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)

Laws of nature are puzzling because they have a 'modal character'—they seem to be 'necessary-ish'—even though they also seem to be metaphysically contingent. And it is hard to understand how contingent truths could have such a modal character. Scientific essentialism is a doctrine that seems to dissolve this puzzle, by showing that laws of nature are actually metaphysically necessary. I argue that even if the metaphysics of natural kinds and properties offered by scientific essentialism is correct, there are still some (...) metaphysically contingent truths that share the modal character of the laws of nature. I argue that these contingent truths should be considered laws of nature. So even if scientific essentialism is true, at least some laws of nature are metaphysically contingent. (shrink)

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)

This essay, which was originally presented at the first Coloquio Internacional at the Guadalajara Campus of the Universidad Panamericana, Mexico, October 8-10, is a short introduction to Newman’s writings in six areas—autobiography, philosophy, theology, literature, education and spirituality—along with some suggestions for additional reading, particularly for those beginning Newman studies.

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)

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

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)

What is the reason for the continued interest in Newman’s theology? This article’s reply that Newman was a contextual theologian is based on a consideration of three questions:Was Newman a theologian? What was the context of his theology? What are the reasons for Newman’s theological longevity?

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)

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)

This paper contains portions of Baldwin’s talk at the Set Theory and Model Theory Conference and a detailed proof that in a suitable extension of ZFC, there is a complete sentence of \ that has maximal models in cardinals cofinal in the first measurable cardinal and, of course, never again.

The growth of esports as a recognized, organized, competitive activity in North America and Europe has evolved steadily from one of the most prominent sport industries in several Asian countries. Esports, which is still pursuing a widely accepted governance structure, has struggled to control the factors that typically act as a breeding ground for sport corruption. Within the esports industry, there is alleged widespread use of both prescription and off-label use of stimulants, such as modafinil, methylphenidate, and dextroamphetamine. Anti-doping policy (...) implementation in this environment may result in either the abuse of the Therapeutic Use Exemptions system or excluding too many competitors who have a legitimate need for these medications. In this paper, we contextualize esports and substance use within this emerging industry. Subsequently, we outline the specific challenges faced by esports organizations in crafting policies to address PEDs—one of the industry’s most pressing issues. Furt... (shrink)

ABSTRACT Hope is a complex social-psychological phenomenon. It combines cognitive and affective dimensions, and it is temporally extended, drawing upon the past in order to orient the present toward the future. In conversation with various texts, ranging from Ernst Bloch to Cornel West to Patrick Shade, the article offers a multidimensional account of hope, arguing that it is integral to human action and possibility.

The projective plane of Baldwin 695) is model complete in a language with additional constant symbols. The infinite rank bicolored field of Poizat 1339) is not model complete. The finite rank bicolored fields of Baldwin and Holland 371; Notre Dame J. Formal Logic , to appear) are model complete. More generally, the finite rank expansions of a strongly minimal set obtained by adding a ‘random’ unary predicate are almost strongly minimal and model complete provided the strongly minimal set is ‘well-behaved’ (...) and admits ‘exactly rank k formulas’. The last notion is a geometric condition on strongly minimal sets formalized in this paper. (shrink)

We provide a general framework for studying the expansion of strongly minimal sets by adding additional relations in the style of Hrushovski. We introduce a notion of separation of quantifiers which is a condition on the class of expansions of finitely generated models for the expanded theory to have a countable ω-saturated model. We apply these results to construct for each sufficiently fast growing finite-to-one function μ from 'primitive extensions' to the natural numbers a theory T μ of an expansion (...) of an algebraically closed field which has Morley rank 2. Finally, we show that if μ is not finite-to-one the theory may not be ω-stable. (shrink)

Since the mid‐1950s, the various research programs within cognitive science have advanced our basic understanding of human mental function. Over the past 20 years, this basic science of mind has also contributed to the genesis of an applied science of learning and teaching that can powerfully inform educational practice and dramatically improve educational outcomes. Classroom practice based on this applied science differs from traditional instruction in several ways. Instruction based on cognitive theory envisions learning as an active, strategic process. It (...) assumes that learning follows developmental trajectories within subject‐matter domains. It recognizes that learning is guided by the learners' introspective awareness and control of their mental processes. It emphasizes that learning is facilitated by social, collaborative settings that value self‐directed student dialogue. (shrink)

