The simplest quantified modal logic combines classical quantification theory with the propositional modal logic K. The models of simple QML relativize predication to possible worlds and treat the quantifier as ranging over a single fixed domain of objects. But this simple QML has features that are objectionable to actualists. By contrast, Kripke-models, with their varying domains and restricted quantifiers, seem to eliminate these features. But in fact, Kripke-models also have features to which actualists object. Though these philosophers have introduced (...) variations on Kripke-models to eliminate their objectionable features, the most well-known variations all have difficulties of their own. The present authors reexamine simple QML and discover that, in addition to having a possibilist interpretation, it has an actualist interpretation as well. By introducing a new sort of existing abstract entity, the contingently nonconcrete, they show that the seeming drawbacks of the simplest QML are not drawbacks at all. Thus, simple QML is independent of certain metaphysical questions. (shrink)

Karen Bennett has recently argued that the views articulated by Linsky and Zalta (Philos Perspect 8:431–458, 1994) and (Philos Stud 84:283–294, 1996) and Plantinga (The nature of necessity, 1974) are not consistent with the thesis of actualism, according to which everything is actual. We present and critique her arguments. We first investigate the conceptual framework she develops to interpret the target theories. As part of this effort, we question her definition of ‘proxy actualism’. We then discuss her main arguments that (...) the theories carry a commitment to actual entities that do not exist. We end by considering and addressing a worry that might have been the driving force behind Bennett’s claim that Linsky and Zalta’s view is not fully actualistic. (shrink)

Quantified modal logic has reputation for complexity. Completeness results for the various systems appear piecemeal. Different tactics are used for different systems, and success of a given method seems sensitive to many factors, including the specific combination of choices made for the quantifiers, terms, identity, and the strength of the underlying propositional modal logic. The lack of a unified framework in which to view QMLs and their completeness properties puts pressure on those who develop, apply, and teach QML to work (...) with the simplest systems, namely those that adopt the Barcan Formulas and predicate logic rules for the quantifiers. In these systems, the quantifier ranges over a fixed domain of possible individuals, so advocates of these logics are sometimes called possibilists. A literature has grown up rationalizing the choice of possibilist logics despite ordinary intuitions that the resulting theorems are too strong.Williamson even takes the view that the complications to be faced within the weaker logics “are a warning sign of philosophical error”. It is the purpose of this paper to show that abandonment of the weaker QMLs is excessively fainthearted, since most QMLs can be given relatively simple formulations within one general framework. Given the straightforward nature of the systems and their completeness results, the purported complications evaporate, along with any philosophical warnings one might have associated with them. (shrink)

We provide a quantifier-free axiom system for plane hyperbolic geometry in a language containing only absolute geometrically meaningful ternary operations (in the sense that they have the same interpretation in Euclidean geometry as well). Each axiom contains at most 4 variables. It is known that there is no axiom system for plane hyperbolic consisting of only prenex 3-variable axioms. Changing one of the axioms, one obtains an axiom system for plane Euclidean geometry, expressed in the same language, all of whose (...) axioms are also at most 4-variable universal sentences. We also provide an axiom system for plane hyperbolic geometry in Tarski's language L B which might be the simplest possible one in that language. (shrink)

Dependencies are identified in two recently proposed first-order axiom systems for plane hyperbolic geometry. Since the dependencies do not specifically concern hyperbolic geometry, our results yield two simpler axiom systems for absolute geometry.

Using the axiom system provided by Carsten Augat in [1], it is shown that the only 6-variable statement among the axioms of the axiom system for plane hyperbolic geometry (in Tarski's language L B =), we had provided in [3], is superfluous. The resulting axiom system is the simplest possible one, in the sense that each axiom is a statement in prenex form about at most 5 points, and there is no axiom system consisting entirely of at most 4-variable (...) statements. (shrink)

A low linear order with no computable copy constructed by C. Jockusch and R. Soare has Hausdorff rank equal to $2$. In this regard, the question arises, how simple can be a low linear order with no computable copy from the point of view of the linear order type? The main result of this work is an example of a low strong $\eta $ -representation with no computable copy that is the simplest possible example.

