Conscious mental states are states we are in some way aware of. I compare higher-order theories of consciousness, which explain consciousness by appeal to such higher-order awareness (HOA), and first-order theories, which do not, and I argue that higher-order theories have substantial explanatory advantages. The higher-order nature of our awareness of our conscious states suggests an analogy with the metacognition that figures in the regulation of psychological processes and behaviour. I argue that, although both consciousness (...) and metacognition involve higher-order psychological states, they have little more in common. One thing they do share is the possibility of misrepresentation; just as metacognitive processing can misrepresent one’s cognitive states and abilities, so the HOA in virtue of which one’s mental states are conscious can, and sometimes does, misdescribe those states. A striking difference between the two, however, has to do with utility for psychological processing. Metacognition has considerable benefit for psychological processing; in contrast, it is unlikely that there is much, if any, utility to mental states’ being conscious over and above the utility those states have when they are not conscious. (shrink)

This chapter provides a critical overview of several influential proposals about the epistemic function of higher-order evidence. I start by criticizing accounts of higher-order evidence that appeal to evidential defeat (§1), epistemic conflicts (§2), and unreasonable knowledge (§3). Next, I propose an alternative account that appeals to a combination of improper basing (§4) and non-ideal rationality (§5). Finally, I conclude by summarizing my reasons for preferring this account of higher-order evidence to the alternatives (§6).

This paper begins the study of first-order functions, which are a generalization of truth-functions. The concepts of truth-table and systems of truth-functions, both introduced in propositional logic by Post, are also generalized and studied in the quantificational setting. The general facts about these concepts are given in the first five sections, and constitute a “general theory” of first-order functions. The central theme of this paper is the relation of definition among notions expressed by formulas of first-order logic. (...) We emphasize that logic is not concerned only with the consequence relation among notions expressed by formulas. It also attends to the relation of definition among notions, where a notion is defined from other notions. Sections 5 and 6 deal exclusively with the relation of definition among notions expressed by formulas of first-order logic. In these sections, we study the systems of first-order functions, which are the sets of first-order functions closed under definitions. Sections 7 and 8 are concerned with the relativization of first-order functions to a class of structures. The relativization to a class of structures is a fundamental operation which is used in order to relate the theory of first-order functions with set theory and first-order model theory, a subject which we have barely scratched the surface. The apparatus developed in this paper enables us to define what is a vehicle for the foundation of classical mathematics in set theory, and, in Sect. 8, we prove that first-order logic with one binary predicate variable is not a minimal vehicle for the foundation of classical mathematics in set theory. Sections 9 and 10 introduce further operations and ideals of first-order functions. Besides some results on the influence of the arguments of a first-order function, a result about definability is proved in Sect. 10.1. It is this theorem that provides necessary and sufficient conditions for a first-order function to be in a finitely generated ideal. In Sect. 11, this result is applied to the problem of predicate definability in classes of structures, the problem with which Beth’s theorem dealt in the case of elementary classes. (shrink)

One of the most basic functions of human language is to convey who did what to whom. In the world's languages, the order of these three constituents (subject [S], verb [V], and object [O]) is uneven, with SOV and SVO being most common. Recent experiments using experimentally elicited pantomime provide a possible explanation of the prevalence of SOV, but extant explanations for the prevalence of SVO could benefit from further empirical support. Here, we test whether SVO might emerge because (...) (a) SOV is not well suited for describing reversible events (a woman pushing a boy) and (b) pressures to be efficient and mention subjects before objects conspire to rule out many other alternatives. We tested this by asking participants to describe reversible and non‐reversible events in pantomime, and we instructed some participants to be consistent in the form of their gestures and to teach them to the experimenter. These manipulations led to the emergence of SVO in speakers of both English (SVO) and Turkish (SOV). (shrink)

We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.

From proofs in any classical first-order theory that proves the existence of at least two elements, one can eliminate definitions in polynomial time. From proofs in any classical first-order theory strong enough to code finite functions, including sequential theories, one can also eliminate Skolem functions in polynomial time.

