Some scientific categories seem to correspond to genuine features of the world and are indispensable for successful science in some domain; in short, they are natural kinds. This book gives a general account of what it is to be a natural kind and puts the account to work illuminating numerous specific examples.

Some philosophers understand natural kinds to be the categories which are constraints on enquiry. In order to elaborate the metaphysics appropriate to such an account, I consider the complicated history of scurvy, citrus, and vitamin C. It may be tempting to understand these categories in a shallow way (as mere property clusters) or in a deep way (as fundamental properties). Neither approach is adequate, and the case instead calls for middle-range ontology: starting from categories which we identify in the world (...) and elaborating their structure, but not pretending to jump ahead to a complete story about fundamental being. (shrink)

The Argument from Inductive Risk (AIR) is taken to show that values are inevitably involved in making judgements or forming beliefs. After reviewing this conclusion, I pose cases which are prima facie counterexamples: the unreflective application of conventions, use of black-boxed instruments, reliance on opaque algorithms, and unskilled observation reports. These cases are counterexamples to the AIR posed in ethical terms as a matter of personal values. Nevertheless, it need not be understood in those terms. The values which load a (...) theory choice may be those of institutions or past actors. This means that the challenge of responsibly handling inductive risk is not merely an ethical issue, but is also social, political, and historical. (shrink)

We analyse the extent of possible computations following Hogarth ([2004]) conducted in Malament–Hogarth (MH) spacetimes, and Etesi and Németi ([2002]) in the special subclass containing rotating Kerr black holes. Hogarth ([1994]) had shown that any arithmetic statement could be resolved in a suitable MH spacetime. Etesi and Németi ([2002]) had shown that some relations on natural numbers that are neither universal nor co-universal, can be decided in Kerr spacetimes, and had asked specifically as to the extent of computational limits there. (...) The purpose of this note is to address this question, and further show that MH spacetimes can compute far beyond the arithmetic: effectively Borel statements (so hyperarithmetic in second-order number theory, or the structure of analysis) can likewise be resolved: Theorem A. If H is any hyperarithmetic predicate on integers, then there is an MH spacetime in which any query ? n H ? can be computed. In one sense this is best possible, as there is an upper bound to computational ability in any spacetime, which is thus a universal constant of that spacetime. Theorem C. Assuming the (modest and standard) requirement that spacetime manifolds be paracompact and Hausdorff, for any spacetime there will be a countable ordinal upper bound, , on the complexity of questions in the Borel hierarchy computable in it. Introduction 1.1 History and preliminaries Hyperarithmetic Computations in MH Spacetimes 2.1 Generalising SADn regions 2.2 The complexity of questions decidable in Kerr spacetimes An Upper Bound on Computational Complexity for Each Spacetime CiteULike Connotea Del.icio.us What's this? (shrink)

forall x: Calgary is a full-featured textbook on formal logic. It covers key notions of logic such as consequence and validity of arguments, the syntax of truth-functional propositional logic TFL and truth-table semantics, the syntax of first-order (predicate) logic FOL with identity (first-order interpretations), symbolizing English in TFL and FOL, and Fitch-style natural deduction proof systems for both TFL and FOL. It also deals with some advanced topics such as modal logic, soundness, and functional completeness. Exercises with solutions are available. (...) It is provided in PDF (for screen reading, printing, and a special version for dyslexics), HTML, and in LaTeX source code. (shrink)

We consider various concepts associated with the revision theory of truth of Gupta and Belnap. We categorize the notions definable using their theory of circular definitions as those notions universally definable over the next stable set. We give a simplified account of varied revision sequences-as a generalised algorithmic theory of truth. This enables something of a unification with the Kripkean theory of truth using supervaluation schemes.