Several recent commentators argue that Thomas Hobbes’s account of the nature of science is conventionalist. Engaging in scientific practice on a conventionalist account is more a matter of making sure one connects one term to another properly rather than checking one’s claims, e.g., by experiment. In this paper, I argue that the conventionalist interpretation of Hobbesian science accords neither with Hobbes’s theoretical account in De corpore and Leviathan nor with Hobbes’s scientific practice in De homine and elsewhere. Closely tied to (...) the conventionalist interpretation is the deductivist interpretation, on which it is claimed that Hobbes believed sciences such as optics are deduced from geometry. I argue that Hobbesian science places simplest conceptions as the foundation for geometry and the sciences in which we use geometry, which provides strong evidence against both the conventionalist and deductivist interpretations. (shrink)

A relaxed and short road to peace of mind uncomplicated by the intellect and personal history. This renowned German teacher advocates deconstructing the tyrants called "feelings" and the egocentered programming of many lifetimes.

The simple concept of a SIC poses a very deep problem in algebraic number theory, as soon as the dimension of Hilbert space exceeds three. A detailed description of the simplest possible example is given.

Norton describes how a Maxwell’s demon can be exorcised merely by considerations of the conservation of phase volume in classical physics. This exorcism is generalized here to quantum physics.

Inanimate explanation is to be analysed in terms of substances having powers and liabilities to exercise their powers under certain conditions; while personal explanation is to be analysed in terms of persons, their beliefs, powers, and purposes. A crucial criterion for an explanation being probably true is that it is (among explanations leading us to expect the data) the simplest one. Simplicity is a matter of few substances, few kinds of substances, few properties (including powers and liabilities), few kinds (...) of properties, and mathematically simple relations between properties. Explanation of the existence of the universe by the agency of God provides the simplest kind of personal explanation there can be, and one simpler than any inanimate explanation. I defend this view more thoroughly than previously in light of recent challenges. (shrink)

Drawing on drafts and other material from the Harvey Sacks archive this paper examines the development of one of the defining papers of Conversation Analysis, _A Simplest Systematics for the Organization of Turn-Taking for Conversation_ (Sacks, Schegloff, and Jefferson 1974). The discussion examines four drafts of the paper along with correspondence between the authors and with William Bright, the editor of the journal _Language_ where it was to be published. The four drafts trace the development of the paper from (...) a 13-page draft to the final 106-page final draft submitted to the journal. By exploring the drafts as they evolved the discussion highlights the development of the central ideas in the paper, the distinctive style of the paper as it is revised, the changes of authorship, and the role of the editor of _Language,_ William Bright, in helping to shape the paper through his own detailed reviews. (shrink)

I have argued over many years that theism provides a probably true explanation of the existence and most general features of the universe. A major reason for this, I have claimed, is that it is simpler than other explanations. The present paper seeks to amplify and defend this latter claim in the light of some recent challenges.

Long since, people tried to solve the mystery of the way that led to the appearance and propagation of living entities. However, no harmonious understanding of this mystery existed, because neither the scientifically grounded source minerals nor the ambient conditions were proposed and because it was groundlessly taken that the process of living matter origination is endothermal. The Life Origination Hydrate Theory (LOH-Theory) first suggests the chemical way capable of leading from the specified abundant natural minerals to origination of multitudes (...) of multitudes of simplest living entities and gives an original explanation for the phenomena of chirality and racemization delay. The LOH-Theory covers the period up to origination of the genetic code. The LOH-Theory is grounded on the following three discoveries based on the available information and on the results of our experimental works performed using original instrumentation and computer simulations. (1) There is the only one triad of natural minerals applicable for exothermal thermodynamically possible chemical syntheses of simplest living-matter components. (2) N-base, ribose, and phosphdiester radicals and nucleic acids as whole are size-compatible with structural gas-hydrate cavities. (3) The gas-hydrate structure arises around amido-groups in cooled undisturbed systems consisting of water and highly-concentrated functional polymers with amido-groups.The natural conditions and historic periods favorable for simplest living matter origination are revealed. The LOH-Theory is supported by results of observations, biophysical and biochemical experiments, and wide application of original three-dimensional and two-dimensional computer simulations of biochemical structures within gas-hydrate matrix. The instrumentation and procedures for experimental verification of the LOH-Theory are suggested. If future experiments are successful, they, possibly, could be the first step on the way to industrial synthesis of food from minerals, i.e., to execution of the work that is performed by plants. (shrink)

This collection explicates one of the core ideas underpinning Minimalist theory--explanation via simplification. It introduces and advances Minimalist theory for students and scholars in linguistics and related sub-disciplines of psychology, philosophy, and cognitive science.

