In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablity and show that this lies strictly between VC-minimality and dp-minimality. To do this we prove a general result about set systems with independence dimension ≤ 1. Next, we define the notion of weak VC-minimality, show it lies strictly between VC-minimality and dependence, and show that all unstable weakly VC-minimal theories interpret an infinite linear order. Finally, we define the notion (...) full VC-minimality, show that this lies strictly between weak o-minimality and VC-minimality, and show that theories that are fully VC-minimal have low VC-density. (shrink)

In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show that this is enough to characterize many algebraic theories. For example, dp-small ordered groups are abelian divisible and dp-small ordered fields are real closed.

We consider VC-minimal theories admitting unpackable generating families, and show that in such theories, forking of formulae over a model M is equivalent to containment in global types definable over M, generalizing a result of Dolich on o-minimal theories in [4].

We show that any formula with two free variables in a Vapnik–Chervonenkis (VC) minimal theory has VC-codensity at most 2. Modifying the argument slightly, we give a new proof of the fact that, in a VC-minimal theory where acleq= dcleq, the VC-codensity of a formula is at most the number of free variables (from the work of Aschenbrenner et al., the author, and Laskowski).

We show that in the theory of infinite trees the VC-function is optimal. This generalizes a result of Simon showing that trees are dp-minimal.

We compute that the index set of PAC-learnable concept classes is m-complete Σ30\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Sigma^{0}_{3}}$$\end{document} within the set of indices for all concept classes of a reasonable form. All concept classes considered are computable enumerations of computable Π10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Pi^{0}_{1}}$$\end{document} classes, in a sense made precise here. This family of concept classes is sufficient to cover all standard examples, and also has the property that (...) PAC learnability is equivalent to finite VC dimension. (shrink)

A theory $T$ is shown to have an ICT pattern of depth $k$ in $n$ variables iff it interprets some $k$ -maximum VC class in $n$ parameters.

This essay demonstrates a previously unnoticed connection between formal and statistical learning theory with regard to Nelson Goodman’s new riddle of induction. Discussions of Goodman’s riddle in formal learning theory explain how conjecturing “all green” before “all grue” can enhance efficient convergence to the truth, where efficiency is understood in terms of minimizing the maximum number of retractions or “mind changes.” Vapnik-Chervonenkis (VC) dimension is a central concept in statistical learning theory and is similar to Popper’s notion of degrees of (...) testability. I show that for a class inductive problems of which Goodman’s riddle is one example, a reliable inductive method minimizes the maximum number of mind changes exactly if it always conjectures the hypothesis from the set with lowest VC dimension consistent with the data. I also discuss the relevance of these results to language invariance and curve fitting. (shrink)

It has consistently been shown that agents judge the intervals between their actions and outcomes as compressed in time, an effect named intentional binding. In the present work, we investigated whether this effect is result of prior bias volunteers have about the timing of the consequences of their actions, or if it is due to learning that occurs during the experimental session. Volunteers made temporal estimates of the interval between their action and target onset , or between two events . (...) Our results show that temporal estimates become shorter throughout each experimental block in both conditions. Moreover, we found that observers judged intervals between action and outcomes as shorter even in very early trials of each block. To quantify the decrease of temporal judgments in experimental blocks, exponential functions were fitted to participants’ temporal judgments. The fitted parameters suggest that observers had different prior biases as to intervals between events in which action was involved. These findings suggest that prior bias might play a more important role in this effect than calibration-type learning processes. (shrink)

That humans can categorize in different ways does not imply that there are qualitatively distinct underlying natural kinds or that the field of concepts splinters. Rather, it implies that the unitary goal of forming concepts is important enough that it receives redundant expression in cognition. Categorization science focuses on commonalities involved in concept learning. Eliminating makes this more difficult.

We discuss in what sense the decay-scattering system is a minimal phenomenological theory for particle decay and resonance scattering.

