This paper is about how to interpret and evaluate purported evidence for predicativism about proper names. I aim to point out some underappreciated thorny issues and to offer both predicativists and non-predicativists some advice about how best to pursue their respective projects. I hope to establish three related claims: that non-predicativists have to posit relatively exotic, though not entirely implausible, polysemic mechanisms to capture the range of data that predicativists have introduced ; that neither referentialism nor extant versions of predicativism (...) can offer a very plausible account of the interpretive possibilities for singular unmodified definite descriptions containing names ; and that the most plausible version of predicativism would treat bare names as non-anaphoric definite descriptions. (shrink)

Among the virtues of relationist approaches to Frege’s puzzle is that they put us in a position to outline structural features of the puzzle that were only implicit in earlier work. In particular, they allow us to frame questions about the relation between the explanatory roles of sense and sameness of sense. In this paper, I distinguish a number of positions about that relation which have not been clearly distinguished. This has a few pay-offs. It allows us to shed light (...) on recent controversies about the ‘essential indexical’, and it also allows us to see what’s at stake between relationists and their opponents. When we see what’s at stake, we can see that we have reason to adopt an account of cognitive significance that incorporates elements of both relationist and Fregean approaches. (shrink)

Frege's puzzle is a fundamental challenge for accounts of mental and linguistic representation. This piece surveys a family of recent approaches to the puzzle that posit representational relations. I identify the central commitments of relational approaches and present several arguments for them. I also distinguish two kinds of relationism—semantic relationism and formal relationism—corresponding to two conceptions of representational relations. I briefly discuss the consequences of relational approaches for foundational questions about propositional attitudes, intentional explanation, and compositionality.

Fregeanism and Relationism are competing families of solutions to Frege’s Puzzle, and by extension, competing theories of propositional representation. My aim is to clarify what is at stake between them by characterizing and evaluating a Relationist argument. Relationists claim that it is cognitively possible for distinct token propositional attitudes to be, in a sense, qualitatively indistinguishable: to differ in no intrinsic representational features. The idea of an ‘intrinsic representational feature’ is not, however, made especially clear in the argument. I clarify (...) it here and, having done so, offer reason to doubt the argument. This will put us in a position to draw some lessons about the relation between object-directed and representation-internal aspects of cognitive significance. (shrink)

Predicativists hold that proper names have predicate-type semantic values. They face an obvious challenge: in many languages names normally occur as, what appear to be, grammatical arguments. The standard version of predicativism answers this challenge by positing an unpronounced determiner in bare occurrences. I argue that this is a mistake. Predicativists should draw a distinction between two kinds of semantic type—underived semantic type and derived semantic type. The predicativist thesis concerns the underived semantic type of proper names and underdetermines a (...) view about the semantic type of bare occurrences. I’ll argue that predicativists should hold that bare names are derived individual-denoting expressions. I end by considering what this result means for the relationship between predicativism and other metalinguistic theories of names. (shrink)

It is commonly argued that the fact that our universe is fine-tuned for life favors both a design hypothesis as well as a non-teleological multiverse hypothesis. The claim that the fine-tuning of this universe supports a non-teleological multiverse hypothesis has been forcefully challenged however by Ian Hacking and Roger White. In this paper we take this challenge even further by arguing that if it succeeds, then not only does the fine-tuning of this universe fail to support a multiverse hypothesis, but (...) it tends to favor a single-universe hypothesis instead. (shrink)

Frege's Puzzle is a founding problem in analytic philosophy. It lies at the intersection of central topics in the philosophy of language and mind: the theory of reference, the nature of propositional attitudes, the nature of semantic theorizing, the relation between semantics and pragmatics, etc. This chapter is an overview of the puzzle and of the space of contemporary approaches to it.

A theme running through Katherine Hawley’s recent works on trust and trustworthiness is that thinking about the relations between these and Miranda Fricker’s notion of testimonial injustice offers a perspective from which we can see several limitations of Fricker’s own account of testimonial injustice. This paper clarifies the aspects of Fricker’s account that Hawley’s criticisms target, focusing on her objections to Fricker’s proposal that its primary harm involves a kind of epistemic objectification and her characterization of testimonial injustice in terms (...) of prejudicial credibility deficits. I also offer an assessment of the potency of Hawley’s objections, concluding that they do point to genuine limitations of Fricker’s account, but that we can appreciate Hawley’s points without adopting her trust-centric approach to testimonial injustice, or her specific commitment-based accounts of trust and trustworthiness. However, in the last section I examine the positive picture of testimonial injustice that emerges from Hawley’s discussion of unequally distributed obstacles to both being trustworthy and maintaining a reputation for trustworthy testimony in her recent book How To Be Trustworthy, considering how this picture contrasts with Fricker’s account and where it might have important affinities with other accounts in the literature. (shrink)

