After reviewing various natural bi-interpretations in urelement set theory, including second-order set theories with urelements, we explore the strength of second-order reflection in these contexts. Ultimately, we prove, second-order reflection with the abundant atom axiom is bi-interpretable and hence also equiconsistent with the existence of a supercompact cardinal. The proof relies on a reflection characterization of supercompactness, namely, a cardinal κ is supercompact if and only if every Π11 sentence true in a structure M (of any size) containing κ in (...) a language of size less than κ is also true in a substructure m≺M of size less than κ with m∩κ∈κ. (shrink)

We study reflection principles in Kelley-Morse set theory with urelements (KMU). We first show that First-Order Reflection Principle is not provable in KMU with Global Choice. We then show that KMU + Limitation of Size + Second-Order Reflection Principle is mutually interpretable with KM + Second-Order Reflection Principle. Furthermore, these two theories are also shown to be bi-interpretable with parameters. Finally, assuming the existence of a κ+-supercompact cardinal κ in KMU, we construct a model of KMU + Second-Order Reflection Principle (...) where Limitation of Size fails. (shrink)

We explore Boolean-valued models of set theory with a class of urelements. In an existing construction, which we call UB, every urelement is its own B-name. We prove the fundamental theorem of UB in the context of ZFUR (i.e., ZF with urelements formulated with Replacement). In particular, UB is shown to preserve Replacement and hence ZFUR. Moreover, UB can both destroy axioms, such as the DCω1-scheme, and recover axioms, such as the Collection Principle. One drawback of UB is that it (...) does not permit mixing names, resulting in a lack of fullness. To address this, we introduce a new construction, UB‾, which is closed under mixtures. We prove that there is an elementary embedding from UB to UB‾. Over ZFUR with the Axiom of Choice, UB‾ is full for every complete Boolean algebra B just in case the Collection Principle holds. (shrink)

Two principles regarding agents' specific ability are proposed. The first claims that ordinary agents always lack the ability to do otherwise in the past, while the second principle observes that it is at least possible for some agent to have the ability to perform some action in the past. These two principles further give rise to three desiderata for a true account of ability. Two accounts of ability in the literature—the conditional analysis and the dispositional account—are then examined but they (...) both fail to meet the desiderata simultaneously. A modal principle of ability is motivated at the end. (shrink)

I propose a new theory of mereology based on a mereological reflection principle. Reflective mereology has natural fusion principles but also refutes certain principles of classical mereology such as Universal Fusion and Fusion Uniqueness. Moreover, reflective mereology avoids Uzquiano’s cardinality problem–the problem that classical mereology tends to clash with set theory when they both quantify over everything. In particular, assuming large cardinals, I construct a model of reflective mereology and second-order ZFCU with Limitation of Size. In the model, classical mereology (...) holds when the quantifiers are restricted to the urelements. (shrink)

This thesis aims to solve two metaphysical puzzles about ability. The first belongs to the free will debate: is determinism compatible with the ability to do otherwise? The second pertains to time travel: what things can a backward time traveler do in the past? By introducing two principles about an agent’s ability regarding the past, I defend the following modal principle about ability: what an agent can do must be compossible with the past. This principle generates solutions to the two (...) puzzles. (shrink)

We replicated and extended the findings of Yao et al. [(2018). Differential emotional processing in concrete and abstract words. Journal of Experimental Psychology: Learning, Memory, and Cognition, 44(7), 1064–1074] regarding the interaction of emotionality, concreteness, and imageability in word processing by measuring eye fixation times on target words during normal reading. A 3 (Emotion: negative, neutral, positive) × 2 (Concreteness: abstract, concrete) design was used with 22 items per condition, with each set of six target words matched across conditions in (...) terms of word length and frequency. Abstract (e.g. shocking, reserved, fabulous) and concrete (e.g. massacre, calendar, treasure) target words appeared (separately) within contextually neutral, plausible sentences. Sixty-three participants each read all 132 experimental sentences while their eye movements were recorded. Analyses using Gamma generalised linear mixed models revealed significant effects of both Emotion and Concreteness on all fixation measures, indicating faster processing for emotional and concrete words. Additionally, there was a significant Emotion × Concreteness interaction which, critically, was modulated by Imageability in early fixation time measures. Emotion effects were significantly larger in higher-imageability abstract words than in lower-imageability ones, but remained unaffected by imageability in concrete words. These findings support the multimodal induction hypothesis and highlight the intricate interplay of these factors in the immediate stages of word processing during fluent reading. (shrink)

姚伯茂(1937~ ),浙江诸暨人,上海工业大学人文学院院长、教授,中国辩证唯物主义研究会理事,上海市哲学学会常务理事.

This dissertation aims to provide a comprehensive account of set theory with urelements. In Chapter 1, I present mathematical and philosophical motivations for studying urelement set theory and lay out the necessary technical preliminaries. Chapter 2 is devoted to the axiomatization of urelement set theory, where I introduce a hierarchy of axioms and discuss how ZFC with urelements should be axiomatized. The breakdown of this hierarchy of axioms in the absence of the Axiom of Choice is also explored. In Chapter (...) 3, I investigate forcing with urelements and develop a new approach that addresses a drawback of the existing machinery. I demonstrate that forcing can preserve, destroy, and recover the axioms isolated in Chapter 2 and discuss how Boolean ultrapowers can be applied in urelement set theory. Chapter 4 delves into class theory with urelements. I first discuss the issue of axiomatizing urelement class theory and then explore the second-order reflection principle with urelements. In particular, assuming large cardinals, I construct a model of second-order reflection where the principle of limitation of size fails. (shrink)