party do the things they do? Why are things so unfair? It just doesn’t make sense! -/- Many people think that if we just got together and talked it through, (...) we can resolve our differences. But man has been talking for thousands of years. That isn’t working. This paper is not about resolving those differences. It is about understanding why those differences exist. (shrink)

The philosophical world has long attempted to reconcile determinism with the notion of free will. Everything we have observed above the sub-atomic level appears to operate in a strictly causal relationship with other objects. This appears to indicate that all events are completely causally determined. On the other hand, we each clearly sense that we are more than mere causal automatons. We make choices, and we exercise free will, and these choices affect our future. Thus, the notions of determinism and (...) free will are at odds. This paper will thoroughly reconcile those two notions. (shrink)

This essay presents an ideal for modern Western romantic love.The basic ideas are the following: people want to form a distinctive sort of plural subject with another, what Nozick has called a "We", they want to be loved for properties of certain kinds, and they want this love to establish and sustain a special sort of commitment to them over time.

This essay explores the notion of truth and how it is relative to the available facts.

Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...) work in numerical cognition and ontogenetic studies. (shrink)

This paper explores connections between theories of morality and theories of properties. It argues that (1) moral realism is in tension with predicate, class and mereological nominalism; (2) moral non-naturalism is incompatible with standard versions of resemblance nominalism, immanent realism and trope theory; and (3) the standard semantic arguments for property realism do not support moral realism. I also raise doubts about trope-theoretic explanations of moral supervenience and argue against one version of the principle that we should accept theories that (...) maintain neutrality. (shrink)

This essay outlines the different forms of meditation, how they are performed, and what their benefits are.

I argue that one intends that ϕ if one has a desire that ϕ and an appropriately related means-end belief. Opponents, including Setiya and Bratman, charge that this view can't explain three things. First, intentional action is accompanied by knowledge of what we are doing. Second, we can choose our reasons for action. Third, forming an intention settles a deliberative question about what to do, disposing us to cease deliberating about it. I show how the desire- belief view can explain (...) why these phenomena occur when they occur, and why they don't when they don't. (shrink)

Spinoza's attributes are explained in a simple and clear manner.

In this chapter, we argue for three theses: (1) we lack the power to form beliefs at will (i.e., directly); at very least, we lack the power to form at will beliefs of the kind that proponents of doxastic voluntarism have in mind; but (2) we possess a propensity to form beliefs for non-epistemic reasons; and (3) these propensities—once we come to know we have them—entail that we have obligations similar to those we would have were doxastic voluntarism true. Specifically, (...) we will argue that we have obligations to avoid triggering these propensities to form beliefs that are unwarranted or even immoral. (shrink)

This chapter considers the nature of imagination and belief, exploring how deeply these two states of mind differ. It first addresses a range of cognitive and motivational differences between imagination and belief which suggest that they're fundamentally different states of mind. Then it addresses imaginative immersion, delusions, and the different norms we apply to the two mental states, which some theorists regard as providing support for a more unified picture of imagination and belief.

This paper argues that a counterpart-theoretic treatment of events, combined with a counterfactual theory of causation, can help resolve three puzzles from the causation literature. First, CCT traces the apparent contextual shifts in our causal attributions to shifts in the counterpart relation which obtains in those contexts. Second, being sensitive to shifts in the counterpart relation can help diagnose what goes wrong in certain prominent examples where the transitivity of causation appears to fail. Third, CCT can help us resurrect the (...) much-maligned fragility response to the problems of late pre-emption by understanding fragility in counterpart-theoretic terms. Some reasons to prefer this CCT approach to rivals are discussed. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...) to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions. (shrink)

It is commonly assumed that causation is transitive and in this paper I aim to reconcile this widely-held assumption with apparent evidence to the contrary. I will discuss a familiar approach to certain well-known counterexamples, before introducing a more resistant sort of case of my own. I will then offer a novel solution, based on Yablo’s proportionality principle, that succeeds in even these more resistant cases. There is a catch, however. Either proportionality is a constraint on which causal claims are (...) true, and the solution works, or it is not and causation is not transitive after all. I will argue that the first horn has unacceptable consequences and should be rejected, but that the second horn is less costly than it might initially appear. (shrink)

This paper argues that qualia share their physical correlates' locations. The first premise comes from the theory of relativity: If something shares a time with a physical event in all reference frames, it shares that physical event’s location. The second premise is that qualia share times with their correlates in all reference frames. Having qualia and correlates share locations makes relations between them easier to explain, improving both physicalist and dualist theories.