We consider certain linear orders with a function on them, and discuss for which types of functions the resulting structure is or is not computably categorical. Particularly, we consider computable copies of the rationals with a fixed-point free automorphism, and also ω with a non-decreasing function.

It is shown how the strong ordinal notation systems that figure in proof theory and have been previously defined by employing large cardinals, can be developed directly on the basis of their recursively large counterparts. Thereby we provide a completely new approach to well-ordering proofs as will be exemplified by determining the proof-theoretic ordinal of the systemKPM of [R91].

We consider the problem of constructing first-order definitions in the language of rings of holomorphy rings of one-variable function fields of characteristic 0 in their integral closures in finite extensions of their fraction fields and in bigger holomorphy subrings of their fraction fields. This line of questions is motivated by similar existential definability results over global fields and related questions of Diophantine decidability.

In this paper we develop a differential analogue of o-minimal cell decomposition for the theory CODF of closed ordered differential fields. Thanks to this differential cell decomposition we define a well-behaving dimension function on the class of definable sets in CODF. We conclude this paper by proving that this dimension is closely related to both the usual differential transcendence degree and the topological dimension associated, in this case, with a natural differential topology on ordered differential fields.

In eighteenth-century French natural history, the notion of preformation was not only a model for a small preexisting embryo that gradually extended its shape through the influx of particles, but also for an order that coordinated the dynamic relation between organic parts. Preformation depended therefore also on a hidden order behind the continuity of visible forms. Louis Bourguet, Charles Bonnet, and Georges Cuvier distinguished three organizational levels: First, the synchronic or functional order of organic systems; second, the (...) diachronic order of the initiation of mechanical processes; and third, the hierarchical order that regulates the interaction of organic parts. In this essay, I reconstruct and compare the three organizational levels in the writings of Bourguet, Bonnet and Cuvier, relate their models of organic unity to the principle of perfection, and contrast these models with Georges Buffon's critique of system theories. (shrink)

We define a quasi-order on Borel functions from a zero-dimensional Polish space into another that both refines the order induced by the Baire hierarchy of functions and generalises the embeddability order on Borel sets. We study the properties of this quasi-order on continuous functions, and we prove that the closed subsets of a zero-dimensional Polish space are well-quasi-ordered by bi-continuous embeddability.

Living systems employ several mechanisms and behaviors to achieve robustness and maintain themselves under changing internal and external conditions. Regulation stands out from them as a specific form of higher-order control, exerted over the basic regime responsible for the production and maintenance of the organism, and provides the system with the capacity to act on its own constitutive dynamics. It consists in the capability to selectively shift between different available regimes of self-production and self-maintenance in response to specific signals (...) and perturbations, due to the action of a dedicated subsystem which is operationally distinct from the regulated ones. The role of regulation, however, is not exhausted by its contribution to maintain a living system’s viability. While enhancing robustness, regulatory mechanisms play a fundamental role in the realization of an autonomous biological organization. Specifically, they are at the basis of the remarkable integration of biological systems, insofar as they coordinate and modulate the activity of distinct functional subsystems. Moreover, by implementing complex and hierarchically organized control architectures, they allow for an increase in structural and organizational complexity while minimizing fragility. Finally, they endow living systems, from their most basic unicellular instances, with the capability to control their own internal dynamics to adaptively respond to specific features of their interaction with the environment, thus providing the basis for the emergence of minimal forms of cognition. (shrink)

We introduce a new typed combinatory calculus with a type constructor that, to each type σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}, associates the star type σ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma ^*$$\end{document} of the nonempty finite subsets of elements of type σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}. We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star combinatory (...) calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements. (shrink)

We analyze the representation of binary relations in general, and in particular of functions and of total antisymmetric relations, in monadic third order logic, that is, the simple typed theory of sets with three types. We show that there is no general representation of functions or of total antisymmetric relations in this theory. We present partial representations of functions and of total antisymmetric relations which work for large classes of these relations, and show that there is an adequate representation (...) of cardinality in this theory. The relation of our work to similar work by Henrard and Allen Hazen is discussed. This work can be understood as part of a program of assessing the capabilities of weak logical frameworks: our results are applicable for example, to the framework in David Lewis’s Parts of Classes. (shrink)

