In this paper, we provide a new characterization of Keisler’s order in terms of saturation of Boolean ultrapowers. To do so, we apply and expand the framework of ‘separation of variables’ recently developed by Malliaris and Shelah. We also show that good ultrafilters on Boolean algebras are precisely the ones which capture the maximum class in Keisler’s order, answering a question posed by Benda in 1974.

We show that the analysis of Keisler’s order can be localized to the study of φ-types. Specifically, if is a regular ultrafilter on λ such that and M is a model whose theory is countable, then is λ+-saturated iff it realizes all φ-types of size λ.

There is a Turing functional $\Phi $ taking $A^\prime $ to a theory $T_A$ whose complexity is exactly that of the jump of A, and which has the property that $A \leq _T B$ if and only if $T_A \trianglelefteq T_B$ in Keisler’s order. In fact, by more elaborate means and related theories, we may keep the complexity at the level of A without using the jump.

Gaifman's normal form theorem showed that every first-order sentence of quantifier rank n is equivalent to a Boolean combination of “scattered local sentences”, where the local neighborhoods have radius at most 7n−1. This bound was improved by Lifsches and Shelah to 3×4n−1. We use Ehrenfeucht–Fraïssé type games with a “shrinking horizon” to get a spectrum of normal form theorems of the Gaifman type, depending on the rate of shrinking. This spectrum includes the result of Lifsches and Shelah, with a (...) more easily understood proof and with the bound on the radius improved to 4n−1. We also obtain bounds for a normal form theorem of Schwentick and Barthelmann. (shrink)

This paper studies the expressive power that an extra first order quantifier adds to a fragment of monadic second order logic, extending the toolkit of Janin and Marcinkowski [JM01].We introduce an operation existsn on properties S that says "there are n components having S". We use this operation to show that under natural strictness conditions, adding a first order quantifier word u to the beginning of a prefix class V increases the expressive power monotonically in u. As (...) a corollary, if the first order quantifiers are not already absorbed in V, then both the quantifier alternation hierarchy and the existential quantifier hierarchy in the positive first order closure of V are strict.We generalize and simplify methods from Marcinkowski [Mar99] to uncover limitations of the expressive power of an additional first order quantifier, and show that for a wide class of properties S, S cannot belong to the positive first order closure of a monadic prefix class W unless it already belongs to W.We introduce another operation alt on properties which has the same relationship with the Circuit Value Problem as reach has with the Directed Reachability Problem. We use alt to show that Πn⊈ FO, Σn⊈ FO, and Δn+1⊈ FOB, solving some open problems raised in [Mat98]. (shrink)

First order reasoning about hyperintegers can prove things about sets of integers. In the author’s paper Nonstandard Arithmetic and Reverse Mathematics, Bulletin of Symbolic Logic 12 100–125, it was shown that each of the “big five” theories in reverse mathematics, including the base theory, has a natural nonstandard counterpart. But the counterpart of has a defect: it does not imply the Standard Part Principle that a set exists if and only if it is coded by a hyperinteger. In this (...) paper we find another nonstandard counterpart, *RCA0′, that does imply the Standard Part Principle. (shrink)

In prior work [7] we considered networks of agents who have knowledge bases in first order logic, and report facts to their neighbors that are in their common languages and are provable from their knowledge bases, in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any deciderʼs sentence that can be proved from the combined knowledge base. This paper (...) introduces a more general setting where new observations may be added to knowledge bases and the decider must choose a sentence from a set of alternatives. We consider the question of when it is possible to prepare in advance a finite plan to generate reports within the network. We obtain conditions under which such a plan exists and is guaranteed to produce the right choice under any new observations. (shrink)

First order reasoning about hyperintegers can prove things about sets of integers. In the author’s paper Nonstandard Arithmetic and Reverse Mathematics, Bulletin of Symbolic Logic 12 100–125, it was shown that each of the “big five” theories in reverse mathematics, including the base theory , has a natural nonstandard counterpart. But the counterpart of has a defect: it does not imply the Standard Part Principle that a set exists if and only if it is coded by a hyperinteger. In (...) this paper we find another nonstandard counterpart, *RCA0′, that does imply the Standard Part Principle. (shrink)

