I asked the people at LaRouchePAC to read the book Gödel Versus Wittgenstein, and was given this in reply:

“I read a couple of chapters of it, but his writing style included many interesting concepts and conclusions that didn’t compel belief.  That is, I was able to get a sense of things the author thought, but they weren’t made necessary by what he wrote about them.  So I just had to stop after a bit, I didn’t think it was repaying the reading.  Had we been doing the previously-usual roundtable format, it could have been a good example to bring up of contrasts between right conclusions and right reasoning, but it’s been Leibniz-city recently.”

This was my reply:

I re-read the beginning of the book to see what it was like if one hadn’t already been indoctrinated into the author’s philosophy, and found that I agree that much of it would be difficult to take at face value.  However, the point can be summed up with these excerpts:

“…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.”

“If math isn’t about energy then it must be a manmade abstraction, and, in that case, it’s incomprehensible how it can be used in science to study energy, assuming science purports to be about reality. Either math is about energy or math is a ridiculous fantasy that’s no more relevant to the structure and operations of the universe than the Chinese language is. The prevailing mathematical, scientific and philosophical establishment has failed to understand the true nature of math, and this has had catastrophic consequences for the advancement of human knowledge. Pythagoras was more right 2,500 years ago than almost 100% of “intellectuals” today. [Pythagoras said: “All is number; number rules all.”] Those 2,500 years have therefore been wasted. It’s not just religion that has held us back in that time, it’s also scientific, philosophical and mathematical empiricism. Empiricism (based on the worship of the human senses) is as much an enemy of reason as faith (based on the worship of human feelings).”

I asked the relevant question to LaRouche at one time, and the question was featured in a public webcast back when LaRouche was still speaking at those things – the question being basically: what is the arche, what is reality made of, what does mathematics have to do with this given that science is so dependent upon mathematics?

As you well know, LaRouche has a great disliking for the “mathematicsts”, for those who try to reduce the fundamentals of reality to purely mathematical mechanics.  LaRouche doesn’t like this because, in his understanding, it takes away the role of free-will, of human thinking, and human mental intuition and discovery, and similar things.  Mathematics doesn’t in itself within some context ever indicate a need for a phase change in the comprehension of reality, for example in the need to go from Ptolemy to Kepler; the problem there was empirical and in comprehension, and there were no fundamental principles of mathematics which could show the way to the answer to resolve that empirical problem (of the correct prediction of the positions of the planets).  The same happened with the empirical problem of the precession of Mercury, being solved only with a new comprehension of the structure of reality (going from Newtonian gravity to General Relativity).

That all being what has happened, the question is actually about what is the arche?  What is reality made of?  You must be aware of the philosophical concept of “substance dualism”, and the problem that if reality were made out of two or more truly independent and unique substances, then it would be an unsolvable problem as to how these substances could ever interact with each other unless there were something common to all of them, in which case they would not be truly independent and unique substances relative to each other because there would be a third-thing, a commonality, that mediated between them.  For example, consider the “substance” of electricity, and magnetism, and then consider the “substance” of the weak and strong nuclear forces: all of these are apparently, by empirical impression, different substances, however, all of these substances are actually manifestations of a single higher-order reality which are unified at a higher phase change or phase space of very high energy flux density.

Of course if we extend this concept to include one more force of nature, gravity, as people are working on, then all manifestations of reality reduce to a single unified “substance” which merely has multiple sense or empirical appearances.  Of course the philosophical argument already made the point: if there were truly unique substances, they couldn’t interact, and would exist in essentially different universes; if you live in a universe where it appears that there are different substances, they must actually be the same substance within that universe.

But if there could be more than one fundamental substance and different universes, then what would stop there from being an infinite number?  What if there were infinite separate substances?  Then one must consider the fundamental properties of what it is to be an “existent”.  What property(s) must something have to be an existent?  Consider Hegel’s statement: “That which is rational exists, what exists is rational.”  Sparing the many paragraphs to explain: whatever is an existent must partake of the form or “substance” of reason, otherwise its own contradictions would destroy itself and prevent its existence.  So if there were multiple existent substances, they must all partake of reason and be rational, and hence would actually reduce to a singular substance of reason, to a singular substance of the rational.

