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If a constituent C has the potential for a type of movement M, a structurally lower constituent cannot undergo M across C in certain contexts, as reported in Li, Shields and Lin (2012). Neither the Relativized Minimality Condition nor the Minimal Link Condition alone can account for this new fact. It is argued that an empirically adequate model of UG may keep the MLC but must also include two more mechanisms. Ternary-valued features accommodate potential movability. The Feature Value Assignment Protocol relies on computational cost to regulate how the inherent values of any given feature are actually represented in syntactic operations. While this theory offers a unified account of all known facts of minimality (wh-island, potentiality-related movements of adverbs, superiority, super-raising, local and long head movements), it also bears on more fundamental concerns of theoretical simplicity and data idealization. It is argued with both linguistic cases like minimality and the previously axiomatic notion of government and cases of physics (friction, Maxwell’s equations) that the understanding of simplicity often found in syntactic theorization is overly simplistic.
This chapter examines Aquinas’s doctrine of divine simplicity, situating it within the broader landscape of classical theism in contrast to theistic personalism. After outlining Aquinas’s conviction that while God’s existence can be demonstrated, God’s essence remains incomprehensible, the discussion turns to Summa Theologiae, 1a, 3, where Aquinas denies that God is composite in any respect. He argues that God is not a body, nor composed of form and matter, essence and existence, substance and accidents, or genus and difference. Instead, God is pure actuality, identical with his essence and existence, and thus utterly simple. The chapter compares these claims with parallel treatments in the Sentences, Summa Contra Gentiles, and Compendium Theologiae. Finally, it surveys modern objections – particularly from Alvin Plantinga, Richard Swinburne, and others – that divine simplicity undermines God’s personhood, freedom, or responsiveness. The chapter concludes that many such criticisms misrepresent Aquinas, who presents simplicity chiefly as a way of ruling out what God cannot be.
Aquinas argues that, abstracting from divine revelation, God's existence can be argued for successfully, and that God is the source of the existence of all that is not divine for as long as it exists. His philosophical thought about God has been seminal for later thinkers, but can be hard to grasp as it is scattered across a broad range of his writings. This book provides a comprehensive and accessible single-volume account of Aquinas's philosophy of God which also evaluates it in the light both of various criticisms that have been made of it, and of philosophical thought more generally. It situates Aquinas's thinking about God in relation to major philosophers of the past and a number of important philosophers writing today, which will enable readers to understand Aquinas's philosophy of God in the context of centuries of philosophical thought.
We prove that if a Hölder continuous fiber-bunched cocycle $\hat {A}$ over an invertible hyperbolic transitive shift $\hat {\Sigma }$ satisfies an appropriate strong irreducibility condition on Grassmannians, then $\hat {\Sigma }$ admits an ergodic measure $\hat {\mu }$ with full support and product structure with simple Lyapunov spectrum if and only if any other ergodic measure with full support and product structure also has simple Lyapunov spectrum.
This paper defends a broadly Thomistic understanding of simplicity against a range of contemporary criticisms. Critics of divine simplicity argue that simplicity leads us to identify God with an abstract property and that it renders theological language semantically vacuous because divine simplicity cannot ground a plurality of true intrinsic predicates. I defuse these criticisms by employing some central Fregean distinctions – specifically, the distinctions between object and concept, predication and identification, and sense and reference. While these Fregean distinctions help to dissolve initial logical difficulties, they do not by themselves explain how theological predicates can have determinate content or truth-conditions. I therefore situate the relevant Fregean diagnostics within the Thomistic metaphysical framework of analogy. This framework supplies principled constraints on theological predication without reintroducing composition into God. I conclude by arguing that the Thomistic doctrine of analogy does not eliminate semantic openness but renders theological language sufficiently determinate for meaning and practice, grounding meaningful God-talk in both metaphysics and the formative practices of religious life.
Let T be an algebraically bounded theory. We consider the $L(\bar \delta )$-expansions of T by a tuple $\bar {\delta }$ of derivations (which may be commuting or not). We investigate the model completion of either of the above theories, whose existence has been established in [21], with particular attention to its model-theoretic properties, including $\omega $-stability, simplicity, open core, and elimination of imaginaries.
