We extend the gap 1 cardinal transfer theorem → to any language of cardinality ≤λ, where λ is a regular cardinal. This transfer theorem has been proved by Chang under GCH for countable languages and by Silver in some cases for bigger languages . We assume the existence of a coarse -morass instead of GCH.

Let ℒ be a first-order language of cardinality κ++ with a distinguished unary predicate symbol U. In this paper we prove, working on L, the two cardinal transfer theorem (κ⁺,κ) ⇒ (κ++,κ⁺) for this language. This problem was posed by Chang and Keisler more than twenty years ago.

BackgroundSocial cognition and competence are a key part of daily interactions and essential for satisfying relationships and well-being. Pediatric neurological and psychological conditions can affect social cognition and require assessment and remediation of social skills. To adequately approximate the complex and dynamic nature of real-world social interactions, innovative tools are needed. The aim of this study was to document the performance of adolescents on two versions of a serious video game presenting realistic, everyday, socio-moral conflicts, and to explore whether their (...) performance is associated with empathy or sense of presence, factors known to influence social cognition.MethodsParticipants first completed a pre-test measure of socio-moral reasoning based on three dilemmas from a previously validated computer task. Then, they either played an evaluative version or an adaptive version of a video game presenting nine social situations in which they made socio-moral decisions and provided justifications. In the evaluative version, participants’ audio justifications were recorded verbatim and coded manually to obtain a socio-moral reasoning maturity score. In the adaptive version, tailored feedback and social reinforcements were provided based on participant responses. An automatic coding algorithm developed using artificial intelligence was used to determine socio-moral maturity level in real-time and to provide a basis for the feedback and reinforcements in the game. All participants then completed a three-dilemma post-test assessment.ResultsThose who played the adaptive version showed improved SMR across the pre-test, in-game and post-test moral maturity scores, F = 9.81, pHF < 0.001, ϵ2 = 0.21, but those who played the Evaluative version did not. Socio-moral reasoning scores from both versions combined did not correlate with empathy or sense of presence during the game, though results neared significance. The study findings support preliminary validation of the game as a promising method for assessing and remediating social skills during adolescence. (shrink)

We define a structure which is much simpler than a morass, but whose existence is equivalent to the existence of a morass.

The problem of statistical inference based on a partial measurement (“coarse-graining”) requires the specification of an a priori distribution. We reformulate the ordinary theory such as to encompass systematically a wide range of a priori distributions (“relative coarse-graining”). This is done in a mathematical setting which admits an interpretation in both classical probability and quantum mechanics. The formalism is illustrated in a few simple examples, such as the die whose geometrical shape is known, the spin in thermal equilibrium (...) with an unknown reservoir, and the position measurement of a one-dimensional particle. It is shown that some of the limitations of the usual theory are a consequence of the fact that it is restricted to “equidistributed” (symmetric) a priori states. (shrink)

In this paper I first argue that the objection which is most commonly levelled against the coarse-graining approach-viz. that it introduces an element of subjectivity into what ought to be a purely objective formalism-is ultimately unfounded. I then proceed to argue that two different objections to the coarse-graining approach indicate that it is an inadequate approach to statistical mechanics. The first objection is based on the fact that the appeal to appearances by the coarse-graining approach fails to (...) justify the coarse-graining strategy of ignoring the physical differences between so-called quasi-equilibrium distributions and equilibrium distributions. The second objection is centred on the notion of a coarse-grained entropy. I will argue that the required increase in the coarse-grained entropy is obtained by disregarding the dynamical constraints on the system. This undermines the very task statistical mechanics has set out to accomplish, viz. to provide a microdynamical underpinning of thermodynamics. (shrink)

