We present a novel method, called graph sparse nonnegative matrix factorization, for dimensionality reduction. The affinity graph and sparse constraint are further taken into consideration in nonnegative matrix factorization and it is shown that the proposed matrix factorization method can respect the intrinsic graph structure and provide the sparse representation. Different from some existing traditional methods, the inertial neural network was developed, which can be used to optimize our proposed matrix factorization problem. By adopting one parameter in the neural network, (...) the global optimal solution can be searched. Finally, simulations on numerical examples and clustering in real-world data illustrate the effectiveness and performance of the proposed method. (shrink)

In this essay, I will compare the character, scientific style, and writing style of the American physicist Josiah Willard Gibbs and the French physicist Pierre Maurice Duhem. I begin with biographical notes to portray some significant moments of their lives. I will contrast their characters and scientific styles as manifested in their social and scientific activity influenced by the cultural traditions of their countries and the social and scientific milieu of their time. Also, in these sections, I will discuss features (...) of their familial relationships that affected their youth, their psychology, and the shaping of their characters. I will compare their writing styles emphasizing the differences observed between Gibbs’s dense and austere style, unlike Duhem’s detailed and informative way of writing his essays. I will further examine the way by which each physicist used Mach's doctrine of the economy of thought in shaping their writing style. A final contrast is reserved for their pedagogical styles. In this case, I will let their students and colleagues speak for them, while I comment on why they did not leave behind a school of thought. (shrink)

The social, ethical and legal implications of discoveries in the neurosciences.

What role does our knowledge about the ideal society play in guiding policymaking in the real world? One intuitive answer is to approximate. Namely, we have a duty to approximate the ideal within the relevant constraints of feasibility. However, political philosophers seem to have what might be called ‘approximatophobia'. Many philosophers, including idealists such as David Estlund, warn against approximation. Their criticism is chiefly motivated by ‘the problem of second best’, which points out that your second-best option may not be (...) closest to your best option. This paper aims to dispel ‘approximatophobia'. The difficulty posed by the problem of second best is often overstated. More positively, I present a novel defence of approximation, arguing that approximation of an ideal can be a reasonably reliable default strategy of action guidance in the real world. Difficulties that may afflict the project of approximation can be mitigated by sophistication of the project of approximation. After showing that critics of approximation overstep their mark in issuing the strong or moderate warning against approximation, I propose an account of sophisticated approximation. It seeks a series of reforms that make existing social institutions closer to the ideal based on careful selection of frame of analysis. Three virtuous correlations are identified as indicators for successful project of approximation, linking descriptive similarity to desirability, feasibility and knowledge of the ideal. I also explain a two-staged strategy of sophisticating the way you approximate the ideal, with an expected positive feedback effect. (shrink)

Kant’s published arguments for the non-spatiotemporality of things in themselves have not been well received. I argue that Kant has available to himself an argument for the non-spatiotemporality of things in themselves that is premised upon a disparity between the compositional structure of the intelligible world and the structure of space and time. I argue that Kant was unwaveringly committed to the premises of this argument throughout his career and that he was aware of their idealistic implications. I also argue (...) that this argument is consistent with Kant’s restrictive mature epistemology. If my argument is successful, then even if Kant’s published arguments for transcendental idealism fail, we need not regard his ambitious metaphysical project as a failure. (shrink)

Kant rejects the ontological argument on the grounds that the ontological argument inescapably must assume that existence is a “determination” or “real predicate,” which it is not. Most understand Kant’s argument for this claim to be premised upon his distinctive proto-Fregean theory of existence. But this leaves Kant dialectically vulnerable: the defender of the ontological argument can easily reject this as question-begging. I show that Kant relies upon two distinct arguments, both of which contend that the claim that existence is (...) a determination is inconsistent with bedrock ontological set pieces assumed by rationalist defenders of the ontological argument. (shrink)