There is a history of thinking that photographs provide a special kind of access to the objects depicted in them, beyond the access that would be provided by a painting or drawing. What is included in the photograph does not depend on the photographer’s beliefs about what is in front of the camera. This feature leads Kendall Walton to argue that photographs literally allow us to see the objects which appear in them. Current generative algorithms produce images in response to (...) users’ text prompts. Depending on the parameters, the output can resemble specific people or things which are named in the prompt. This resemblance does not depend on the user’s beliefs, so generated images are in this sense like photographs. Given this parallel, how should we think about AI-generated images? (shrink)

It is now commonly held that values play a role in scientific judgment, but many arguments for that conclusion are limited. First, many arguments do not show that values are, strictly speaking, indispensable. The role of values could in principle be filled by a random or arbitrary decision. Second, many arguments concern scientific theories and concepts which have obvious practical consequences, thus suggesting or at least leaving open the possibility that abstruse sciences without such a connection could be value-free. Third, (...) many arguments concern the role values play in inferring from evidence, thus taking evidence as given. This paper argues that these limitations do not hold in general. There are values involved in every scientific judgment. They cannot even conceivably be replaced by a coin toss, they arise as much for exotic as for practical sciences, and they are at issue as much for observation as for explicit inference. (shrink)

A critical note on Christopher Bartel and Jack M. C. Kwong, ‘Pluralism, Eliminativism, and the Definition of Art’, Estetika 58 (2021): 100–113. Art pluralism is the view that there is no single, correct account of what art is. Instead, art is understood through a plurality of art concepts and with considerations that are different for particular arts. Although avowed pluralists have retained the word ‘art’ in their discussions, it is natural to ask whether the considerations that motivate pluralism should lead (...) us to abandon art talk altogether; that is, should pluralism lead to eliminativism? This paper addresses arguments both for and against this move. We ultimately argue that pluralism allows one to retain the word ‘art’, if one wants it, but only in a loose, conversational sense. The upshot of pluralism is that talk of art in general cannot be asked to do theoretical and philosophical work. (shrink)

We show that Leitgeb’s dependence operator of Leitgeb is a \-operator and that this is best possible.

William James’ argument against William Clifford in The Will to Believe is often understood in terms of doxastic efficacy, the power of belief to influence an outcome. Although that is one strand of James’ argument, there is another which is driven by ampliative risk. The second strand of James’ argument, when applied to scientific cases, is tantamount to what is now called the Argument from Inductive Risk. Either strand of James’ argument is sufficient to rebut Clifford's strong evidentialism and show (...) that it is sometimes permissible to believe in the absence of compelling evidence. However, the two considerations have different scope and force. Doxastic efficacy applies in only some cases but allows any values to play a role in determining belief; risk applies in all cases but only allows particular conditional values to play a role. (shrink)

This discussion note addresses Caleb Hazelwood’s ‘Practice-Centered Pluralism and a Disjunctive Theory of Art’. Hazelwood advances a disjunctive definition of art on the basis of an analogy with species concept pluralism in the philosophy of biology. We recognize the analogy between species and art, we applaud attention to practice, and we are bullish on pluralism—but it is a mistake to take these as the basis for a disjunctive definition.

We have begun work on two separate but related ontologies for the study of neurological diseases. The first, the Neurological Disease Ontology (ND), is intended to provide a set of controlled, logically connected classes to describe the range of neurological diseases and their associated signs and symptoms, assessments, diagnoses, and interventions that are encountered in the course of clinical practice. ND is built as an extension of the Ontology for General Medical Sciences — a high-level candidate OBO Foundry ontology that (...) provides a set of general classes that can be used to describe general aspects of medical science. ND is being built with classes utilizing both textual and axiomatized definitions that describe and formalize the relations between instances of other classes within the ontology itself as well as to external ontologies such as the Gene Ontology, Cell Ontology, Protein Ontology, and Chemical Entities of Biological Interest. In addition, references to similar or associated terms in external ontologies, vocabularies and terminologies are included when possible. Initial work on ND is focused on the areas of Alzheimer’s and other diseases associated with dementia, multiple sclerosis, and stroke and cerebrovascular disease. Extensions to additional groups of neurological diseases are planned. The second ontology, the Neuro-Psychological Testing Ontology (NPT), is intended to provide a set of classes for the annotation of neuropsychological testing data. The intention of this ontology is to allow for the integration of results from a variety of neuropsychological tests that assay similar measures of cognitive functioning. Neuro-psychological testing is an important component in developing the clinical picture used in the diagnosis of patients with a range of neurological diseases, such as Alzheimer’s disease and multiple sclerosis, and following stroke or traumatic brain injury. NPT is being developed as an extension to the Ontology for Biomedical Investigations. (shrink)