For [Formula: see text], the coarse similarity class of A, denoted by [Formula: see text], is the set of all [Formula: see text] such that the symmetric difference of A and B has asymptotic density 0. There is a natural metric [Formula: see text] on the space [Formula: see text] of coarse similarity classes defined by letting [Formula: see text] be the upper density of the symmetric difference of A and B. We study the metric space of (...) class='Hi'>coarse similarity classes under this metric, and show in particular that between any two distinct points in this space there are continuum many geodesic paths. We also study subspaces of the form [Formula: see text] where [Formula: see text] is closed under Turing equivalence, and show that there is a tight connection between topological properties of such a space and computability-theoretic properties of [Formula: see text]. We then define a distance between Turing degrees based on Hausdorff distance in the metric space [Formula: see text]. We adapt a proof of Monin to show that the Hausdorff distances between Turing degrees that occur are exactly 0, [Formula: see text], and 1, and study which of these values occur most frequently in the senses of Lebesgue measure and Baire category. We define a degree a to be attractive if the class of all degrees at distance [Formula: see text] from a has measure 1, and dispersive otherwise. In particular, we study the distribution of attractive and dispersive degrees. We also study some properties of the metric space of Turing degrees under this Hausdorff distance, in particular the question of which countable metric spaces are isometrically embeddable in it, giving a graph-theoretic sufficient condition for embeddability. Motivated by a couple of issues arising in the above work, we also study the computability-theoretic and reverse-mathematical aspects of a Ramsey-theoretic theorem due to Mycielski, which in particular implies that there is a perfect set whose elements are mutually 1-random, as well as a perfect set whose elements are mutually 1-generic. Finally, we study the completeness of [Formula: see text] from the perspectives of computability theory and reverse mathematics. (shrink)

After many years of enduring the drought and famine of Quinean ontology and Carnapian meta-ontology, the notion of ground, with its distinctively philosophical flavor, finally promises to give metaphysicians something they can believe in again and around which they can rally: their very own metaphysical explanatory connection which apparently cannot be reduced to, or analyzed in terms of, other familiar idioms such as identity, modality, parthood, supervenience, realization, causation or counterfactual dependence. Often, phenomena such as the following are cited as (...) putative examples of grounding connections: systematic connections between entire realms of facts (mental/physical; moral/natural; etc.); truthmaking (e.g., the relation between the truth of the proposition that snow is white and snow’s being white); logical cases (e.g., the connection between conjunctive facts or disjunctive facts and their constituent facts); the determinate/determinable relation (e.g., the relation between something’s being maroon and its being red). I argue in this paper that classifying all of these phenomena as exhibiting grounding connections does not achieve much in the way of illumination. In fact, by treating a collection of phenomena which is in fact heterogeneous as though it were homogeneous, we have, if anything, taken a dialectical step backward. (shrink)

The paper discusses various relationships between the concepts mentioned in the title. In Section 1 Todorcevic functions are shown to arise from both morasses and square. In Section 2 the theme is of supplements to morasses which have some of the flavour of square. Distinctions are drawn between differing concepts. In Section 3 forcing axioms related to the ideas in Section 2 are discussed.

Explaining the emergence of individuality in the process of evolution remains a challenge; it faces the difficulty of characterizing adequately what ‘emergence’ amounts to. Here, I present a pragmatic account of individuality in which I take up this challenge. Following this account, individuals that emerge from an evolutionary transition in individuality are coarse-grained entities: entities that are summaries of lower-level evolutionary processes. Although this account may _prima facie_ appear to ultimately rely on epistemic considerations, I show that it can (...) be used to vindicate the emergence of individuals in a quasi-ontological sense. To this end, I discuss a recent account of evolutionary transitions in individuality proposed by Godfrey-Smith and Kerr (Brit J Philos Sci 64(1):205–222, 2013) where a transition occurs through several stages, each with an accompanying model. I focus on the final stage where higher-level entities are ascribed a separate fitness parameter, while they were not in the previous stages. In light of my account, I provide some justification for why such a change in parameters is necessary and cannot be dismissed as merely epistemic. (shrink)

Let S∞ denote the topological group of permutations of the natural numbers. A closed subgroup G of S∞ is called oligomorphic if for each n, its natural action on n-tuples of natural numbers has onl...

