This note adduces three passages in Seneca the Elder to reinforce a demonstration in CQ 69, 793–8001 that the text of Plin. HN 7.117 has suffered corruption in one of its clauses and requires emendation to restore Pliny's intent. This additional evidence concerns a trope employed by declaimers which could have predisposed a scribe to alter Pliny's text to state that Cicero proscribed Mark Antony. Such a statement has no place in a list of achievements that otherwise all belong to (...) Cicero's consulship twenty years earlier in 63 b.c. (shrink)

This paper will examine the circumstances that inspired the famous utterance attributed to the haruspex Spurinna, ‘Beware the Ides of March!'1 Recently the argument has been made that this warning to Caesar was based upon an astrological calculation, rather than on the usual arts of an haruspex who read signs of the future by inspecting the entrails of sacrificial animals or by interpreting bolts of lightning and portents . As intriguing as this astrological theory is, I am convinced that it (...) is fatally flawed, and I intend to show why it must ultimately be rejected. The question is not merely an academic one, having to do with the methods employed by a particular seer on a given occasion. Rather, if it can be established as even probable that Spurinna based his prophecy upon an astrological calculation, which helped convince the conspirators that Caesar was vulnerable to attack on the Ides as being an unlucky day for him according to the stars, then we are presented with a very significant and hitherto unsuspected instance of astrology influencing the course of public affairs at Rome several decades before astrology came into its own under the early emperors. According to such a reconstruction, astrology played a key role in determining the date of one of the most fateful murders in Roman history. It is the contention of this paper, on the contrary, that there is no reason whatsoever to attribute Spurinna's prophecy to an astrological calculation. (shrink)

This paper will examine the circumstances that inspired the famous utterance attributed to the haruspex Spurinna, ‘Beware the Ides of March!'1Recently the argument has been made that this warning to Caesar was based upon an astrological calculation, rather than on the usual arts of an haruspex who read signs of the future by inspecting the entrails of sacrificial animals (exta) or by interpreting bolts of lightning (fulgura) and portents (ostenta). As intriguing as this astrological theory is, I am convinced that (...) it is fatally flawed, and I intend to show why it must ultimately be rejected. The question is not merely an academic one, having to do with the methods employed by a particular seer on a given occasion. Rather, if it can be established as even probable that Spurinna based his prophecy upon an astrological calculation, which helped convince the conspirators that Caesar was vulnerable to attack on the Ides as being an unlucky day for him according to the stars, then we are presented with a very significant and hitherto unsuspected instance of astrology influencing the course of public affairs at Rome several decades before astrology came into its own under the early emperors. According to such a reconstruction, astrology played a key role in determining the date of one of the most fateful murders in Roman history. It is the contention of this paper, on the contrary, that there is no reason whatsoever to attribute Spurinna's prophecy to an astrological calculation. (shrink)

Pliny's celebration of Cicero's consular achievements contains a striking anomaly, namely the assertion that Cicero proscribed Marcus Antonius(HN7.117). That statement turns Cicero, the victim of Antonius’ murderous vendetta, into the one who wielded the executioner's axe, and it abruptly shifts the focus of the passage from 63 to 43b.c.Two slight corrections to the Latin text can eliminate the intrusion of the proscriptions by substituting a reference to the control Cicero exercised in 63 over Gaius Antonius, his consular colleague and an (...) old ally of Catiline. In hisIn Pisonem(§5), Cicero takes credit for combatting the threat posed by his colleague, and it is highly probable thatHN7.117 mentioned Gaius (not Marcus) Antonius as well, since Pliny's summary of Cicero's consular deeds and honours is nearly identical to the one found inPis. 4–6. The beauty of the emended text is that it restores both historical fact and a logical progression to the overall structure of Pliny's encomium. (shrink)

The aim of this paper is to propose a new and more satisfactory context for a fragment from one of Ennius’ tragedies preserved in Cicero and discussed by a late scholiast on the Ciceronian passage. It will be shown that the scholiast, or more likely the source upon which he drew, had in front of him a bit more of the Ennian passage than the partial line preserved in Cicero and that the scholiast drew a false conclusion concerning the identity (...) of one of the interlocutors from the way in which one speaker addressed the other. Previous scholars have sought to remove the inconsistency in the scholiast's sketch of the scene either by changing the locale of the dialogue or by correcting the scholiast's identification of the out-of-place speaker. It will be shown that a more productive line of investigation is to seek to discover the underlying cause of the scholiast's apparent error. The identification of the cause not only sheds light on the fate of Ennius’ text in Late Antiquity but permits us to restore, by means of conjecture, an additional word to the corpus of Ennius’ tragedies, a word that is a favourite of his in the Annales, but until now has not been attested in a Roman tragedy before the age of Seneca. (shrink)

