What are the features of a good scientific theory? Samuel Schindler's book revisits this classical question in the philosophy of science and develops new answers to it. Theoretical virtues matter not only for choosing theories 'to work with', but also for what we are justified in believing: only if the theories we possess are good ones can we be confident that our theories' claims about nature are actually correct. Recent debates have focussed rather narrowly on a theory's capacity to predict (...) new phenomena successfully, but Schindler argues that the justification for this focus is thin. He discusses several other theory properties such as testability, accuracy, and consistency, and highlights the importance of simplicity and coherence. Using detailed historical case studies and careful philosophical analysis, Schindler challenges the received view of theoretical virtues and advances arguments for the view that science uncovers reality through theory. (shrink)

Deflationists claim that the truth predicate was introduced into our language merely to full a certain logico-linguistic function. Oddly enough, the question what this function exactly consists in has received little attention. We argue that the best way of understanding the function of the truth predicate is as enabling us to mimic higher-order quantification in a first-order framework. Indeed, one can show that the full simple theory of types is reducible to disquotational principles of truth. Our analysis has important consequences (...) for our understanding of truth. In this paper, we can only touch on one of them: we will argue that the insubstantiality of truth does not imply a conservativity requirement on our best theories of truth. (shrink)

Theoretical virtues play an important role in the acceptance and belief of theories in science and philosophy. Philosophers have well-developed views on which virtues ought and ought not to influence one’s acceptance and belief. But what do scientists think? This paper presents the results of a quantitative study with scientists from the natural and social sciences and compares their views to those held by philosophers. Some of the more surprising results are: all three groups have a preference order regarding theoretical (...) virtues, making theory choice a much more determinate matter than what has sometimes been suggested; the preference orders are very similar for the three groups; simplicity is viewed as an epistemic virtue particularly by social scientists ; and syntactic parsimony is preferred to ontological parsimony by all three groups. (shrink)

One of the main logical functions of the truth predicate is to enable us to express so-called ‘infinite conjunctions’. Several authors claim that the truth predicate can serve this function only if it is fully disquotational, which leads to triviality in classical logic. As a consequence, many have concluded that classical logic should be rejected. The purpose of this paper is threefold. First, we consider two accounts available in the literature of what it means to express infinite conjunctions with a (...) truth predicate and argue that they fail to support the necessity of transparency for that purpose. Second, we show that, with the aid of some regimentation, many expressive functions of the truth predicate can actually be performed using truth principles that are consistent in classical logic. Finally, we suggest a reconceptualisation of deflationism, according to which the principles that govern the use of the truth predicate in natural language are largely irrelevant for the question of what formal theory of truth we should adopt. Many philosophers think that the paradoxes pose a special problem for deflationists; we will argue, on the contrary, that deflationists are in a much better position to deal with the paradoxes than their opponents. (shrink)

What requirements must deflationary formal theories of truth satisfy? This chapter argues against the widely accepted view that compositional and Tarskian theories of truth are substantial or otherwise unacceptable to deflationists. First, two purposes that a formal truth theory can serve are distinguished: one descriptive, the other logical (i.e., to characterise the correctness of inferences involving ‘true’). The chapter argues that the most compelling arguments for the incompatibility of compositional and Tarskian theories concern descriptive theories only. -/- Second, two requirements (...) that any deflationist truth theory intended to serve a logical purpose must satisfy are put forward. These requirements, it is argued, suggest that (i) many well-known compositional and Tarskian theories are acceptable from a deflationist standpoint (including CT); (ii) certain other popular theories of truth (including KF and FS) are not similarly acceptable; (iii) there are no conclusive reasons to impose a conservativeness requirement on deflationary theories of truth. (shrink)

The so-called expertise defence against sceptical challenges from experimental philosophy has recently come under attack: there are several studies claiming to have found direct evidence that philosophers’ judgments in thought experiments are susceptible to erroneous effects. In this paper, we distinguish between the customary ‘immune experts’ version of the expertise defence and an ‘informed experts’ version. On the informed expertise defence, we argue, philosophers’ judgments in thought experiments could be preferable to those by the folk even if it were true (...) that philosophers’ judgments are no less immune to confounders than judgments by the folk are. We present results from an experimental study comparing philosophers and non-philosophers (n = 484), which support this version of the expertise defence. (shrink)