It can seem surprising that there is something rather than nothing because, as Leibniz famously put it, nothing is “simpler and easier” than something. The idea seems to be that, in virtue of its relative simplicity, an empty world is the default. In Chapters 5-7 I will question this assumption. An empty world is not obviously simpler than a world in which things exist. A world in which nothing exists would still hold various truths. We might call these “nonontological truths” because they are not truths regarding existing things. If something were to exist, however, then it could in principle simplify matters considerably by grounding, and so unifying, the various nonontological truths. The simplification at work here is similar to the simplification involved in postulating a common ancestor to explain homologous traits in different species that happen to be similar to one another. Similarly, in postulating some existing thing that unifies the various nonontological truths, we avoid having to postulate disparate nonontological truths that obtain for no reason. If that is right, then a world in which something exists might very well be simpler than a world in which nothing exists.
This chapter will examine whether we should expect an explanation for the Question. Does the fact that there is something rather than nothing call out for explanation? The answer to this question depends on what it takes for some phenomenon to call out for explanation. Here I will engage with some extant accounts of this notion of a phenomenon calling out for explanation, as well as the principle of sufficient reason, which in its strongest form claims that every fact must have an explanation. I will also develop my own account of when some fact calls out for explanation. I will propose that in asking whether some fact calls out for explanation we simply ask: What is the probability of that fact’s having an explanation? And here we employ the criteria of theory choice (i.e., the criteria governing our probability assignments) that we make in other contexts. To the extent that the probability that some fact has an explanation is greater than 0.5, we should expect the fact in question to have an explanation. In the case of the fact that there is something rather than nothing, the main factors relevant to determining the probability in question will be examined in subsequent chapters.
The doctrine of divine simplicity is an important element of major monotheistic religions; not only Islamic and Jewish but also Christian theologians have affirmed and defended the doctrine. However, the historic doctrine is the subject of intense debate within these traditions. Historic expressions of the doctrine are surveyed, important objections are considered, and arguments in favor of the doctrine are summarized.
This chapter traces the development of ideas concerning the divine nature over the course of the early scholastic period. In particular, it traces a shift which occurred over the course of the period, at the start of which scholastic theologians generally described God's nature as fundamentally simple, but over the course of which members of the Franciscan order in particular began to speak of God's nature as primarily infinite.
Cross-category harmony is one of the most well-known typological universals. It describes a trend of consistent alignment of different syntactic categories across phrases within a language. Explanations for this universal vary as to whether cognitive factors play a role or the tendency is instead due to mechanisms of language change alone. In this article we report a series of artificial language learning experiments that aim to test a hypothesized link between cognition and cross-category harmony. As with the typological tendency itself, we find mixed evidence for harmony across different types of phrases. Specifically, learners are biased in favor of consistent alignment of the verb in the verb phrase and the adposition in the adpositional phrase. However, the bias for consistent alignment of the verb in the verb phrase and the adjective in the noun phrase depends on the semantic similarity between adjectives and verbs. When adjectives are active and therefore more verb-like (e.g. broken), we find harmony; when they are stative and therefore less verb-like (e.g. blue), we do not. These results suggest that the bias for cross-category harmony is not purely based on the syntactic notions of head and dependent, but reflects the interaction between a general cognitive bias favoring consistent order and cross-category similarity.
In this chapter I explore theories, models, and methods. The narrative turn in the social sciences and in the analysis of world politics has been fostered by and drawn attention to McCloskey’s work and the importance of story-telling (section 1). Theories and models tell stories that are created by acts of individual imagination and that exist as collective imaginaries (section 2). Experiments and experimentation are different ways of testing and test-driving scientific theories and models in a world that is both risky and uncertain (section 3). And the simplicity or complexity of the stories told by theories and models always grapples with the risk-uncertainty conundrum (section 4).
This chapter proposes that singular compositional abduction has four features shared by at least many other instances of abduction: (1) abduction is sometimes used for confirmation, (2) abduction is sometimes used to postulate entities that are qualitatively distinct from the entities cited in the supporting evidence, (3) abduction may rely on background beliefs, and (4) abduction is sometimes used to postulate entities that are not directly empirically detected. It also indicates why scientists take abduction to be truth conducive. It shows how compositional abduction may serve as an alternative to the theory of hypothetico-deductive confirmation. Finally, it suggests a broad range of scientific cases in cognitive science that might be understood in terms of singular compositional abduction.