This paper seeks to dispel the notion that Mark Antony and the Senate indulged in a cat-and-mouse game over the control of Caesar's archives in the weeks immediately following the Ides of March. At stake was whether unpublished documents drawn up by Caesar before his death should be ratified and put into force. The belief that the Senate and Antony contended over this issue and that Antony got the upper hand rests primarily on what I hope to show is a (...) misinterpretation of two key passages in the Philippics. Moreover, since the standard interpretation of these two passages appears to be supported by Dio's account of how Antony cajoled the Senate into permitting him a freer hand to review and publish documents found in Caesar's archives, it will be necessary to have a closer look at Dio's probable sources for this particular section of his history. (shrink)

This paper seeks to dispel the notion that Mark Antony and the Senate indulged in a cat-and-mouse game over the control of Caesar's archives in the weeks immediately following the Ides of March. At stake was whether unpublished documents drawn up by Caesar before his death should be ratified and put into force. The belief that the Senate and Antony contended over this issue and that Antony got the upper hand rests primarily on what I hope to show is a (...) misinterpretation of two key passages in the Philippics. Moreover, since the standard interpretation of these two passages appears to be supported by Dio's account of how Antony cajoled the Senate into permitting him a freer hand to review and publish documents found in Caesar's archives, it will be necessary to have a closer look at Dio's probable sources for this particular section of his history. (shrink)

With Discourse of Miracles and part of A Third Letter Concerning Toleration.

Conditionals that contain a modality in the consequent give rise to a particular semantic phenomenon whereby the antecedent of the conditional blocks possibilities when interpreting the modality in the consequent. This explains the puzzling logical behaviour of constructions like "If you don't buy a lottery ticket, you can't win", "If you eat that poison, it is unlikely that you will survive the day" and "If you kill Harry, you ought to kill him gently". In this paper it is argued that (...) a semantic version of the Ramsey Test provides a key in the analysis of such constructions. The logic for this semantics is axiomatized and some examples are studied, among them a well-known puzzle for contrary-to-duty obligations. (shrink)

I argue that the most promising approach to understanding J.J. Gibson's "affordances" takes affordances themselves as ontological primitives, instead of treating them as dispositional properties of more primitive things, events, surfaces, or substances. These latter are best treated as coalescences of affordances present in the environment (or "coalescences of use-potential," as in Sanders (1994) and Hilditch (1995)). On this view, even the ecological approach's stress on the complementary organism/environment pair is seen as expressing a particular affordance relation between the world (...) and the analyst. That the world is parsed in any way among events and objects, perceivers and worlds, etc., reflects equally features of certain real or possible perspectives on the world and features of the world itself. In section 1, I begin by contending that, contrary to the apparent expectations of some in the field, the bare existence of affordances is surely quite uncontroversial. In section 2, I argue that the most reasonable approach to foundational ontology is a relativistic one. In section 3, I address the claim that affordances must be ontologically complemented by effectivities for the sake of completeness, and I shall argue against that claim on grounds that I take to reflect some of Gibson's most important insights. This work will help to clarify the way affordances are to be used in the fourth and final section, where I argue that ontological work, even within special sciences, should not be merely "regional," and that the most attractive general approach to ontological questions is one that is based on affordances, rather than upon things, events, surfaces, and the like. (shrink)