The emergence of macroscopic variables can be effected through coarse graining. Despite practical and fundamental benefits conveyed by this partitioning of state space, the apparently subjective nature of the selection of coarse grains has been considered problematic. We provide objective selection methods, deriving from the existence of relatively slow dynamical time scales. Using a framework for nonequilibrium statistical mechanics developed by us, we show the emergence of both spatial variables and order parameters. Although significant objective criteria are introduced (...) in the coarse graining, we do not provide a unique prescription. Most significantly, the grains, and by implication entropy, are only defined modulo a characteristic time scale of observation. (shrink)

The renormalization group has been characterized as merely a coarse-graining procedure that does not illuminate the microscopic content of quantum field theory but merely gets us from that content, as given by axiomatic QFT, to macroscopic predictions. I argue that in the constructive field theory tradition, RG techniques do illuminate the microscopic dynamics of a QFT, which are not automatically given by axiomatic QFT. RG techniques in constructive field theory are also rigorous, so one cannot object to their foundational (...) import on grounds of lack of rigor. (shrink)

The renormalization group has been characterized as merely a coarse-graining procedure that does not illuminate the microscopic content of quantum field theory, but merely gets us from that content, as given by axiomatic QFT, to macroscopic predictions. I argue that in the constructive field theory tradition, RG techniques do illuminate the microscopic dynamics of a QFT, which are not automatically given by axiomatic QFT. RG techniques in constructive field theory are also rigorous, so one cannot object to their foundational (...) import on grounds of lack of rigor. (shrink)

This chapter discusses why the grounding idiom does not perform as well as we have been led to believe in providing a plausible approach to relative fundamentality. Grounding suffers from some of same deficiencies as supervenience: most prominently, grounding also fails to be sufficiently fine-grained to do its intended explanatory work. In addition, there is doubt as to whether the phenomena collected together under the rubric of grounding are really unified by the presence of a single relation. Grounding turns out (...) not to be helpful in capturing and illuminating what is philosophically important about the traditional substance/non-substance distinction. Although grounding performs better than supervenience in some ways, it does not solve all of the problems to which a supervenience-based approach to relative fundamentality falls prey. (shrink)

We prove that in the Cohen extension adding ℵ3 generic reals to a model of containing a simplified (ω1, 2)‐morass, gap‐2 morass‐definable η1‐orderings with cardinality ℵ3 are order‐isomorphic. Hence it is consistent that and that morass‐definable η1‐orderings with cardinality of the continuum are order‐isomorphic. We prove that there are ultrapowers of over ω that are gap‐2 morass‐definable. The constructions use a simplified gap‐2 morass, and commutativity with morass‐maps and morass‐embeddings, to extend a transfinite (...) back‐and‐forth construction of order‐type ω1 to an order‐preserving bijection between objects of cardinality ℵ3. (shrink)

Frank and Nagel are very interested in the causes and consequences of moralizing about addiction. If addiction is a disease, moralistic concerns are sidelined. If it's a choice, we'd better identify clear reasons to absolve addicts from blame. While these are interesting considerations, they don't have much to do with the model of addiction I put forward in the target article.

The rise of appeals to intuitive theories in many areas of cognitive science must cope with a powerful fact. People understand the workings of the world around them in far less detail than they think. This illusion of knowledge depth has been uncovered in a series of recent studies and is caused by several distinctive properties of explanatory understanding not found in other forms of knowledge. Other experimental work has shown that people do have skeletal frameworks of expectations that constrain (...) richer ad hoc theory construction on the fly. These frameworks are supplemented by an ability to evaluate and rely on the division of cognitive labour in one's culture, an ability shown to be present even in young children. (shrink)

Feynman's sum-over-histories formulation of quantum mechanics has been considered a useful calculational tool in which virtual Feynman histories entering into a coherent quantum superposition cannot be individually measured. Here we show that sequential weak values, inferred by consecutive weak measurements of projectors, allow direct experimental probing of individual virtual Feynman histories, thereby revealing the exact nature of quantum interference of coherently superposed histories. Because the total sum of sequential weak values of multitime projection operators for a complete set of orthogonal (...) quantum histories is unity, complete sets of weak values could be interpreted in agreement with the standard quantum mechanical picture. We also elucidate the relationship between sequential weak values of quantum histories with different coarse graining in time and establish the incompatibility of weak values for nonorthogonal quantum histories in history Hilbert space. Bridging theory and experiment, the presented results may enhance our understanding of both weak values and quantum histories. (shrink)