When evaluating competing hypotheses in archaeology, researchers frequently invoke the principle of parsimony, which states that simpler hypotheses should be preferred. However, the criteria for measuring simplicity and the rationale for labeling a hypothesis as most parsimonious often remain unclear. More broadly, the epistemic merit of parsimony and its relevance to archaeological reasoning are generally assumed but rarely clarified. This article explores how archaeologists use parsimony in ethnographic analogy and formal model selection. In the first context, it is usually uncertain how simplicity should be measured or why increased simplicity raises the plausibility of an ethnographic analogy. We contend that discussions of ethnographic analogy are better characterized under inference to the best explanation, where parsimony is only one heuristic among others. In the second context, simplicity is assessed by the relative complexity, rather than the quantity, of postulates in a model. This approach to parsimony, which does track plausibility under certain conditions, helps prevent false positives in archaeological interpretation. However, it also heightens the risk of rejecting alternative, complex causes. We argue that parsimony can aid in evaluating the relative likelihood of competing models and, more importantly, serve as a guide to clarify the complex histories of archaeological phenomena.
This chapter identifies and explores a central feature of automated legal guidance: “simplexity.” As this chapter introduces this term, simplexity occurs when the government presents clear and simple explanations of the law without highlighting its underlying complexity or reducing this complexity through formal legal changes. Automated legal guidance inherently relies on simplexity as a result of the tension between the complexity of the law and the need of agencies to explain the law in simple terms. In creating the law, the federal government must address complex problems, and it often does so by creating legislation that is replete with errors, ambiguities, and problems. This disconnect between complex federal law and agencies’ need to explain the law to the public in simple and understandable ways forces agencies to rely on simplexity. Automated legal guidance only exacerbates the need for simplexity, because when individuals use automated online tools offered by government agencies, they expect the explanations to be even simpler, more straightforward, and easier to apply than would be the case if they were relying upon written agency publications.
This paper experimentally investigates the effect of introducing unavailable alternatives and irrelevant information regarding the alternatives on the optimality of decisions in choice problems. We find that the presence of unavailable alternatives and irrelevant information generates suboptimal decisions with the interaction between the two amplifying this effect. Irrelevant information in any dimension increases the time costs of decisions. We also identify a “preference for simplicity” beyond the desire to make optimal decisions or minimize time spent on a decision problem.
Transforming the core array in Tucker three-way component analysis to simplicity is an intriguing way of revealing structures in between standard Tucker three-way PCA, where the core array is unconstrained, and CANDECOMP/PARAFAC, where the core array has a generalized diagonal form. For certain classes of arrays, transformations to simplicity, that is, transformations that produce a large number of zeros, can be obtained explicitly by solving sets of linear equations. The present paper extends these results. First, a method is offered to simplifyJ ×J × 2 arrays. Next, it is shown that the transformation that simplifies anI ×J ×K array can be used to also simplify the (complementary) arrays of order (JK −I) ×J ×K, of orderI × (IK −J) ×K and of orderI ×J × (IJ −K). Finally, the question of what constitutes the maximal simplicity for arrays (the maximal number of zero elements) will be considered. It is shown that cases of extreme simplicity, considered in the past, are, in fact, cases of maximal simplicity.
We introduce non-associative skew Laurent polynomial rings and characterize when they are simple. Thereby, we generalize results by Jordan, Voskoglou, and Nystedt and Öinert.
Young children often lack words for what they want to talk about. To fill the gaps in their lexicon, they coin new words. They rely on compounding and derivation to do this. This means identifying and analyzing parts of words – roots or stems, and affixes – and learning their meanings, as well as which combinations are possible. Some languages favor compounding and some derivation in word formation. Children are sensitive to which options are the most productive and adopt those first. Two-year-olds offer analyses of word meanings, as in running-stick (I run with it) or high-chair (it is high), and provide analyses of novel compounds where they take account of language structure (head noun first in Hebrew, second in English). They also analyze derived forms with agentive endings. They start to produce novel words from as young as age two, whether compounds in Germanic languages, or derived forms in Romance and Semitic. They begin with simple forms (minimal or no change to the root), advance to compound or derived word forms that are transparent in meaning, and opt for the most productive options in the adult language, with the goal of finding the right words to convey the child-speaker’s meaning.