Fool-proof proofs of God?

Summary Two claims have been explored, the first, that fool-proof proofs of the sort that there could be if there were a God like the God of Abraham, Isaac and Jacob are not to be expected, on good religious grounds (a claim I found wanting); and second, that there cannot be philosophical proofs of God which work beyond reasonable doubt.The argument that there cannot be philosophical proofs beyond a reasonable doubt is supported by an examination of some of the fundamental issues in the traditional discussions of proofs for God's existence, and by claims about the relativity of methodological rules to world-views which, I maintain, the traditional discussions indicate. I do not claim to have proved that relativity, only to have illustrated the claim that it is there.It is my further opinion, but I do not claim really to have proved it, that the failure of religious excuses for the lack of public demon strations constitutes a good reason for concluding that there is no God of the sort described as the God of Abraham, Isaac and Jacob; hence that if there is a God, it must be the God of the philosophers. However I admit that there might be sufficient hidden reasons which would offer persuasive excuses for the God of the ordinary believer.Lastly, I have made some comments about what I think is the more valuable way to view the proofs for God. Such an interpretation does justice to the otherwise baffling and continual philosophical disagreements better than rival theories. It is time we take these disagreements with utmost seriousness, and one can hardly do that while treating basic metaphysical arguments as fool-proof proofs.Readers of the literature on proofs will recognize many of the historical and current discussions on which comment is being made. To provide sources for all the comments would be not only cumbersome but impossible because they are found in so many different places and are not the property of any one in particular.     

The heart of consequentialism

Conclusion My goal in this paper was to argue that consequentialism should be construed as the view that the better a state of affairs the better the action that produces it and the more moral reason there is to perform that action. I call this view BETTER. I tried to show that treating this rather than a claim about the right as crucial to consequentialism had significant advantages. Finally, I demonstrated the relevance of my account to the issue of whether consequentialism is correct. It doesn't provide a conclusive answer to that question (we should be suspicious if it did) but allows us to see it in a new light and hopefully, suggests new and fruitful ways to tackle it.I am grateful to Daniel Howard-Snyder for help with this paper and to David McNaughton and Piers Rawling for correspondence regarding some of their views. Thanks also to an anonymous referee atPhilosophical Studies for comments.     

What is a Correspondence Theory of Truth?

It is often thought that instances of the T-schema such as snow is white is true if and only if snow is white state correspondences between sentences andthe world, and that therefore such sentences play a crucial role in correspondence theories oftruth. I argue that this assumption trivializes the correspondence theory: even a disquotationaltheory of truth would be a correspondence theory on this conception. This discussionallows one to get clearer about what a correspondence theory does claim, and toward the end of thepaper I discuss what a true correspondence theory of truth would involve.     

Quark quantum numbers and the problem of microphysical observation

The main question addressed in this essay is whether quarks have been observed in any sense and, if so, what might be meant by this use of the term, observation. In the first (or introductory) section of the paper, I explain that well-known researchers are divided on the answers to these important questions. In the second section, I investigate microphysical observation in general. Here I argue that Wilson's analogy between observation by means of high-energy accelerators and observation by means of microscopes is misleading, for at least three reasons. Moreover, so long as high-energy observation is accomplished by means of spark or bubble chambers, then sentences about these observations do not meet Maxwell's criterion, that observation statements are quickly decidable. I argue, however, that this criterion is not a good norm for what is observable in high-energy physics, both because it would result in our describing a great many allegedly observed particle events as unobserved or theoretical, and because it fails to distinguish the reasons why some observation statements might not be quickly decidable. Most important, Maxwell's criterion fails because, contrary to Hanson's analysis, it presupposes that seeing does not involve both seeing as and seeing that.With this background concerning what is meant by general microphysical observation, in the third section of the essay, I discuss what might be meant by a more particular type of observation, that of the quark via scattering events. I employ Feinberg's distinction concerning observation of manifest, versus existent, particles and claim that the alleged indirect observation of quarks as existent particles is really based on a retroductive inference. I explain which premise in the retroductive argument appears most open to the charge of being theoretical (in a damaging sense) and less substantiated by observation.In the fourth section of the essay, I discuss two different types of observation of quarks: detection of overt and hidden quark charm. Although this is only one illustration of alleged quark observation, I argue that the difference between the two types of observation of charm provides insight into which observations are less theoretical in a damaging sense. I claim that this case reveals, paradoxically, that an observation may be both more theory laden, but less theoretical in a damaging sense; that there is no real opposition between theory and observation (which is nothing new); that it might be wrong to think of an observation-theory continuum; and that who discovered charmed quarks is a function of what is meant by observation.Finally, in the fifth and concluding section of the paper, I suggest that theoretical terms are essentially dynamic and that observations never really verify a theory. I close by suggesting why microphysical observations are becoming more theoretical, but not necessarily in a damaging sense. Both cosmological and microphysical observation demand that what is observed be seen in a very abstract way.     

