Numerical Expressions in Chinese: Syntax and Semantics

Numerical expressions are linguistic forms related to numbers or quantities, which directly reflect the relationship between linguistic symbols and mathematical cognition. Featuring some unique properties, numeral systems are somewhat distinguished from other language subsystems. For instance, numerals can appear in various grammatical positions, including adjective positions, determiner positions, and argument positions. Thus, linguistic research on numeral systems, especially the research on the syntax and semantics of numerical expressions, has been a popular and recurrent topic. For the syntax of complex numerals, two analyses have been proposed in the literature. The traditional constituency analysis maintains that complex numerals are phrasal constituents, which has been widely accepted and defended as a null hypothesis. The nonconstituency analysis, by contrast, claims that a complex numeral projects a complementative structure in which a numeral is a nominal head selecting a lexical noun or a numeral-noun combination as its complement. As a consequence, additive numerals are transformed from full NP coordination. Whether numerals denote numbers or sets has aroused a long-running debate. The number-denoting view assumes that numerals refer to numbers, which are abstract objects, grammatically equivalent to nouns. The primary issue with this analysis comes from the introduction of a new entity, numbers, into the model of ontology. The set-denoting view argues that numerals refer to sets, which are equivalent to adjectives or quantifiers in grammar. One main difficulty of this view is how to account for numerals in arithmetic sentences.

How Things Are

This work is designed to introduce some of the more important fruits of Indian Buddhist metaphysical theorizing to philosophers with little or no prior knowledge of classical Indian philosophy. It is widely known among non-specialists that Buddhists deny the existence of a self. Less widely appreciated among philosophers currently working in metaphysics is the fact that the Indian Buddhist tradition contains a wealth of material on a broad assortment of other issues that have also been foci of recent debate. Indian Buddhist philosophers have argued for a variety of interesting claims about the nature of the causal relation, about persistence, about abstract objects, about the consequences of presentism, about the prospects for a viable ontological emergentism. They engaged in a spirited debate over illusionism in the philosophy of consciousness. Some espoused global anti-realism while others called its coherence into question. And so on. This work is meant to introduce the views of such major Buddhist philosophers as Vasubandhu, Dharmakīrti, and Nāgārjuna on these and other issues. And it presents their arguments and analyses in a manner meant to make them accessible to students of philosophy who lack specialist knowledge of the Indian tradition. Analytic metaphysicians who are interested in moving beyond the common strategy of appealing to the intuitions of “the folk” should find much of interest here.

Abstract Objects in the Causal Order

<p>Abstract entities have long been viewed as entities that lack causal powers; that is, they cannot be constitutive of causes or effects. This thesis aims to reject this claim and argue that abstract objects are indeed part of the causal order. I will call this thesis ‘AOCO’ for short. In the first chapter I argue that other philosophers have committed themselves to the claim that some abstract objects have been caused to come into existence. In the second chapter, I argue that the best solution to Benacerraf’s problem is to concede that abstract objects have a causal influence on what we believe. In the third chapter I examine and evaluate objections to AOCO.</p>

Abstract Objects in the Causal Order

<p>Abstract entities have long been viewed as entities that lack causal powers; that is, they cannot be constitutive of causes or effects. This thesis aims to reject this claim and argue that abstract objects are indeed part of the causal order. I will call this thesis ‘AOCO’ for short. In the first chapter I argue that other philosophers have committed themselves to the claim that some abstract objects have been caused to come into existence. In the second chapter, I argue that the best solution to Benacerraf’s problem is to concede that abstract objects have a causal influence on what we believe. In the third chapter I examine and evaluate objections to AOCO.</p>

Classification Using 3D Point Cloud and 2D Image on Abstract Objects

While classification using machine learning is exceptionally successful with 2D images, it is more challenging to classify 3D objects. However, 3D objects classification is critical because of its application in autonomous vehicles and robotics. This paper compared neural networks with similar structures using 3D point clouds and 2D images on the same objects. We also generated objects with abstract design and input them into the neural networks we created. We find clear disadvantages with classifying abstract objects compared to ordinary objects for both neural networks. We believe having contextual information will help to address this problem. We also observed that the neural network based on images performs worse than that based on point clouds. However, image based classification takes less time to train compared to point cloud based classification.

Challenges Regarding Scientific Transcription in Virtual Office Hours

Mathematics teachers face great difficulties during virtual communication with their students, mainly because scientific and technical subjects use a great many mathematical symbols, abstract objects and a wide variety of technical nomenclatures that are not directly represented on the keyboards of computers, tablets or other communication devices. This paper aims to facilitate oral and written communication between teachers and students in mathematics subjects. In this regard, we describe realistic procedures for use in virtual office hours. We analyse different methods that combine the use of computers, tablets, webcams and an institutional video lecture system. The improvement in oral and written communication will have a positive effect on academic performance and decrease the dropout rate in distance learning courses, because the students feel more closely accompanied in their learning.

Sense Logic

Traditional mathematical logic is "what follows from what".Sense logic - "what belongs to what".Traditional mathematical logic is "a collection of abstract objects not related to the outside world."Sense logic is "a set of objects and events that describe the state of the real world."Below, we present a new paradigm of logic based on semantic connections between the considered objects of any nature. The Sense Logic is not a part of traditional mathematics. Its main task is to describe the phenomena of the real world from the standpoint of their semantic coherence.