I critically examine some deflationary theories of properties, according to which properties are ‘shadows of predicates’ and quantification over them serves a mere quasi-logical function. I start by considering Hofweber’s internalist theory, and pose a problem for his account of inexpressible properties. I then introduce a theory of properties that closely resembles Horwich’s minimalist theory of truth. This theory overcomes the problem of inexpressible properties, but its formulation presupposes the existence of various kinds of abstract objects. I discuss some ways (...) to reduce these existence assumptions, but ultimately suggest that deflationists can hardly avoid quantification over abstract objects of one sort or another. I conclude that property deflationism is perhaps not as deflationary as some philosophers want it to be, but that it’s still apt to call the position ‘deflationary’. (shrink)

We introduce a framework for a graph-theoretic analysis of the semantic paradoxes. Similar frameworks have been recently developed for infinitary propositional languages by Cook and Rabern, Rabern, and Macauley. Our focus, however, will be on the language of first-order arithmetic augmented with a primitive truth predicate. Using Leitgeb’s notion of semantic dependence, we assign reference graphs (rfgs) to the sentences of this language and define a notion of paradoxicality in terms of acceptable decorations of rfgs with truth values. It is (...) shown that this notion of paradoxicality coincides with that of Kripke. In order to track down the structural components of an rfg that are responsible for paradoxicality, we show that any decoration can be obtained in a three-stage process: first, the rfg is unfolded into a tree, second, the tree is decorated with truth values (yielding a dependence tree in the sense of Yablo), and third, the decorated tree is re-collapsed onto the rfg. We show that paradoxicality enters the picture only at stage three. Due to this we can isolate two basic patterns necessary for paradoxicality. Moreover, we conjecture a solution to the characterization problem for dangerous rfgs that amounts to the claim that basically the Liar- and the Yablo graph are the only paradoxical rfgs. Furthermore, we develop signed rfgs that allow us to distinguish between ‘positive’ and ‘negative’ reference and obtain more fine-grained versions of our results for unsigned rfgs. (shrink)

The thesis of theory-ladenness of observations, in its various guises, is widely considered as either ill-conceived or harmless to the rationality of science. The latter view rests partly on the work of the proponents of New Experimentalism who have argued, among other things, that experimental practices are efficient in guarding against any epistemological threat posed by theory-ladenness. In this paper I show that one can generate a thesis of theory-ladenness for experimental practices from an influential New Experimentalist account. The notion (...) I introduce for this purpose is the concept of ‘theory-driven data reliability judgments’, according to which theories which are sought to be tested with a particular set of data guide reliability judgments about those very same data. I provide various prominent historical examples to show that TDRs are used by scientists to resolve data conflicts. I argue that the rationality of the practices which employ TDRs can be saved if the independent support of the theories driving TDRs is construed in a particular way. (shrink)

Deflationary positions have been defended in many areas of philosophy. Most prominent are semantic deflationism about truth and reference, and meta-ontological deflationism, according to which existence has no deep nature and the standard neo-Quinean approach to ontology is misguided. Although both kinds of views have generated much discussion, surprisingly little attention has been paid to the question of how they relate to each other. Are they independent, is it advisable to hold them all at once, or do they even entail (...) each other? One exception is Amie Thomasson, who has argued that semantic deflationism actually entails meta-ontological deflationism. This is unexpected, since semantic deflationism is usually regarded as much less controversial than meta-ontological deflationism. In our paper, we will argue that Thomasson’s argument fails though, and that the connection between the views is in fact weaker than she makes them out to be. (shrink)

Admiration and adoration have been considered as emotions with the power to change people, yet our knowledge of the specific nature and function of these emotions is quite limited. From an interdisciplinary perspective, we present a prototype approach to admiration and what has variously been labelled adoration, worship, or reverence. Both admiration and adoration contribute to the formation of personal and collective ideals, values, and identities, but their workings differ. We offer a detailed theoretical account of commonalities and differences in (...) the appraisal patterns and action tendencies associated with the two emotions. This analysis reveals that admiration motivates the internalisation and emulation of ideals embodied by an outstanding role model. Adoration motivates adherence to the teachings and expectations of a meaning maker and benefactor perceived as superhuman or sacred. Thus, the primary function of admiration is to promote individual learning and change, whereas adoration primarily serves to bind communities together. (shrink)