Ethical Phenomenology and Metaethics

In recent times, comments have been made and arguments advanced in support of metaethical positions based on the phenomenology of ethical experience – in other words, the feel that accompanies our ethical experiences. In this paper I cast doubt on whether ethical phenomenology supports metaethical positions to any great extent and try to tease out what is involved in giving a phenomenological argument. I consider three such positions: independent moral realism (IMR), another type of moral realism – sensibility theory – and noncognitivism. Phenomenological arguments have been used in support of the first two positions, but my general claim is that ethical phenomenology supports no metaethical position over any other.I discuss two types of phenomenological argument that might be offered in support of different types of moral realism, although I couch my debate in terms of IMR. The first argument asserts that ethical properties are not experienced in the way that rivals to IMR say we experience them. Against this I claim that it is odd to think that one could experience ethical properties as any metaethical theory characterizes them. The second argument is more complicated: the general thought is that an adequate metaethical theory should not distort our ethical experience unduly. I consider one aspect of our ethical experience – that there is some ethical authority to which our judgements answer – in order to illustrate this idea. I discuss why IMRealists might think that this phenomenon supports their position. Against them I claim that other metaethical positions might be able to accommodate the phenomenon of ethical authority. Even if they cannot, then, secondly, I argue that there are other aspects of our ethical experience that sit more naturally with other metaethical positions. Hence, one cannot argue that ethical phenomenology as a whole supports one theory over any others.     

On the ontology of branching quantifiers

Conclusion Still, some may still want to say it. If so, my replies may gain nothing better than a stalemate against such persistence, though I can hope that earlier revelations will discourage others from persisting. But two replies are possible. Both come down, one circuitously, to an issue with us from the beginning: whether the language of the right side of (10) is suspect. For if (10) is to support instances for (6) which are about objects, that clause must itself be about objects. (These would be ones assigned by variants of I it mentions to constants it mentions.) Yet Barwise and I would call it implicitly about functions. Ironically, the discussion surrounding (10), hoping to settle that issue, could only do so if the issue were already settled, revealing decisively the ontology of (10). If irritating, this is also inevitable, given the Tarskian spirit of the ensivioned semantics for QLB.A second reply begins by noting that a QLB semantics which implies (10) cannot simply be assumed. Even a QL semantics augmented to imply (11) is not trivial to frame, as I will let readers confirm. On the QLB project, Barwise comments thus:It is not possible to explain the meaning of an essential use of branching quantification ... inductively, by treating one quantifier at a time in a first-order fashion. Some use of higher-type abstract objects is essential. (BQE75)But believers in a modest ontology for QLB can claim a non sequitur here. For (10), as they read it, succeeds without mentioning abstract objects, though not in the one quantifier at a time way which Barwise rightly finds impossible. This is not yet to say the same about a QLB semantics implying (10). But that too can be said, as it happens, with as good a conscience as with (10). A suitable treatment can begin by somehow linearizing non QL sentences like (6). Still assuming prefixes whose rows each consist, speaking loosely, of n universal quantifiers followed by a single existential, we could simply line up these rows in any order, with unique deconcatenatability being assured. From then on, it gets both tedious and complex. A full syntax is essential, and some surprising categories arose in mine. I will spare readers all details, except to say that one can indeed treat one quantifier at a time, if not in first-order fashion: schematic rules for treating n quantifiers at once can be eschewed. Unsurprisingly, heavy use is made of the depending only on idiom seen in (10). Nor does it surprise me that this semantics can succeed, with that idiom available. Roughly, if open talk about functions works in a semantics for QLF, what I read as implicit talk about them should work in a semantics for QLB.So even from a bare sketch, we can see that this new semantics settles nothing. It just leads back to the stalemate. Barwise and I will read crucial clauses as talking implicitly about functions, but this general charge against an idiom is equally deniable wherever the idiom occurs: in a reading for (6), say, or in the metalanguage can hardly repress a motherhood slogan: better dead than obscurely read. But that just denies the denial, unhelpfully. A better comment is the reminder that the claim stays alive only in a form which no one has ever imagined for it. The QLB quantifiers that cannot be shown not to range over objects are not the items anyone would ever have pointed to in illustrating the unkillable claim.