We further develop a previously introduced method of constructing forcing notions with the help of morasses. There are two new results: (1) If there is a simplified (ω 1 , 1)-morass, then there exists a ccc forcing of size ω 1 that adds an ω 2 -Suslin tree. (2) If there is a simplified (ω 1 , 2)-morass, then there exists a ccc forcing of size ω 1 that adds a 0-dimensional Hausdorff topology τ on ω 3 which (...) has spread s(τ) = ω 1 . While (2) is the main result of the paper, (1) is only an improvement of a previous result, which is based on a simple observation. Both forcings preserve GCH. To show that the method can be changed to produce models where CH fails, we give an alternative construction of Koszmider's model in which there is a chain 〈X α | α < ω 2 〉 such that X α ⊆ ω 1 , X β — X α is finite and X α — X β has size ω 1 for all β < α < ω 2. (shrink)

This paper concerns the theory of morasses. In the early 1970s Jensen defined (κ,α)-morasses for uncountable regular cardinals κ and ordinals $\alpha . In the early 1980s Velleman defined (κ, 1)-simplified morasses for all regular cardinals κ. He showed that there is a (κ, 1)-simplified morass if and only if there is (κ, 1)-morass. More recently he defined (κ, 2)-simplified morasses and Jensen was able to show that if there is a (κ, 2)-morass then there is a (...) (κ, 2)-simplified morass. In this paper we prove the converse of Jensen's result, i.e., that if there is a (κ, 2)-simplified morass then there is a (κ, 2)-morass. (shrink)

This paper concerns the theory of morasses. In the early 1970s Jensen defined -morasses for uncountable regular cardinals $\kappa$ and ordinals $\alpha < \kappa$. In the early 1980s Velleman defined -simplified morasses for all regular cardinals $\kappa$. He showed that there is a -simplified morass if and only if there is -morass. More recently he defined -simplified morasses and Jensen was able to show that if there is a -morass then there is a -simplified morass. In (...) this paper we prove the converse of Jensen's result, i.e., that if there is a -simplified morass then there is a -morass. (shrink)

The Martin-Steel coarse inner model theory is employed in obtaining new results in descriptive set theory. $\underset{\sim}{\Pi}$ determinacy implies that for every thin Σ 1 2 equivalence relation there is a Δ 1 3 real, N, over which every equivalence class is generic--and hence there is a good Δ 1 2 (N ♯ ) wellordering of the equivalence classes. Analogous results are obtained for Π 1 2 and Δ 1 2 quasilinear orderings and $\underset{\sim}{\Pi}^1_2$ determinacy is shown to imply (...) that every Π 1 2 prewellorder has rank less than $\underset{\sim}{\delta}^1_2$. (shrink)

This paper concerns the theory of morasses. In the early 1970s Jensen defined -morasses for uncountable regular cardinals $\kappa$ and ordinals $\alpha < \kappa$. In the early 1980s Velleman defined -simplified morasses for all regular cardinals $\kappa$. He showed that there is a -simplified morass if and only if there is -morass. More recently he defined -simplified morasses and Jensen was able to show that if there is a -morass then there is a -simplified morass. In (...) this paper we prove the converse of Jensen's result, i.e., that if there is a -simplified morass then there is a -morass. (shrink)

We show how to construct Gitik’s short extenders gap-3 forcing using a morass, and that the forcing notion is of Prikry type.

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.

In this chapter, I discuss the possibility of using genome editing technologies in the context of assisted reproduction. I present the most prominent arguments in favour of and against this use of genome editing technologies, and explore two strategies used in bioethics in the event of moral disagreement to analyse the questions at hand and to develop morally sound policies. These strategies are: the clarification of the facts regarding a new technology and the formulation of the best philosophical argument. I (...) contend that both approaches are theoretically flawed and might result in states of affairs that fail to promote peoples’ well-being. I then argue that we should focus instead on finding at least some common ground in order to move forward in the debate on genome editing, building a regulatory framework that lightens “the burden of human existence”, whilst still accommodating opposing views as much as possible. Furthermore, I argue that insights from moral psychology and democratic governance can assist us in these challenges. (shrink)