We prove the following result which is due to the third author. Let [Formula: see text]. If [Formula: see text] determinacy and [Formula: see text] determinacy both hold true and there is no [Formula: see text]-definable [Formula: see text]-sequence of pairwise distinct reals, then [Formula: see text] exists and is [Formula: see text]-iterable. The proof yields that [Formula: see text] determinacy implies that [Formula: see text] exists and is [Formula: see text]-iterable for all reals [Formula: see text]. A consequence is (...) the Determinacy Transfer Theorem for arbitrary [Formula: see text], namely the statement that [Formula: see text] determinacy implies [Formula: see text] determinacy. (shrink)

We prove the following result which is due to the third author. Let [Formula: see text]. If [Formula: see text] determinacy and [Formula: see text] determinacy both hold true and there is no [Formula: see text]-definable [Formula: see text]-sequence of pairwise distinct reals, then [Formula: see text] exists and is [Formula: see text]-iterable. The proof yields that [Formula: see text] determinacy implies that [Formula: see text] exists and is [Formula: see text]-iterable for all reals [Formula: see text]. A consequence is (...) the Determinacy Transfer Theorem for arbitrary [Formula: see text], namely the statement that [Formula: see text] determinacy implies [Formula: see text] determinacy. (shrink)

This paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is loosely based on the Gödel–Russell idea (...) of limited ranges of significance. It is shown how to derive the second-order Dedekind–Peano axioms within that theory. I conclude by discussing whether the theory can be used as a solution to the problem of unrestricted quantification. In an appendix, I prove the consistency of the class theory relative to Zermelo–Fraenkel set theory. (shrink)

In this paper we study several translations that map models and formulae of the language of second-order arithmetic to models and formulae of the language of truth. These translations are useful because they allow us to exploit results from the extensive literature on arithmetic to study the notion of truth. Our purpose is to present these connections in a systematic way, generalize some well-known results in this area, and to provide a number of new results. Sections 3 and 4 contain (...) some recursion- and proof-theoretic results about Kripke-style fixed-point theories of truth. Section 5 shows how to derive full second-order arithmetic from principles of truth. Section 6 investigates the proof-theoretic strength of disquotation without an arithmetical base theory. (shrink)

In this article I argue that a methodological challenge to an integrated history and philosophy of science approach put forth by Ronald Giere almost forty years ago can be met by what I call the Kuhnian mode of History and Philosophy of Science (HPS). Although in the Kuhnian mode of HPS norms about science are motivated by historical facts about scientific practice, the justifiers of the constructed norms are not historical facts. The Kuhnian mode of HPS therefore evades the naturalistic (...) fallacy which Giere’s challenge is a version of. Against the backdrop of a discussion of Laudan’s normative naturalism I argue that the Kuhnian mode of HPS is a superior form of naturalism: it establishes contact to the practice of science without making itself dependent on its contingencies. (shrink)

Predictivism is the view that successful predictions of “novel” evidence carry more confirmational weight than accommodations of already known evidence. Novelty, in this context, has traditionally been conceived of as temporal novelty. However temporal predictivism has been criticized for lacking a rationale: why should the time order of theory and evidence matter? Instead, it has been proposed, novelty should be construed in terms of use-novelty, according to which evidence is novel if it was not used in the construction of a (...) theory. Only if evidence is use-novel can it fully support the theory entailing it. As I point out in this paper, the writings of the most influential proponent of use-novelty contain a weaker and a stronger version of use-novelty. However both versions, I argue, are problematic. With regard to the appraisal of Mendeleev’ periodic table, the most contentious historical case in the predictivism debate, I argue that temporal predictivism is indeed supported, although in ways not previously appreciated. On the basis of this case, I argue for a form of so-called symptomatic predictivism according to which temporally novel predictions carry more confirmational weight only insofar as they reveal the theory’s presumed coherence of facts as real. (shrink)