This paper offers a general characterization of underdetermination and gives a prima facie case for the underdetermination of the topology of the universe. A survey of several philosophical approaches to the problem fails to resolve the issue: the case involves the possibility of massive reduplication, but Strawson on massive reduplication provides no help here; it is not obvious that any of the rival theories are to be preferred on grounds of simplicity; and the usual talk of empirically equivalent theories misses (...) the point entirely. (If the choice is underdetermined, then the theories are not empirically equivalent!) Yet the thought experiment is analogous to a live scientific possibility, and actual astronomy faces underdetermination of this kind. This paper concludes by suggesting how the matter can be resolved, either by localizing the underdetermination or by defeating it entirely. Introduction A brief preliminary Around the universe in 80 days Some attempts at resolving the problem 4.1 Indexicality 4.2 Simplicity 4.3 Empirical equivalence 4.4 Is this just a philosophers' fantasy? Move along... ...nothing to see here 6.1 Rules of repetition 6.2 Some possible replies Conclusion. (shrink)

Many enhancement technologies are distributed by healthcare professionals—by physicians—who are held to the Hippocratic Oath and the goals of medicine. While the ethics of enhancement has been widely discussed with regard to the social justice, humanism, morals and normative values of these interventions, their place in medicine has not attracted a great deal of attention. This paper investigates the potential for enhancement technologies to fulfil the goals of medicine, arguing that they play a role in promoting the health of individuals, (...) and thus, an unavoidable place in medicine. It also warns of potential dangers, suggesting a set of guidelines to initiate conversations regarding the role and responsibilities of physicians practising in an era of enhancement. (shrink)

Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.

Cover songs are a familiar feature of contemporary popular music. Musicians describe their own performances as covers, and audiences use the category to organize their listening and appreciation. However, until now philosophers have not had much to say about them. This book explores how to think about covers, appreciating covers, and the metaphysics of covers and songs. Along the way, it explores a range of issues raised by covers, from the question of what precisely constitutes a cover, to the history (...) and taxonomy of the category, the various relationships that hold between songs, performances, and tracks, and the appreciation and evaluation of covers. (shrink)

Although some authors hold that natural kinds are necessarily relative to disciplinary domains, many authors presume that natural kinds must be absolute, categorical features of the reality —often assuming that without even mentioning the alternative. Recognizing both possibilities, one may ask whether the difference especially matters. I argue that it does. Looking at recent arguments about natural kind realism, I argue that we can best make sense of the realism question by thinking of natural kindness as a relation that holds (...) between a category and a domain. (shrink)

We show that the set of ultimately true sentences in Hartry Field's Revenge-immune solution model to the semantic paradoxes is recursively isomorphic to the set of stably true sentences obtained in Hans Herzberger's revision sequence starting from the null hypothesis. We further remark that this shows that a substantial subsystem of second-order number theory is needed to establish the semantic values of sentences in Field's relative consistency proof of his theory over the ground model of the standard natural numbers: -CA0 (...) (second-order number theory with a -comprehension axiom scheme) is insufficient. We briefly consider his claim to have produced a solution to the semantic paradoxes by introducing this conditional. We remark that the notion of a operator can be introduced in other settings. (shrink)

When we ask what natural kinds are, there are two different things we might have in mind. The first, which I’ll call the taxonomy question, is what distinguishes a category which is a natural kind from an arbitrary class. The second, which I’ll call the ontology question, is what manner of stuff there is that realizes the category. Many philosophers have systematically conflated the two questions. The confusion is exhibited both by essentialists and by philosophers who pose their accounts in (...) terms of similarity. It also leads to misreading philosophers who do make the distinction. Distinguishing the questions allows for a more subtle understanding of both natural kinds and their underlying metaphysics. (shrink)

Kyle Stanford has recently claimed to offer a new challenge to scientific realism. Taking his inspiration from the familiar Pessimistic Induction (PI), Stanford proposes a New Induction (NI). Contra Anjan Chakravartty’s suggestion that the NI is a ‘red herring’, I argue that it reveals something deep and important about science. The Problem of Unconceived Alternatives, which lies at the heart of the NI, yields a richer anti-realism than the PI. It explains why science falls short when it falls short, and (...) so it might figure in the most coherent account of scientific practice. However, this best account will be antirealist in some respects and about some theories. It will not be a sweeping antirealism about all or most of science. (shrink)

P D Walsh; Value Education in a Pluralist Society, Journal of Philosophy of Education, Volume 10, Issue 1, 30 May 2006, Pages 24–33, https://doi.org/10.1111/j.1.