The failure of Einstein’s co-authored “EPR” attempt to show the incompleteness of quantum theory is demonstrated directly for spatial degrees of freedom using only elementary notions. A GHZ construction is realized in the position properties of three particles whose quantum waves are distributed over three two-chambered boxes. The same system is modeled more realistically using three spatially separated, singly ionized hydrogen molecules.

What inductive biases must be incorporated into multi-agent artificial intelligence models to get them to capture high-fidelity imitation? We think very little is needed. In the right environments, both instrumental- and ritual-stance imitation can emerge from generic learning mechanisms operating on non-deliberative decision architectures. In this view, imitation emerges from trial-and-error learning and does not require explicit deliberation.

Einstein proclaimed that we could discover true laws of nature by seeking those with the simplest mathematical formulation. He came to this viewpoint later in his life. In his early years and work he was quite hostile to this idea. Einstein did not develop his later Platonism from a priori reasoning or aesthetic considerations. He learned the canon of mathematical simplicity from his own experiences in the discovery of new theories, most importantly, his discovery of general relativity. Through his (...) neglect of the canon, he realised that he delayed the completion of general relativity by three years and nearly lost priority in discovery of its gravitational field equations. (shrink)

William of Ockham wrote, ‘It is futile to do with more things that which can be done with fewer .’ But what if each option uses less than its predecessor but no option uses the least? A scale perfectly balanced between a pair of kilogram weights can be tipped by adding half a kilogram to one side, or a quarter of a kilogram, or an eighth of a kilogram, or … For any choice, there is an option that gets the (...) job done with less. Relative futility does not entail absolute futility. The job can get done – but only if we use superfluous means. Is this a refutation of Ockham’s Razor or just a close shave? (shrink)

This paper describes an approach for reasoning in a dynamic domain with nondeterministic actions in which an agent’s beliefs correspond to the simplest, or most plausible, course of events consistent with the agent’s observations and beliefs. The account is based on an epistemic extension of the situation calculus, a first-order theory of reasoning about action that accommodates sensing actions. In particular, the account is based on a qualitative theory of nondeterminism. Our position is that for commonsense reasoning, the world (...) is most usefully regarded as deterministic, and that nondeterminism is an epistemic phenomenon, arising from an agent’s limited awareness and perception. The account offers several advantages: an agent has a set of categorical beliefs, yet can deal with equally-likely outcomes or with outcomes of differing plausibility. The agent maintains as its set of contingent beliefs the most plausible, or simplest, picture of the world, consistent with its beliefs and actions it believes it executed; yet it may modify these in light of later information. (shrink)

This study presents a modified simplest equation method to investigate some real and exact solutions of conformable time fractional Benjamin-Bona-Mahony equation and Chan-Hilliard equation. We use traveling wave transformation to obtain the results in the form of series solution. Some calculations are performed through Mathematica software to analyze the accuracy of this approach. Graphical representations are reported for more significant results at different fractional-order which demonstrates that this approach is very simple, adequate, and legitimate.

Einstein proclaimed that we could discover true laws of nature by seeking those with the simplest mathematical formulation. He came to this viewpoint later in his life. In his early years and work he was quite hostile to this idea. Einstein did not develop his later Platonism from a priori reasoning or aesthetic considerations. He learned the canon of mathematical simplicity from his own experiences in the discovery of new theories, most importantly, his discovery of general relativity. Through his (...) neglect of the canon, he realised that he delayed the completion of general relativity by three years and nearly lost priority in discovery of its gravitational field equations. (shrink)

Commentary on: Olaf Blanke, Thomas Metzinger, Full-body illusions and minimal phenomenal selfhood, Trends in Cognitive Sciences, Volume 13, Issue 1, January 2009, Pages 7-13, ISSN 1364-6613, DOI: 10.1016/j.tics.2008.10.003.

From three simple Peircean semeiotic principles, the general formula is derived for the number of definable sign-types from the number of semeiotic trichotomies to be used in defining the sign-types. If k is the number of such trichotomies, then [ ]/2 is the number of sign-types definable by appealing to them. The significance of the derivation lies in its setting constraints on particular detailed theories of sign-types.