Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The Map/Territory distinction is a foundational part of the scientific method and, in fact, underlies all of thought, and even reality itself. This fascinating and fundamental topic is addressed here by some of the world’s leading thinkers and intellectual giants, whose accessible essays cover six and more fields of endeavor. It is imperative to distinguish the Map from the Territory when analyzing any subject, yet we often mistake the map for the territory; the meaning for the reference; a computational tool for what it computes. Representations are so handy and tempting that we often end up committing the category error of over-associating the representation with the thing it represents, so much so that the distinction between them is lost. This error, whose roots frequently lie in pedagogy, generates a plethora of paradoxes/confusions which hinder a proper understanding of the subject. What are wave functions? Fields? Forces? Numbers? Sets? Classes? Operators? Functions? Alphabets and Sentences? Are they a part of our map (theory/representation)? Or do they actually belong to the territory (reality)? A researcher, like a cartographer, clothes (or creates?) the reality by stitching together numerous co-existing maps. Is there a reality out there apart from these maps? How do these various maps interact or combine with each other to produce a coherent reality that we interact with? Or do they not? Does our brain use its own internal maps to facilitate the “physicist/mathematician” in us to construct, in turn, the maps about the external realm? If so, what is the nature of these internal maps? Are there meta-maps? Evolution definitely fences in our perception and thereby our ability to construct maps, revealing to us only those aspects beneficial for our survival. But to what extent? Is there a way out of this metaphorical Plato’s cave erected around us by the nature? Alfred Korzybski once remarked “The Map is not the Territory”: Join us in this journey to explore the many questions, concepts and interpretations that this claim engenders. .

Science --- Thought and thinking --- Philosophy. --- Physics. --- Epistemology. --- Mathematical logic. --- History and Philosophical Foundations of Physics. --- Philosophical and Historical Foundations of Science. --- Popular Science in Philosophy. --- Mathematical Logic and Foundations. --- Mind --- Thinking --- Thoughts --- Educational psychology --- Philosophy --- Psychology --- Intellect --- Logic --- Perception --- Psycholinguistics --- Self --- Normal science --- Philosophy of science --- Genetic epistemology. --- Science—Philosophy. --- Science—History. --- Logic, Symbolic and mathematical. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Developmental psychology --- Knowledge, Theory of --- Mental philosophy --- Humanities --- Epistemology --- Theory of knowledge --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book explores the premise that a physical theory is an interpretation of the analytico-canonical formalism. Throughout the text, the investigation stresses that classical mechanics in its Lagrangian formulation is the formal backbone of theoretical physics. The authors start from a presentation of the analytico-canonical formalism for classical mechanics, and its applications in electromagnetism, Schrödinger's quantum mechanics, and field theories such as general relativity and gauge field theories, up to the Higgs mechanism. The analysis uses the main criterion used by physicists for a theory: to formulate a physical theory we write down a Lagrangian for it. A physical theory is a particular instance of the Lagrangian functional. So, there is already an unified physical theory. One only has to specify the corresponding Lagrangian (or Lagrangian density); the dynamical equations are the associated Euler-Lagrange equations. The theory of Suppes predicates as the main tool in the axiomatization and examples from the usual theories in physics. For applications, a whole plethora of results from logic that lead to interesting, and sometimes unexpected, consequences. This volume looks at where our physics happen and which mathematical universe we require for the description of our concrete physical events. It also explores if we use the constructive universe or if we need set-theoretically generic spacetimes.

Mathematical logic --- Philosophy of science --- wetenschapsfilosofie --- wiskunde --- logica