Reply to Duncan Pritchard and John Campbell

An epistemological how-possible question asks how knowledge, or knowledge of some specific kind, is possible. The main contention of Duncan Pritchard‟s stimulating comments is that what I call „explanatory minimalism‟ appears to offer us just what we are seeking when we ask such a question. This looks like a problem for me given that I defend a version of explanatory anti-minimalism. Pritchard outlines a version of minimalism inspired by the writings of John McDowell and does not find it obvious that this position is lacking in any relevant respect. Nor do I. My minimalism is moderate rather than extreme but Pritchard‟s objections to anti-minimalism are objections to extreme anti-minimalism. Indeed, his comments do not seem to me to have any direct bearing on what I take to be the fundamental disagreement between minimalism and anti-minimalism

An improved lower bound for the maximal length of a multivector

A new lower bound for the maximal length of a multivector is obtained. It is much closer to the best known upper bound than previously reported lower bound estimates. The maximal length appears to be unexpectedly large for $n$-vectors, with n>2, since the few exactly known values seem to grow linearly with vector space dimension, whereas the new lower bound has a polynomial order equal to n-1 like the best known upper bound. This result has implications for quantum chemistry

What is knowledge?

What would a good answer to this question – call it (WK) – look like? What I’m going to call the standard analytic approach (SA) says that: (A) The way to answer WK is to analyse the concept of knowledge. (B) To analyse the concept of knowledge is to come up with noncircular necessary and sufficient conditions for someone to know that something is the case. Is the standard analytic approach to WK the right approach? If not, what would be a better way of doing things? These are the questions I’m going to tackle here. I want to look at some criticisms of SA and consider the prospects for a different, non-standard analytic approach (NA) to WK

Generalization of the concepts of seniority number and ionicity

We present generalized versions of the concepts of seniority number and ionicity. These generalized numbers count respectively the partially occupied and fully occupied shells for any partition of the orbital space into shells. The Hermitian operators whose eigenspaces correspond to wave functions of definite generalized seniority or ionicity values are introduced. The generalized seniority numbers (GSNs) afford to establish refined hierarchies of configuration interaction (CI) spaces within those of fixed ordinary seniority. Such a hierarchy is illustrated on the buckminsterfullerene molecule

A Fast Algorithm for the Construction of Integrity Bases Associated to Symmetry-Adapted Polynomial Representations. Application to Tetrahedral XY4 Molecules

Invariant theory provides more efficient tools, such as Molien generating functions and integrity bases, than basic group theory, that relies on projector techniques for the construction of symmetry--adapted polynomials in the symmetry coordinates of a molecular system, because it is based on a finer description of the mathematical structure of the latter. The present article extends its use to the construction of polynomial bases which span possibly, non--totally symmetric irreducible representations of a molecular symmetry group. Electric or magnetic observables can carry such irreducible representations, a common example is given by the electric dipole moment surface. The elementary generating functions and their corresponding integrity bases, where both the initial and the final representations are irreducible, are the building blocks of the algorithm presented in this article, which is faster than algorithms based on projection operators only. The generating functions for the full initial representation of interest are built recursively from the elementary generating functions. Integrity bases which can be used to generate in the most economical way symmetry--adapted polynomial bases are constructed alongside in the same fashion. The method is illustrated in detail on XY4 type of molecules. Explicit integrity bases for all five possible final irreducible representations of the tetrahedral group have been calculated and are given in the supplemental material associated with this paper

Intellectual vice and self-awareness

To what extent are we able to recognise our own intellectual shortcomings, asks Quassim Cassa

Diagnostic error, overconfidence and self-knowledge

According to the overconfidence hypothesis (OH), physician overconfidence is a major factor contributing to diagnostic error in medicine. This paper argues that (OH) can be read as offering a personal, a sub-personal or a systemic explanation of diagnostic error. It is argued that personal level overconfidence is an ‘epistemic vice’. The hypothesis that diagnostic errors due to overconfidence can be remedied by increasing physician self-knowledge is shown to be questionable. Some epistemic vices or cognitive biases, including overconfidence, are ‘stealthy’ in the sense that they obstruct their own detection. Even if the barriers to self-knowledge can be overcome, some problematic traits are so deeply entrenched that even well-informed and motivated individuals might be unable to correct them. One such trait is overconfidence. Alternative approaches to ‘debiasing’ are considered and it is argued that overconfidence is blameworthy only if it is understood as a personal level epistemic vice rather than a sub-personal cognitive bias