The law-governed world-picture -- A remarkable idea about the way the universe is cosmos and compulsion -- The laws as the cosmic order : the best-system approach -- The three ways : no-laws, non-governing-laws, governing-laws -- Work that laws do in science -- An important difference between the laws of nature and the cosmic order -- The picture in four theses -- The strategy of this book -- The meta-theoretic conception of laws -- The measurability approach to laws -- What (...) comes where -- In defense of some received views -- Some assumptions that will be in play -- The laws are propositions -- The laws are true -- The logically contingent consequences of the laws are laws themselves -- At least some laws are metaphysically contingent -- The meta-theoretic conception of laws -- Laws of nature, laws of science, laws of theories -- The first-order conception versus the meta-theoretic conception -- What is a law of nature? -- Some examples of meta-theoretic accounts -- The virtues of the meta-theoretic conception -- Weighing the virtues and shortcomings of the meta-theoretic conception -- An epistemological argument for the meta-theoretic conception of laws -- The discoverability thesis, the governing thesis, and the first-order conception -- The main argument -- The objection from bad company -- The objection from inference to the best explanation -- The objection from bayesianism -- The objection from contextualist epistemology -- The objection from the threat of inductive skepticism -- Laws, governing, and counterfactuals -- Where we are now -- What would things have to be like in order for the laws of nature to govern the universe? -- Lawhood, inevitability, counterfactuals -- What is it for a proposition to be inevitably true? -- What is it for a whole class of propositions to be inevitably true? -- What is it for lawhood to confer inevitability? -- NP and supporting counterfactuals -- The worry about context-variability -- A solution and a look ahead -- When would the laws have been different? -- Where we are now -- The God cases -- Other counterexamples to NP -- A moral-theoretic counterexample to NP -- Scientific contexts and non-scientific contexts -- Scientific God cases? -- Lewisian non-backtracking counterexamples -- Where things stand now -- How could science show that the laws govern? -- Why the law-governed world-picture must include the science-says-so thesis -- What is extra-scientific? -- How can the science-says-so thesis be true? -- NP as a consequence of the presuppositions in any scientific context -- Np as true in all possible scientific contexts -- But how could it be so? -- Attack of the actual-factualists -- Measurement and counterfactuals -- Where we are now -- Measurements, reliability, counterfactuals -- A general principle that captures the relation between measurement and counterfactuals -- What we can learn about lawhood from what we have learned about the counterfactual commitments of science -- A first-order account of laws or a meta-theoretic account of laws? -- What methods are presupposed to be legitimate measurement procedures? -- Why we must adopt a meta-theoretic account of laws -- What lawhood is -- Where we are now -- The measurability account of laws -- Brief review of the case for the mal -- A note about hedged laws -- How plausible is the mal? -- What if we don't care about the law-governed world-picture? -- Newton's God and Laplace's demon -- Beyond humean and non-humean -- Two views of laws -- Humean supervenience and the meta-theoretic conception -- Alleged counterexamples to humean supervenience -- Governing and non-trivial necessity -- How the mal lets us have it all -- Humeanism? non-humeanism? -- What is the significance of the idea of the law-governed universe? -- Where in the world are the laws of nature? -- Appendix: The mal in action : a few examples -- Of scientific theories and their laws -- Newton's theory as a paradigm example -- Classical special-force laws -- Geometrical optics and one of its laws -- Local deterministic field theories. (shrink)

John Taurek has argued that, where choices must be made between alternatives that affect different numbers of people, the numbers are not, by themselves, morally relevant. This is because we "must" take "losses-to" the persons into account (and these don't sum), but "must not" consider "losses-of" persons (because we must not treat persons like objects). I argue that the numbers are always ethically relevant, and that they may sometimes be the decisive consideration.

Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the impact (...) of model theory on contemporary algebraic geometry, number theory, combinatorics, and differential equations. This comprehensive and detailed book will interest logicians and mathematicians as well as those working on the history and philosophy of mathematics. (shrink)

There is a great deal that might be said about justice in property claims. The strategy that I shall employ focuses attention upon the initial acquisition of property -- the most sensitive and most interesting area of property theory. Every theory that discusses property claims favorably assumes that there is some justification for transforming previously unowned resources into property. It is often this assumption which has seemed, to one extent or another, to be vulnerable to attack by critics of particular (...) justifications of property. Nevertheless, this assumption is frequently left undefended by property theorists, and where it is defended, the defense is often remarkably weak. That some initial claim to property be defensible is required by any theory which holds that certain present distributions may be justified, that certain transfers of property are justified, or that restitution ought to be made for previous injustice in transfer or acquisition. The initial acquisition of property, and its justification, is crucial to the remainder of property theory. (shrink)