Keisler in [7] proved that for a strong limit cardinal κ and a singular cardinal λ, the transfer relation κ → λ holds. We analyze the λ -like models produced in the proof of Keisler's transfer theorem when κ is further assumed to be regular. Our main result shows that with this extra assumption, Keisler's proof can be modified to produce a λ -like model M with built-in Skolem functions that satisfies the following two properties: M is generated by a (...) subset C of order-type λ. M can be written as union of an elementary end extension chain 〈Ni: i < δ 〉 such that for each i < δ, there is an initial segment Ci of C with Ci ⊆ Ni, and Ni ∩ = ∅. (shrink)

We characterize some large cardinal properties, such as μ-measurability and P 2 (κ)-measurability, in terms of ultrafilters, and then explore the Rudin-Keisler (RK) relations between these ultrafilters and supercompact measures on P κ (2 κ ). This leads to the characterization of 2 κ -supercompactness in terms of a measure on measure sequences, and also to the study of a certain natural subset, Full κ , of P κ (2 κ ), whose elements code measures on cardinals less than κ. (...) The hypothesis that Full κ is stationary (a weaker assumption than 2 κ -supercompactness) is equivalent to a higher order Lowenheim-Skolem property, and settles a question about directed versus chain-type unions on P κ λ. (shrink)

A 2-affable ultrafilter has only finitely many predecessors in the Rudin-Keisler ordering of isomorphism classes of ultrafilters over the natural numbers. If the continuum hypothesis is true, then there is an ℵ 1 -sequence of ultrafilters D α such that the strict Rudin-Keisler predecessors of D α are precisely the isomorphs of the D β 's for $\beta.

We consider the question, of longstanding interest, of realizing types in regular ultrapowers. In particular, this is a question about the interaction of ultrafilters and theories, which is both coarse and subtle. By our prior work it suffices to consider types given by instances of a single formula. In this article, we analyze a class of formulas φ whose associated characteristic sequence of hypergraphs can be seen as describing realization of first- and second-order types in ultrapowers on one hand, (...) and properties of the corresponding ultrafilters on the other. These formulas act, via the characteristic sequence, as points of contact with the ultrafilter D, in the sense that they translate structural properties of ultrafilters into model-theoretically meaningful properties and vice versa. Such formulas characterize saturation for various key theories , yet their scope in Keisler’s order does not extend beyond Tfeq. The proof applies Shelah’s classification of second-order quantifiers. (shrink)

We examine Paul Halmos’ comments on category theory, Dedekind cuts, devil worship, logic, and Robinson’s infinitesimals. Halmos’ scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the words of an MAA biography, Halmos thought that mathematics is “certainty” and “architecture” yet 20th century logic teaches us is that mathematics is full of uncertainty or more precisely incompleteness. If the term architecture meant to imply that mathematics is one great solid castle, then modern logic tends to (...) teach us the opposite lesson, namely that the castle is floating in midair. Halmos’ realism tends to color his judgment of purely scientific aspects of logic and the way it is practiced and applied. He often expressed distaste for nonstandard models, and made a sustained effort to eliminate first-order logic, the logicians’ concept of interpretation, and the syntactic vs semantic distinction. He felt that these were vague, and sought to replace them all by his polyadic algebra. Halmos claimed that Robinson’s framework is “unnecessary” but Henson and Keisler argue that Robinson’s framework allows one to dig deeper into set-theoretic resources than is common in Archimedean mathematics. This can potentially prove theorems not accessible by standard methods, undermining Halmos’ criticisms. (shrink)

Let L(Q) be first order logic with Keisler's quantifier, in the λ + interpretation (= the satisfaction is defined as follows: $M \models (\mathbf{Q}x)\varphi(x)$ means there are λ + many elements in M satisfying the formula φ(x)). Theorem 1. Let λ be a singular cardinal; assume □ λ and GCH. If T is a complete theory in L(Q) of cardinality at most λ, and p is an L(Q) 1-type so that T strongly omits $p (= p$ has no support, (...) to be defined in $\S1$ ), then T has a model of cardinality λ + in the λ + interpretation which omits p. Theorem 2. Let λ be a singular cardinal, and let T be a complete first order theory of cardinality λ at most. Assume □ λ and GCH. If Γ is a smallness notion then T has a model of cardinality λ + such that a formula φ(x) is realized by λ + elements of M iff φ(x) is not Γ-small. The theorem is proved also when λ is regular assuming $\lambda = \lambda^{ . It is new when λ is singular or when |T| = λ is regular. Theorem 3. Let λ be singular. If $\operatorname{Con}(ZFC + GCH + (\exists\kappa)$ [κ is a strongly compact cardinal]), then the following in consistent: ZFC + GCH + the conclusions of all above theorems are false. (shrink)

