Artículos con la etiqueta ‘Jerarquía de los predicados’

Hierarchical Economic Agents and their Interactions

Por • 1 ene, 2014 • Category: sociologia

We present a new type of spin market model, populated by hierarchical agents, represented as configurations of sites and arcs in an evolving network. We describe two analytic techniques for investigating the asymptotic behavior of this model: one based on the spectral theory of Markov chains and another exploiting contingent submartingales to construct a deterministic cellular automaton that approximates the stochastic dynamics. Our study of this system documents a phase transition between a sub-critical and a super-critical regime based on the values of a coupling constant that modulates the tradeoff between local majority and global minority forces. In conclusion, we offer a speculative socioeconomic interpretation of the resulting distributional properties of the system.



Satisfaction is not absolute

Por • 9 dic, 2013 • Category: Filosofía

We prove that the satisfaction relation N⊨φ[a ⃗ ] of first-order logic is not absolute between models of set theory having the structure N and the formulas φ all in common. Two models of set theory can have the same natural numbers, for example, and the same standard model of arithmetic ⟨N,+,⋅,0,1,<⟩ , yet disagree on their theories of arithmetic truth; two models of set theory can have the same natural numbers and the same arithmetic truths, yet disagree on their truths-about-truth, at any desired level of the iterated truth-predicate hierarchy; two models of set theory can have the same natural numbers and the same reals, yet disagree on projective truth; two models of set theory can have the same ⟨H ω 2 ,∈⟩ or the same rank-initial segment ⟨V δ ,∈⟩ , yet disagree on which assertions are true in these structures. On the basis of these mathematical results, we argue that a philosophical commitment to the determinateness of the theory of truth for a structure cannot be seen as a consequence solely of the determinateness of the structure in which that truth resides. The determinate nature of arithmetic truth, for example, is not a consequence of the determinate nature of the arithmetic structure N={0,1,2,…} itself, but rather, we argue, is an additional higher-order commitment requiring its own analysis and justification.