In this chapter, we defend an explanationist version of proper functionalism. After explaining proper functionalism’s initial appeal, we note two major objections to proper functionalism: creatures with no design plan who appear to have knowledge (Swampman) and creatures with malfunctions that increase reliability. We then note how proper functionalism needs to be clarified because there are cases of what we call warrant-compatible malfunction. We then formulate our own view: explanationist proper functionalism, which explains the warrant-compatible malfunction cases and helps to (...) block the above objections. We also advance a positive argument for explanationist proper functionalism. (shrink)

This paper reassesses the case against Evidential Externalism, the thesis that one's evidence fails to supervene on one's non-factive mental states, focusing on two objections to Externalism due by Nicholas Silins: the armchair access argument and the supervenience argument. It also examines Silins's attempt to undermine the force of one major source of motivation for Externalism, namely that the rival Internalist picture of evidence is implicated in some central arguments for scepticism. While Silins concludes that the case against Evidential Externalism (...) is surprisingly strong, reassessing the arguments supports the opposite conclusion; the objections to Externalism are weak, and for all Silins has shown it may well have unmatched advantages when it comes to resisting scepticism. (shrink)

In this chapter, I grant Jc Beall’s assertion that the best understanding of the doctrine of the incarnation posits that Christ is a contradictory being, in the sense that it has him satisfying complementary pairs of predicates. I also argue, however, that by attending to a distinction between predicate negation and sentence negation, this view can be upheld without positing any classical logical contradictions. I argue that the resulting Christological view has several advantages over Beall’s: It is more conservative about (...) avoiding contradiction, exhibits greater logical neutrality, and comports better with Christian tradition. (shrink)

We draw attention to a series of implicit assumptions that have structured the debate about Frege’s Puzzle. Once these assumptions are made explicit, we rely on them to show that if one focuses exclusively on the issues raised by Frege cases, then one obtains a powerful consideration against a fine-grained conception of propositional-attitude content. In light of this consideration, a form of Russellianism about content becomes viable.

in the treatise, hume claims to identify many “fictions of the imagination” among both “vulgar” and philosophical beliefs. To name just a few, these include the fiction of one aggregate composed of many parts,1 the fiction of a material object’s identity through change, and the fiction of a human mind’s identity through change and interruption in its existence. Hume claims that these fictions and others like them are somehow defective: in his words, they are “improper,” “inexact,” or not “strict”. I (...) will argue that this claim conflicts with other commitments.. (shrink)

We offer an interpretation of the mental files framework that eliminates the metaphor of files, information being contained in files, etc. The guiding question is whether, once we move beyond the metaphors, there is any theoretical role for files. We claim not. We replace the file-metaphor with two theses: the semantic thesis that there are irreducibly relational representational facts (viz. facts about the coordination of representations); and the metasemantic thesis that processes tied to information-relations ground those facts. In its canonical (...) statement, the ‘file’-theory makes reference to a certain kind of relational representational feature, and a certain kind of mental activity. Mental files need not come into it. In short, we posit mental filing without mental files. Our interpretation avoids awkward problems that arise on the standard interpretation and clarifies the explanatory commitments of the theory. (shrink)

This essay gives a new interpretation of Hume's second thoughts about minds in the Appendix, based on a new interpretation of his view of composition. In Book 1 of the Treatise, Hume argued that, as far as we can conceive it, a mind is a whole composed by all its perceptions. But—this essay argues—he also held that several perceptions form a whole only if the mind to which they belong supplies a “connexion” among them. In order to do so, it (...) must contain a further perception or perceptions. But when the perceptions in question are all of those belonging to a given mind—as in the section “Of personal identity” and the Appendix—there cannot be a further perception in that mind, and so those perceptions do not form a whole. Hence, Hume's views were inconsistent. This essay argues that, unlike most others, this interpretation explains his retreat to skepticism in the Appendix. (shrink)

