This paper deals with a construction, which we dub Non-Agreeing Degree (NAD) constructions, with the distinguishing property that the agreement pattern between subjects and degree predicates is optionally disrupted, even in languages (like Spanish) where verbs commonly agree with their subjects. We show that the agreeing versus non-agreeing alternation comes with important semantic differences for the interpretation of the degree construction. We provide a first systematic description of this type of constructions and postulate a formal syntactic and semantic analysis. We argue that NAD constructions are characterized by degree predicates that introduce a non-conventional nominal scale and by subjects that are interpreted as equally non-conventional units of measurement. We postulate an intensionalization process on the subject of NAD constructions, which we capture via a general nominalization function that allows a default as well as an ordinary agreement pattern between subject and copula.

Let $f : X \to S$ be a family of smooth projective algebraic varieties over a smooth connected quasi-projective base $S$, and let $\mathbb {V} = R^{2k} f_{*} \mathbb {Z}(k)$ be the integral variation of Hodge structure coming from degree $2k$ cohomology it induces. Associated to $\mathbb {V}$ one has the so-called Hodge locus $\textrm {HL}(S) \subset S$, which is a countable union of ‘special’ algebraic subvarieties of $S$ parametrizing those fibres of $\mathbb {V}$ possessing extra Hodge tensors (and so, conjecturally, those fibres of $f$ possessing extra algebraic cycles). The special subvarieties belong to a larger class of so-called weakly special subvarieties, which are subvarieties of $S$ maximal for their algebraic monodromy groups. For each positive integer $d$, we give an algorithm to compute the set of all weakly special subvarieties $Z \subset S$ of degree at most $d$ (with the degree taken relative to a choice of projective compactification $S \subset \overline {S}$ and very ample line bundle $\mathcal {L}$ on $\overline {S}$). As a corollary of our algorithm we prove conjectures of Daw–Ren and Daw–Javanpeykar–Kühne on the finiteness of sets of special and weakly special subvarieties of bounded degree.

What's wrong with joining corona parties? In this article, I defend the idea that reasons to avoid such parties (or collective harms, more generally) come in degrees. I approach this issue from a participation-based perspective. Specifically, I argue that the more people are already joining the party, and the more likely it is that the virus will spread among everyone, the stronger the participation-based reason not to join. In defense of these degrees, I argue that they covary with the expression of certain attitudes.

Philosophers commonly say that beliefs come in degrees (or that beliefs are graded or that there are partial beliefs). Drawing from the literature, I make precise three arguments for this claim: an argument from degrees of confidence, an argument from degrees of firmness, and an argument from natural language. I show that they all fail. I also advance three arguments that beliefs do not come in degrees: an argument from natural language, an argument from intuition, and an argument from the metaphysics of degrees. On the basis of these arguments, I conclude that beliefs do not come in degrees.