Temporal Topos Methods for the Philosophy of Natural Sciences

This book is afirst attempt tounify and explain, through thelanguageofpure mathematics called categories and sheaves, themechanism ofmental activities. Humanities and philosophymeet physics and mathematicsatbothlevels ofthemicrocosm and macrocosm. Thepurpose ofthis book is toprovide systematic and unifying methods forthephysical and thecognitive aspects ofa conscious entity. Thephilosophical thoughts oftheWest and theEast will be formulated and presented in terms ofcategories and sheavesusingpure mathematics. Adefinition-based rigorous approach and method using categorical sheaf theory is a completely new attemptto formulatetheontological philosophies, which must be consistent withquantum physics. For example, it is theauthor's intent tocapture realityas a pair ofthecognitive realm and thephysical realm, forwhich theauthoruses thenotion of(temporal) topos theory, as a pair ofan initial object and a terminal object oftemporal topos. This book allows philosophers and natural scientists tointeracttodiscuss and observe thephysical world and thecognitive world. That is, a brain existing in thephysical world is simultaneously functioning in thecognitive world. Theauthorprovides detailed descriptions fortheprocess fromthesmall tothelarge, which is a part ofdescent-sheaf theory in mathematics by gluing thelocal data toobtain a global object. Adescription ofa process of"understanding" (and realizing-recognizing-discovering) is also formulated in terms oftemporal topos language. Theauthorprovides alltheneeded mathematical backgroundso that readers whose main interests are in humanities can enjoy and appreciate therigorousness and theharmony ofhumanities and natural sciences.