Hume’s discussion of space in the Treatise addresses two main topics: divisibility and vacuum. It is widely recognized that his discussion of divisibility contains an answer to Bayle, whose Dictionary article “Zeno of Elea” presents arguments about divisibility as support for fideism. It is not so widely recognized that, elsewhere in the same article, Bayle presents arguments about vacuum as further support for fideism. This paper aims to show that Hume’s discussion of vacuum contains an answer to these vacuum-based fideistic (...) arguments. Key to this answer is a distinction between two ways in which vacuum was conceived in the early modern period: i) as a genuine thing that has spatial properties, and yet is immobile, indivisible, and penetrable ; ii) as a mere absence of spatial things. This paper also aims to provide a novel defense of Hume against the long-standing objection that he is inconsistent in denying that we can conceive of a vacuum, while allowing that we can conceive of “invisible and intangible distance.” As I interpret him, Hume consistently denies that we can conceive of a positive vacuum, while allowing that we can conceive of two or more objects’ being arranged so as to have privative vacuum between them. (shrink)

Many Jews, Christians, and Muslims adhere to the following three claims: First, God has comprehensive knowledge of all that is, was, and will be. Second, God makes use of this knowledge in order to exercise providential control over the world. Third, human beings have free will. This combination of views raises philosophical puzzles. My aim in this chapter is to explore how historic Jewish reflection on these puzzles relates to treatment of them by contemporary analytic philosophers.

According to proper functionalist theories of warrant, a belief is warranted only if it is formed by cognitive faculties that are properly functioning according to a good, truth-aimed design plan, one that is often thought to be specified either by intentional design or by natural selection. A formidable challenge to proper functionalist theories is the Swampman objection, according to which there are scenarios involving creatures who have warranted beliefs but whose cognitive faculties are not properly functioning, or are poorly designed, (...) or are not aimed at truth. In this paper, we draw lessons from cognitive science in order to develop a novel argument for the conclusion that the Swampman objection fails against proper functionalist theories of warrant. Our argument not only shows that the underlying, central intuition motivating Swampman-like scenarios is false but also motivates proper function as a necessary condition for warrant, thereby lending support to the claim that any theory of knowledge that lacks a proper function requirement is false. (shrink)

Skeptical theists have been charged with being committed to global skepticism. I consider this objection as it applies to a common variety of skeptical theism based on an epistemological principle that Stephen Wykstra labeled “CORNEA.” I show how a recent reformulation of CORNEA (provided by Stephen Wykstra and Timothy Perrine) affords us with a formal apparatus that allows us to see just where this objection gets a grip on that view, as well as what is needed for an adequate response. (...) I conclude by arguing that, given some plausible, modest, and independently motivated anti-skeptical principles, this objection poses no threat to Wykstra’s brand of skeptical theism. (shrink)

A computer simulation is used to study collective judgements that an expert panel reaches on the basis of qualitative probability judgements contributed by individual members. The simulated panel displays a strong and robust crowd wisdom effect. The panel's performance is better when members contribute precise probability estimates instead of qualitative judgements, but not by much. Surprisingly, it doesn't always hurt for panel members to interpret the probability expressions differently. Indeed, coordinating their understandings can be much worse.

Usage of the Greek verb ‘to be’ is generally divided into three broad categories — the predicative use, the existential and the veridical—and these usages often inform the way we understand Being in ancient philosophy. This article challenges this approach by arguing that Being is not the product of linguistic reflection in Parmenides, Plato and Aristotle; rather, these thinkers treat Being as the ontological and epistemological primary. Though this may overlap with the linguistic senses, it is not the same thing. (...) The article is divided into three sections: the first one raises several basic issues with the predicative interpretation of Being, the second argues that Being is unified and singular in a significant sense and the third brings out the special pre-immanence of Being. (shrink)

Proponents of the no-miracles argument contend that scientific realism is “the only philosophy that doesn’t make the success of science a miracle.” Bas van Fraassen argued, however, that the success of our best theories can be explained in Darwinian terms—by the fact they are survivors of a winnowing process in which unsuccessful theories are rejected. Critics of this selectionist explanation complain that while it may account for the fact we have chosen successful theories, it does not explain why any particular (...) one of those theories succeeds. Against this I defend the claim that if selectionists manage to account for the former, they have no burden to account for the latter; the success of any particular one of our best theories might as well be an extraordinary coincidence. I refer to this enhanced selectionist reply as “coincidentalism” and argue that it is a serious but underappreciated response to the no-miracles argument. More generally, I argue the considerations raised in favor of this response show that versions of the no-miracles argument focusing on the success of particular theories are misguided. (shrink)

Some thoughts on moral relativism, and its relation to moral phenomenology and truth.

