AUTONOMY AND HIERARCHY

2003 ◽  
Vol 20 (2) ◽  
pp. 156-176 ◽  
Author(s):  
Michael E. Bratman
Keyword(s):  
Free Will ◽  
Higher Order ◽  
Second Order ◽  
Original Version ◽  
Autonomous Action ◽  
Original Proposal

In autonomous action the agent herself directs and governs the action. But what is it for the agent herself to direct and to govern? One theme in a series of articles by Harry G. Frankfurt is that we can make progress in answering this question by appeal to higher-order conative attitudes. Frankfurt's original version of this idea is that in acting of one's own free will, one is not acting simply because one desires so to act. Rather, it is also true that this desire motivates one's action because one desires that this desire motivate one's action. This latter desire about the motivational role of one's desire is a second-order desire. It is, in particular, what Frankfurt calls a second-order “volition.” And, according to Frankfurt's original proposal, acting of one's own free will involves in this way such second-order, and sometimes yet higher order, volitions.

Frankfurt and the Problem of Self-Control

2020 ◽  
pp. 421-433
Author(s):  
Ryan Cummings ◽  
Adina L. Roskies
Keyword(s):  
Free Will ◽  
Higher Order ◽  
Second Order ◽  
Self Control ◽  
Infinite Regress ◽  
Structural Account ◽  
The Will

Frankfurt’s compatibilist account of free will considers an individual to be free when her first- and second-order volitions align. This structural account of the will, this chapter argues, fails to engage with the dynamics of will, resulting in two shortcomings: (1) the problem of directionality, or that Frankfurtian freedom obtains whenever first- and second-order volitions align, regardless of which desire was made to change, and (2) the potential for infinite regress of higher-order desires. The authors propose that a satisfying account of the genesis of second-order volitions can resolve these issues. To provide this they draw from George Ainslie’s mechanistic account of self-control, which relies on intertemporal bargaining wherein an individual’s self-predictions about future decisions affect the value of her current choices. They suggest that second-order volitions emerge from precisely this sort of process, and that a Frankfurt-Ainslie account of free will avoids the objections previously raised.

On the role of higher-order nonlinearities in implementing second-order hologram-based associative memories

2015 ◽  
Vol 24 (3) ◽  
pp. 230-234 ◽  
Author(s):  
P. V. Polyanskii ◽  
Ch. V. Felde ◽  
A. V. Konovchuk ◽  
M. V. Oleksyuk
Keyword(s):  
Higher Order ◽  
Second Order ◽  
Associative Memories

scholarly journals Cortical Contributions to Higher-Order Conditioning: A Review of Retrosplenial Cortex Function

2021 ◽  
Vol 15 ◽  
Author(s):  
Danielle I. Fournier ◽  
Han Yin Cheng ◽  
Siobhan Robinson ◽  
Travis P. Todd
Keyword(s):  
Brain Structures ◽  
Neutral Stimulus ◽  
Higher Order ◽  
Retrosplenial Cortex ◽  
Second Order ◽  
Future Research ◽  
Cortical Region ◽  
Sensory Preconditioning ◽  
Order Conditioning

In higher-order conditioning paradigms, such as sensory preconditioning or second-order conditioning, discrete (e.g., phasic) or contextual (e.g., static) stimuli can gain the ability to elicit learned responses despite never being directly paired with reinforcement. The purpose of this mini-review is to examine the neuroanatomical basis of high-order conditioning, by selectively reviewing research that has examined the role of the retrosplenial cortex (RSC) in sensory preconditioning and second-order conditioning. For both forms of higher-order conditioning, we first discuss the types of associations that may occur and then review findings from RSC lesion/inactivation experiments. These experiments demonstrate a role for the RSC in sensory preconditioning, suggesting that this cortical region might contribute to higher-order conditioning via the encoding of neutral stimulus-stimulus associations. In addition, we address knowledge gaps, avenues for future research, and consider the contribution of the RSC to higher-order conditioning in relation to related brain structures.

