Embedded Attitudes

This paper presents a puzzle involving embedded attitude reports. We resolve the puzzle by arguing that attitude verbs take restricted readings: in some environments the denotation of attitude verbs can be restricted by a given proposition. For example, when these verbs are embedded in the consequent of a conditional, they can be restricted by the proposition expressed by the conditional’s antecedent. We formulate and motivate two conditions on the availability of verb restrictions: a constraint that ties the content of restrictions to the “dynamic effects” of sentential connectives and a constraint that limits the availability of restriction effects to present tense verbs with first-person subjects. However, we also present some cases that make trouble for these conditions, and outline some possible ways of modifying the view to account for the recalcitrant data. We conclude with a brief discussion of some of the connections between our semantics for attitude verbs and issues concerning epistemic modals and theories of knowledge

Knowledge embedded

How should we account for the contextual variability of knowledge claims? Many philosophers favour an invariantist account on which such contextual variability is due entirely to pragmatic factors, leaving no interesting context-sensitivity in the semantic meaning of ‘know that.’ I reject this invariantist division of labor by arguing that pragmatic invariantists have no principled account of embedded occurrences of ‘S knows/doesn’t know that p’: Occurrences embedded within larger linguistic constructions such as conditional sentences, attitude verbs, expressions of probability, comparatives, and many others, I argue, give rise to a threefold problem of embedded implicatures

Embedded Monopoles

Using the embedded defect method, we classify the possible embeddings of a 't Hooft-Polyakov monopole in a general gauge theory. We then discuss some similarities with embedded vortices and relate our results to fundamental monopoles.Comment: 6 pages, LaTe

Embedded Vortices

We present a discussion of embedded vortices in general Yang-Mills theories. The origin of a family structure of solutions is shown to be group theoretic in nature and a procedure for its determination is developed. Vortex stability can be quantified into three types: Abelian topological stability, non-Abelian topological stability, and dynamical stability; we relate these to the family structure of vortices, in particular discussing how Abelian topological and dynamical stability are related. The formalism generally encompasses embedded domain walls and embedded monopoles also.Comment: final corrections. latex fil

Stable embedded solitons

Stable embedded solitons are discovered in the generalized third-order nonlinear Schroedinger equation. When this equation can be reduced to a perturbed complex modified KdV equation, we developed a soliton perturbation theory which shows that a continuous family of sech-shaped embedded solitons exist and are nonlinearly stable. These analytical results are confirmed by our numerical simulations. These results establish that, contrary to previous beliefs, embedded solitons can be robust despite being in resonance with the linear spectrum.Comment: 2 figures. To appear in Phys. Rev. Let

Detaching embedded points

We show that if $D \subset \mathbb P^N$ is obtained from a codimension two local complete intersection $C$ by adding embedded points of multiplicity $\leq 3$, then $D$ is a flat limit of $C$ and isolated points. As applications, we determine the irreducible components of Hilbert schemes of space curves with high arithmetic genus, show the smoothness of the Hilbert component whose general member is a plane curve union a point in $\mathbb P^3$, and construct a Hilbert component whose general member has an embedded point.Comment: 16 pages, amsart style. New examples added to show that hypotheses of main theorem are necessary, showing sharpness of resul