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“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 G�del’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 G�del’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.
- Sales Rank: #452258 in eBooks
- Published on: 2015-08-11
- Released on: 2015-08-11
- Format: Kindle eBook
Most helpful customer reviews
5 of 5 people found the following review helpful.
Mathematics = Transcendence/Immanence/Ontology/Epistomology/Tautology
By Brad Gumm
"Godel Versus Wittgenstein" is the 29th book in the reality revealing book series known as "The God Series" and it, like all of the books written by the three preeminent authors of the Pythagorean Illuminati, is a work of pure genius. On the surface, this book may appear to you to simply be about the great intellectual battle that Kurt Godel and Ludwig Wittgenstein had concerning the proper definition of mathematics but, once you begin reading, you'll quickly come to the realization that it is SO much more than that.
Of course, if you're thinking about purchasing this book because you are curious about this extremely interesting intellectual battle that took place between Wittgenstein and Godel then you're in luck; this book will not only show you what was truly going on in that battle, it will show you what Godel's incompleteness theorems truly proved.
In this book, the Pythagorean Illuminati take us on a journey back to the early 20th century. We are taken back to a time when the genius Kurt Godel struggled mightily to prove what he intuited to be True about mathematics, namely that mathematics wasn't a human invention. Godel wanted to prove that mathematics had an autonomous existence all its own. You see, Kurt Godel was a Platonist. He believed that mathematics truly existed, but in a separate transcendent domain, a domain of pure and perfect mathematical forms as Plato would say. Godel believed that this separate but real mathematical domain could only be accessed imperfectly by the human mind. So, in other words, Godel believed that mathematics actually exists, but in a domain separated from our material reality and only partially accessible to this material reality. It was this Platonist idea of mathematics that Godel was struggling mightily to defend against the onslaught of overly sensory and autistic people that had invaded and overtaken the study and discipline of mathematics.
These extreme sensory and autistic individuals included the likes of Bertrand Russell, David Hilbert, A.N. Whitehead, and Ludwig Wittgenstein. These strange people, each with an undeniable genius when it came to the technical aspects of mathematics, were attempting to prove that mathematics was some sub-set of human made logic and was an entirely human made invention. Godel, like anybody who KNOWS that mathematics could NEVER be invented by humans, couldn't abide this horrendous autistic definition of mathematics, so he went on the intellectual warpath.
Godel's path was the most honorable of them all, he was defending the integrity of mathematics against people completely enthrall to their senses. These nihilists were trying to shrink mathematics down to a fragile shell of its True self. Godel was trying to prove the majesty of the Truth of mathematics which he was intuiting.
It is a shame that Godel wasn't a Pythagorean as opposed to a Platonist. If Godel were to have learned more of Pythagoras, the prototype of a True mathematician, he would have realized his mistake in interpreting his own incompleteness theorem. You see, Pythagoras taught that mathematics was not only transcendent, as Plato learned from the students of Pythagoras, but it was also immanent, meaning that EVERYTHING is mathematics (this is something that Plato was never taught and was unable to intuit for himself). If Godel would have studied the master (Pythagoras) and not the student (Plato), he would have realized that both him, and his rival Wittgenstein, were partially right and partially wrong concerning their opposed conceptions of what mathematics actually is, and what form it Truly exists in. Be that as it is, the Truth of mathematics can be gleaned from studying the intellectual confrontation these two geniuses (Godel and Wittgenstein) had.
Anyway, back to it. What Godel proved was astounding, though almost zero percent of the intellectual community (and that includes Godel himself) understood what his theorems were proving, much less the ramifications of this proof. What Godel's incompleteness theorems proved was that any attempt to define mathematics in human made terms would always generate a contradiction, an incompleteness within the human constructed system of mathematics.
As I said, the intellectual community completely misunderstood Godel's incompleteness theorems and took them to mean that mathematics, in itself, is either inconsistent, incomplete, or both. This is a patently absurd notion. What the Pythagorean Illuminati demonstrate in this book, even though Godel himself didn't realize it, is that his theorems proved two things: 1) mathematics is absolutely NOT human made, and 2) Godel's theorems proved what his rival Wittgenstein was saying about mathematics all along; namely, mathematics is completely tautological, i.e. every statement of mathematics is simply a statement that says the same thing, but in two different ways. If we extend this line of thinking (that mathematics is tautological) to its omega point (though Wittgenstein didn't perform this exercise of hyperreason), then we find that mathematics, as a true tautology, must be contained within one equation and expressed by one principle. This equation is known as The God Equation, and this principle is known as The Principle of Sufficient Reason.