Let T 1 , T 2 be countable first-order theories, M i ⊨ T i , and ������ any regular ultrafilter on λ ≥ $\aleph_{0}$ . A longstanding open problem of Keisler asks when T 2 is more complex than T 1 , as measured by the fact that for any such λ, ������, if the ultrapower (M 2 ) λ /������ realizes all types over sets of size ≤ λ, then so must the ultrapower (M 1 ) λ (...) /������. In this paper, building on the author's prior work [12] [13] [14], we show that the relative complexity of first-order theories in Keisler's sense is reflected in the relative graph-theoretic complexity of sequences of hypergraphs associated to formulas of the theory. After reviewing prior work on Keisler's order, we present the new construction in the context of ultrapowers, give various applications to the open question of the unstable classification, and investigate the interaction between theories and regularizing sets. We show that there is a minimum unstable theory, a minimum TP 2 theory, and that maximality is implied by the density of certain graph edges (between components arising from Szemerédi-regular decompositions) remaining bounded away from 0, 1. We also introduce and discuss flexible ultrafilters, a relevant class of regular ultrafilters which reflect the sensitivity of certain unstable (non low) theories to the sizes of regularizing sets, and prove that any ultrafilter which saturates the minimal TP 2 theory is flexible. (shrink)

Martin’s conjecture is an attempt to classify the behavior of all definable functions on the Turing degrees under strong set theoretic hypotheses. Very roughly it says that every such function is either eventually constant, eventually equal to the identity function or eventually equal to a transfinite iterate of the Turing jump. It is typically divided into two parts: the first part states that every function is either eventually constant or eventually above the identity function and the second part states that (...) every function which is above the identity is eventually equal to a transfinite iterate of the jump. If true, it would provide an explanation for the unique role of the Turing jump in computability theory and rule out many types of constructions on the Turing degrees.In this thesis, we will introduce a few tools which we use to prove several cases of Martin’s conjecture. It turns out that both these tools and these results on Martin’s conjecture have some interesting consequences both for Martin’s conjecture and for a few related topics.The main tool that we introduce is a basis theorem for perfect sets, improving a theorem due to Groszek and Slaman. We also introduce a general framework for proving certain special cases of Martin’s conjecture which unifies a few pre-existing proofs. We will use these tools to prove three main results about Martin’s conjecture: that it holds for regressive functions on the hyperarithmetic degrees, that part 1 holds for order preserving functions on the Turing degrees, and that part 1 holds for a class of functions that we introduce, called measure preserving functions.This last result has several interesting consequences for the study of Martin’s conjecture. In particular, it shows that part 1 of Martin’s conjecture is equivalent to a statement about the Rudin-Keisler order on ultrafilters on the Turing degrees. This suggests several possible strategies for working on part 1 of Martin’s conjecture, which we will discuss.The basis theorem that we use to prove these results also has some applications outside of Martin’s conjecture. We will use it to prove a few theorems related to Sacks’ question about whether it is provable in $\mathsf {ZFC}$ that every locally countable partial order of size continuum embeds into the Turing degrees. We will show that in a certain extension of $\mathsf {ZF}$, this holds for all partial orders of height two, but not for all partial orders of height three. Our proof also yields an analogous result for Borel partial orders and Borel embeddings in $\mathsf {ZF}$, which shows that the Borel version of Sacks’ question has a negative answer.We will end the thesis with a list of open questions related to Martin’s conjecture, which we hope will stimulate further research.prepared by Patrick Lutz.E-mail: pglutz@berkeley.edu. (shrink)

Given the complexity and generalizability of motor skills, it is difficult to account for learning in this area without incorporating the concept of unconscious abstraction. A model based solely on association does not seem to account for data in this domain; specifically, instances that require learners to execute a practiced motor skill in a novel situation.