Minimalism about truth is one of the main contenders for our best theory of truth, but minimalists face the charge of being unable to properly state their theory. Donald Davidson incisively pointed out that minimalists must generalize over occurrences of the same expression placed in two different contexts, which is futile. In order to meet the challenge, Paul Horwich argues that one can nevertheless characterize the axioms of the minimalist theory. Sten Lindström and Tim Button have independently argued that Horwich’s (...) attempt to formulate minimalism remains unsuccessful. We show how to properly state Horwich’s axioms by appealing to propositional functions that are given by definite descriptions. Both Lindström and Button discuss proposals similar to ours and conclude that they are unsuccessful. Our new suggestion avoids these objections. (shrink)

What does it mean for a hypothesis to be ad hoc? One prominent account has it that ad hoc hypotheses have no independent empirical support. Others have viewed ad hoc judgements as subjective. Here I critically review both of these views and defend my own Coherentist Conception of Ad hocness by working out its conceptual and descriptive attractions.

Horwich proposes a solution to the liar paradox that relies on a particular notion of grounding—one that, unlike Kripke’s notion of grounding, does not invoke any “Tarski-style compositional principles”. In this short note, we will formalize Horwich’s construction and argue that his solution to the liar paradox does not justify certain generalizations about truth that he endorses. We argue that this situation is not resolved even if one appeals to the \-rule. In the final section, we briefly discuss how Horwich (...) might respond to the situation. (shrink)

In this article I assess Alisa Bokulich’s idea that explanatory model fictions can be genuinely explanatory. I draw attention to a tension in her account between the claim that model fictions are explanatorily autonomous, and the demand that model fictions be justified in order for them to be genuinely explanatory. I also explore the consequences that arise from Bokulich’s use of Woodward’s account of counterfactual explanation and her abandonment of Woodward’s notion of an intervention. As it stands, Bokulich’s account must (...) be deemed unworkable. (shrink)

We axiomatize Leitgeb's (2005) theory of truth and show that this theory proves all arithmetical sentences of the system of ramified analysis up to $\epsilon_0$. We also give alternative axiomatizations of Kripke's (1975) theory of truth (Strong Kleene and supervaluational version) and show that they are at least as strong as the Kripke-Feferman system KF and Cantini's VF, respectively.

This book examines the evidential status and use of linguistic intuitions, a topic that has seen increased interest in recent years. Linguists use native speakers' intuitions - such as whether or not an utterance sounds acceptable - as evidence for theories about language, but this approach is not uncontroversial. The two parts of this volume draw on the most recent work in both philosophy and linguistics to explore the two major issues at the heart of the debate. Chapters in the (...) first part address the 'justification question', critically analysing and evaluating the theoretical rationale for the evidential use of linguistic intuitions. The second part discusses recent developments in the domain of experimental syntax, focusing on the question of whether formal and systematic models of gathering intuitions are epistemically and methodologically superior to the informal methods that have traditionally been used. -/- The volume provides valuable insights into whether and how linguistic intuitions can be used in theorizing about language, and will be of interest to graduate students and researchers in linguistics, philosophy, and cognitive science. (shrink)

If the Bounded Proper Forcing Axiom BPFA holds, then Mouse Reflection holds at N₂ with respect to all mouse operators up to the level of Woodin cardinals in the next ZFC-model. This yields that if Woodin's ℙ max axiom (*) holds, then BPFA implies that V is closed under the "Woodin-in-the-next-ZFC-model" operator. We also discuss stronger Mouse Reflection principles which we show to follow from strengthenings of BPFA, and we discuss the theory BPFA plus "NS ω1 is precipitous" and strengthenings (...) thereof. Along the way, we answer a question of Baumgartner and Taylor. [2, Question 6.11]. (shrink)

In a recent book and an article, Carl Craver construes the relations between different levels of a mechanism, which he also refers to as constitutive relations, in terms of mutual manipulability (MM). Interpreted metaphysically, MM implies that inter-level relations are symmetrical. MM thus violates one of the main desiderata of scientific explanation, namely explanatory asymmetry. Parts of Craver’s writings suggest a metaphysical interpretation of MM, and Craver explicitly commits to constitutive relationships being symmetrical. The paper furthermore explores the option of (...) interpreting MM epistemologically, as a means for individuating mechanisms. It is argued that MM then is redundant. MM should therefore better be abandoned. (shrink)

