In order to present this result, we approach it by proving some preliminary theorems about different forcings which capture the main ideas in a simpler setting. For the entirety of the notes we work with an increasing sequence of large cardinals 〈κn | n < ω〉 with κ =def supn<ω κn. The large cardinal hypothesis that we use varies with the forcing. A recurring theme is the idea of a cell. A cell ...

Baker (Mind 114:223–238, 2005; Brit J Philos Sci 60:611–633, 2009) has recently defended what he calls the “enhanced” version of the indispensability argument for mathematical Platonism. In this paper I demonstrate that the nominalist can respond to Baker’s argument. First, I outline Baker’s argument in more detail before providing a nominalistically acceptable paraphrase of prime-number talk. ...

This paper looks at the need for a better understanding of the impediments to critical thinking in relation to graduate student work. The paper argues that a distinction is needed between two vectors that influence student writing: (1) the word-level sentence-level vector; and (2) the grammar inferencing vector. It is suggested that much of the work being done to assist students is only done on...

The argument from fine tuning is supposed to establish the existence of God from the fact that the evolution of carbon-based life requires the laws of physics and the boundary conditions of the universe to be more or less as they are. We demonstrate that this argument fails. In particular, we focus on problems associated with the role probabilities play in the argument. We show that, even grant...

A coamoeba is the image of a subvariety of a complex torus under the argument map to the real torus. We describe the structure of the boundary of the coamoeba of a variety, which we relate to its logarithmic limit set. Detailed examples of lines in three-dimensional space illustrate and motivate these results.

We consider the canonical symplectic form for sine-Gordon evaluated explicitly on the solitons of the model. The integral over space in the form, which arises because the canonical argument uses the Lagrangian density, is done explicitly in terms of functions arising in the group doublecrossproduct formulation of the inverse scattering procedure, and we are left with a simple expression given b...

The design argument is one of three main arguments for the existence of God; the others are the ontological argument and the cosmological argument. Unlike the ontological argument, the design argument and the cosmological argument are a posteriori. And whereas the cosmological argument can focus on any present event to get the ball rolling (arguing that it must trace back to a first cause, name...

For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...

Argument visualisation (AV) tools facilitate structured debates utilising elements such as issues, positions and arguments. In this way, AV tools seem promising for improving eParticipation e.g. by avoiding repetition and enhancing clarity in debates. In this paper we present and discuss citizens’ opinion on utilising an AV platform for eParticipation, specifically for discussing the emerging t...

This essay is about how four deeply important Kantian ideas can significantly illuminate some essentially intertwined issues in philosophical theology, philosophical logic, the metaphysics of agency, and above all, morality. These deeply important Kantian ideas are: (1) Kant’s argument for the impossibility of the Ontological Argument, (2) Kant’s first “postulate of pure practical reason,” immo...