In this article we, given a free ultrafilter p on ω, consider the following classes of ultrafilters:(1) T(p) - the set of ultrafilters Rudin-Keisler equivalent to p,(2) S(p)={q ∈ ω*:∃ f ∈ ω ω , strictly increasing, such that q=f β (p)},(3) I(p) - the set of strong Rudin-Blass predecessors of p,(4) R(p) - the set of ultrafilters equivalent to p in the strong Rudin-Blass order,(5) P RB (p) - the set of Rudin-Blass predecessors of p, and(6) P RK (...) (p) - the set of Rudin-Keisler predecessors of p,and analyze relationships between them. We introduce the semi-P-points as those ultrafilters p ∈ ω* for which P RB (p)=P RK (p), and investigate their relations with P-points, weak-P-points and Q-points. In particular, we prove that for every semi-P-point p its α-th left power α p is a semi-P-point, and we prove that non-semi-P-points exist in ZFC. Further, we define an order ⊴ in T(p) by r⊴q if and only if r ∈ S(q). We prove that (S(p),⊴) is always downwards directed, (R(p),⊴) is always downwards and upwards directed, and (T(p),⊴) is linear if and only if p is selective.We also characterize rapid ultrafilters as those ultrafilters p ∈ ω* for which R(p)∖S(p) is a dense subset of ω*.A space X is M-pseudocompact (for ) if for every sequence (U n ) n < ω of disjoint open subsets of X, there are q ∈ M and x ∈ X such that x=q-lim (U n ); that is, for every neighborhood V of x. The P RK (p)-pseudocompact spaces were studied in [ST].In this article we analyze M-pseudocompactness when M is one of the classes S(p), R(p), T(p), I(p), P RB (p) and P RK (p). We prove that every Frolik space is S(p)-pseudocompact for every p ∈ ω*, and determine when a subspace with is M-pseudocompact. (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)

We study the Rudin–Keisler pre-order on Fréchet–Urysohn ideals on $\omega $. We solve three open questions posed by S. García-Ferreira and J. E. Rivera-Gómez in the articles [5] and [6] by establishing the following results: •For every AD family $\mathcal {A},$ there is an AD family $\mathcal {B}$ such that $\mathcal {A}^{\perp } <_{{\textsf {RK}}}\mathcal {B}^{\perp }.$ •If $\mathcal {A}$ is a nowhere MAD family of size $\mathfrak {c}$ then there is a nowhere MAD family $\mathcal {B}$ such that (...) $\mathcal {I}\left $ and $\mathcal {I}\left $ are Rudin–Keisler incomparable.•There is a family $\left \{ \mathcal {B}_{\alpha }\mid \alpha \in \mathfrak {c}\right \} $ of nowhere MAD families such that if $\alpha \neq \beta $, then $\mathcal {I}\left $ and $\mathcal {I}\left $ are Rudin–Keisler incomparable.Here $\mathcal {I}$ denotes the ideal generated by an AD family $\mathcal {A}$.In the context of hyperspaces with the Vietoris topology, for a Fréchet–Urysohn-filter $\mathcal {F}$ we let $\mathcal {S}_{c}\left \right ) $ be the hyperspace of nontrivial convergent sequences of the space consisting of $\omega $ as discrete subset and only one accumulation point $\mathcal {F}$ whose neighborhoods are the elements of $\mathcal {F}$ together with the singleton $\{\mathcal {F}\}$. For a FU-filter $\mathcal {F}$ we show that the following are equivalent: • $\mathcal {F}$ is a FUF-filter.• $\mathcal {S}_{c}\left \right ) $ is Baire. (shrink)