Philosophers use historical case studies to support wide-ranging claims about science. This practice is often criticized as problematic. In this paper we suggest that the function of case studies can be understood and justified by analogy to a well-established practice in biology: the investigation of model organisms. We argue that inferences based on case studies are no more problematic than inferences from model organisms to larger classes of organisms in biology. We demonstrate our view in detail by reference to a (...) case study with a long history: Semmelweis’s discovery of the cause of childbed fever. (shrink)

We show that either of the following hypotheses imply that there is an inner model with a proper class of strong cardinals and a proper class of Woodin cardinals. 1) There is a countably closed cardinal k ≥ N₃ such that □k and □(k) fail. 2) There is a cardinal k such that k is weakly compact in the generic extension by Col(k, k⁺). Of special interest is 1) with k = N₃ since it follows from PFA by theorems of (...) Todorcevic and Velickovic. Our main new technical result, which is due to the first author, is a weak covering theorem for the model obtained by stacking mice over $K^c ||k.$. (shrink)

Background Although it is the moral duty of physicians to protect vulnerable patients, there are no data on how vulnerability is perceived in clinical practice. This study explores how physicians classify someone as “vulnerable”. Method Thirty-three physicians were initially questioned about resource allocation problems in their work. The results of these interviews were examined with qualitative study software to identify characteristics associated with vulnerability in patients. Data were conceptualized, classified and cross-linked to highlight the major determinants of vulnerability. The findings (...) revealed the principal factors that make patients vulnerable in clinical practice, according to our definition of vulnerability: the likelihood of having one’s interests unjustly considered. Results Vulnerability can arise as a result of a mismatch between the characteristics of patients and physicians, the healthcare system, the treatment, or the communication between physicians and patients. Vulnerability appears as a gap between a patient’s needs and the means intended to meet them. Vulnerability can further be the result of doing too little or too much for patients. This result suggests that structures provided by healthcare systems are not as differentiated as they should be to cover all situations. Our initial definition of vulnerability was illustrated and supported by our results, showing that it encompasses all factors involved, not solely personal characteristics, indicating the need for a more pragmatic approach for use in clinical practice. Conclusion Vulnerability is not due to a single factor but appears under certain circumstances when there is a discrepancy between a patient’s interests and the care provided, despite existing compensation systems. (shrink)

How is admiration different from adoration? We provided one answer to this question by examining the pathways through which admiration and adoration linked to self-expansion in a questionnaire and an experimental (autobiographical recall of emotion episodes) study. Both emotions were associated with increased potential efficacy to accomplish goals (i.e., self-expansion), but different action tendencies accounted for these links. While our emotion inductions did not successfully distinguish between admiration and adoration, we could statistically disentangle their effects through mediator models. In both (...) studies, self-reported admiration linked to self-expansion through the tendency to emulate admired others. Adoration related to self-expansion through the tendency to affiliate with adored others. These findings were obtained after controlling for other emotions in response to the target person (awe, love, hope, benign envy) and mutuality of the relationship. Our findings also suggest that considering specific emotions (rather than undifferentiated positive affect) helps uncover different pathways to self-expansion. (shrink)

Truth predicates are widely believed to be capable of serving a certain logical or quasi-logical function. There is little consensus, however, on the exact nature of this function. We offer a series of formal results in support of the thesis that disquotational truth is a device to simulate higher-order resources in a first-order setting. More specifically, we show that any theory formulated in a higher-order language can be naturally and conservatively interpreted in a first-order theory with a disquotational truth or (...) truth-of predicate. In the first part of the paper we focus on the relation between truth and full impredicative sentential quantification. The second part is devoted to the relation between truth-of and full impredicative predicate quantification. (shrink)

In this paper I inquire into Bogen and Woodward’s data/phenomena distinction, which in a similar way to Cartwright’s construal of the model of superconductivity —although in a different domain—argues for a ‘bottom-up’ construction of phenomena from data without the involvement of theory. I criticise Bogen and Woodward’s account by analysing their melting point of lead example in depth, which is usually cited in the literature to illustrate the data/phenomenon distinction. Yet, the main focus of this paper lies on Matthias Kaiser’s (...) case study of the plate tectonic revolution, the most extensive case study that has been put forth to support the bottom-up construction of phenomena. On the basis of new historical evidence, which has been overlooked not only by Kaiser but also by the entire historical literature on the plate tectonic revolution, I demonstrate that phenomena are not constructed from the bottom-up but rather, admittedly counter-intuitively, from the top-down.Keywords: Data; Phenomena; Bottom-up; Theory-ladenness; Plate tectonic revolution. (shrink)