A choice set for a computable linear ordering is a set which contains one element from each maximal block of the ordering. We obtain a partial characterization of the computable linear order-types for which each computable model has a computable choice set, and a full characterization in the relativized case; Every model of the linear order-type α of degree ≤ d has a choice set of degree ≤ d iff α can written as a finite sum of (...) class='Hi'>order-types, each of which either has finitely many blocks, or has order-type n · η for some integer n. (shrink)

Let \({\mathcal {R}}\) be a polynomially bounded o-minimal expansion of the real field. Let _f_(_z_) be a transcendental entire function of finite order \(\rho \) and type \(\sigma \in [0,\infty ]\). The main purpose of this paper is to show that if ( \(\rho ) or ( \(\rho =1\) and \(\sigma =0\) ), the restriction of _f_(_z_) to the real axis is not definable in \({\mathcal {R}}\). Furthermore, we give a generalization of this result for any \(\rho \in (...) [0,\infty )\). (shrink)

Although Boyle has been regarded as a champion of the seventeenth century Cartesian mechanical philosophy, I defend the position that Boyle’s views conciliate between a strictly mechanistic conception of fundamental matter and a non-reductionist conception of chemical qualities. In particular, I argue that this conciliation is evident in Boyle’s ontological distinction between fundamental corpuscles endowed with mechanistic properties and higher-level corpuscular concretions endowed with chemical properties. Some of these points have already been acknowledged by contemporary scholars, and I actively engage (...) with their ideas in this paper. However I attempt to contribute to the debate over Boyle’s mechanical philosophy by arguing that Boyle’s writings suggest an emergentist, albeit still mechanistic, notion of chemical properties. I contrast Boyle’s views against those of strict reductionist mechanical philosophers, focusing on the famous debate with Spinoza over the redintegration of niter, and argue that Boyle’s complex chemical ontology provides a more satisfactory understanding of chemical phenomena than is provided by a strictly reductionist and Cartesian mechanical philosophy. (shrink)

This paper contains a formal theory of functional parthood. Since the relation of functional parthood is defined here by means of the notion of design, the theory of functional parthood turns out to be a theory of design. The formal theory of design I defend here is a result of introducing a number of constraints that are to express the rational aspects of designing practice. The ontological background for the theory is provided by a conception of states of affairs. The (...) theory is accompanied with a formal model. I prove that the theory is sound and complete with respect to this model. (shrink)

The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have a definable choice function (by a monadic formula with parameters)? A natural dichotomy arises where the trees that fall in the first class don't have a definable choice function and the trees in the second class have even a definable well ordering of their elements. This has a (...) close connection to the uniformization problem. (shrink)

ObjectiveVirtual reality grasping exercise training helps patients participate actively in their recovery and is a critical approach to the rehabilitation of hand dysfunction. This study aimed to explore the effects of active participation and VR grasping on brain function combined with the kinematic information obtained during VR exercises.MethodsThe cerebral oxygenation signals of the prefrontal cortex, the motor cortex, and the occipital cortex were measured by functional near-infrared spectroscopy in 18 young people during the resting state, grasping movements, and VR (...) grasping movements. The EPPlus plug-in was used to collect the hand motion data during simulated interactive grasping. The wavelet amplitude of each cerebral cortex and the wavelet phase coherence of each pair of channels were calculated by wavelet analysis. The total difference in acceleration difference of the hand in the VR grasping movements was calculated to acquire kinematic characteristics. The cortical activation and brain functional connectivity of each brain region were compared and analyzed, and a significant correlation was found between VR grasping movements and brain region activation.ResultsCompared with the resting state, the WA values of LPFC, RPFC, LMC, RMC, and ROC increased during the grasping movements and the VR grasping movements, these changes were significant in LPFC and LMC. The WA values of LMC in the VR grasping movements were significantly higher than those in the grasping movements. The WPCO of the cerebral cortex increased during grasping exercise compared with the resting state. Nevertheless, the number of significant functional connections during VR grasping decreased significantly, and only the WPCO strength between the LPFC and LMC was enhanced. The increased WA of the LPFC, RPFC, LMC, and RMC during VR grasping movements compared with the resting state showed a significant negative correlation with KCs.ConclusionThe VR grasping movements can improve the activation and FC intensity of the ipsilateral brain region, inhibit the FC of the contralateral brain region, and reduce the quantity of brain resources allocated to the task. Thus, ordered grasping exercises can enhance active participation in rehabilitation and help to improve brain function. (shrink)