This paper develops the model theory of ordered structures that satisfy Keisler’s regularity scheme and its strengthening REF ${(\mathcal{L})}$ (the reflection scheme) which is an analogue of the reflection principle of Zermelo-Fraenkel set theory. Here ${\mathcal{L}}$ is a language with a distinguished linear order <, and REF ${(\mathcal {L})}$ consists of formulas of the form $$\exists x \forall y_{1} < x \ldots \forall y_{n} < x \varphi (y_{1},\ldots ,y_{n})\leftrightarrow \varphi^{ < x}(y_1, \ldots ,y_n),$$ where φ is an ${\mathcal{L}}$ (...) -formula, φ order theory T in a countable language ${\mathcal{L}}$ with a distinguished linear order:Some model of T has an elementary end extension with a first new element.T ⊢ REF ${(\mathcal{L})}$ .T has an ω 1-like model that continuously embeds ω 1.For some regular uncountable cardinal κ, T has a κ-like model that continuously embeds a stationary subset of κ.For some regular uncountable cardinal κ, T has a κ-like model ${\mathfrak{M}}$ that has an elementary extension in which the supremum of M exists.Moreover, if κ is a regular cardinal satisfying κ = κ <κ , then each of the above conditions is equivalent to: T has a κ + -like model that continuously embeds a stationary subset of κ. (shrink)

We consider several variants of Keisler’s isomorphism theorem. We separate these variants by showing implications between them and cardinal invariants hypotheses. We characterize saturation hypotheses that are stronger than Keisler’s theorem with respect to models of size $\aleph _1$ and $\aleph _0$ by $\mathrm {CH}$ and $\operatorname {cov}(\mathsf {meager}) = \mathfrak {c} \land 2^{<\mathfrak {c}} = \mathfrak {c}$ respectively. We prove that Keisler’s theorem for models of size $\aleph _1$ and $\aleph _0$ implies $\mathfrak {b} = \aleph (...) _1$ and $\operatorname {cov}(\mathsf {null}) \le \mathfrak {d}$ respectively. As a consequence, Keisler’s theorem for models of size $\aleph _0$ fails in the random model. We also show that for Keisler’s theorem for models of size $\aleph _1$ to hold it is not necessary that $\operatorname {cov}(\mathsf {meager})$ equals $\mathfrak {c}$. (shrink)

Shelah's theory of forking is generalized in a way which deals with measures instead of complete types. This allows us to extend the method of forking from the class of stable theories to the larger class of theories which do not have the independence property. When restricted to the special case of stable theories, this paper reduces to a reformulation of the classical approach. However, it goes beyond the classical approach in the case of unstable theories. Methods from ordinary forking (...) theory and the Loeb measure construction from nonstandard analysis are used. (shrink)

We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [3] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles which are equivalent in strength to weaker theories in second order arithmetic.

Upshot: Second-order cybernetics is an important field for the scientific enterprise but it has difficulty explaining itself to those outside the field and defining itself to those inside the field.

In a nonstandard universe, the $\kappa$-saturation property states that any family of fewer than $\kappa$ internal sets with the finite intersection property has a nonempty intersection. An ordered field $F$ is said to have the $\lambda$-Bolzano-Weierstrass property iff $F$ has cofinality $\lambda$ and every bounded $\lambda$-sequence in $F$ has a convergent $\lambda$-subsequence. We show that if $\kappa < \lambda$ are uncountable regular cardinals and $\beta^\alpha < \lambda$ whenever $\alpha < \kappa$ and $\beta < \lambda$, then there is a $\kappa$-saturated nonstandard (...) universe in which the hyperreal numbers have the $\lambda$-Bolzano-Weierstrass property. The result also applies to certain fragments of set theory and second order arithmetic. (shrink)

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell’s Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes that.

The purpose of Pope John Paul''s encyclicalCentesimus Annus (CA) is to propound the foundations of a just economic order and to sketch its essential characteristics. As such he essentially provides an orientation or moral compass for the political economy rather than a precise road map. This article first reviews the principal components of CA and then analyzes and evaluates its central contentions on both cultural and economic grounds.

§0. Introduction. In [16], Barwise described his graduate study at Stanford. He told of his interactions with Kreisel and Scott, and said how he chose Feferman as his advisor. He began working on admissible fragments of infinitary logic after reading and giving seminar talks on two Ph.D. theses which had recently been completed: that of Lopez-Escobar, at Berkeley, on infinitary logic [46], and that of Platek [58], at Stanford, on admissible sets.Barwise's work on infinitary logic and admissible sets is described (...) in his thesis [4], the book [13], and papers [5]—[16]. We do not try to give a systematic review of these papers. Instead, our goal is to give a coherent introduction to infinitary logic and admissible sets. We describe results of Barwise, of course, because he did so much. In addition, we mention some more recent work, to indicate the current importance of Barwise's ideas. Many of the central results are stated without proof, but occasionally we sketch a proof, to indicate how the ideas fit together.Chapters 1 and 2 describe infinitary logic and admissible sets at the time Barwise began his work, circa 1965. From Chapter 3 on, we survey the developments that took place after Barwise appeared on the scene.§1. Background on infinitary logic. In this chapter, we describe the situation in infinitary logic at the time that Barwise began his work. We need some terminology. By a vocabulary, we mean a set L of constant symbols, and relation and operation symbols with finitely many argument places. As usual, by an L-structureM, we mean a universe set M with an interpretation for each symbol of L. (shrink)

