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Difficulties of Simplicity
This paper attempts to show that the doctrine of divine simplicity suffers from difficulties which undermine its plausibility. The main difficulties explored are Plantinga’s problem of double identification, Pruss’ multiple attributes problem, and Schmitt’s co-specificity problem. In more recent years, defenders of the doctrine have offered a way out of these problems by interpreting it in light of a truthmaker account of predication. This paper analyzes this recent defense, among others, and attempts to show that this new interpretation of divine simplicity still has problems which undermine the plausibility of the doctrine
The Ambiguity of Simplicity
A system's apparent simplicity depends on whether it is represented
classically or quantally. This is not so surprising, as classical and quantum
physics are descriptive frameworks built on different assumptions that capture,
emphasize, and express different properties and mechanisms. What is surprising
is that, as we demonstrate, simplicity is ambiguous: the relative simplicity
between two systems can change sign when moving between classical and quantum
descriptions. Thus, notions of absolute physical simplicity---minimal structure
or memory---at best form a partial, not a total, order. This suggests that
appeals to principles of physical simplicity, via Ockham's Razor or to the
"elegance" of competing theories, may be fundamentally subjective, perhaps even
beyond the purview of physics itself. It also raises challenging questions in
model selection between classical and quantum descriptions. Fortunately,
experiments are now beginning to probe measures of simplicity, creating the
potential to directly test for ambiguity.Comment: 7 pages, 6 figures, http://csc.ucdavis.edu/~cmg/compmech/pubs/aos.ht
Pseudofinite structures and simplicity
We explore a notion of pseudofinite dimension, introduced by Hrushovski and
Wagner, on an infinite ultraproduct of finite structures. Certain conditions on
pseudofinite dimension are identified that guarantee simplicity or
supersimplicity of the underlying theory, and that a drop in pseudofinite
dimension is equivalent to forking. Under a suitable assumption, a
measure-theoretic condition is shown to be equivalent to local stability. Many
examples are explored, including vector spaces over finite fields viewed as
2-sorted finite structures, and homocyclic groups. Connections are made to
products of sets in finite groups, in particular to word maps, and a
generalization of Tao's algebraic regularity lemma is noted
COMPLEXITY * SIMPLICITY * SIMPLEXITY
“In the midst of order, there is chaos; but in the midst of chaos, there is order”, John Gribbin wrote in his book Deep Simplicity (p.76). In this dialectical spirit, we discuss the generative tension between complexity and simplicity in the theory and practice of management and organization. Complexity theory suggests that the relationship between complex environments and complex organizations advanced by the well-known Ashby’s law, may be reconsidered: only simple organization provides enough space for individual agency to match environmental turbulence in the form of complex organizational responses. We suggest that complex organizing may be paradoxically facilitated by a simple infrastructure, and that the theory of organizations may be viewed as resulting from the interplay between simplicity and complexity. JEL codes:
Simplicity in simplicial phase space
A key point in the spin foam approach to quantum gravity is the
implementation of simplicity constraints in the partition functions of the
models. Here, we discuss the imposition of these constraints in a phase space
setting corresponding to simplicial geometries. On the one hand, this could
serve as a starting point for a derivation of spin foam models by canonical
quantisation. On the other, it elucidates the interpretation of the boundary
Hilbert space that arises in spin foam models.
More precisely, we discuss different versions of the simplicity constraints,
namely gauge-variant and gauge-invariant versions. In the gauge-variant
version, the primary and secondary simplicity constraints take a similar form
to the reality conditions known already in the context of (complex) Ashtekar
variables. Subsequently, we describe the effect of these primary and secondary
simplicity constraints on gauge-invariant variables. This allows us to
illustrate their equivalence to the so-called diagonal, cross and edge
simplicity constraints, which are the gauge-invariant versions of the
simplicity constraints. In particular, we clarify how the so-called gluing
conditions arise from the secondary simplicity constraints. Finally, we discuss
the significance of degenerate configurations, and the ramifications of our
work in a broader setting.Comment: Typos and references correcte
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