The no-miracles argument and the pessimistic induction are arguably the main considerations for and against scientific realism. Recently these arguments have been accused of embodying a familiar, seductive fallacy. In each case, we are tricked by a base rate fallacy, one much-discussed in the psychological literature. In this paper we consider this accusation and use it as an explanation for why the two most prominent `wholesale' arguments in the literature seem irresolvable. Framed probabilistically, we can see very clearly why realists (...) and anti-realists have been talking past one another. We then formulate a dilemma for advocates of either argument, answer potential objections to our criticism, discuss what remains (if anything) of these two major arguments, and then speculate about a future philosophy of science freed from these two arguments. In so doing, we connect the point about base rates to the wholesale/retail distinction; we believe it hints at an answer of how to distinguish profitable from unprofitable realism debates. In short, we offer a probabilistic analysis of the feeling of ennui afflicting contemporary philosophy of science. (shrink)

The accepted narrative treats John Stuart Mill’s Kinds as the historical prototype for our natural kinds, but Mill actually employs two separate notions: Kinds and natural groups. Considering these, along with the accounts of Mill’s nineteenth-century interlocutors, forces us to recognize two distinct questions. First, what marks a natural kind as worthy of inclusion in taxonomy? Second, what exists in the world that makes a category meet that criterion? Mill’s two notions offer separate answers to the two questions: natural groups (...) for taxonomy and Kinds for ontology. This distinction is ignored in many contemporary debates about natural kinds and is obscured by the standard narrative that treats our natural kinds just as a development of Mill’s Kinds. (shrink)

Introduction 1 P. D. Magnus and Jacob Busch 1. Form-driven vs. Content-driven Arguments for Realism 8 Juha Saatsi 2. Optimism about the Pessimistic Induction 29 Sherrilyn Roush 3. Metaphysics between the Sciences and Philosophies of Science 59 Anjan Chakravartty 4. Nominalism and Inductive Generalizations 78 Jessica Pfeifer 5. Models and Scientific Representations 94 Otávio Bueno 6. The Identical Rivals Response to Underdetermination 112 Gregory Frost-Arnold and P. D. Magnus 7. Scientific Representation and the Semiotics of Pictures 131 Laura Perini 8. (...) Philosophy of the Environmental Sciences 155 Jay Odenbaugh 9. Value Judgements and the Estimation of Uncertainty in Climate Modeling 172 Justin Biddle and Eric Winsberg 10. Feminist Standpoint Empiricism: Rethinking the Terrain in Feminist Philosophy of Science 198 Kristen Intemann 11. Naturalism and the Enlightenment Ideal: Rethinking a Central Debate in the Philosophy of Social Science 226 Daniel Steel 12. New Approaches to the Division of Cognitive Labor 250 Michael Weisberg. (shrink)

We show how in the hierarchies${F_\alpha }$of Fieldian truth sets, and Herzberger’s${H_\alpha }$revision sequence starting from any hypothesis for${F_0}$ that essentially each${H_\alpha }$ carries within it a history of the whole prior revision process.As applications we provide a precise representation for, and a calculation of the length of, possiblepath independent determinateness hierarchiesof Field’s construction with a binary conditional operator. We demonstrate the existence of generalized liar sentences, that can be considered as diagonalizing past the determinateness hierarchies definable in Field’s recent (...) models. The ‘defectiveness’ of such diagonal sentences necessarily cannot be classified by any of the determinateness predicates of the model. They are ‘ineffable liars’. We may consider them a response to the claim of Field that ‘the conditional can be used to show that the theory is not subject to “revenge problems”.’. (shrink)

Homeostatic property clusters (HPCs) are offered as a way of understanding natural kinds, especially biological species. I review the HPC approach and then discuss an objection by Ereshefsky and Matthen, to the effect that an HPC qua cluster seems ill-fitted as a description of a polymorphic species. The standard response by champions of the HPC approach is to say that all members of a polymorphic species have things in common, namely dispositions or conditional properties. I argue that this response fails. (...) Instances of an HPC kind need not all be similar in their exhibited properties. Instead, HPCs should instead be understood as unified by the underlying causal mechanism that maintains them. The causal mechanism can both produce and explain some systematic differences between a kind’s members. An HPC kind is best understood not as a single cluster of properties maintained in stasis by causal forces, but as a complex of related property clusters kept in relation by an underlying causal process. This approach requires recognizing that taxonomic systems serve both explanatory and inductive purposes. (shrink)

