This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a sub stantial course on abstract algebra. Consequently, our treatment ofthe sub ject is algebraic. Although we assurne a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of . the exercises. We also assurne (...) a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model oflogic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based-rather, any conclusions to be drawn about the foundations of mathematics co me only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory. (shrink)

Participation in research is supposed to be voluntary and informed. Yet it is difficult to ensure people are adequately informed about the potential uses of their biological materials when they donate samples for future research. We propose a novel consent framework which we call “demonstrated consent” that leverages blockchain technology and generative AI to address this problem. In a demonstrated consent model, each donated sample is associated with a unique non-fungible token (NFT) on a blockchain, which records in its metadata (...) information about the planned and past uses of the sample in research, and is updated with each use of the sample. This information is accessible to a large language model (LLM) customized to present this information in an understandable and interactive manner. Thus, our model uses blockchain and generative AI technologies to track, make available, and explain information regarding planned and past uses of donated samples. (shrink)

This book is available either individually, or as part of the specially-priced Arguments of the Philosphers Collection.

The Global Workspace Theory and Information Integration Theory are two of the most currently accepted consciousness models; however, these models do not address many aspects of conscious experience. We compare these models to our previously proposed consciousness model in which the thalamus fills-in processed sensory information from corticothalamic feedback loops within a proposed 3D default space, resulting in the recreation of the internal and external worlds within the mind. This 3D default space is composed of all cells of the body, (...) which communicate via gap junctions and electrical potentials to create this unified space. We use 3D llustrations to explain how both visual and non-visual sensory information may be filled-in within this dynamic space, creating a unified seamless conscious experience. This neural sensory memory space is likely generated by baseline neural oscillatory activity from the default mode network, other salient networks, brainstem, and reticular activating system. (shrink)

Aristotle's Politics is widely recognized as one of the classics of the history of political philosophy, and like every other such masterpiece, it is a work about which there is deep division.