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Against Global Egalitarianism

This article attacks the view that global justice should be understood in terms of a global principle of equality. The principle mainly discussed is global equality of opportunity – the idea that people of similar talent and motivation should have equivalent opportunity sets no matter to which society they belong. I argue first that in a culturally plural world we have no neutral way of measuring opportunity sets. I then suggest that the most commonly offered defences of global egalitarianism – the cosmopolitan claim that human lives have equal value, the argument that a persons nationality is a morally arbitrary characteristic, and the more empirical claim that relationships among fellow-nationals are no longer special in a way that matters for justice – are all defective. If we fall back on the idea of equality as a default principle, then we have to recognize that pursuing global equality of opportunity systematically would leave no space for national self-determination. Finally, I ask whether global inequality might be objectionable for reasons independent of justice, and argue that the main reason for concern is the inequalities of power that are likely to emerge in a radically unequal world.I am very grateful to Gillian Brock and Kok-Chor Tan for their helpful comments on an earlier draft of this article.     

Tooley's solution to the inference problem

Conclusion Tooley's speculative theory, I have tried to show, is beset with difficulties. I warned that this theory threatens to fail in its goal of illuminating the possible nature of a necessitation relation if it employs radical principles about parts and wholes and universals. Secondly, I argued that regardless of how we interpret the crucial phrase existing only as a part of, the speculative theory cannot solve the inference problem without appealing to such radical principles. Finally, I considered and rejected a version of Tooley's speculative theory that attempts to solve the inference problem using the Indiscernibility of Identicals.I conclude that the speculative theory fails. Tooley must fall back to the stipulative theory and live with the lack of an illuminating solution to the inference problem. But this is not to admit defeat. While it would be nice to have a more complete account of its workings, we may view the introduction of the necessitation relation as a theoretical posit, analogous to the positing of subatomic particles in physics to account for various data.I would like to thank Phillip Bricker for his persistent help with this paper. I would also like to thank David Lewis and an anonymous referee for Philosophical Studies for their comments.     

Deontological evidentialism and <Emphasis Type="Italic">ought</Emphasis> implies <Emphasis Type="Italic">can</Emphasis>

Deontological evidentialism is the claim that S ought to form or maintain S’s beliefs in accordance with S’s evidence. A promising argument for this view turns on the premise that consideration c is a normative reason for S to form or maintain a belief that p only if c is evidence that p is true. In this paper, I discuss the surprising relation between a recently influential argument for this key premise and the principle that ought implies can. I argue that anyone who antecedently accepts or rejects this principle already has a reason to resist either this argument’s premises or its role in support of deontological evidentialism.     

Quantum entanglement and nonideal measurements: A critique of Margenau's objections to the projection postulate

I defend the projection postulate against two of Margenau's criticisms. One involves two types of nonideal measurements, measurements that disturb and measurements that annihilate. Such measurements cannot be characterized using the original version of the projection postulate. This is one of the most interesting and powerful objections to the projection postulate since most realistic measurements are nonideal, in Margenau's sense. I show that a straightforward generalization of the projection postulate is capable of handling the more realistic kinds of measurements considered by Margenau. His other objection involves the EPR (Einstein-Podolsky-Rosen) situation. He suggests that there is a significant potential for violations of the no-superluminalsignals requirement of the special theory of relativity, if projections occur in this situation and others like it. He also suggests that what is paradoxical about this situation disappears if the projection postulate is rejected. I show that it is not possible to use measurements on pairs of spatially-separated systems whose states are entangled to transmit information superluminally, and generalize this result to include nonideal measurements. I also show that EPR's dilemma does not really depend on the projection postulate.I would like to thank three anonymous referees, two from Synthese and one from Foundations of Physics, for their critical comments on preliminary versions of this essay, and for bringing to my attention several articles concerning quantum mechanics and the impossibility of faster-than-light communication.     

The myth of the categorical counterfactual

I aim to show that standard theories of counterfactuals are mistaken, not in detail, but in principle, and I aim to say what form a tenable theory must take. Standard theories entail a categorical interpretation of counterfactuals, on which to state that, if it were that A, it would be that C is to state something, not relative to any supposition or hypothesis, but categorically. On the rival suppositional interpretation, to state that, if it were that A, it would be that C is to state that it would be that C relative to the supposition that it were that A. The two interpretations make incompatible predictions concerning the correct evaluation of counterfactuals. I argue that the suppositional interpretation makes the correct prediction.