A provocative ontological-cum-semantic position asserting that the right ontology is austere in its exclusion of numerous common-sense and scientific posits and that many statements employing such posits are nonetheless true. The authors of Austere Realism describe and defend a provocative ontological-cum-semantic position, asserting that the right ontology is minimal or austere, in that it excludes numerous common-sense posits, and that statements employing such posits are nonetheless true, when truth is understood to be semantic correctness under contextually operative semantic standards. (...) Terence Horgan and Matjaz Potrc argue that austere realism emerges naturally from consideration of the deep problems within the naive common-sense approach to truth and ontology. They offer an account of truth that confronts these deep internal problems and is independently plausible: contextual semantics, which asserts that truth is semantically correct affirmability. Under contextual semantics, much ordinary and scientific thought and discourse is true because its truth is indirect correspondence to the world. After offering further arguments for austere realism and addressing objections to it, Horgan and Potrc consider various alternative austere ontologies. They advance a specific version they call "blobjectivism"--the view that the right ontology includes only one concrete particular, the entire cosmos, which, although it has enormous local spatiotemporal variability, does not have any proper parts. The arguments in Austere Realism are powerfully made and concisely and lucidly set out. The authors' contentions and their methodological approach--products of a decade-long collaboration--will generate lively debate among scholars in metaphysics, ontology, and philosophy. (shrink)

The authors of Austere Realism describe and defend a provocative ontological-cum-semantic position, asserting that the right ontology is minimal or austere, in that it excludes numerous common-sense posits, and that statements employing such posits are nonetheless true, when truth is understood to be semantic correctness under contextually operative semantic standards. Terence Horgan and Matjaz [hacek over z] Potrc [hacek over c] argue that austere realism emerges naturally from consideration of the deep problems within the naive common-sense approach to truth (...) and ontology. They offer an account of truth that confronts these deep internal problems and is independently plausible: contextual semantics, which asserts that truth is semantically correct affirmability. Under contextual semantics, much ordinary and scientific thought and discourse is true because its truth is indirect correspondence to the world. After offering further arguments for austere realism and addressing objections to it, Horgan and Potrc [hacek over c] consider various alternative austere ontologies. They advance a specific version they call "blobjectivism"--the view that the right ontology includes only one concrete particular, the entire cosmos, which, although it has enormous local spatiotemporal variability, does not have any proper parts. The arguments in Austere Realism are powerfully made and concisely and lucidly set out. The authors' contentions and their methodological approach--products of a decade-long collaboration--will generate lively debate among scholars in metaphysics, ontology, and philosophy. Terence E. Horgan is Professor of Philosophy at the University of Arizona. Matjaz [hacek over z] Potrc [hacek over c] is Professor of Philosophy at the University of Ljubljana. (shrink)

Vagueness is given a philosophically neutral definition in terms of an epistemic notion of tolerance. Such a notion is intended to capture the thesis that vague terms draw no known boundary across their range of signification and contrasts sharply with the semantic notion of tolerance given by Wright (1975, 1976). This allows us to distinguish vagueness from superficially similar but distinct phenomena such as semantic incompleteness. Two proofs are given which show that vagueness qua epistemic tolerance and vagueness qua borderline (...) cases (when properly construed to exclude terms which are stipulated to give rise to borderline cases) are in fact conceptually equivalent dimensions of vagueness, contrary to what might initially be expected. It is also argued that the common confusion of tolerance and epistemic tolerance has skewed the vagueness debate in favour of indeterminist over epistemic conceptions of vagueness. Clearing up that confusion provides an indirect argument in favour of epistemicism. Finally, given the equation of vagueness with epistemic tolerance, it is shown that there must be radical higher-order vagueness, contrary to what many authors have argued. (shrink)

Our aim in the present paper is to approach the nature of life from the perspective of autonomy, showing that this perspective can be helpful for overcoming the traditional Cartesian gap between the physical and cognitive domains. We first argue that, although the phenomenon of life manifests itself as highly complex and multidimensional, requiring various levels of description, individual organisms constitute the core of this multifarious phenomenology. Thereafter, our discussion focuses on the nature of the organization of individual living entities, (...) proposing autonomy as the main concept to grasp it. In the second part of the article we show how autonomy is also fundamental to explaining major evolutionary transitions, in an attempt to rethink evolution from the point of view of the organizational structure of the entities/organisms involved. This gives further support to the idea of autonomy not only as a key to understanding life in general but also the complex expressions of it that we observe on our planet. Finally, we suggest a possible general principle that underlies those evolutionary transitions, which allow for the open-ended redefinition of autonomous systems: namely, the relative dynamic decoupling that must be articulated among distinct parts, modules or modes of operation in these systems. (shrink)