Some thoughts on our moral experience and moral phenomenology, asking whether it can be justified or whether it is misleading.

Proponents of the explanatory indispensability argument for mathematical platonism maintain that claims about mathematical entities play an essential explanatory role in some of our best scientific explanations. They infer that the existence of mathematical entities is supported by way of inference to the best explanation from empirical phenomena and therefore that there are the same sort of empirical grounds for believing in mathematical entities as there are for believing in concrete unobservables such as quarks. I object that this inference depends (...) on a false view of how abductive considerations mediate the transfer of empirical support. More specifically, I argue that even if inference to the best explanation is cogent, and claims about mathematical entities play an essential explanatory role in some of our best scientific explanations, it doesn’t follow that the empirical phenomena that license those explanations also provide empirical support for the claim that mathematical entities exist. (shrink)

The problem of multi-peer disagreement concerns the reasonable response to a situation in which you believe P1 … Pn and disagree with a group of ‘epistemic peers’ of yours, who believe ∼P1 … ∼Pn, respectively. However, the problem of multi-peer disagreement is a variant on the preface paradox; because of this the problem poses no challenge to the so-called ‘steadfast view’ in the epistemology of disagreement, on which it is sometimes reasonable to believe P in the face of peer disagreement (...) about P. After some terminology is defined (§1), Peter van Inwagen's challenge to the steadfast view will be presented (§2). The preface paradox will then be presented and diagnosed (§3), and it will be argued that van Inwagen's challenge relies on the same principle that generates the preface paradox (§4). The reasonable response to multi-peer disagreement will be discussed (§5), and an objection addressed (§6). (shrink)

Easy-road mathematical fictionalists grant for the sake of argument that quantification over mathematical entities is indispensable to some of our best scientific theories and explanations. Even so they maintain we can accept those theories and explanations, without believing their mathematical components, provided we believe the concrete world is intrinsically as it needs to be for those components to be true. Those I refer to as “mathematical surrealists” by contrast appeal to facts about the intrinsic character of the concrete world, not (...) to explain why our best mathematically imbued scientific theories and explanations are acceptable in spite of having false components, but in order to replace those theories and explanations with parasitic, nominalistically acceptable alternatives. I argue that easy-road fictionalism is viable only if mathematical surrealism is and that the latter constitutes a superior nominalist strategy. Two advantages of mathematical surrealism are that it neither begs the question concerning the explanatory role of mathematics in science nor requires rejecting the cogency of inference to the best explanation. (shrink)

Paradigmatic examples of logical arguments from evil are attempts to establish that the following claims are inconsistent with one another: (1) God is omnipotent, omniscient and wholly good. (2) There is evil in the world. Alvin Plantinga’s free will defense resists such arguments by providing a positive case that (1) and (2) are consistent. A weakness in Plantinga’s free will defense, however, is that it does not show that theism is consistent with the proposition that there are non-moral evils in (...) the world (i.e., that there obtain morally bad states of affairs for which no creature is morally responsible). But many of us firmly believe that there are evils of that sort. I show how Plantinga’s free will defense can be extended so as to redress this weakness. (shrink)

The development of causal modelling since the 1950s has been accompanied by a number of controversies, the most striking of which concerns the Markov condition. Reichenbach's conjunctive forks did satisfy the Markov condition, while Salmon's interactive forks did not. Subsequently some experts in the field have argued that adequate causal models should always satisfy the Markov condition, while others have claimed that non-Markovian causal models are needed in some cases. This paper argues for the second position by considering the multi-causal (...) forks, which are widespread in contemporary medicine (Section 2). A non-Markovian causal model for such forks is introduced and shown to be mathematically tractable (Sections 6, 7, and 8). The paper also gives a general discussion of the controversy about the Markov condition (Section 1), and of the related controversy about probabilistic causality (Sections 3, 4, and 5). (shrink)

Existentialism concerning singular propositions is the thesis that singular propositions ontologically depend on the individuals they are directly about in such a way that necessarily, those propositions exist only if the individuals they are directly about exist. Haecceitism is the thesis that what non-qualitative facts there are fails to supervene on what purely qualitative facts there are. I argue that existentialism concerning singular propositions entails the denial of haecceitism and that this entailment has interesting implications for debates concerning the philosophy (...) of language, the nature of propositions, and the metaphysics of modality. (shrink)

