Related papers: Mathematical Responses to the Hole Argument: Then …
We make some remarks on the mathematics and metaphysics of the hole argument, in response to a recent article in this journal by Weatherall ([2018]). Broadly speaking, we defend the mainstream philosophical literature from the claim that…
I argue that the Hole Argument is based on a misleading use of the mathematical formalism of general relativity. If one is attentive to mathematical practice, I will argue, the Hole Argument is blocked.
This paper reviews the hole argument as an argument against spacetime substantivalism. After a careful presentation of the argument itself I review possible responses.
The authors discuss various objections and rejoinders in the collected responses [math.HO/9404229,math.HO/9404236] to their original article on the relationship between mathematics and theoretical physics [math.HO/9307227].
In this two-part paper, we review, and then develop, the assessment of the hole argument for general relativity. This first Part reviews the literature hitherto, focussing on the philosophical aspects. It also introduces two main ideas we…
In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.
The canonical formalism of general relativity affords a particularly interesting characterisation of the infamous hole argument. It also provides a natural formalism in which to relate the hole argument to the problem of time in classical…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
Jim Weatherall has suggested that Einstein's hole argument, as presented by Earman and Norton (1987), is based on a misleading use of mathematics. I argue on the contrary that Weatherall demands an implausible restriction on how mathematics…
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
In this two-part paper we review, and then develop, the assessment of the hole argument for general relativity. The review (in Part I) discussed how to compare points in isomorphic spacetimes, i.e. models of the theory. This second Part…
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
We give a brief overview of the black hole information problem emphasizing fundamental issues and recent proposals for its resolution. The focus is on broad perspective and providing a guide to current literature rather than presenting full…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
The large scale binary black hole effort in numerical relativity has led to an increasing distinction between numerical and mathematical relativity. This note discusses this situation and gives some examples of succesful interactions…
Although black holes are objects of central importance across many fields of physics, there is no agreed upon definition for them, a fact that does not seem to be widely recognized. Physicists in different fields conceive of and reason…
I examine the debate between substantivalists and relationalists about the ontological character of spacetime and conclude it is not well posed. I argue that the so-called Hole Argument does not bear on the debate, because it provides no…
Mathematical proofs should be paired with formal proofs, whenever feasible.
We consider the angle in mathematics and arrive at a conclusion that there are two concepts on the issue. One is a descriptive geometrical one, while the other is from functional analysis. They are somewhat different, allow for different…
An attempt is made in order to clarify the so called regular black holes issue. It is revisited that if one works within General Relativity minimally coupled with non linear source, mainly of electromagnetic origin, and within a static…