Against liberty

Conclusion There are no private particular actions that should be altogether free of social interference. No absolute distinction can be made between types of actions affecting others and those affecting only the agent. Relative to a purpose in formulating an act of law, for instance, such a distinction can, however, be made. The idea of social freedom could therefore be thought to imply that even if there are no absolutely private particular actions, and even if society could interfere for any purpose to regulate the actions of the individual, not any reason for such interference is acceptable from the point of view of liberty. Acts of law should not be made unnecessarily inclusive with respect to their purpose and they should be designed to further public security. Not even in this weak formulation, however, can the principle of social liberty be defended against moral criticism. Some illiberal laws, in this sense, should after all be passed. Examples can be found in taxation law.The only reasonable conclusion to draw from all this is that there is no tenable principle of liberty.That there is no tenable principle of liberty does not mean that everything that has been condemned in the name of liberty should now be regarded as right. Many things said to result in a limitation of freedom could be wrong for other reasons. But probably not all of them are. So it will, I think, have some effects on our political views in general, if we accept the conclusion of this essay.     

Contractualism,Person-Affecting Wrongness and the Non-identity Problem

A number of theorists have argued that Scanlon's contractualist theory both "gets around" and "solves" the non-identity problem. They argue that it gets around the problem because hypothetical deliberation on general moral principles excludes the considerations that lead to the problem. They argue that it solves the problem because violating a contractualist moral principle in one's treatment of another wrongs that particular other, grounding a person-affecting moral claim. In this paper, I agree with the first claim but note that all it shows is that the act is impersonally wrong. I then dispute the second claim. On Scanlon's contractualist view, one wrongs a particular other if one treats the other in a way that is unjustifiable to that other on reasons she could not reasonably reject. We should think of person-affecting wronging in terms of the reasons had by the actual agent and the actual person affected by the agent's action. In non-identity cases, interpersonal justifiability is therefore shaped both by the reason to reject the treatment provided by the bad suffered and the reason to affirm the treatment provided by the goods had as a result of existing. I argue it would be reasonable for the actual person to find the treatment justifiable, and so I conclude that Scanlon's contractualist metaethics does not provide a narrow person-affecting solution to the non-identity problem on its own terms. I conclude that the two claims represent a tension within Scanlon's contractualist theory itself.     

Between fiction and reflection: Foucault and the experience-book

Foucault notoriously suggests that his historical analyses are fictions. Commentators typically interpret this claim in a negative light to mean that Foucault's works are not, strictly speaking, true. In this paper, I present a positive interpretation of Foucault's claim, basing my argument on a hitherto marginalized aspect of his work: the experience-book. An experience-book is defined as a use of fiction in the practice of critique with desubjectifying effects. My argument for this interpretation proceeds in three steps. First, to prepare a preliminary account of Foucault's concept of fiction and its effects, I look at Blanchot's ontological interpretation of the work of literature in The Space of Literature. Blanchot, I suggest, provides a template for understanding Foucault's concept of the experience-book. Second, I identify traces of Blanchot's concept of fiction in Foucault's study of Jules Verne, Behind the Fable. I argue that Foucault's critique of fiction, in this paper, anticipates and prefigures his later use of fiction in the practice of critique. Third, pursuing this intuition, I develop an interpretation of Discipline and Punish understood as a use of fiction and experience-book. This interpretation provides a new, immanent perspective on Foucault's critique, and mitigates the epistemological skepticism of the claim that his works are fictions.     

Duties to the Distant: Aid, Assistance, and Intervention in the Developing World

In his classic article, Famine, Affluence, and Morality (Philosophy and Public Affairs 1 (1972), pp. 229–243), Peter Singer claimed that affluent people in the developed world are morally obligated to transfer large amounts of resources to poor people in the developing world. For present purposes I will not call Singers argument into question. While people can reasonably disagree about exactly how demanding morality is with respect to duties to the desperate, there is little question in my mind that it is much more demanding than common sense morality or our everyday behavior suggests. Even someone who disagrees with this might still find some interest in seeing what a demanding morality would imply for well-off residents of the rich countries of the world. I proceed in the following way. First, I survey humanitarian aid, development assistance, and intervention to protect human rights as ways of discharging duties to the desperate. I claim that we should be more cautious about such policies than is often thought. I go on to suggest two principles that should guide our actions, based on an appreciation of our roles, relationships, and the social and political context in which we find ourselves.     