The randomization of a complete first-order theory [Formula: see text] is the complete continuous theory [Formula: see text] with two sorts, a sort for random elements of models of [Formula: see text] and a sort for events in an underlying atomless probability space. We study independence relations and related ternary relations on the randomization of [Formula: see text]. We show that if [Formula: see text] has the exchange property and [Formula: see text], then [Formula: see text] has a strict (...) independence relation in the home sort, and hence is real rosy. In particular, if [Formula: see text] is o-minimal, then [Formula: see text] is real rosy. (shrink)

A general metatheorem is proved which reduces a wide class of statements about continuous time stochastic processes to statements about discrete time processes. We introduce a strong language for stochastic processes, and a concept of forcing for sequences of discrete time processes. The main theorem states that a sentence in the language is true if and only if it is forced. Although the stochastic process case is emphasized in order to motivate the results, they apply to a wider class (...) of random variables. At the end of the paper we illustrate how the theorem can be used with three applications involving submartingales. (shrink)

We define two maps, one map from the set of conditional probability systems (CPS’s) onto the set of lexicographic probability systems (LPS’s), and another map from the set of LPS’s with full support onto the set of CPS’s. We use these maps to establish a relationship between strong belief (defined on CPS’s) and assumption (defined on LPS’s). This establishes a relationship at the abstract level between these two widely used notions of belief in an extended probability-theoretic setting.

Any great new theoretical framework has an epistemological and an ontological aspect to its philosophy as well as an axiological one, and one needs to understand all three aspects in order to grasp the deep aspiration and idea of the theoretical framework. Presently, there is a widespread effort to understand C. S. Peirce's (1837–1914) pragmaticistic semeiotics, and to develop it by integrating the results of modern science and evolutionary thinking; first, producing a biosemiotics and, second, by integrating it with (...) the progress in cybernetics, information science, and system theory to create a cybersemiotics. In this paper, we focus on the understanding of the evolution of the universe that Peirce produced as an alternative to the mechanistic view underlying classical physics and try to place man in an evolving universe as a creative, aesthetical agent. It is true that modern non-equilibrium physics has made a modern foundation for a profound physical understanding of the basic evolutionary processes in the universe. But science still has not produced a theory that can explain how the creativity of the universe could produce signification, interpretation, and first-person consciousness. To this end, Peirce's thoughts on agapastic evolution coupled with the aesthetically influence of the growth of ideas and reasonableness on man could make a contribution. (shrink)

This essay details the resurgence of wellness program as employed by large corporations with the aim of reducing healthcare costs. The essay narrows in on a discussion of how Big Data collection practices are being utilized in wellness programs and the potential negative impact on the worker in regards to privacy and employment discrimination. The essay offers an ethical framework to be adopted by wellness program vendors in order to conduct wellness programs that would achieve cost-saving goals without undue (...) burdens on the worker. The essay also offers some innovative approaches to wellness that may well better serve the goals of healthcare cost reduction. (shrink)

This is a case study on a series of at least thirty-four sixteenth-century notebooks from the Sloane collection, which reconsiders early modern note taking techniques and the organisation of knowledge. These notebooks were written by an anonymous compiler, a physician who read widely in the alchemical and medical literature available in his lifetime, the late sixteenth century. In the alchemica, he devotes individual volumes to specific alchemical substances, which are connected with each other by means of a complex system of (...) cross-referencing; they are constantly revised and change appearance according to the physician's latest ideas about alchemical medicines. As a result, the notebooks not only preserve received information — they also represent an equivalent to the alchemical workshop, where the combination of different textual elements generates knowledge. (shrink)

Upshot: The work that scientists do, particularly social scientists, is currently constrained by their conception of science. Expanding the conception of science would lead to more innovative work and more rapid social progress.