Some proponents of the indispensability argument for mathematical realism maintain that the empirical evidence that confirms our best scientific theories and explanations also confirms their pure mathematical components. I show that the falsity of this view follows from three highly plausible theses, two of which concern the nature of mathematical application and the other the nature of empirical confirmation. The first is that the background mathematical theories suitable for use in science are conservative in the sense outlined by Hartry Field. (...) The second is that the empirical relevance of mathematical statements suitable for use in science is mediated by their non-mathematical consequences. The third is that statements receive additional empirical confirmation only by way of generating additional empirical expectations. Since each of these is a thesis we have good reason to endorse, my argument poses a challenge to anyone who argues that science affords empirical grounds for mathematical realism. (shrink)

Historically, Nelson Goodman’s paradox involving the predicates ‘grue’ and ‘bleen’ has been taken to furnish a serious blow to Carl Hempel’s theory of confirmation in particular and to purely formal theories of confirmation in general. In this paper, I argue that Goodman’s paradox is no more serious of a threat to Hempel’s theory of confirmation than is Hempel’s own paradox of the ravens. I proceed by developing a suggestion from R. D. Rosenkrantz into an argument for the conclusion that these (...) paradoxes are, in fact, equivalent. My argument, if successful, is of both historical and philosophical interest. Goodman himself maintained that Hempel’s theory of confirmation was capable of handling the paradox of the ravens. And Hempel eventually conceded that Goodman’s paradox showed that there could be no adequate, purely syntactical theory of confirmation. The conclusion of my argument entails, by contrast, that Hempel’s theory of confirmation is incapable of handling Goodman’s paradox if and only if it is incapable of handling the paradox of the ravens. It also entails that for any adequate solution to one of these paradoxes, there is a corresponding and equally adequate solution to the other. (shrink)

This paper examines how the prevailing knowledge systems of the West reduce and divide us within and between ourselves. It also highlights how these are paralleled by the Wisdom tradition in theology which allows for a more inclusive model of relationality and becoming. The author sets out before us how western systems create and dictate the underlying binary oppositions by which we, almost unconsciously, live out our lives. New ways are suggested and new horizons plotted.

Making good decisions depends on having accurate information – quickly, and in a form in which it can be readily communicated and acted upon. Two features of medical practice can help: deliberation in groups and the use of scores and grades in evaluation. We study the contributions of these features using a multi-agent computer simulation of groups of physicians. One might expect individual differences in members’ grading standards to reduce the capacity of the group to discover the facts on which (...) well-informed decisions depend. Observations of the simulated groups suggest on the contrary that this kind of diversity can in fact be conducive to epistemic performance. Sometimes, it is adopting common standards that may be expected to result in poor decisions. (shrink)

Biomarkers are widely used not only as prognostic or diagnostic indicators, or as surrogate markers of disease in clinical trials, but also to formulate theories of pathogenesis. We identify two problems in the use of biomarkers in mechanistic studies. The first problem arises in the case of multifactorial diseases, where different combinations of multiple causes result in patient heterogeneity. The second problem arises when a pathogenic mediator is difficult to measure. This is the case of the oxidative stress (OS) theory (...) of disease, where the causal components are reactive oxygen species (ROS) that have very short half-lives. In this case, it is usual to measure the traces left by the reaction of ROS with biological molecules, rather than the ROS themselves. Borrowing from the philosophical theories of signs, we look at the different facets of biomarkers and discuss their different value and meaning in multifactorial diseases and system medicine to inform their use in patient stratification in personalized medicine. (shrink)

Hartry Field argues that conservative rather than true mathematical sentences facilitate deductions in nominalist (i.e., abstracta-free) science without prejudging its empirical outcomes. In this paper, I identify one branch of mathematics as nonconservative, for its indispensable role in enabling nominalist language about a fundamental scientific property, in a fictional scientific community. The fundamental property is electromagnetic reflectance, and the mathematics is Fourier analysis, which renders reflectance ascribable, and nominalist reflectance claims utterable, by this community. Using a recent characterization of conservativeness (...) by Kenneth Boyce, I argue that infinitudes can be rendered inherently mathematical and non-nominalizable in the fictional community, and that rendering infinitudes inherently mathematical for all real communities would yield a convincing counterexample to Fieldian conservativeness. (shrink)

