Gödel Versus Wittgenstein (The God Series Book 29)

“Without mathematics we cannot penetrate deeply into philosophy. Without philosophy we cannot penetrate deeply into mathematics. Without both we cannot penetrate deeply into anything.” – Leibniz In intellectual history, perhaps nothing has been more misinterpreted than Gödel’s incompleteness theorems. Stephen Hawking, adopting the popular misconception, said, “Thus mathematics is either inconsistent, or incomplete. The smart money is on incomplete.” This book is about the titanic struggle for the soul of mathematics, and reflects two immense battles in which mathematics is immersed to this day. Firstly, if mathematics is tautology, as Wittgenstein said, mathematics cannot be inconsistent and/or incomplete, and so Gödel’s work cannot be about mathematics. If mathematics is not tautological, mathematics is necessarily mired in inconsistency and/or incompleteness, just as Stephen Hawking said, hence is wholly unreliable. Secondly, if mathematics is non-ontological, it cannot say anything about reality. If mathematics is ontological, it’s the only thing that can say anything true about reality. There can’t be a world where math is a bit true and a bit false. Either the world is wholly mathematical – in which case math and not science is how we must study the world – or the world isn’t mathematical at all, in which case it’s absurd for science to use math in its attempts to account for, or model, reality. Math presents a deadly challenge to science. If math is real, we don’t need science. If math isn’t real, then science, which is so heavily reliant on math, is nonsense! The greatest challenge facing science isn’t to define and understand the universe, but to define and understand math. Of course, it turns out that math and the universe are one and the same. Only if the universe is mathematical can it be rational and intelligible. It must be entirely mathematical since a universe that is partly mathematical and partly something else would be irrational and unintelligible given that mathematical things cannot interact with non-mathematical things (this would constitute a version of Cartesian dualism where two incompatible substances cannot interact since they have no common ground). To understand what math actually is, you must strip all non-mathematical considerations from it. Are you ready to ponder existence in itself - bare existence - shorn of all subjective experiences, feelings, desires, sensations, perceptions, mystical intuitions, beliefs, opinions, and interpretations? What is naked existence? What is existence in its rawest, oldest, most primitive and primordial state? Until you understand that, you will have no idea what it is when you impose an appearance on it. Gödel Versus Wittgenstein Table of Contents Introduction Move Out of the Way Diagonalization Wittgenstein, Gödel and Tautology The View from Nowhere Truthful Atoms? Sons of Men and Sons of God No Answer Above and Below: All Is One The Martyrs’ Death Club The Philosophy of Mathematics The Reaper List The Problem With Science Gödel versus Wittgenstein Paradoxes The Triumph of Reason Manmade Languages The Big Picture Black Holes Monism The War To Come Autistics No Final Theory of Science? The Soul Camera The Higher World of Reason Star Trek The Tax On Beauty The Island of Magicians The Wrong Foundations The Best Minds The Danger Words versus Numbers Ontology Incommensurate Minds Genuine Importance The Black Sun The Principle of Cartesian Dualism How and Why Two Logics The Wrong Approach Ontology versus Logic The Smartest Person in the Room Binary Jokes Wittgenstein – Non-Soul Man Perception and Reality “Objectivism” The Riddle The Mystery of Death The Farce Fail No Shame The Force Gödel – Soul Man The Truth The Impossible Project Nature’s Language Epic Fail What Is Math? Logopolis: The City of Reason The Establishment Human Knowledge Conclusion