Some twenty years ago, Bogen and Woodward challenged one of the fundamental assumptions of the received view, namely the theory-observation dichotomy and argued for the introduction of the further category of scientific phenomena. The latter, Bogen and Woodward stressed, are usually unobservable and inferred from what is indeed observable, namely scientific data. Crucially, Bogen and Woodward claimed that theories predict and explain phenomena, but not data. But then, of course, the thesis of theory-ladenness, which has it that our observations are (...) influenced by the theories we hold, cannot apply. On the basis of two case studies, I want to show that this consequence of Bogen and Woodward’s account is rather unrealistic. More importantly, I also object against Bogen and Woodward’s view that the reliability of data, which constitutes the precondition for data-to-phenomena inferences, can be secured without the theory one seeks to test. The case studies I revisit have figured heavily in the publications of Bogen and Woodward and others: the discovery of weak neutral currents and the discovery of the zebra pattern of magnetic anomalies. I show that, in the latter case, data can be ignored if they appear to be irrelevant from a particular theoretical perspective (TLI) and that, in the former case, the tested theory can be critical for the assessment of the reliability of the data (TLA). I argue that both TLI and TLA are much stronger senses of theory-ladenness than the classical thesis and that neither TLI nor TLA can be accommodated within Bogen and Woodward’s account. (shrink)

Minimalism about truth is one of the main contenders for our best theory of truth, but minimalists face the charge of being unable to properly state their theory. Donald Davidson incisively pointed out that minimalists must generalize over occurrences of the same expression placed in two different contexts, which is futile. In order to meet the challenge, Paul Horwich argues that one can nevertheless characterize the axioms of the minimalist theory. Sten Lindström and Tim Button have independently argued that Horwich’s (...) attempt to formulate minimalism remains unsuccessful. We show how to properly state Horwich’s axioms by appealing to propositional functions that are given by definite descriptions. Both Lindström and Button discuss proposals similar to ours and conclude that they are unsuccessful. Our new suggestion avoids these objections. (shrink)

Let L[E] be an iterable tame extender model. We analyze to which extent L[E] knows fragments of its own iteration strategy. Specifically, we prove that inside L[E], for every cardinal K which is not a limit of Woodin cardinals there is some cutpoint t K > a>ω1 are cardinals, then ◊$_{K.\lambda }^* $ holds true, and if in addition λ is regular, then ◊$_{K.\lambda }^* $ holds true.

The present paper investigates the power of proper forcings to change the shape of the universe, in a certain well-defined respect. It turns out that the ranking among large cardinals can be used as a measure for that power. However, in order to establish the final result I had to isolate a new large cardinal concept, which I dubbed “remarkability.” Let us approach the exact formulation of the problem—and of its solution—at a slow pace.Breathtaking developments in the mid 1980s found (...) one of its culminations in the theorem, due to Martin, Steel, and Woodin, that the existence of infinitely many Woodin cardinals with a measurable cardinal above them all implies that AD, the axiom of determinacy, holds in the least inner model containing all the reals, L. One of the nice things about AD is that the theory ZF + AD + V = L appears as a choiceless “completion” of ZF in that any interesting question seems to find an at least attractive answer in that theory. Beyond that, AD is very canonical as may be illustrated as follows.Let us say that L is absolute for set-sized forcings if for all posets P ∈ V, for all formulae ϕ, and for all ∈ ℝ do we have thatwhere is a name for the set of reals in the extension. (shrink)

The current paper proves the results announced in [5]. We isolate a new large cardinal concept, "remarkability." Consistencywise, remarkable cardinals are between ineffable and ω-Erdos cardinals. They are characterized by the existence of "O # -like" embeddings; however, they relativize down to L. It turns out that the existence of a remarkable cardinal is equiconsistent with L(R) absoluteness for proper forcings. In particular, said absoluteness does not imply Π 1 1 determinacy.

The main result of this paper is the following theorem: Let M be a premouse with a top extender, F. Suppose that (a) M is linearly coarsely iterable via hitting F and its images, and (b) if M * is a linear iterate of M as in (a), then M * is coarsely iterable with respect to iteration trees which do not use the top extender of M * and its images. Then M is coarsely iterable.