While there are numerous differences between the approaches taken by Maurice Merleau-Ponty and James J. Gibson, the basic motivation of the two thinkers, as well as the internal logic of their respective views, is extraordinarily close. Both were guided throughout their lives by an attempt to overcome the dualism of subject and object, and both devoted considerable attention to their "Gestaltist" predecessors. There can be no doubt but that it is largely because of this common cause that the subsequent development (...) of their ideas is so similar. It is not my objective in what follows merely to demonstrate a similarity between two lines of thought. Instead, I will try to show that each approach gains considerably from attention to the other. There are numerous ways to begin such a project, each about as arbitrary as the next. For present purposes, I shall take as of central importance the question of the character of the perceived world, both in relation to the traditionally opposed mental and material "substances", and in relation to its identification and individuation of things vis a vis one another and vis a vis ourselves. This will implicate especially Gibson's "affordances" and Merleau-Ponty's thesis concerning the "materiality of meaning.". (shrink)

Subcreative sets, introduced by Blum, are known to coincide with the effectively speedable sets. Subcreative sets are shown to be the complete sets with respect to S-reducibility, a special case of Turing reducibility. Thus a set is effectively speedable exactly when it contains the solution to the halting problem in an easily decodable form. Several characterizations of subcreative sets are given, including the solution of an open problem of Blum, and are used to locate the subcreative sets with respect to (...) the complete sets of other reducibilities. It is shown that q-cylindrification is an order-preserving map from the r.e. T-degrees to the r.e. S-degrees. Consequently, T-complete sets are precisely the r.e. sets whose q-cylindrifications are S-complete. (shrink)

I try in this essay to accomplish two things. First I offer some first thoughts toward a clarification of the ethical foundations of private property rights that avoids pitfalls common to more strictly Lockean theories, and is thus better prepared to address arguments posed by critics of standard private property arrangements. Second, I'll address one critical argument that has become pretty common over the years. While versions of the argument can be traced back at least to Pierre Joseph Proudhon, I'll (...) focus on a formulation given it by Jeremy Waldron. The basic idea is that the only sound arguments for private property rights lead to the conclusion that society has an obligation to insure that every citizen possess private property. In Waldron's formulation, what is justifiable is a general, rather than a special, right to private property. I shall try to suggest that this conclusion is unwarranted. (shrink)

As complicated an affair as it may be to give a fully acceptable general characterization of professional codes of ethics that will capture every nuance, one theme that has attracted widespread attention portrays them as contrivances whose primary function is to secure certain obligations of professionals to clients, or to the external community. In contrast to such an "externalist" characterization of professional codes, it has occasionally been contended that, first and foremost, they should be understood as internal conventions, adopted among (...) professionals as a device for securing the "interests" of the professionals themselves. In what follows, I will argue that both of these lines are incomplete. As important as service to the community and the interests of professionals may be in the full understanding of the multiple role that "codes of ethics" play in many professions, it is equally important to see them as expressive of the romance of a profession. Professional codes should be understood not only in terms of their utility to the community, or in terms of their utility to practitioners, but as expressions of callings. Analyses of professional codes of ethics that do not take into consideration their role in evoking the romance of a professional calling are thus not entirely adequate. Professional standards and codes can be fully understood only if one appreciates that they are designed to contribute to and evoke feelings of dignity, self-worth-and, for better or for worse, even the superiority--of the professionals themselves; the code may seem to them to express essential features of what the profession really is. (shrink)

Hrushovski originated the study of “flat” stable structures in constructing a new strongly minimal set and a stable 0-categorical pseudoplane. We exhibit a set of axioms which for collections of finite structure with dimension function δ give rise to stable generic models. In addition to the Hrushovski examples, this formalization includes Baldwin's almost strongly minimal non-Desarguesian projective plane and several others. We develop the new case where finite sets may have infinite closures with respect to the dimension function δ. In (...) particular, the generic structure need not be ω-saturated and so the argument for stability is significantly more complicated. We further show that these structures are “flat” and do not interpret a group. (shrink)

In Anarchy, State and Utopia, Robert Nozick argues, first, that free-market anarchism is unstable -that it will inevitably lead back to the state; and, second, that without a certain "redistributive" proviso, the model is unjust. If either of these things is the case, the model defeats itself, for its justification purports to be that it provides a morally acceptable alternative to government (and therefore to the state). I argue, against Nozick's contention, that his "dominant protection agency" neither meets his monopoly (...) condition for statehood nor need run afowl of his redistributive requirement. This being the case, his argument against free market anarchism fails. (shrink)

First published in 1969, this volume presents a survey of the contemporary national education system in Latin American countries. Laurence Gale describes the uneven provision of schools for different sections of the community and the problems which arise with the racial, cultural and geographical difficulties. He examines the main features in education throughout Latin America, areas of co-operation and agreement and differences of policy and provision.

