We present a set of algorithms for automated simplification of symbolic constants of the form ∑iαixi with αi rational and xi complex. The included algorithms, called SimplifySum2 and implemented in Mathematica, remove redundant terms, attempt to make terms and the full expression real, and remove terms using repeated application of the multipair PSLQ integer relation detection algorithm. Also included are facilities for making substitutions according to user-specified identities. We illustrate this toolset by giving some real-world examples of its usage, (...) including one, for instance, where the tool reduced a symbolic expression of approximately 100 000 characters in size enough to enable manual manipulation to one with just four simple terms.2Available from https://github.com/alexkaiser/SimplifySum. (shrink)

The modal completeness proofs of Guaspari and Solovay (1979) for their systems R and R – are improved and the relationship between R and R – is clarified.

Nelson Goodman has constructed two theories of simplicity: one of predicates; one of hypotheses. I offer a simpler theory by generalization and abstraction from his. Generalization comes by dropping special conditions Goodman imposes on which unexcluded extensions count as complicating and which excluded extensions count as simplifying. Abstraction is achieved by counting only nonisomorphic models and subinterpretations. The new theory takes into account all the hypotheses of a theory in assessing its complexity, whether they were projected prior to, or result (...) from, projection of a given hypothesis. It assigns simplicity post-projection priority over simplicity pre-projection. It better orders compound conditionals than does the theory of simplicity of hypotheses, and it does not inherit an anomaly of the theory of simplicity of predicates — its failure to order the ordering relations. Drop Goodman's special conditions, and the problems fall away with them. (shrink)

We propose a modification of the exhaustivity operator from Fox Presupposition and implicature in compositional semantics, Palgrave Macmillan, London, pp 71–120, 2007. https://doi.org/10.1057/9780230210752_4) that on top of negating all the Innocently Excludable alternatives affirms all the ‘Innocently Includable’ ones. The main result of supplementing the notion of Innocent Exclusion with that of Innocent Inclusion is that it allows the exhaustivity operator to identify cells in the partition induced by the set of alternatives whenever possible. We argue for this property of (...) ‘cell identification’ based on the simplification of disjunctive antecedents and the effects on free choice that arise as the result of the introduction of universal quantifiers. We further argue for our proposal based on the interaction of only with free choice disjunction. (shrink)

Languages spoken in larger populations are relatively simple. A possible explanation for this is that languages with a greater number of speakers tend to also be those with higher proportions of non‐native speakers, who may simplify language during learning. We assess this explanation for the negative correlation between population size and linguistic complexity in three experiments, using artificial language learning techniques to investigate both the simplifications made by individual adult learners and the potential for such simplifications to influence group‐level language (...) characteristics. In Experiment 1, we show that individual adult learners trained on a morphologically complex miniature language simplify its morphology. In Experiment 2, we explore how these simplifications may then propagate through subsequent learning. We use the languages produced by the participants of Experiment 1 as the input for a second set of learners, manipulating (a) the proportion of their input which is simplified and (b) the number of speakers they receive their input from. We find, contrary to expectations, that mixing the input from multiple speakers nullifies the simplifications introduced by individuals in Experiment 1; simplifications at the individual level do not result in simplification of the population's language. In Experiment 3, we focus on language use as a mechanism for simplification, exploring the consequences of the interaction between individuals differing in their linguistic competence (as native and non‐native speakers might). We find that speakers who acquire a more complex language than their partner simplify their language during interaction. We ultimately conclude that adult learning can result in languages spoken by more people having simpler morphology, but that idiosyncratic simplifications by non‐natives do not offer a complete explanation in themselves; accommodation—by comparatively competent non‐natives to less competent speakers, or by native speakers to non‐natives—may be a key linking mechanism. (shrink)

An opinionated history of neuroscience, which argues that--due to the brain's complexity--neuroscientific theories have only captured partial truths, and therefore "neurophilosophy" is unlikely to be achieved.

The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise brings the investigation of the soundness of the argument into better focus. Also, (...) the simpler representation of the argument brings out clearly how the ontological argument constitutes an early example of a ?diagonal argument? and, moreover, one used to establish a positive conclusion rather than a paradox. (shrink)

This note discusses P. Oppenheimer and E. Zalta's ?A Computationally-Discovered Simplification of the Ontological Argument? [this journal, 2011]. I try to explain why the simplification presented there was successful and comment on the technical aspects of the method they applied.

With the ever-growing quality of observational data in astronomy, the complexity of astrophysical models has been increasing in turn. This trend raises the question: Are there still reasons to prefer simpler models if the final goal is an actual model-target comparison? I argue for two aspects in which astrophysical research may favor models having reduced complexity: first, to address the problem of determining the values of adjustable parameters and, second, to pave the way for a validation of the model based (...) on the modeler’s understanding of the scope of the model and the critical processes on the target’s side. (shrink)

The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise brings the investigation of the soundness of the argument into better focus. Also, (...) the simpler representation of the argument brings out clearly how the ontological argument constitutes an early example of a ‘diagonal argument’ and, moreover, one used to establish a positive conclusion rather than a paradox. (shrink)

(2006). Flexible heuristics for simplification with conditional lemmas by marking formulas as forbidden, mandatory, obligatory, and generous. Journal of Applied Non-Classical Logics: Vol. 16, No. 1-2, pp. 209-239.

Le Programme de cе Congrès, pour unifier la diversité des communications, propose six problèmes et six thèmes, formant un tout cohérent. Tout ensemble compliqué, étant dénombré, est réductible en un complexe qui d’autant mieux qu’il est plus ordonné, forme une simple unité. Discernons dans chacune et dans l’ensemble des notions, les trois acceptions les plus antinomiques, partant complémentaires, réunissons-les moyennant une plus générale, les autres seront coordonnées entre ces quatre, formant un complexe tétra-univoque. La coordination unitaire-trinitaire, la seule complète, est (...) la plus simple méthode des méthodes. (shrink)