So, this brings me to why I said that this book is so much more than simply a history lesson. As you can see from my short description of just a small portion of the information contained within "Godel Versus Wittgenstein", this is a book about True mathematics--a.k.a. ontological mathematics, transcendental mathematics, monadic mathematics--and it is absolutely unlike any other book on mathematics, science, or reality out there.
This book, and all of the books written by the Pythagorean Illuminati, is and are, 100% unique; you won't find any other books like them. The whole point of the books written by the Pythagorean Illuminati is to reveal to humanity, for the very first time in history, what reality is. Reality IS mathematics; mathematics is and has always been, mathematics is eternal and a priori, mathematics is the universe and, last but not least, mathematics is your very own soul. It's mathematics that guarantees us all immortality and life after "death", not any absurd religion.
Depending on how your brain is wired, those last two sentences will either anger you, make you laugh, intrigue you, or you'll recognize them as Truth and your life will begin to change. But, however the reality of mathematics equaling existence makes you feel is neither here nor there. Mathematics doesn't care what any of our opinions are on it. What we think or feel about mathematics doesn't change the Truth of hyperreason, namely: mathematics = one equation = our souls = existence = life, mind, body, and everything.
As you can see, I couldn't think any higher of these books by the Pythagorean Illuminati. I can't recommend them enough to those of you out there who are still holding onto your reason. I just simply can't say enough about how incredibly amazing these books are, and how much they've improved my mind and life.
So, the bottom line is this: if you consider yourself a rational person who loves mathematics, and who KNOWS that there is so much more to mathematics than what some crappy teachers taught you in school, then these are the books for you. On the other hand, if your brain is infected by any ideology--religious, philosophical, political, or otherwise--then you should most definitely steer clear of these books. If you do attempt to read them though, be forewarned: the reading of the books by Mike Hockney, Adam Weishaupt, or Michael Faust (otherwise known as the Pythagorean Illuminati) might cause you to learn something for once in your life, and I know how much you irrational dogs hate that.
5 of 7 people found the following review helpful.
Incompleteness versus Tautology
By Cuore
This book offers a radical and yet very sensible perspective with regards to a controversial and unsettled debate within the philosophy of mathematics: the ontological status of G�del's incompleteness theorems. In his direct and incisive style, Hockney addresses the disagreement between G�del and Wittgenstein and argues persuasively that both great geniuses were having a mere verbal disagreement and misunderstood the nature of their disagreement in the first place by not being able to address the ontological status of mathematics.
In a nutshell, this book makes the claim that metamathematics and mathematics are patently NOT the same thing, and that mathematical logic's valid status within mathematics is to describe mathematical structures, but not to replace mathematics wholesale since mathematical logic cannot reduce math to itself without having to introduce extraneous concepts such as elementhood, sequents, etc. Formalism and other axiomatic approaches are shown to be inadequate as a result.
Hockney claims that Wittgenstein was correct in that he said mathematics was pure tautology, while G�del was correct in saying that metamathematics is insufficient for mathematics itself and that math is a real thing and not a mere abstraction. Hockney then goes to say that G�del was also wrong in taking a more mystical approach, while Wittgenstein was wrong for being an extreme empiricist. The gist of it is that if mathematics is ontological and pure analytic tautology (as shown in previous books in this series), then it MUST be complete and consistent — the incomplete and/or inconsistent approaches are the varying constructivist frameworks that try to reduce math to non-mathematical systems. Math is primal, metamath is man-made.
Other topics covered include interesting arguments regarding a comparison between axiomatic approaches to systems and ontological substance pluralism, as well as addressing the need for a double-aspect theory in order to overcome the mind-body problem.
This book offers a fresh perspective, and I highly recommend it.
0 of 1 people found the following review helpful.
excellent logic-focused mathematicist rationalist idealist book in the best modern philosophy series
By David Melik
This is the best (along with his others and those of the two associated writers) introductory modern series on rationalist idealism in Classical Greek & Cartesian & German Idealist philosophy & postmodernism, including Pythagoreanism/Illumination, Platonism, Hermetism, Gnosticism, Leibnizianism, Hegelianism, formal & natural & social science, religion, and the arts, in this case such as mathematics/mathematicism, logic and the nature of mathematical-logical language & meaning, and more in-depth philosophy analysis. This is the best series that explains reality more clearly than anything else.
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