Much recent attention has been paid to Kant’s account of the unity of space in the Critique of Pure Reason, not least because of the significant implications of that view for other key critical-period doctrines. But far less attention has been paid to the development of Kant’s account of the unity of space. This paper aims to offer a systematic account of Kant’s pre-critical account of the unity of space. On the view presented herein, Kant’s early account of the unity (...) of space is deeply rooted in his pre-critical cosmological views. In particular, I argue that Kant sees the unity of space as grounded in the cosmological unity of the world of substances, which is itself rooted in the divine conservation of all substances in relations of mutual causal dependence. I contend that the seeds of this view are present in the late 1740s and 1750s, but that this view receives its fullest and most complete expression in the 1770 Inaugural Dissertation. The final section of the paper considers the fate of Kant’s pre-critical account of the unity of space. I contend that the theory is excluded from the Critique of Pure Reason in light of the strict epistemological strictures adopted in that text. But considerable textual evidence shows that Kant continues to aver the theory throughout the 1770s and 1780s in the looser epistemic context of his lectures. I contend, then, that this theory is not abandoned at all. Rather, like Kant’s 1763 proof of the existence of God, it is epistemically demoted: it is Kant’s preferred view, but one that falls short of the demanding epistemic standards of the critical philosophy. (shrink)

Kant describes the concept of freedom as "the keystone of the whole structure of a system of pure reason, even of speculative reason." Kant's theory of freedom thus plays a foundational and unifying role in all aspects of his philosophy and is thus of significant interest to historians of Kant's philosophy. Kant's theory of freedom has also played a significant role in contemporary debates in metaphysics, normative ethics, and metaethics. This volume brings historians of Kant's philosophy into conversation with contemporary (...) metaphysicians and ethicists with the aim of representing the current state of scholarship on Kant's and Kantian accounts of freedom while at the same time opening new avenues of exploration. The Idea of Freedom includes papers by leading scholars on a range of historical and contemporary topics centrally related to the Kantian theory of freedom, including transcendental idealism, determinism, Kant's normative ethical theory, Kant's conception of cognition, Kant's theory of beauty, Kant's conception of logic, and many others. (shrink)

In considering Kant’s response to the Leibnizian theory of space in the Transcendental Aesthetic, scholars have overwhelmingly emphasized Kant’s response to Leibniz’s relationalism. They have largely missed the metaphysically realistic aspects of Leibniz’s theory with which Kant is primarily concerned. As such, scholars have failed to appreciate the threat Leibniz’s theory poses to Kant’s idealism, a point made publicly as early as 1786 by H. A. Pistorius. I argue that the Aesthetic does indeed contain a compelling argument against the Leibnizian (...) theory of space. This argument crucially depends upon Kant’s claim that space is monistic: that the whole of space is prior to the parts of space and, as such, spatial representations are not decomposable. (shrink)

Typically, fair machine learning research focuses on a single decision maker and assumes that the underlying population is stationary. However, many of the critical domains motivating this work are characterized by competitive marketplaces with many decision makers. Realistically, we might expect only a subset of them to adopt any non-compulsory fairness-conscious policy, a situation that political philosophers call partial compliance. This possibility raises important questions: how does partial compliance and the consequent strategic behavior of decision subjects affect the allocation outcomes? (...) If k% of employers were to voluntarily adopt a fairness-promoting intervention, should we expect k% progress (in aggregate) towards the benefits of universal adoption, or will the dynamics of partial compliance wash out the hoped-for benefits? How might adopting a global (versus local) perspective impact the conclusions of an auditor? In this paper, we propose a simple model of an employment market, leveraging simulation as a tool to explore the impact of both interaction effects and incentive effects on outcomes and auditing metrics. Our key findings are that at equilibrium: (1) partial compliance by k% of employers can result in far less than proportional (k%) progress towards the full compliance outcomes; (2) the gap is more severe when fair employers match global (vs local) statistics; (3) choices of local vs global statistics can paint dramatically different pictures of the performance vis-a-vis fairness desiderata of compliant versus non-compliant employers; (4) partial compliance based on local parity measures can induce extreme segregation. Finally, we discuss implications for auditors and insights concerning the design of regulatory frameworks. (shrink)