The foundations of epistemological probability

Epistemological probability is the kind of probability relative to a body of evidence. Many philosophers, including Henry Kyburg and Roderick Chisholm, hold that all epistemological probabilities reflect a relation between an evidential body of propositions and other propositions. But this article argues that some epistemological probabilities for empirical propositions must be relative to non-propositional evidence, specifically the contents of non-propositional perceptual states. In doing so, the article distinguishes between internalism and externalism regarding epistemological probability, and argues for a version of awareness internalism. The article draws three main concluding lessons. First, epistemological probability is not to be identified with the sort of objective, experience-independent probability that is familiar from statistical and propensity interpretations of probability. Second, it is doubtful that epistemological probability is measurable, in any useful way, by real numbers, even if it admits of comparative assessments. Third, contrary to the familiar claim of C. I. Lewis, epistemological probability should not be viewed as requiring a basis of certainty.     

The explanatory power of local miracle compatibilism

Local miracle compatibilists claim that we are sometimes able to do otherwise than we actually do, even if causal determinism obtains. When we can do otherwise, it will often be true that if we were to do otherwise, then an actual law of nature would not have been a law of nature. Nevertheless, it is a compatibilist principle that we cannot do anything that would be or cause an event that violates the laws of nature. Carl Ginet challenges this nomological principle, arguing that it is not always capable of explaining our inability to do otherwise. In response to this challenge, I point out that this principle is part of a defense against the charge that local miracle compatibilists are committed to outlandish claims. Thus it is not surprising that the principle, by itself, will often fail to explain our inability to do otherwise. I then suggest that in many situations in which we are unable to do otherwise, this can be explained by the compatibilist’s analysis of ability, or his criteria for the truth of ability claims. Thus, the failure of his nomological principle to explain the falsity of certain ability claims is no strike against local miracle compatibilism.     

A priori judgments and the argument from design

Conclusions At the outset of this discussion, I undertook to present an argument from design which would follow Swinburne's example in making use of a priori judgments, while avoiding some of the objections which have been posed in response to his treatment of these issues. So we need to ask: how does this approach to the question of design compare with Swinburne's?Swinburne argues that a chaotic world is a priori more likely than an ordered world: this consideration provides one central reason, on his account, for giving an explanation of some sort for the world's regularity. The other central argument he advances for this claim is the argument from analogy (in terms of the coins) which we noted earlier. The approach I have taken offers an alternative route to this same conclusion. In particular, it substitutes the simpler a priori judgments recorded in (i) and (ii) for the rather difficult and contentious claim that chaos is a priori more likely than order. In place of this claim, I have offered the judgment that order, or recurrence, is more likely given the activity of a common source or common kind of source than otherwise: this proposal does not commit us to a view either way on the question of whether order is a priori likely per se. Moreover, in place of Swinburne's analogical argument, I have offered an a priori approach, with the advantages I have noted.Given that recurrence is to be explained, we might ask: why offer an explanation in terms of design? On this point, Swinburne argues, for instance, that no other explanation of temporal regularity is even possible a priori. Again, the a priori principles which I have used, in (iv) and (v), may be less ambitious, but at the same time more persuasive. In support of this same idea, Swinburne also cites various ideas to do with the predictive power of the idea of design. I have tried to bring out the role of this sort of consideration in terms of my principle (v). Principle (iv) has no place in Swinburne's account, in view of his reliance on the principle of simplicity as a measure of prior probability.Lastly, we may ask: if we are to cite a designer, are there reasons for attributing to this agent more powers than are needed for the production of the effect to be explained? On this point, Swinburne cites the principle of simplicity. Again, my approach avoids what has proved to be a relatively controversial judgment about the nature of a priori probabilities, offering in place of the principle of simplicity the less ambitious principle recorded in (iii). At this point, I have moreover inverted the logical sequence of Swinburne's argument: it seems to me that, in the ways I have indicated, it is helpful to consider the extent of the powers of the source of recurrence before addressing the question of design.In these various ways, I hope I have made good my undertaking to present an argument which avoids some of the controversy surrounding the particular measures of a priori probability which figure in Swinburne's argument. Moreover, I hope that this approach provides an indication of how a priori judgments may function in a relatively unproblematic way within an argument from design, in so far as (i)–(v) are all rather modest proposals. In sum, the argument I have presented is distinguished by its explicit use of the a priori judgments recorded in (i)–(v), by its attempt to buttress in this fashion analogical forms of argument, and by the logical role it gives to the idea that the source of regularity possesses more powers than are required for the production of this effect.Lastly, we might ask: how persuasive is this argument? Of course, the cogency of the idea of design depends upon the balance of debate in other areas of the philosophy of religion, especially upon our ability to provide some account of the existence of evil. In this paper, I have been concerned to argue simply that recurrence by kind provides evidence for design: I have not addressed the question of whether other features of the world provide good evidence against the idea of (benevolent) design. However, if we confine our attention to this one phenomenon, there is it seems to me good evidence for the idea of design, (i) and (ii) suggest that recurrence surely calls for some explanation; (iii), together with the existence in nature of statistical irregularities, suggests that whatever provides this explanation could have brought about other effects besides; and design seems the only clear explanation of why this effect should have been brought about, if (as I have argued) analogies drawn from vegetable and animal reproduction fail, and if we cannot explain the effect satisfactorily by reference to the conditions of observation. Moreover, I have argued that there are reasons for supposing that the probability a priori of design is relatively high in relation to the probability a priori of any rival hypothesis of equivalent predictive power. In brief, this is because the design hypothesis (unlike the hypothesis of theism) can cite an agent of relatively indeterminate power in order to account for the phenomenon to be explained. In this regard, it is less precisely defined than any rival hypothesis of equivalent predictive power. If all of this is so, then as philosophers from early times have supposed, temporal regularity provides the basis for a powerful argument in favour of design. It remains true, of course, that its import can be judged in full only when we have taken into account the relevance of other phenomena, many of which are apparently less favourable to the idea of design.     