This article examines cognitive process models of human sentence comprehension based on the idea of informed search. These models are rational in the sense that they strive to find a good syntactic analysis quickly. Informed search derives a new account of garden pathing that handles traditional counterexamples. It supports a symbolic explanation for local coherence as well as an algorithmic account of entropy reduction. The models are expressed in a broad framework for theories of human sentence comprehension.

I describe a problem about the relations among symmetries, laws and measurable quantities. I explain why several ways of trying to solve it will not work, and I sketch a solution that might work. I discuss this problem in the context of Newtonian theories, but it also arises for many other physical theories. The problem is that there are two ways of defining the space-time symmetries of a physical theory: as its dynamical symmetries or as its empirical symmetries. The two (...) definitions are not equivalent, yet they pick out the same extension. This coincidence cries out for explanation, and it is not clear what the explanation could be. The Puzzle: Symmetries, Measurability and Invariance 1.1 The symmetries and the measurable quantities of Newtonian mechanics 1.2 The puzzle Two Easy Answers Another Unsuccessful Solution: Appeal to Geometrical Symmetries Locating the Puzzle The Relation between Laws and Measurability A Possible Solution CiteULike Connotea Del.icio.us What's this? (shrink)

This collection addresses the central issue of political philosophy or, in a couple of cases, issues very close to the heart of that question: Is government justified? This ancient question has never been more alive than at the present time, in the midst of continuing political and social upheaval in virtually every part of the world. Only two of the pieces collected here have been published previously. All the other contributions were, at the time of the inception of the volume, (...) fresh from the pens, or still to emerge from the pens, of their authors. (shrink)

Thesis: The exclusion of organized labor/management issues from the principal arenas for business ethics study and discussions needs to be remedied. The paper develops this thesis in three steps: 1) Exclusion: A careful examination of select textbooks, journals, and conferences provides evidence as to the virtual absence of unions and such crucial organized labor/management issues as labor organizing and collective bargaining; 2) Inclusion: A series of brief arguments favoring inclusion of these issues in business ethics based on the notion of (...) privileged institutions, adversarial posturing, the societal benefits, and globalization; 3) Suggestions: Some practical, cooperative initiatives involving the academy, management and labor, such as, labor officials as guest speakers and members of business school committees, internships in labor organizations, training workshops in business ethics for labor leaders, fora for joint management/labor discussions of issues each group faces in the economy and the legislatures. (shrink)

We use κ-free but not Whitehead Abelian groups to constructElementary Classes (AEC) which satisfy the amalgamation property but fail various conditions on the locality of Galois-types. We introduce the notion that an AEC admits intersections. We conclude that for AEC which admit intersections, the amalgamation property can have no positive effect on locality: there is a transformation of AEC's which preserves non-locality but takes any AEC which admits intersections to one with amalgamation. More specifically we have: Theorem 5.3. There is (...) an AEC with amalgamation which is not (N₀, N₁)-tame but is 2(N0, ∞)-tame; Theorem 3.3. It is consistent with ZFC that there is an AEC with amalgamation which is not (≤ N₂, ≤ N₂)-compact. (shrink)

My objective in this paper is to address a handful of issues that typically get raised in discussions of philosophical anarchism. Some of these issues arise in discussions among partisans of anarchism, and some are more likely to be raised in efforts to defend the state against its opponents. My hope is to focus the argument in such a way as to make clearer the main issues that are at stake from the point of view of at least one version (...) of philosophical anarchism. (shrink)