In the Discourses on Livy, Machiavelli claims that writers who are afraid to condemn Caesar instead criticize Catiline. I argue that Machiavelli follows this advice by inverting it. He openly condemns Caesar and the empire he founded while signaling that he has in mind another inimical example: the Church. He signals his intention by echoing Cicero’s fourth Catilinarian oration, imitating Cicero’s image of the ruin of Rome if Catiline’s conspiracy were to succeed through his own vision of the Italy wrought (...) by wicked Roman emperors who succeeded Caesar. The reader of Machiavelli who recognizes this echo is in a position to see Machiavelli’s own Catilinarian oration against another successor of Caesar. In making my argument, I draw on Rex Stem’s treatment of the functions of exemplementarity as employed by authors of texts and as received by their readers. (shrink)

We study when classes can have the disjoint amalgamation property for a proper initial segment of cardinals. Theorem A For every natural number k, there is a class $K_k $ defined by a sentence in $L_{\omega 1.\omega } $ that has no models of cardinality greater than $ \supset _{k - 1} $ , but $K_k $ has the disjoint amalgamation property on models of cardinality less than or equal to $\mathfrak{N}_{k - 3} $ and has models of cardinality $\mathfrak{N}_{k (...) - 1} $ . More strongly, we can have disjoint amalgamation up to $\mathfrak{N}_\alpha $ for α > ω, but have a bound on size of models. Theorem B For every countable ordinal a, there is a class $K_\alpha $ defined by a sentence in $L_{\omega 1.\omega } $ that has no models of cardinality greater than $ \supset _{\omega 1} $ , but K does have the disjoint amalgamation property on models of cardinality less than or equal to $\mathfrak{N}_\alpha $ . Finally we show that we can extend the $\mathfrak{N}_\alpha $ to $ \supset _\alpha $ in the second theorem consistently with ZFC and while having $\mathfrak{N}_i \ll \supset _i $ for 0 > i < α. Similar results hold for arbitrary ordinals α with |α|= K and $L_{k + ,\omega } $. (shrink)

Let T be a complete countable first order theory and λ an uncountable cardinal. Theorem 1. If T is not superstable, T has 2 λ resplendent models of power λ. Theorem 2. If T is strictly superstable, then T has at least $\min(2^\lambda,\beth_2)$ resplendent models of power λ. Theorem 3. If T is not superstable or is small and strictly superstable, then every resplendent homogeneous model of T is saturated. Theorem 4 (with Knight). For each μ ∈ ω ∪ {ω, (...) 2 ω } there is a recursive theory in a finite language which has μ resplendent models of power κ for every infinite κ. (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)

We describe techniques for constructing models of size continuum inωsteps by simultaneously building a perfect set of enmeshed countable Henkin sets. Such models have perfect, asymptotically similar subsets. We survey applications involving Borel models, atomic models, two-cardinal transfers and models respecting various closure relations.

Jeremy Waldron, Torture, Terror, and Trade-offs: Philosophy for the White House, viii + 357 pp. In Torture, Terror, and Trade-offs, Jeremy Waldron assesses s...

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)

We have argued against a standard way of defining Humean supervenience about laws, and in favor of an alternative definition. Skow says that our argument against the standard definition makes a big mistake. He is right about this. But that mistake is correctable. Skow also argues that our alternative definition is seriously flawed. We think he is wrong about this.

I address some specific problems in the two target articles offered here (Rao and Palmer/Alcock: Parapsychology review and critique), which are indicative of more general problems that plague the larger debate. Because such problems are rather typical of scientific conflict, I address general problems of assessment in a second section. In a final section. I make some comments about the future of this debate.

In Part I of this paper we argued that the first-order systems HP5 and EG are modest complete descriptive axiomatization of most of Euclidean geometry. In this paper we discuss two further modest complete descriptive axiomatizations: Tarksi’s for Cartesian geometry and new systems for adding $$\pi$$. In contrast we find Hilbert’s full second-order system immodest for geometrical purposes but appropriate as a foundation for mathematical analysis.

This paper ties together much of the model theory of the last 50 years. Shelah's attempts to generalize the Morley theorem beyond first order logic led to the notion of excellence, which is a key to the structure theory of uncountable models. The notion of Abstract Elementary Class arose naturally in attempting to prove the categoricity theorem for L ω 1 ,ω (Q). More recently, Zilber has attempted to identify canonical mathematical structures as those whose theory (in an appropriate logic) (...) is categorical in all powers. Zilber's trichotomy conjecture for first order categorical structures was refuted by Hrushovski, by the introducion of a special kind of Abstract Elementary Class. Zilber uses a powerful and essentailly infinitary variant on these techniques to investigate complex exponentiation. This not only demonstrates the relevance of Shelah's model theoretic investigations to mainstream mathematics but produces new results and conjectures in algebraic geometry. (shrink)