McGrew, McGrew and Vestrup (MMV) have argued that the fine-tuning anthropic principle argument for the existence of God fails because no probabilities can be assigned to the likelihood that physical constants fall in some finite interval. In particular, the fine-tuning argument that, say, some constant must lie in the range (1.000,1.001) in order for intelligent life to be possible is no better than a seemingly absurd coarse-tuning argument based on the need for that constant to lie in the range (...) (0.001, 10000000). The author of this piece defends the coarse tuning argument as a rational piece of reasoning, and, further, argues that the countable additivity assumption in the MMV paper can be dropped in favor of finite additivity. (shrink)

Dariusz Łukasiewicz has investigated in depth the “Argument from Chance” which argues that the data revealing chance in the world are incompatible with Divine Providence. Łukasiewicz agrees that these data undermine the traditional model of Providence—a fine-grained model in which every single detail is controlled by God—but maintains that they are not incompatible with a coarse-grained model—in which God leaves to chance many aspects of history (including some horrendous evils). Furthermore, Łukasiewicz provides independent reasons to prefer this coarse-grained (...) model. Even though I agree that a maximally fine-grained model is undermined by the scientific data, I argue that this is no sufficient reason to adopt a model as coarse-grained as Łukasiewicz’s. I propose a model of intermediate level of fine-grainedness which could avoid the drawbacks of both extremes, and seems to me to provide a more traditional approach to the problem of evil. (shrink)

ABSTRACT McCabe [2021: 137–40] identifies a crucial ambiguity in the terms ‘learns’ and ‘knows’. Such terms can be read as either ‘perfective’ or ‘imperfective’. This is an aspect difference. The former indicates a settled state, the latter a directed process. McCabe uses this insight to show how Socrates can rebut the sophists’ view of meaning, render compelling Socrates’ self-refutation arguments, and explain the Socratic connections between learning, knowledge, and how one should live. In the final section of the Euthydemus, Euthydemus (...) offers the ‘Omniscience Sophism’, and the related, rather cheeky, ‘Father Sophisms’. McCabe [ibid.: 140–2] suggests that the Omniscience Sophism might be addressed by identifying an aspect ambiguity, but does not follow up her point in detail. In this response, I argue that McCabe’s instinct is good and that a relative term, such as ‘knowledgeable’, can be understood as having two senses. That distinction is between what I call ‘fine-grained’ and ‘coarse-grained’ senses of ‘knowledgeable’. I suggest that this distinction that tracks McCabe’s aspect distinction between senses of ‘learns’ and best explains the fallacy committed in the Omniscience Sophism. (shrink)

What position on dualism does medicine require? Our understanding of that ques- tion has been dictated by holism, as defined by the biopsychosocial model, since the late twentieth century. Unfortunately, holism was characterized at the start with con- fused definitions of ‘dualism’ and ‘reductionism’, and that problem has led to a deep, unrecognized conceptual split in the medical professions. Some insist that holism is a nonreductionist approach that aligns with some form of dualism, while others insist it’s a reductionist view (...) that sets out to eradicate dualism. It’s important to consider each version. Nonreductive holism is philosophically consistent and clinically unprob- lematic. Reductive holism, however, is conceptually incoherent—yet it is the basis for the common idea that the boundary between medical and mental health disorders must be vague. When we trace that idea through to its implementation in medical practice, we find evidence that it compromises the safety of patient care in the large portion of cases where clinicians grapple with diagnosis at the boundary between psychiatry and medicine. Having established that medicine must embrace some form of nonreduc- tionism, I argue that Chalmers’ naturalistic dualism is a stronger prima facie candidate than the nonreductive alternatives. Regardless of which form of nonreductionism we prefer, some philosophical corrections are needed to give medicine a safe and coherent foundation. (shrink)

By using the notion of a simplified (κ,1)-morass, we construct κ-thin-tall, κ-thin-thick and, in a forcing extension, κ-very thin-thick superatomic Boolean algebras for every infinite regular cardinal κ.