This paper examines two different, but closely related, classes of problems. The first part deals with whistleblowers, and the difficulties and dangers that they have often faced, although their actions, in the rare cases where they become necessary, are indispensable for the maintenance of honest science. The problems are illustrated by discussion of several specific cases from 1960 to 1990. The second part deals with problems that face many young scientists today, and the stresses to which they are exposed in (...) an increasingly competitive atmosphere. There are powerful pressures for premature publication, and many gifted scientists are driven to spend an inordinate amount of time in writing grant applications that are turned down for lack of funds, while receiving high praise from reviewers. Correction of conditions is an important matter for science policy; it is also important, among other things, to relieve pressures that would tend to encourage deviations from the standards necessary for trustworthy science. (shrink)

Previous discussions of addiction have often focused on the question of whether addiction is a disease. This discussion distinguishes that question – the disease question – from the question of whether addiction is a disability. I argue that, however one answers the disease question, and indeed on almost any credible account of addiction, addiction is a disability. I then consider the implications of this view, or why it matters that addiction is a disability. The disease model of addiction has led (...) many to see addiction as primarily a medical problem, and to make medical treatment of the addicted person the first priority in addressing addiction. Once addiction is viewed as a disability, different concerns are foregrounded. The problem of addiction resides not only in the addicted person, but also in the social environment in which the addicted person finds herself. The fundamental ethical question about addiction is not how addicted persons can be treated or otherwise changed, but how a just society can make reasonable accommodations for addicted persons. (shrink)

CHAPTER 1 Combinatorial Geometries and Infinitary Logics In this chapter we introduce two of the key concepts that are used throughout the text. ...

Against David Schenck's interpretation, I argue that it is not absolutely clear that Merleau-Ponty ever meant to replace what Schenck refers to as the "unity of meanings" interpretation of "structure" with a "material meanings" interpretation. A particular problem-setting -- for example, an attempt to understand the "truth in naturalism" or the "truth in dualism" -- may very well require a particular mode of expression. I argue that the mode of expression chosen by Merleau-Ponty for these purposes, while unfortunate in some (...) of its apparent implications, need not be interpreted as recommitting him to the doctrine he spent his life working to renounce. I have argued that this would have been clearer had he been able to avail himself of James J. Gibson's notion of affordances, which capture perfectly what he was reaching for. (shrink)

We give a general account of the goals of axiomatization, introducing a variant on Detlefsen’s notion of ‘complete descriptive axiomatization’. We describe how distinctions between the Greek and modern view of number, magnitude, and proportion impact the interpretation of Hilbert’s axiomatization of geometry. We argue, as did Hilbert, that Euclid’s propositions concerning polygons, area, and similar triangles are derivable from Hilbert’s first-order axioms. We argue that Hilbert’s axioms including continuity show much more than the geometrical propositions of Euclid’s theorems and (...) thus are an immodest complete descriptive axiomatization of that subject. (shrink)

Christian responses to the developing field of evolutionary psychology tend to be defensive, focusing on the task of showing that Christians have not beenpresented with any reason to abandon any central beliefs of the Christian faith. A more positive response would seek to show that evolutionary psychologycan provide some sort of epistemic support for one or more distinctively Christian doctrines. This paper is an attempt to supply such a response by focusing on the distinctively Christian doctrine of original sin, which (...) presents itself as an especially likely candidate for support from evolutionary psychology. I consider five versions of the doctrine in order of increasing content, arguing that all but the last can receive such support. However, in order to argue for the fourth version (which includes the doctrine traditionally described as “original guilt”), I enlist the aid of a Molinist understanding of divine providence. A consequence of this application of Molinism is that God holds us morally accountable, not only for what we actually do, but also for what we would do in any non-actual conditions, and that He acts on His knowledge of what we would do in such conditions. Because many may find this consequence problematic, I also argue that it is both morally acceptableand necessary for the perfection of the relationship between God and human beings. The last version of original sin that I consider insists that it must be thecausal product of the first sin of the first human being(s), but I argue that this is not a reasonable alternative if original sin is to be equated with behavioraltendencies inherited from an evolutionary ancestry. (shrink)

We explore Shelah's model‐theoretic dividing line methodology. In particular, we discuss how problems in model theory motivated new techniques in model theory, for example classifying theories by their potential (consistently with Zermelo–Fraenkel set theory with the axiom of choice (ZFC)) spectrum of cardinals in which there is a universal model. Two other examples are the study (with Malliaris) of the Keisler order leading to a new ZFC result on cardinal invariants and attempts to clarify the “main gap” by reducing the (...) dependence of certain versions on (highly independent) cardinal arithmetic. (shrink)