A good book may have the power to change the way we see the world, but a great book actually becomes part of our daily consciousness, pervading our thinking to the point that we take it for granted, and we forget how provocative and challenging its ideas once were—and still are. _The Structure of Scientific Revolutions _is that kind of book. When it was first published in 1962, it was a landmark event in the history and philosophy of science. Fifty (...) years later, it still has many lessons to teach. With _The Structure of Scientific Revolutions, _Kuhn challenged long-standing linear notions of scientific progress, arguing that transformative ideas don’t arise from the day-to-day, gradual process of experimentation and data accumulation but that the revolutions in science, those breakthrough moments that disrupt accepted thinking and offer unanticipated ideas, occur outside of “normal science,” as he called it. Though Kuhn was writing when physics ruled the sciences, his ideas on how scientific revolutions bring order to the anomalies that amass over time in research experiments are still instructive in our biotech age. This new edition of Kuhn’s essential work in the history of science includes an insightful introduction by Ian Hacking, which clarifies terms popularized by Kuhn, including paradigm and incommensurability, and applies Kuhn’s ideas to the science of today. Usefully keyed to the separate sections of the book, Hacking’s introduction provides important background information as well as a contemporary context. Newly designed, with an expanded index, this edition will be eagerly welcomed by the next generation of readers seeking to understand the history of our perspectives on science. (shrink)

What are mental states? When we talk about people’s beliefs or desires, are we talking about what is happening inside their heads? If so, might cognitive science show that we are wrong? Might it turn out that mental states do not exist? Mental fictionalism offers a new approach to these longstanding questions about the mind. Its core idea is that mental states are useful fictions. When we talk about mental states, we are not formulating hypotheses about people’s inner machinery. Instead, (...) we simply talk "as if" people had certain inner states, such as beliefs or desires, in order to make sense of their behaviour. This is the first book dedicated to exploring mental fictionalism. Featuring contributions from established authors as well as up-and-coming scholars in this burgeoning field, the book reveals the exciting potential of a fictionalist approach to the mind, as well as the challenges it faces. In doing so, it offers a fresh perspective on foundational debates in the philosophy of mind, such as the nature of mental states and folk psychology, as well as hot topics in the field, such as embodied cognition and mental representation. Mental Fictionalism: Philosophical Explorations essential reading for advanced undergraduates, postgraduates and professionals alike. (shrink)

The notion that it is useful to specify norms progressively in order to resolve doubts about what to do, which I developed initially in a 1990 article, has been only partly assimilated by the bioethics literature. The thought is not just that it is helpful to work with relatively specific norms. It is more than that: specification can replace deductive subsumption and balancing. Here I argue against two versions of reliance on balancing that are prominent in recent bioethical discussions. (...) Without meaning to address the substance or the overall merits of either view I criticize, I attack Gert, Culver and Clouser's implicit reliance on some overall dimension of balancing as a basis of resolving conflicts among norms and Beauchamp and Childress's residual acceptance of 'justified balancing'. The former authors' description of resolving conflicts depends upon a type of value commensurability that (as they otherwise seem to admit) does not obtain, while the latter authors' role for justified balancing would be better served by continued specification. (shrink)

In the debates regarding the ethics of human organoid biobanking, the locus of donor autonomy has been identified in processes of consent. The problem is that, by focusing on consent, biobanking processes preclude adequate engagement with donor autonomy because they are unable to adequately recognise or respond to factors that determine authentic choice. This is particularly problematic in biobanking contexts associated with organoid research or the clinical application of organoids because, given the probability of unforeseen and varying purposes for which (...) a donor’s organoids could be employed and given the different ways in which a donor can relate to her biospecimens, a donor can value her organoids differently in different contexts and her reasons for autonomously permitting use of her cells and tissues in one case may not support an autonomous decision in another. In response, this paper has three aims: firstly, to make the case for why organoid biobanks ought to respect donor autonomy conceived as authentic choice; secondly, to explore the autonomy-respecting limits of established and widely prevalent models of biobank consent; and thirdly, to propose certain conditions that organoid biobanks ought to support or facilitate in order to respect donor autonomy. (shrink)