We give a direct and elementary proof of the fact that every real-valued probability measure can be approximated—up to an infinitesimal—by a hyperreal-valued one which is regular and defined on the whole powerset of the sample space.

A theory’s fertility is one of the standard theoretical virtues. But how is it to be construed? In current philosophical discourse, particularly in the realism debate, theoretical fertility is usually understood in terms of novel success: a theory is fertile if it manages to make successful novel predictions. Another, more permissible, notion of fertility can be found in the work of Ernan McMullin. This kind of fertility, McMullin claims, gives us just as strong grounds for realism. My paper critically assesses (...) McMullin’s notion of fertility and its realist rationale. It concludes that McMullin’s preferred example, namely the fertile development of the Bohr-Sommerfeld model of the atom, does not support McMullin’s argument for realism. Although the implications for the realism debate are as of yet unclear, the case study offers some important methodological lessons. (shrink)

LetZ2,Z3, andZ4denote 2nd, 3rd, and 4thorder arithmetic, respectively. We let Harrington’s Principle, HP, denote the statement that there is a realxsuch that everyx-admissible ordinal is a cardinal inL. The known proofs of Harrington’s theorem “$Det\left$implies 0♯exists” are done in two steps: first show that$Det\left$implies HP, and then show that HP implies 0♯exists. The first step is provable inZ2. In this paper we show thatZ2+ HP is equiconsistent with ZFC and thatZ3+ HP is equiconsistent with ZFC + there exists a remarkable (...) cardinal. As a corollary,Z3+ HP does not imply 0♯exists, whereas Z4+ HP does. We also study strengthenings of Harrington’s Principle over 2ndand 3rdorder arithmetic. (shrink)

Let N be a transitive model of ZFC such that ωN ⊂ N and P(R) ⊂ N. Assume that both V and N satisfy "the core model K exists." Then KN is an iterate of K. i.e., there exists an iteration tree J on K such that J has successor length and $\mathit{M}_{\infty}^{\mathit{J}}=K^{N}$. Moreover, if there exists an elementary embedding π: V → N then the iteration map associated to the main branch of J equals π ↾ K. (This answers (...) a question of W. H. Woodin, M. Gitik, and others.) The hypothesis that P(R) ⊂ N is not needed if there does not exist a transitive model of ZFC with infinitely many Woodin cardinals. (shrink)

We introduce 0• as a sharp for an inner model with a proper class of strong cardinals. We prove the existence of the core model K in the theory “ does not exist”. Combined with work of Woodin, Steel, and earlier work of the author, this provides the last step for determining the exact consistency strength of the assumption in the statement of the 12th Delfino problem pp. 221–224)).

In this paper I comment on a recent paper by [Scerri, E., & Worrall, J. . Prediction and the periodic table. Studies in History and Philosophy of Science, 32, 407–452.] about the role temporally novel and use-novel predictions played in the acceptance of Mendeleev’s periodic table after the proposal of the latter in 1869. Scerri and Worrall allege that whereas temporally novel predictions—despite Brush’s earlier claim to the contrary—did not carry any special epistemic weight, use-novel predictions did indeed contribute to (...) the acceptance of the table. Although I agree with their first claim, I disagree with their second. In order to spell out my disagreement, I not only revisit Scerri and Worrall’s interpretation of crucial historical evidence they have cited in support of the ‘heuristic account’ of use-novel predictions, but I also criticise the latter on general grounds.Keywords: Periodic table; Dmitri Mendeleev; Noble gases; Use-novel predictions; Heuristic account; Ad hoc hypotheses. (shrink)

We show that L absoluteness for semi-proper forcings is equiconsistent with the existence of a remarkable cardinal, and hence by [6] with L absoluteness for proper forcings. By [7], L absoluteness for stationary set preserving forcings gives an inner model with a strong cardinal. By [3], the Bounded Semi-Proper Forcing Axiom is equiconsistent with the Bounded Proper Forcing Axiom , which in turn is equiconsistent with a reflecting cardinal. We show that Bounded Martin's Maximum is much stronger than BSPFA in (...) that if BMM holds, then for every X ∈ V , X# exists. (shrink)