Some philosophers (including Urmson, Humberstone, Shah, and Velleman) hold that believing that p distinctively involves applying a norm according to which the truth of p is a criterion for the success or correctness of the attitude. On this view, imagining and assuming differ from believing in that no such norm is applied. I argue against this view with counterexamples showing that applying the norm of truth is neither necessary nor sufficient for distinguishing believing from imagining and assuming. Then I argue (...) that the different functional properties of these mental states are enough to distinguish them, and that norm-application doesn't help us draw the functional distinctions. (shrink)

Here I advance a unified account of the structure of the epistemic normativity of assertion, action, and belief. According to my Teleological Account, all of these are epistemically successful just in case they fulfill the primary aim of knowledgeability, an aim which in turn generates a host of secondary epistemic norms. The central features of the Teleological Account are these: it is compact in its reliance on a single central explanatory posit, knowledge-centered in its insistence that knowledge sets the fundamental (...) epistemic norm, and yet fiercely pluralistic in its acknowledgment of the legitimacy and value of a rich range of epistemic norms distinct from knowledge. Largely in virtue of this pluralist character, I argue, the Teleological Account is far superior to extant knowledge-centered accounts. (shrink)

Ethical reductionism is the best version of naturalistic moral realism. Reductionists regard moral properties as identical to properties appearing in successful scientific theories. Nonreductionists, including many of the Cornell Realists, argue that moral properties instead supervene on scientific properties without identity. I respond to two arguments for nonreductionism. First, nonreductionists argue that the multiple realizability of moral properties defeats reductionism. Multiple realizability can be addressed in ethics by identifying moral properties uniquely or disjunctively with properties of the special sciences. Second, (...) nonreductionists argue that irreducible moral properties explain empirical phenomena, just as irreducible special-science properties do. But since irreducible moral properties don't successfully explain additional regularities, they run the risk of being pseudoscientific properties. Reductionism has all the benefits of nonreductionism, while also being more secure against anti-realist objections because of its ontological simplicity. (shrink)

I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the syllogistic is (...) a fragment of my system of Core Logic. Then I introduce my main innovation: the use of binary quantifiers, governed by introduction and elimination rules. The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. I conclude with some comments and results about grammatical generativity, ecthesis, perfect validity, skeletal validity and Aristotle's chain principle. (shrink)

Response to commentary. We are grateful to Crockett and Craigie for their interesting remarks on our paper. We accept Crockett’s claim that there is a need for caution in drawing inferences about patient groups from work on healthy volunteers in the laboratory. However, we believe that the evidence we cited established a strong presumption that many of the patients who are routinely taking a medication, including many people properly prescribed the medication for a medical condition, have morally significant aspects of (...) their cognition and behavior modified in a way that is unintended and may sometimes be unwelcome. Crockett notes that in some cases the effects of long-term drug use may differ, sometimes markedly, from the effects of short-term use. However, if acute use of a drug affects a neural system involved in mediating moral cognition or behavior, this nevertheless provides some evidence that chronic use of the drug may affect that same system and thus have morally significant effects. It is also plausible, in some cases, that an acute moral effect would give rise to a chronic moral effect via cognitive mechanisms. ... (shrink)

Philosophers from Hart to Lewis, Johnston and Bennett have expressed various degrees of reservation concerning the doctrine of double effect. A common concern is that, with regard to many activities that double effect is traditionally thought to prohibit, what might at first look to be a directly intended bad effect is really, on closer examination, a directly intended neutral effect that is closely connected to a foreseen bad effect. This essay examines the extent to which the commonsense concept of intention (...) supports a reasonably consistent and coherent application of double effect. Two important conclusions are these: (1) a number of traditionally proscribed activities involve a kind of “targeting” of innocents that can be taken to exhibit a direct intention to harm them; (2) a direct intention to harm need not involve a desire to harm in any ordinary sense of the latter expression. (shrink)

This paper applies the theory of teleosemantics to the issue of moral content. Two versions of teleosemantics are distinguished: input-based and output-based. It is argued that applying either to the case of moral judgements generates the conclusion that such judgements have both descriptive (belief-like) and directive (desire-like) content, intimately entwined. This conclusion directly validates neither descriptivism nor expressivism, but the application of teleosemantics to moral content does leave the descriptivist with explanatory challenges which the expressivist does not face. Since teleosemantics (...) ties content to function, the paper also offers an account of the evolutionary function of moral judgements. (shrink)

Bayesian models of legal arguments generally aim to produce a single integrated model, combining each of the legal arguments under consideration. This combined approach implicitly assumes that variables and their relationships can be represented without any contradiction or misalignment, and in a way that makes sense with respect to the competing argument narratives. This paper describes a novel approach to compare and ‘average’ Bayesian models of legal arguments that have been built independently and with no attempt to make them consistent (...) in terms of variables, causal assumptions or parameterization. The approach involves assessing whether competing models of legal arguments are explained or predict facts uncovered before or during the trial process. Those models that are more heavily disconfirmed by the facts are given lower weight, as model plausibility measures, in the Bayesian model comparison and averaging framework adopted. In this way a plurality of arguments is allowed yet a single judgement based on all arguments is possible and rational. (shrink)

