Horwich on meaning and use

Paul Horwich claims that theories of meaning ought to accommodate the commonsense intuition that meanings play a part in explaining the use of words. Further, he argues that the view that best does so is that according to which the meaning of a word is constituted by a disposition to accept, in some circumstances, sentences in which it features. I argue that if meanings are construed thus, they will in fact fail to explain the use of words. I also argue that if we insist, as Horwich does, on the commonsense assumption that meanings are a species of entity, all versions of the view that meaning is constituted by our dispositions to use words will have to be rejected. I do not, however, claim that such theories ought to be rejected. My point is that they are incompatible with the requirements of commonsense. Further, I suggest that it is premature to impose such requirements on theories of meaning

Dispositions and the principle of least action

My aim is to argue for the incompatibility of one of the central principles of physics, namely the principle of least action (PLA), with the increasingly popular view that the world is, ultimately, merely something like a conglomerate of objects and irreducible dispositions. First, I argue that the essentialist implications many suppose this view has are not compatible with the PLA. Second, I argue that, irrespective of whether this view has any essentialist implications, it is not compatible with the kind of explanation that the PLA affords

On what powers cannot do

Dispositionalism is the view that the world is, ultimately, just a world of objects and their irreducible dispositions, and that such dispositions are, ultimately, the sole explanatory ground for the occurrence of events. This view is motivated, partly, by arguing that it affords, while non-necessitarian views of laws of nature do not afford, an adequate account of our intuitions about which regularities are non-accidental. I, however, argue that dispositionalism cannot adequately account for our intuitions about which regularities are non-accidental. Further, I argue that, intuitions aside, if we suppose that our world contains objects along with their irreducible dispositions, we must suppose, on pain of logical incoherence, that it contains laws of nature that are incompatible with a dispositionalist ontology. Indeed, if we sup ose a world of objects and irreducible dispositions, we will have to suppose that the most prominent views of laws of nature currently on offer are all inadequate

Identity, nature and ground

What does the qualitative identity of objects consist in? A standard response is that it consists in the possession of properties and relations. If all of an object’s properties and relations are specified, all there is to be specified about its qualitative as opposed to its numerical identity will have been specified. Another response adds that kinds, conceived of as an irreducible category of entity, also play a part in fixing the qualitative identities of objects. In what follows, two arguments are offered according to which these views are insufficient. Both lead to the conclusion that the qualitative identities of objects consist in part in their natures being grounded in what differs from entities, that is to say in something like conditions for the possibility of entities. The idea of such grounding will be clarified, and some of the criteria of adequacy for theses about it will be spelled out. Further, the implications of the claim that the natures of objects are grounded for the problems of the one and the many will be discussed

Dynamical Inequality in Growth Models

A recent exponent inequality is applied to a number of dynamical growth models. Many of the known exponents for models such as the Kardar-Parisi-Zhang (KPZ) equation are shown to be consistent with the inequality. In some cases, such as the Molecular Beam Equation, the situation is more interesting, where the exponents saturate the inequality. As the acid test for the relative strength of four popular approximation schemes we apply the inequality to the exponents obtained for two Non Local KPZ systems. We find that all methods but one, the Self Consistent Expansion, violate the inequality in some regions of parameter space. To further demonstrate the usefulness of the inequality, we apply it to a specific model, which belongs to a family of models in which the inequality becomes an equality. We thus show that the inequality can easily yield results, which otherwise have to rely either on approximations or general beliefs.Comment: 6 pages, 4 figure

Ellis on the limitations of dispositionalism

FIRST PARAGRAPH I have argued that dispositionalism is incompatible with the Principle of Least Action (PLA) (Katzav 2004). In ‘Katzav on the Limitations of Dispositionalism,’ Brian Ellis responds, arguing that while naïve dispositionalism is incompatible with the PLA, sophisticated dispositionalism is not. Naive dispositionalism, according to Ellis, is the view that the world is ultimately something like a conglomerate of objects and their dispositions, and that, therefore, dispositions are the ultimate ontological units that explain events. Sophisticated dispositionalism, according to Ellis, supposes that, how things are disposed to behave depends also on what kinds of things they are, what kinds of property they have, and how these kinds of things and properties are placed in the natural kinds hierarchies to which they belong (Ellis 2005). Further, it supposes that at the top of each hierarchy of natural kinds there is a global kind. For example, ‘[t]he global natural kind in the category of substance is that of the physical system’ (Ellis 2005). Ellis continues, claiming that the PLA is of the essence of the global kind in the category of objects or substances. If this is so, then, of course, every continuing object must be Lagrangian, i.e. disposed to evolve in accordance with the principle of least action (Ellis 2005). Ellis concludes that, therefore, a sophisticated dispositionalist can accommodate the PLA and its metaphysical necessity

Roughness of tensile crack fronts in heterogenous materials

The dynamics of planar crack fronts in heterogeneous media is studied using a recently proposed stochastic equation of motion that takes into account nonlinear effects. The analysis is carried for a moving front in the quasi-static regime using the Self Consistent Expansion. A continuous dynamical phase transition between a flat phase and a dynamically rough phase, with a roughness exponent $\zeta=1/2$, is found. The rough phase becomes possible due to the destabilization of the linear modes by the nonlinear terms. Taking into account the irreversibility of the crack propagation, we infer that the roughness exponent found in experiments might become history-dependent, and so our result gives a lower bound for $\zeta$.Comment: 7 page

Large Deviations of the Smallest Eigenvalue of the Wishart-Laguerre Ensemble

We consider the large deviations of the smallest eigenvalue of the Wishart-Laguerre Ensemble. Using the Coulomb gas picture we obtain rate functions for the large fluctuations to the left and the right of the hard edge. Our findings are compared with known exact results for $\beta=1$ finding good agreement. We also consider the case of almost square matrices finding new universal rate functions describing large fluctuations.Comment: 4 pages, 2 figure

The probability density function tail of the Kardar-Parisi-Zhang equation in the strongly non-linear regime

An analytical derivation of the probability density function (PDF) tail describing the strongly correlated interface growth governed by the nonlinear Kardar-Parisi-Zhang equation is provided. The PDF tail exactly coincides with a Tracy-Widom distribution i.e. a PDF tail proportional to $\exp( - c w_2^{3/2})$, where $w_2$ is the the width of the interface. The PDF tail is computed by the instanton method in the strongly non-linear regime within the Martin-Siggia-Rose framework using a careful treatment of the non-linear interactions. In addition, the effect of spatial dimensions on the PDF tail scaling is discussed. This gives a novel approach to understand the rightmost PDF tail of the interface width distribution and the analysis suggests that there is no upper critical dimension.Comment: 17 pages, 2 figure

Dynamic stability of crack fronts: Out-of-plane corrugations

The dynamics and stability of brittle cracks are not yet fully understood. Here we use the Willis-Movchan 3D linear perturbation formalism [J. Mech. Phys. Solids {\bf 45}, 591 (1997)] to study the out-of-plane stability of planar crack fronts in the framework of linear elastic fracture mechanics. We discuss a minimal scenario in which linearly unstable crack front corrugations might emerge above a critical front propagation speed. We calculate this speed as a function of Poisson's ratio and show that corrugations propagate along the crack front at nearly the Rayleigh wave-speed. Finally, we hypothesize about a possible relation between such corrugations and the long-standing problem of crack branching.Comment: 5 pages, 2 figures + supplementary informatio