The meaningful character of value-language: A critique of the linguistic foundations of emotivism

Conclusion The above arguments have not conclusively demonstrated the existence of value; nor have they sought to. Rather, they have focused primarily on value-language itself: what it is, what it means, and how men use it. In value-judgements, men intend to speak about reality, and not merely to manifest their feelings to influence others. The conceptual character of value-words gives them a formal objectivity lacking in mere manifestations of feeling; the meaning of value-words contains a claim to objectivity arising from the ontological claim to objectivity of value itself.These facts demonstrate conclusively that value-language differs essentially from emotive manifestations of feeling. Therefore, and in contradiction to both Ayer and Stevenson, even the most abstract of value-words can be used to form legitimate, conceptually meaningful value-judgements. As judgements, value-judgements can be true or false, not because of any factual content, but specifically as conceptually meaningful, pure value-judgements.I have deliberately restricted these investigations to consideration of language, without seriously arguing the ontology of value itself. Thereby, I have met the emotivists on their own ground. Even without demonstrating the existence of value, I have shown their analysis of value-language to be flawed. Further, I have identified a unique claim to objectivity in value-language which argues strongly in favor of the real existence of value as its ultimate foundation.For the simplest, most obvious explanation of this claim to objectivity is that it refers to value, which actually exists. That proof is logically the next step in my argument. A good place to begin would be a more careful, detailed analysis of the structure of human responses such as admiration, love, enthusiasm, etc., seeking to determine what they ontologically presuppose. Proof of the real existence of value would demonstrate the ontological grounds for the claim to objectivity of value-language. It would show that value-language is rooted in the real world, speaking of reality as it is. This would be the last, and most important sense in which value-language is meaningful and objective.

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Anti-foundation and self-reference

This note argues against Barwise and Etchemendy's claim that their semantics for self-reference requires use of Aczel's anti-foundational set theory, AFA, and that any alternative would involve us in complexities of considerable magnitude, ones irrelevant to the task at hand (The Liar, p. 35).Switching from ZF to AFA neither adds nor precludes any isomorphism types of sets. So it makes no difference to ordinary mathematics. I argue against the author's claim that a certain kind of naturalness nevertheless makes AFA preferable to ZF for their purposes. I cast their semantics in a natural, isomorphism invariant form with self-reference as a fixed point property for propositional operators. Independent of the particulars of any set theory, this form is somewhat simpler than theirs and easier to adapt to other theories of self-reference.I thank John Mayberry for discussions of axiomatics which inspired this paper. Jon Barwise's criticism of an earlier draft improved this one as did an anonymous referee.