To the best of our current understanding, quantum mechanics is part of the most fundamental picture of the universe. It is natural to ask how pure and minimal this fundamental quantum description can be. The simplest quantum ontology is that of the Everett or Many-Worlds interpretation, based on a vector in Hilbert space and a Hamiltonian. Typically one also relies on some classical structure, such as space and local configuration variables within it, which then gets promoted to an algebra (...) of preferred observables. We argue that even such an algebra is unnecessary, and the most basic description of the world is given by the spectrum of the Hamiltonian and the components of some particular vector in Hilbert space. Everything else—including space and fields propagating on it—is emergent from these minimal elements. (shrink)

: When children and incapacitated adults are enrolled in research that cannot directly benefit them, they can be exposed to no more than "minimal" risks, according to guidelines accepted around the world. We need a new standard for what "minimal" risks are, howeve--one that recognizes that participating in nonbeneficial research is like participating in a charitable activity. Such a standard appears likely to provide more stringent protections for these vulnerable populations.

To what risks may children participating in research be subjected? Institutional review boards can stand surrogate for parents by filtering out studies whose risk is unacceptably high.

Nonclassical theories of truth have in common that they reject principles of classical logic to accommodate an unrestricted truth predicate. However, different nonclassical strategies give up different classical principles. The paper discusses one criterion we might use in theory choice when considering nonclassical rivals: the maxim of minimal mutilation.

A traditional view of mathematical modeling holds, roughly, that the more details of the phenomenon being modeled that are represented in the model, the better the model is. This paper argues that often times this ‘details is better’ approach is misguided. One ought, in certain circumstances, to search for an exactly solvable minimal model—one which is, essentially, a caricature of the physics of the phenomenon in question.

As patient autonomy expands, a highly controversial issue has emerged. Should the advance directives of refusing life-saving treatments or requesting euthanasia of persons with dementia who express changed minds or are often in a happy state be fulfilled? There are two autonomy-related positions. The mainstream position in philosophical discussions supports the priority of ADs based on precedent autonomy. Buchanan and Brock, and Dworkin represent this view. The other position supports the priority of PWDs’ current wishes based on minimal autonomy (...) represented by Jaworska. By rethinking the theoretical and practical challenges of the two positions and their arguments respectively, the paper concludes that in such a scenario, the priority of ADs is morally indefensible, and it is also challenging to establish minimal autonomy defend the moral priority of PWDs’ current wishes. For PWDs whose past values, beliefs, and preferences fade away but who retain apparent intrinsic sentience of well-being, a modified defined quality-of-life approach serves as another reasonable basis in their medical decision-making, and the ADs and the QoL should be further merged to reduce the uncertainty of the grey zone. (shrink)

When children and incapacitated adults are enrolled in research that cannot directly benefit them, they can be exposed to no more than “minimal” risks, according to guidelines accepted around the world. We need a new standard for what “minimal” risks are, however—one that recognizes that participating in nonbeneficial research is like participating in a charitable activity. Such a standard appears likely to provide more stringent protections for these vulnerable populations.

Despite the lack of invariance problem (the many‐to‐many mapping between acoustics and percepts), human listeners experience phonetic constancy and typically perceive what a speaker intends. Most models of human speech recognition (HSR) have side‐stepped this problem, working with abstract, idealized inputs and deferring the challenge of working with real speech. In contrast, carefully engineered deep learning networks allow robust, real‐world automatic speech recognition (ASR). However, the complexities of deep learning architectures and training regimens make it difficult to use them to (...) provide direct insights into mechanisms that may support HSR. In this brief article, we report preliminary results from a two‐layer network that borrows one element from ASR, long short‐term memory nodes, which provide dynamic memory for a range of temporal spans. This allows the model to learn to map real speech from multiple talkers to semantic targets with high accuracy, with human‐like timecourse of lexical access and phonological competition. Internal representations emerge that resemble phonetically organized responses in human superior temporal gyrus, suggesting that the model develops a distributed phonological code despite no explicit training on phonetic or phonemic targets. The ability to work with real speech is a major advance for cognitive models of HSR. (shrink)