Awarding rights to rivers, forests, and other environmental entities (EEs) is a new and increasingly popular approach to environmental protection. The distinctive feature of such rights of nature (RoN) legislation is that direct duties are owed to the EEs. This paper presents a novel rebuttal of the strongest argument against RoN: the no interest argument. The crux of this argument is that because EEs are not sentient, they cannot possess the kinds of interests necessary to ground direct duties. Therefore, they (...) cannot be legitimate rights-bearers. After considering and rejecting standard responses to this argument, the paper challenges its fundamental assumption: that rights-correlative duties must be grounded in the interests of the rights-bearer. The paper then presents the RoN critic with a dilemma. The critic must either accept that EEs are legitimate rights-bearers, or delegitimise many well-established rights-bearers along with EEs. Either way, the no interest argument loses its force. (shrink)

Multiverse Views in set theory advocate the claim that there are many universes of sets, no-one of which is canonical, and have risen to prominence over the last few years. One motivating factor is that such positions are often argued to account very elegantly for technical practice. While there is much discussion of the technical aspects of these views, in this paper I analyse a radical form of Multiversism on largely philosophical grounds. Of particular importance will be an account of (...) reference on the Multiversist conception, and the relativism that it implies. I argue that analysis of this central issue in the Philosophy of Mathematics indicates that Radical Multiversism must be algebraic, and cannot be viewed as an attempt to provide an account of reference without a softening of the position. (shrink)

This paper outlines a new metasemantic theory of moral reason statements, focused on explaining how the reasons thus stated can be inescapable. The motivation for the theory is in part that it can explain this and other phenomena concerning moral reasons. The account also suggests a general recipe for explanations of conceptual features of moral reason statements. (Published with Open Access.).

This paper is a concise survey of recent expressivist theories of discourse, focusing on the ethical case. For each topic discussed recent trends are summarised and suggestions for further reading provided. Issues covered include: the nature of the moral attitude; ‘hybrid’ views according to which moral judgements express both beliefs and attitudes; the quasi-realist programmes of Simon Blackburn and Allan Gibbard; the problem of creeping minimalism; the nature of the ‘expression’ relation; the Frege-Geach problem; the problem of wishful thinking; the (...) role of moral intuitions; expressivism in aesthetics. (shrink)

In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor (...) sufficiently precise. Instead, we suggest that the process of justification in set theory should not be thought of as neatly divisible in this way, but should rather be understood as a conceptually indivisible notion linked to the goal of explanation. (shrink)

This paper examines the prospects for a conceptual or functional role theory of moral concepts. It is argued that such an account is well-placed to explain both the irreducibility and practicality of moral concepts. Several versions of conceptual role semantics for moral concepts are distinguished, depending on whether the concept-constitutive conceptual roles are wide or narrow normative or non-normative and purely doxastic or conative. It is argued that the most plausible version of conceptual role semantics for moral concepts involves only (...) ‘narrow’ conceptual roles, where these include connections to motivational, desire-like, states. In the penultimate section it is argued, contrary to what Wedgwood, Enoch and others have claimed, that such an account of moral concepts cannot plausibly be combined with the claim that moral concepts refer to robust properties. (Published with Open Access.). (shrink)

Trust not only disposes us to feel betrayed, trust can be betrayed. Understanding what a betrayal of trust is requires understanding how trust can ground an obligation on the part of the trusted person to act specifically as trusted. This essay argues that, since trust cannot ground an appropriate obligation where there is no prior obligation, a betrayal of trust should instead be conceived as the violation of a trust-based obligation to respect an already existing obligation. Two forms of trust (...) are evaluated for their potential to ground such a second-order obligation. One form counts as a gift to the trusted person only because it does not involve an expectation of trustworthiness; the other form cannot count as a gift but confers an honor because it does include an expectation of trustworthiness. Only trust that confers an honor generates a second-order obligation whose violation would be a betrayal of trust. -/- . (shrink)

In this paper we sketch a new version of aesthetic expressivism. We argue that one advantage of this view is that it explains various putative norms on the formation and revision of aesthetic judgement. We begin by setting out our proposed explananda and a sense in which they can be understood as governing the correct response to putative higher-order evidence in aesthetics. We then summarise some existing discussions of expressivist attempts to explain these norms, and objections raised to them. This (...) will allow us to identify the pitfalls that a good expressivist explanation needs to avoid. Finally, we sketch our preferred version of aesthetic expressivism which includes as a crucial part a hypothesis concerning the distinctive expressive function of aesthetic practice. We then consider how this theory can explain the putative aesthetic norms whilst avoiding the previous objections. (shrink)