There is a conceptual crisis in the biomedical sciences that is particularly salient in psychopathology research. Underlying the crisis is a controversy that pertains to the current medical model of disease that largely draws from causal-mechanistic explanations. The bedrock of this model is the analysis of biological part-dysfunctions that aims at unequivocally defining a pathological condition and demarcating it from its neighboring entities. This endeavor has led to a quest for physiological, biochemical, and genetic signatures. Yet, so far there is (...) little evidence for reliable biomarkers for any mental disorder. The contemporary biomedical paradigm largely ignores historical, dynamic, and system-level aspects—a view that has contributed much to the conceptual disjunction of the patient as a person from his/her disease. Notwithstanding the impressive progress in the biomedical sciences, increasingly more critics question whether the constituting framework is sufficient to convey a comprehensive understanding of illnesses, especially mental illnesses. Thus, the medical model urgently requires an update. But rather than revamping it by methodological advancements, it will be necessary to critically review its philosophical roots. The most problematic issues that require reworking are: the preponderance of the biostatistical theory; the undue decoupling of physiological from evolutionary explanations of function; the clinging to the Modern Synthesis ; and the neglect of dynamic and system-level properties. The proposed overhaul requires the heeding of historical explanations that draw from the Extended Evolutionary Synthesis as well as systems biology approaches for tackling multilevel and dynamic phenomena of complex systems. (shrink)

We propose a rudimentary formal framework for reasoning about recursion equations over inductively generated data. Our formalism admits all equational programs , and yet singles out none. While being simple, this framework has numerous extensions and applications. Here we lay out the basic concepts and definitions; show that the deductive power of our formalism is similar to that of Peano's Arithmetic; prove a strong normalization theorem; and exhibit a mapping from natural deduction derivations to an applied λ -calculus, à la (...) Curry–Howard, which provides a transparent proof of Gödel's result that the provably recursive functions of PA are definable by primitive recursion in finite types. Also of interest is the extent, uncommon among similar constructions, to which our mapping is oblivious to first order terms, including first order quantification and equality. Additional applications and extensions of the method will be presented in sequel papers. In particular, the methodology introduced here lends itself to systematic links between natural sub-formalisms and computational complexity classes. Since these sub-formalisms are largely transparent, allowing one to reason formally in the full system while leaving to automatic software tools the task of verifying that restrictions are complied with, the framework is particularly attractive for the development of Feasible Mathematics. (shrink)

We consider the decision problem for cases of first-order temporal logic with function symbols and without equality. The monadic monodic fragment with flexible functions can be decided with EXPSPACE-complete complexity. A single rigid function is sufficient to make the logic not recursively enumerable. However, the monadic monodic fragment with rigid functions, where no two distinct terms have variables bound by the same quantifier, is decidable and EXPSPACE-complete.

It is well known that interval orders are particularly interesting in decision theory, since they are reflexive, complete and nontransitive binary relations which may be fully represented by means of two real-valued functions. In this paper, we discuss the existence of a pair of nonnegative, positively homogeneous and semicontinuous real-valued functionals representing an interval order on a real cone in a topological vector space. We recover as a particular case a result concerning the existence of a nonnegative, positively homogeneous (...) and continuous utility functional for a complete preorder on a real cone in a topological vector space. (shrink)