It has been over two decades since Miranda Fricker labeled epistemic injustice, in which an agent is wronged in their capacity as a knower. The philosophical literature has proliferated with variants and related concepts. By considering cases in popular music, we argue that it is worth distinguishing a parallel phenomenon of art-interpretive injustice, in which an agent is wronged in their creative capacity as a possible artist. In section 1, we consider the prosecutorial use of rap lyrics in court as (...) a central case of this injustice. In section 2, we distinguish art-interpretive injustice from other categories already discussed in recent literature. In section 3, we discuss the relationship between genre discourse and identity prejudice. The case for recognizing the category of art-interpretive injustice is that it allows one to recognize a class of harms as being importantly related in ways that one would otherwise overlook. (shrink)

There are two senses of ‘what scientists know’: An individual sense (the separate opinions of individual scientists) and a collective sense (the state of the discipline). The latter is what matters for policy and planning, but it is not something that can be directly observed or reported. A function can be defined to map individual judgments onto an aggregate judgment. I argue that such a function cannot effectively capture community opinion, especially in cases that matter to us.

According to many philosophers, psychological explanation canlegitimately be given in terms of belief and desire, but not in termsof knowledge. To explain why someone does what they do (so the common wisdom holds) you can appeal to what they think or what they want, but not what they know. Timothy Williamson has recently argued against this view. Knowledge, Williamson insists, plays an essential role in ordinary psychological explanation.Williamson's argument works on two fronts.First, he argues against the claim that, unlike knowledge, (...) belief is``composite'' (representable as a conjunction of a narrow and a broadcondition). Belief's failure to be composite, Williamson thinks, undermines the usual motivations for psychological explanation in terms of belief rather than knowledge.Unfortunately, we claim, the motivations Williamson argues against donot depend on the claim that belief is composite, so what he saysleaves the case for a psychology of belief unscathed.Second, Williamson argues that knowledge can sometimes provide abetter explanation of action than belief can.We argue that, in the cases considered, explanations that cite beliefs(but not knowledge) are no less successful than explanations that citeknowledge. Thus, we conclude that Williamson's arguments fail both coming andgoing: they fail to undermine a psychology of belief, and they fail tomotivate a psychology of knowledge. (shrink)

We characterise explicitly the decidable predicates on integers of Infinite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down $\zeta$, the least ordinal not the length of any eventual output of an Infinite Time Turing machine ; using this the Infinite Time Turing Degrees are considered, and it is shown how the jump operator coincides with the production of mastercodes for the constructible hierarchy; further that the natural ordinals associated with the (...) jump operator satisfy a Spector criterion, and correspond to the L$_\zeta$-stables. It also implies that the machines devised are "$\Sigma_2$ Complete" amongst all such other possible machines. It is shown that least upper bounds of an "eventual jump" hierarchy exist on an initial segment. (shrink)

If two theory formulations are merely different expressions of the same theory, then any problem of choosing between them cannot be due to the underdetermination of theories by data. So one might suspect that we need to be able to tell distinct theories from mere alternate formulations before we can say anything substantive about underdetermination, that we need to solve the problem of identical rivals before addressing the problem of underdetermination. Here I consider two possible solutions: Quine proposes that we (...) call two theories identical if they are equivalent under a reconstrual of predicates, but this would mishandle important cases. Another proposal is to defer to the particular judgements of actual scientists. Consideration of an historical episodethe alleged equivalence of wave and matrix mechanicsshows that this second proposal also fails. Nevertheless, I suggest, the original suspicion is wrong; there are ways to enquire into underdetermination without having solved the problem of identical rivals. (shrink)

