相关论文: On mathematical realism and the applicability of h…

We examine some of Connes' criticisms of Robinson's infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes' own…

Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of…

A discussion of the quantum mechanical use of superposition or entangled states shows that descriptions containing only statements about state vectors and experiments outputs are the most suitable for Quantum Mechanics. In particular, it is…

We analyze recent criticisms of the use of hyperreal probabilities as expressed by Pruss, Easwaran, Parker, and Williamson. We show that the alleged arbitrariness of hyperreal fields can be avoided by working in the Kanovei-Shelah model or…

It is often claimed that analysis with infinitesimals requires more substantial use of the Axiom of Choice than traditional elementary analysis. The claim is based on the observation that the hyperreals entail the existence of nonprincipal…

We comment on, elaborate, and extend the work of Warren Ewens and Herbert Wilf, described in their http://www.pnas.org/content/104/27/11189.full.pdf about the maximum in balls-and-boxes problem. In particular we meta-apply their ingenious…

`Shallow' and `deep' versions of scientific realism may be distinguished as follows: the shallow realist is satisfied with belief in the existence of the posits of our best scientific theories; by contrast, deep realists claim that realism…

This paper explores the options available to the anti-realist to defend a Quinean empirical under-determination thesis using examples of dualities. I first explicate a version of the empirical under-determination thesis that can be brought…

Machine learning practitioners are often ambivalent about the ethical aspects of their products. We believe anything that gets us from that current state to one in which our systems are achieving some degree of fairness is an improvement…

Two typical entanglements will be shown to stand on opposite sides on the issue of \emph{instrumental realism}, the issue of whether (as for EPR in the original form or EPRB, Bohm's versions using spin) or not (as for GHZ) observables have…

Eugene Wigner's much-discussed notion of the "unreasonable effectiveness of mathematics" as applied to describing the physics of empirical reality is simultaneously both trivial and profound. After all, the relevant mathematics was (in the…

Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…

Traditionally, to be a realist about something means believing in the independent existence of that something. In this line of thought, a scientific realist is someone who believes in the objective existence of the entities postulated by…

We define realism using a slightly modified version of the EPR criterion of reality. This version is strong enough to show that relativity is incomplete. We show that this definition of realism is nonetheless compatible with the general…

The Existential Theory of the Reals (ETR) consists of existentially quantified Boolean formulas over equalities and inequalities of polynomial functions of variables in $\mathbb{R}$. In this paper we propose and study the approximate…

Quantum mechanics stands in conflict with local realism only in its treatment of separated systems. A modification of quantum mechanics that changes the handling of separated systems is suggested that can reconcile quantum mechanics with…

In his remarkable paper Formalism64, Robinson defends his philsophocal position as follows: (i) Any mention of infinite totalities is literally meaningless. (ii) We should act as if infinite totalities really existed. Being the originator…

We introduce the E-measure: a measure-like generalization of the E-value to a class of hypotheses. Unlike classical measures, E-measures are closed under infimums instead of addition. They arise from a compatibility axiom with logical…

Much has been discussed in the philosophy of science about how we should understand the scientific enterprise. On the one hand, scientific realists believe that empirically adequate theories can be supplemented by interpretations that can…

Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…