This paper presents two cases demonstrating that theories allowing the environment to partially determine the content of moral concepts provide incorrect truth-conditions for moral terms. While typical Moral Twin Earth cases seek to establish that these theories fail to account formoral disagreement, neither case here essentially involves interpersonal disagreement. Both involve a single person retaining moral beliefs despite recognizing actual or potential mismatches with the purportedly content-determining facts. This lets opponents of such theories grant objections that standard Moral Twin Earth (...) cases fail to demonstrate disagreement, and argue more straightforwardly that they generate implausible truth-conditions for moral claims. (shrink)

This essay makes a number of distinctions between the motives of love and of duty, and argues that ideally they act in concert so as to generate constancy in loving relations. The essay revolves around a case in which a husband or wife is tempted to infidelity. It is argued that resistance to the temptation is optimally grounded in love for the spouse rather than simply in a duty to resist initiated perhaps through promise or vow. This is not, however, (...) to undermine altogether the significance of promises of this sort; it is rather to put a proper emphasis on the sentiment of love as an effective spring to action and to suggest that the sentiment itself ideally brings a past promise or vow of fidelity into present relief in a choice situation. (shrink)

Let's suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes---you've prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that there are some considerations based on a formal notion of restrictiveness which suggest that it is restrictive to hold that there are uncountable sets.

This paper presents the Universality Argument that pleasure is goodness. The first premise defines goodness as what should please all. The second premise reduces 'should' to perceptual accuracy. The third premise invokes a universal standard of accuracy: qualitative identity. Since the pleasure of all is accurate solely about pleasure, pleasure is goodness, or universal moral value. The argument proceeds from a moral sense theory that analyzes moral concepts as concerned with what all should hope for, feel guilty about, and admire. (...) This requires rejecting practical anti-empiricism, the view that moral judgment concerns empirically inaccessible norms governing action. (shrink)

I present a novel objection to fine-tuning arguments for God's existence. On any values of the physical constants, the psychophysical laws could be set to permit intelligent and happy beings, so the specific values of the physical constants in our world provide little evidence for God's existence. For example, even if the physical constants didn't allow carbon or any atoms larger than hydrogen, the psychophysical laws could be set so that charge is sufficient to realize romantic desire. Then every hydrogen (...) atom would be a proton and electron in love. (shrink)

Causal exclusion arguments are taken to threaten the autonomy of the special sciences, and the causal efficacy of mental properties. A recent line of response to these arguments has appealed to “independently plausible” and “well grounded” theories of causation to rebut key premises. In this paper I consider two papers which proceed in this vein and show that they share a common feature: they both require causes to be proportional to their effects. I argue that this feature is a bug, (...) and one that generalises: any attempt to rescue the autonomy of the special sciences, or the efficacy of the mental, from exclusion worries had better not look to proportionality for help. (shrink)

Let mathematical justification be the kind of justification obtained when a mathematician provides a proof of a theorem. Are Gettier cases possible for this kind of justification? At first sight we might think not: The standard for mathematical justification is proof and, since proof is bound at the hip with truth, there is no possibility of having an epistemically lucky justification of a true mathematical proposition. In this paper, I argue that Gettier cases are possible (and indeed actual) in mathematical (...) reasoning. By analysing these cases, I suggest that the Gettier phenomenon indicates some upshots for actual mathematical practice. (shrink)

Actions performed in a state of automatism are not subject to moral evaluation, while automatic actions often are. Is the asymmetry between automatistic and automatic agency justified? In order to answer this question we need a model or moral accountability that does justice to our intuitions about a range of modes of agency, both pathological and non-pathological. Our aim in this paper is to lay the foundations for such an account.

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...) and meta-theoretic properties when comparing first-order and second-order logic. (shrink)

Epistemic akrasia can be rational. I consider a lonely pragmatist who believes that her imaginary friend doesn’t exist, and also believes on pragmatic grounds that she should believe in him. She rationally believes that her imaginary friend doesn’t exist, rationally follows various sources of evidence to the view that she should believe in him to end her loneliness, and rationally holds these attitudes simultaneously. Evidentialism suggests that her ambivalent epistemic state is rational, as considerations grounded in the value of truth (...) justify her beliefs. (shrink)

It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...) the continuum is a proper class. We examine several principles based on maximality considerations in this framework, and show how some (namely Ordinal Inner Model Hypotheses) enable us to incorporate standard set theories (including ZFC with large cardinals added). We conclude that the systems considered raise questions concerning the foundational purposes of set theory. (shrink)