A subset A $\subseteq$ M of a totally ordered structure M is said to be convex, if for any a, b $\in A: [a . A complete theory of first order is weakly o-minimal (M. Dickmann [D]) if any model M is totally ordered by some $\emptyset$ -definable formula and any subset of M which is definable with parameters from M is a finite union of convex sets. We prove here that for any model M of a weakly o- (...) class='Hi'>minimal theory T, any expansion M + of M by a family of unary predicates has a weakly o-minimal theory iff the set of all realizations of each predicate is a union of a finite number of convex sets (Theorem 63), that solves the Problem of Cherlin-Macpherson-Marker-Steinhorn [MMS] for the class of weakly o-minimal theories. (shrink)

The phrase “minimal risk,” as defined in the United States’ federal research regulations, is ambiguous and poorly defined. This article argues that most of the ambiguity that one finds in the phrase stems from the “daily life risks” standard in the definition of minimal risk. In this article, the author argues that the daily life risks standard should be dropped and that “minimal risk” should be defined as simply “the probability and magnitude of the harm or discomfort (...) anticipated in research are not greater than those encountered during the performance of routine physical or psychological examinations or tests”. (shrink)

This paper explicates how we might positively understand the distinctive, nonconceptual experience of our own actions and experiences by drawing on insights from a radically enactive take on phenomenal experience. We defend a late-developing relationalism about the emergence of explicit, conceptually based self-awareness, proposing that the latter develops in tandem with the mastery of self-reflective narrative practices. Focusing on the case of human newborns, Sect. 1 reviews and rejects claims that the capacities of actors to keep track of aspects of (...) themselves—e.g. their bodies, body parts, movements, activities, actions and experiences—when coordinating what they do equates to or is best explained by positing minimal, tacit awareness of their experiences as their own. Section 2 then considers and resists more familiar arguments, based on the so-called reflexivity thesis, that take such minimal self-awareness to be implied wherever there is any kind of phenomenal experience. In place of these ideas, we promote an alternative proposal of what is involved when agents keep track of aspects of themselves, drawing on a radically enactive conception of basic experience. Section 3 concludes by proposing that our first conceptual, explicit sense of self is something that only arrives on the scene once we become able to hold our own—through the support of others—in discursive, narrative practices that give us a conceptual grip on what it is to be a temporally extended self that persists over time. (shrink)

The field of clinical ethics consultation has matured into a multidisciplinary profession, with clinical ethics consultants (CECs) being trained in bioethics, philosophy, theology, law, medicine, n...

An erotetic calculus for a given logic constitutes a sequent-style proof-theoretical formalization of the logic grounded in Inferential Erotetic Logic ). In this paper, a new erotetic calculus for Classical Propositional Logic ), dual with respect to the existing ones, is given. We modify the calculus to obtain complete proof systems for the propositional part of paraconsistent logic CLuN and its extensions CLuNs and mbC. The method is based on dual resolution. Moreover, the resolution rule is non-clausal. According to the (...) authors knowledge, this is the first account of resolution for mbC. Last but not least, as the method is grounded in IEL, it constitutes an important tool for the so-called question-processing. (shrink)

0-categorical o-minimal structures were completely described by Pillay and Steinhorn 565–592), and are essentially built up from copies of the rationals as an ordered set by ‘cutting and copying’. Here we investigate the possible structures which an 0-categorical weakly o-minimal set may carry, and find that there are some rather more interesting examples. We show that even here the possibilities are limited. We subdivide our study into the following principal cases: the structure is 1-indiscernible, in which case all (...) possibilities are classified up to binary structure; the structure is 2-indiscernible, classified up to ternary structure; the structure is 3-indiscernible, in which case we show that it is k-indiscernible for every finite k. We also make some remarks about the possible structures of higher arities which an 0-categorical weakly o-minimal structure may carry. (shrink)

