Does Suppositional Reasoning Solve the Bootstrapping Problem?

In a 2002 article Stewart Cohen advances the “bootstrapping problem” for what he calls “basic justification theories,” and in a 2010 followup he offers a solution to the problem, exploiting the idea that suppositional reasoning may be used with defeasible as well as with deductive inference rules. To curtail the form of bootstrapping permitted by basic justification theories, Cohen insists that subjects must know their perceptual faculties are reliable before perception can give them knowledge. But how is such knowledge of reliability to be acquired if not through perception itself? Cohen proposes that such knowledge may be acquired a priori through suppositional reasoning. I argue that his strategy runs afoul of a plausible view about how epistemic principles function; in brief, I argue that one must actually satisfy the antecedent of an epistemic principle, not merely suppose that one does, to acquire any justification by its means – even justification for a merely conditional proposition

The world problem: on the computability of the topology of 4-manifolds

Topological classification of the 4-manifolds bridges computation theory and physics. A proof of the undecidability of the homeomorphy problem for 4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary Turing machine with an arbitrary input can be encoded into the topology of a 4-manifold, such that the 4-manifold is homeomorphic to a certain other 4-manifold if and only if the corresponding Turing machine halts on the associated input. Physical implications are briefly discussed.Comment: Submitted to Class. Quant. Gra

On Hirzebruch invariants of elliptic fibrations

We compute all Hirzebruch invariants $\chi_q$ for $D_5$, $E_6$, $E_7$ and $E_8$ elliptic fibrations of every dimension. A single generating series $\chi(t,y)$ is produced for each family of fibrations such that the coefficient of $t^{k}y^{q}$ encodes $\chi_q$ over a base of dimension $k$, solely in terms of invariants of the base of the fibration

International Comparisons of Work Disability

Self-reported work disability is analyzed in the US, the UK and the Netherlands. Different wordings of the questions lead to different work disability rates. But even if identical questions are asked, cross-country differences remain substantial. Respondent evaluations of work limitations of hypothetical persons described in vignettes are used to identify the extent to which differences in self-reports between countries or socio-economic groups are due to systematic variation in the response scales. Results suggest that more than half of the difference between the rates of self-reported work disability in the US and the Netherlands can be explained by response scale differences. A similar methodology is used to analyze the reporting bias that arises if respondents justify being on disability benefits by overstating their work limiting disabilities

The Evolutionary Unfolding of Complexity

We analyze the population dynamics of a broad class of fitness functions that exhibit epochal evolution---a dynamical behavior, commonly observed in both natural and artificial evolutionary processes, in which long periods of stasis in an evolving population are punctuated by sudden bursts of change. Our approach---statistical dynamics---combines methods from both statistical mechanics and dynamical systems theory in a way that offers an alternative to current ``landscape'' models of evolutionary optimization. We describe the population dynamics on the macroscopic level of fitness classes or phenotype subbasins, while averaging out the genotypic variation that is consistent with a macroscopic state. Metastability in epochal evolution occurs solely at the macroscopic level of the fitness distribution. While a balance between selection and mutation maintains a quasistationary distribution of fitness, individuals diffuse randomly through selectively neutral subbasins in genotype space. Sudden innovations occur when, through this diffusion, a genotypic portal is discovered that connects to a new subbasin of higher fitness genotypes. In this way, we identify innovations with the unfolding and stabilization of a new dimension in the macroscopic state space. The architectural view of subbasins and portals in genotype space clarifies how frozen accidents and the resulting phenotypic constraints guide the evolution to higher complexity.Comment: 28 pages, 5 figure