The Alagadd?pama Sutta is the 22nd discourse of the Majjhima-nik?ya of the Pali canon. In the sutta itself it is mentioned that the Buddha’s delivery of this discourse was necessitated by the need to refute a wrong view held by one of his disciples named Ari??ha. Parallel versions of the sutta are found preserved in the Chinese?gamas. The two main similes used in the sutta, those of the snake and of the raft, are referred to in the scriptures of a (...) number of non-Therav?da Buddhist traditions as well, showing that the Buddhist doctrine represented in it is early and authentic and the message contained in the sutta was considered to be extremely significant by many early Buddhist traditions. The Alagadd?pama Sutta shows the Buddha’s role as one of the earliest thinkers in the history of philosophy who engaged in a critique of the craving for metaphysics and dogma frequently exhibited in those who propound worldviews. The Buddha did not value a belief or a worldview on grounds of the logical skill with which it was constructed but on grounds of the transformative effect it could have on the character of an individual and the sense of wellbeing it could promote. There are several discourses of the Pali canon which give prominence to this aspect of the Buddha’s teaching. Among them the Brahmaj?la Sutta of the D?gha-nik?ya and the A??hakavagga of the Suttanip?ta need special mention. The Buddha is seen to have consistently avoided engagement in speculative metaphysics, pointing out that the goal of his teaching goes beyond all such engagement. The Buddha himself distinguished his own worldview as a Teaching in the Middle avoiding the common tendency of humankind to be trapped by either of the two extremes, Eternalism or Annihilationism. These distinctive standpoints of the Buddha are all seen to be amply represented in the Alagadd?pama Sutta. (shrink)

This paper gives a characterization of distributed cognition (d-cog) and explores ways that the framework might be applied in studies of science. I argue that a system can only be given a d-cog description if it is thought of as performing a task. Turning our attention to science, we can try to give a global d-cog account of science or local d-cog accounts of particular scientific projects. Several accounts of science can be seen as global d-cog accounts: Robert Merton's sociology (...) of scientific norms, Philip Kitcher's 20th-century account of cognitive labor, and Kitcher's 21st-century notion of well-ordered science. Problems that arise for them arise just because of the way that they attribute a function to science. The paper concludes by considering local d-cog accounts. Here, too, the task is the crux of the matter. (shrink)

According to the standard narrative, natural kind is a technical notion that was introduced by John Stuart Mill in the 1840s and the recent craze for natural kinds, launched by Putnam and Kripke, is a continuation of that tradition. I argue that the standard narrative is mistaken. The Millian tradition of kinds was not particularly influential in the 20th-century, and the Putnam-Kripke revolution did not clearly engage with even the remnants that were left of it. The presently active tradition of (...) natural kinds is less than half a century old. Recognizing this might help us better appreciate both Mill and natural kinds. (shrink)

The underdetermination of theory by evidence is supposed to be a reason to rethink science. It is not. Many authors claim that underdetermination has momentous consequences for the status of scientific claims, but such claims are hidden in an umbra of obscurity and a penumbra of equivocation. So many various phenomena pass for `underdetermination' that it's tempting to think that it is no unified phenomenon at all, so I begin by providing a framework within which all these worries can be (...) seen as species of one genus: A claim of underdetermination involves (at least implicitly) a set of rival theories, a standard of responsible judgment, and a scope of circumstances in which responsible choice between the rivals is impossible. Within this framework, I show that one variety of underdetermination motivated modern scepticism and thus is a familiar problem at the heart of epistemology. I survey arguments that infer from underdetermination to some reëvaluation of science: top-down arguments infer a priori from the ubiquity of underdetermination to some conclusion about science; bottom-up arguments infer from specific instances of underdetermination, to the claim that underdetermination is widespread, and then to some conclusion about science. The top-down arguments either fail to deliver underdetermination of any great significance or (as with modern scepticism) deliver some well-worn epistemic concern. The bottom-up arguments must rely on cases. I consider several promising cases and find them to either be so specialized that they cannot underwrite conclusions about science in general or not be underdetermined at all. Neither top-down nor bottom-up arguments can motivate any deep reconsideration of science. (shrink)

We look at various notions of a class of definability operations that generalise inductive operations, and are characterised as “revision operations”. More particularly we: (i) characterise the revision theoretically definable subsets of a countable acceptable structure; (ii) show that the categorical truth set of Belnap and Gupta’s theory of truth over arithmetic using \emph{fully varied revision} sequences yields a complete \Pi13 set of integers; (iii) the set of \emph{stably categorical} sentences using their revision operator ψ is similarly \Pi13 and which (...) is complete in Gödel’s universe of constructible sets L; (iv) give an alternative account of a theory of truth—realistic variance that simplifies full variance, whilst at the same time arriving at Kripkean fixed points. (shrink)