Higher‐order Logic

2009 ◽  
Author(s):  
Stewart Shapiro
Keyword(s):  
Philosophy Of Mathematics ◽  
Higher Order ◽  
Second Order ◽  
Order Logic ◽  
First Order Logic ◽  
Higher Order Logic ◽  
First Order ◽  
Deductive Systems ◽  
Second Order Logic

The philosophical literature contains numerous claims on behalf of and numerous claims against higher-order logic. Virtually all of the issues apply to second-order logic (vis-à-vis first-order logic), so this article focuses on that. It develops the syntax of second-order languages and present typical deductive systems and model-theoretic semantics for them. This will help to explain the role of higher-order logic in the philosophy of mathematics. It is assumed that the reader has at least a passing familiarity with the theory and metatheory of first-order logic.

Optimal control of higher order differential inclusions with functional constraints

2020 ◽  
Vol 26 ◽  
pp. 37 ◽  
Author(s):  
Elimhan N. Mahmudov
Keyword(s):  
Optimal Control ◽  
Optimality Conditions ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Higher Order ◽  
Second Order ◽  
Sufficient Optimality Conditions ◽  
Functional Constraints ◽  
Complementary Slackness ◽  
Complementary Slackness Conditions

The present paper studies the Mayer problem with higher order evolution differential inclusions and functional constraints of optimal control theory (PFC); to this end first we use an interesting auxiliary problem with second order discrete-time and discrete approximate inclusions (PFD). Are proved necessary and sufficient conditions incorporating the Euler–Lagrange inclusion, the Hamiltonian inclusion, the transversality and complementary slackness conditions. The basic concept of obtaining optimal conditions is locally adjoint mappings and equivalence results. Then combining these results and passing to the limit in the discrete approximations we establish new sufficient optimality conditions for second order continuous-time evolution inclusions. This approach and results make a bridge between optimal control problem with higher order differential inclusion (PFC) and constrained mathematical programming problems in finite-dimensional spaces. Formulation of the transversality and complementary slackness conditions for second order differential inclusions play a substantial role in the next investigations without which it is hardly ever possible to get any optimality conditions; consequently, these results are generalized to the problem with an arbitrary higher order differential inclusion. Furthermore, application of these results is demonstrated by solving some semilinear problem with second and third order differential inclusions.

Introduction

2018 ◽  
Author(s):  
Christopher Evan Franklin
Keyword(s):  
Moral Responsibility ◽  
Free Will ◽  
Human Agency ◽  
Causal Role ◽  
Central Question ◽  
Agent Causation ◽  
The Right

This chapter lays out the book’s central question: Assuming agency reductionism—that is, the thesis that the causal role of the agent in all agential activities is reducible to the causal role of states and events involving the agent—is it possible to construct a defensible model of libertarianism? It is explained that most think the answer is negative and this is because they think libertarians must embrace some form of agent-causation in order to address the problems of luck and enhanced control. The thesis of the book is that these philosophers are mistaken: it is possible to construct a libertarian model of free will and moral responsibility within an agency reductionist framework that silences that central objections to libertarianism by simply taking the best compatibilist model of freedom and adding indeterminism in the right junctures of human agency. A brief summary of the chapters to follow is given.

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

scholarly journals Free will and neurosurgical resections of the supplementary motor area: a critical review

2021 ◽  
Vol 163 (5) ◽  
pp. 1229-1237 ◽  
Author(s):  
Rickard L Sjöberg
Keyword(s):  
Executive Function ◽  
Free Will ◽  
Corticospinal Tract ◽  
Supplementary Motor Area ◽  
Personal Responsibility ◽  
Motor Area ◽  
Simple Motor ◽  
Motor Actions ◽  
Intense Debate

Abstract Background Research suggests that unconscious activity in the supplementary motor area (SMA) precedes not only certain simple motor actions but also the point at which we become aware of our intention to perform such actions. The extent to which these findings have implications for our understanding of the concepts of free will and personal responsibility has been subject of intense debate during the latest four decades. Methods This research is discussed in relation to effects of neurosurgical removal of the SMA in a narrative review. Results Removal of the SMA typically causes a transient inability to perform non-stimulus-driven, voluntary actions. This condition, known as the SMA syndrome, does not appear to be associated with a loss of sense of volition but with a profound disruption of executive function/cognitive control. Conclusions The role of the SMA may be to serve as a gateway between the corticospinal tract and systems for executive function. Such systems are typically seen as tools for conscious decisions. What is known about effects of SMA resections would thus seem to suggest a view that is compatible with concepts of personal responsibility. However, the philosophical question whether free will exists cannot be definitely resolved on the basis of these observations.

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

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