This thesis develops a detailed account of the emergence of for all practical purposes continuous, quasi-classical world histories from the discontinuous, stochastic micro dynamics of Minimal Bohmian Mechanics (MBM). MBM is a non-relativistic quantum theory. It results from excising the guiding equation from standard Bohmian Mechanics (BM) and reinterpreting the quantum equilibrium hypothesis as a stochastic guidance law for the random actualization of configurations of Bohmian particles. On MBM, there are no continuous trajectories linking up individual configurations. Instead, individual (...) configurations are actualized independently of each other, carving out the decoherence-induced branching structure of the universal wave function. Yet, by contrast to the Everett interpretation, branches of the universal wave function are not actualized in parallel, i.e. all at the same time. Rather, world branches, on MBM, are actualized sequentially. -/- For an introduction to MBM, the transition from BM to MBM is described, and their empirical equivalence is established. I present the conditions under which MBM can be classified as a primitive ontology (PO) theory, regarded as crucial for the acceptance of a theory as Bohmian by many proponents of BM. While rendering MBM compatible with the PO approach, it must not fall prey to the problem of communication, arising from the two-space reading of BM. -/- The issue of temporal solipsism, identified by Bell as a serious problem for his “Everett (?) theory” – the historic predecessor of MBM – is discussed. I argue that Barbour’s time capsule approach does not provide a satisfactory solution. In particular, his adopting a more than minimal psychophysical parallelism between brain processes and experience of macroscopic change is argued to be reasonable in light of our current best neuroscience, yet problematic for theories relying solely on time capsules, understood as highly structured, individual, internally static configurations. As a solution, I introduce worlds, and world histories, as key concepts in providing a link between MBM’s micro dynamics and macroscopic phenomena. Worlds, other than time capsules, are coarse-grained regions in phase- or configuration space, defined as sets of possible micro states satisfying a relation of sufficient similarity from a macroscopic perspective, with respect to a given micro state. Hence, worlds may overlap. -/- I argue that worlds thus construed are a reasonable option for replacing the disjoint macro regions of phase space, resulting from the usual way of partitioning phase space in the standard framework of Boltzmannian statistical mechanics. This move solves the issue of discontinuous change of macro variables upon the micro state crossing the boundary between different macro regions. -/- I adapt this move for MBM’s discontinuous micro dynamics in configuration space. Issues revolving around the microscopic-macroscopic distinction, particle identity, impenetrability and haecceity in light of the desideratum of particle number conservation, etc., are discussed. I provide a detailed explanation of how overlapping worlds in MBM form world histories, thereby linking up macroscopically distinct worlds. Thus, the problem of temporal solipsism is resolved in a way that is compatible with a more than minimal psychophysical parallelism. (shrink)

This paper explicates how we might positively understand the distinctive, nonconceptual experience of our own actions and experiences by drawing on insights from a radically enactive take on phenomenal experience. We defend a late-developing relationalism about the emergence of explicit, conceptually based self-awareness, proposing that the latter develops in tandem with the mastery of self-reflective narrative practices. Focusing on the case of human newborns, Sect. 1 reviews and rejects claims that the capacities of actors to keep track of aspects of (...) themselves—e.g. their bodies, body parts, movements, activities, actions and experiences—when coordinating what they do equates to or is best explained by positing minimal, tacit awareness of their experiences as their own. Section 2 then considers and resists more familiar arguments, based on the so-called reflexivity thesis, that take such minimal self-awareness to be implied wherever there is any kind of phenomenal experience. In place of these ideas, we promote an alternative proposal of what is involved when agents keep track of aspects of themselves, drawing on a radically enactive conception of basic experience. Section 3 concludes by proposing that our first conceptual, explicit sense of self is something that only arrives on the scene once we become able to hold our own—through the support of others—in discursive, narrative practices that give us a conceptual grip on what it is to be a temporally extended self that persists over time. (shrink)

Two approaches to understanding the idealizations that arise in the Aharonov–Bohm effect are presented. It is argued that a common topological approach, which takes the non-simply connected electron configuration space to be an essential element in the explanation and understanding of the effect, is flawed. An alternative approach is outlined. Consequently, it is shown that the existence and uniqueness of self-adjoint extensions of symmetric operators in quantum mechanics have important implications for philosophical issues. Also, the alleged indispensable explanatory role of (...) said idealizations is examined via a minimal model explanatory scheme. Last, the idealizations involved in the AB effect are placed in a wider philosophical context via a short survey of part of the literature on infinite and essential idealizations. (shrink)

Michael Moehler’s Minimal Morality is a wonderful and important book, from which I have learned a great deal. It reinvigorates rational choice moral theory in the process of confronting what I see as the most important issue in social and moral philosophy today: can those in a deeply morally divided society endorse a common moral framework to structure social cooperation? Is a rational moral order possible under conditions of deep and wide moral diversity? Minimal Morality’s answers are thoughtful (...) and innovative. I am not, however, entirely persuaded that Minimal Morality can fulfil its promise of grounding a cooperative order when ‘traditional’ modes moral justification cannot. (shrink)