The Iranian prophet and reformer Zarathustra (Greek: Zoroaster) founded his religion in the 6th Century BC. In a series of visions he was taken up to Heaven and Ahura Mazda - creator of all that is good - charged him with enlisting Humanity in the fight against Aura Mainyu - the principle of chaos and destruction - offering Mankind a free choice between Good and Evil. It is hard to overstate the importance of Zoroastrianism. According to Professor of Iranian Studies (...) Dr Mary Boyce: "It was the first to teach the doctrines of an individual judgment, Heaven and Hell, the future resurrection of the body, the general Last Judgment, and life everlasting for the reunited soul and body." 'The Teachings of Zoroaster' is an excellent introduction to this little-known and often misunderstood religion, giving Zoroastrianism its rightful place as the precursor of many Christian, Judaic and Islamic beliefs. (shrink)

In his book, Romaphobia: The Last Acceptable form of Racism, Aidan McGarry gives a powerful analysis of anti-Roma racism in Europe. His aims in the book are to highlight the plight of European Roma and to anal- yse the underlying causes of their persecution. The quandary, as McGarry sees it, is that Roma persecution in Europe has persisted unabated for over six hundred years. As soon as Roma appeared in Europe in the late fourteenth century they were traded as (...) slaves, or targeted by laws calling for assimilation or death. Roma were targeted for mass extermination during the Holocaust, and even now, they face widespread persecution across Europe. Italian interior minister Matteo Salvini, for instance, insists on compiling a “Gypsy Registry” and cleansing Italian neighbour- hoods of Roma camps. The French government targets Roma settlements for demolition and, in defiance of European laws, deports around twenty thousand Roma to other countries every year. Targeted murders of Roma in Hungary, Slovakia, and the Ukraine are encouraged, and ignored. Tabloid newspapers in the UK drum up anti-Roma sentiment. Indeed, the Daily Mail even cite former UK opposition leader Jeremy Corbin’s past attempts to protect Roma from eviction in London as a reason for his unsuitability to become Prime Minister—in modern Britain, compassion for Gypsies is a sign of questionable character. For McGarry, then, this persistence is central to the puzzle of Romaphobia—why does this form of racism remain unchallenged and acceptable? (shrink)

In the recent literature on the nature of knowledge, a rivalry has emerged between modalism and explanationism. According to modalism, knowledge requires that our beliefs track the truth across some appropriate set of possible worlds. Modalists tend to focus on two modal conditions: sensitivity and safety. According to explanationism, knowledge requires only that beliefs bear the right sort of explanatory relation to the truth. In slogan form: knowledge is believing something because it’s true. In this paper, we aim to vindicate (...) explanationism from some recent objections offered by Gualtiero Piccinini, Dario Mortini, and Kenneth Boyce and Andrew Moon. Together, these authors present five purported counterexamples to the sufficiency of the explanationist analysis for knowledge. In addition, Mortini devises a clever argument that explanationism entails the violation of a plausible closure principle on knowledge. We will argue that explanationism is innocent of all these charges against it, and we hope that the strength of the defense we offer of explanationism is evidence in its favor, and a reason to investigate explanationism further as the long-elusive truth about the nature of knowledge. (shrink)

In the debate over whether mathematical facts, properties, or entities explain physical events (in what philosophers call “extra-mathematical” explanations), Aidan Lyon’s (2012) affirmative answer stands out for its employment of the program explanation (PE) methodology of Frank Jackson and Philip Pettit (1990). Juha Saatsi (2012; 2016) objects, however, that Lyon’s examples from the indispensabilist literature are (i) unsuitable for PE, (ii) nominalizable into non-mathematical terms, and (iii) mysterious about the explanatory relation alleged to obtain between the PE’s mathematical explanantia (...) and physical explananda. In this paper, I propose a counterexample to Saatsi’s objections. My counterexample is Frank Jackson’s (1998a) program explanation for color experience, which I argue needs recasting as an extra-mathematical PE due to its implicit reliance on reflectance, a property that suffers conceptual regress unless redefined with Fourier harmonics. Pace Saatsi, I argue that this recast example is an authoritative PE, non-nominalizable, and minimally esoteric. Important for the indispensability debate at large, moreover, is that my counterexample reifies Fourier harmonics without the Enhanced Indispensability Argument (an argument to which Lyon applies PE as a premise). Indispensabilists have long overlooked the conditionalization of a limited mathematical realism on property realism, and my counterexample to Saatsi exploits this conditionalization. (shrink)