What is reality made out of?  What is the substance of the rational?  What substance partakes of reason?  Why does science think that all of reality reduces to a single “grand unified” framework?

Hockney postulates that the substance is something he calls “Ontological Mathematics”.

Of course you fellows at LPAC are all Platonists, and you all consider “mind” to be primary to matter.  And for various reasons, the position that mind is primary reality is correct.  So then it is left to define what mind actually is, rather than to leave it as some mystery, as LaRouche seems in some ways to prefer.  However, defining mind does not mean that we have taken away its free-will, or have limited its abilities to comprehend higher orders of reality, or have taken away its and our meaning, and purpose, etc.

What is reality made out of?  What is mind?  What is the arche?

Let’s go to science: at the fundamental level, science has realized that it cannot define, outside of mathematical properties, what the fundamental particles of nature are, for example.  We have labeled quarks with quite arbitrary names: strange, charm, up, down, top, bottom; we could have labelled quarks with flavors for all it mattered and for all the same meaning as the names they have now: vanilla quark, chocolate quark, sweet quark, sour quark, spicy quark, savory quark.  At the fundamental level, there are no human-experiential words we can give to the things which make up reality at the basis level.  The only thing we have to understand them are mathematical properties.

Mathematical properties of what?  We know that the concept of “hard little balls of material” is incorrect, and that no such “material” actually exists: it is all force fields of energy, all different states, configurations, and manifestations of energy.  Energy is what is at the basis of it all.  Energy.

But how do we define energy?  Science merely states that energy is an abstract concept, and so this is no definition at all.  It’s something abstract, but it has mathematical properties.  It’s something abstract, but it has something to do with mind as we seem unable to remove the importance of mind to this fundamental substance, according to quantum mechanics.

The only solution is to realize, as in the problem and resolution of substance dualism, that these are all the same substance: energy is mind, energy is mathematical, mathematics is mind.  In particular, it is all a mathematical substance called “Ontological Mathematics”, i.e., the mathematics of that which exists, the grand unifying form of mathematics.

The point of the Gödel vs. Wittgenstein book is that what Gödel actually showed was that mathematics is not a language-invention of man, but is rather an independent or sovereign existent in itself.  Bertrand Russel and co. all had been attempting to demonstrate that mathematics was an invention like any other language, that it was simply some axiomatic process similar to Euclid’s axioms of geometry – they wished to demonstrate that mathematics itself was simply an axiomatic invention, simply an arbitrary, but useful, language.  Gödel’s theorems demonstrated that this couldn’t be done, that mathematics couldn’t be invented by another language or by a set of axioms.  It was its own thing.

Well, what the heck can be “its own thing” in a logical reality where there can be no independent own things, where there can be no dualism of things?  There can only be one thing.  Gödel showed that mathematics is a thing, is an existent, not a creation.  The only conclusion is then that mathematics is the arche.

But this is “Ontological Mathematics”, as a substance, as the arche.  And Hockney demonstrates that the fundamental form of this arche is given by Euler’s Equation.  This is not to say that reality is some mindless abstraction, without meaning and purpose, as science would and does say.  Rather, this ontological mathematics, this grand-unifying substance of all reality, is indeed fully minded, capable of self-awareness as in humans, is totally synonymous with mind, and free-will, etc.  Leibniz’ Monadology, which I am sure that you are well aware given your studies of him, plays a central role in this.

And now I appreciate that without knowledge of the role of the Monadology, the arguments which resolve the problems of substance dualism, and mind vs. matter, etc., that indeed, it would be difficult to understand what Hockney is arguing in this book.  Hence, why I suggest reading his whole series.

But to the aforementioned question: “Mathematical properties of what?”

The answer is: The mathematical properties of ontological mathematics.

There are no other ways to define mathematical properties, and that is also the point of the book and Gödel’s work.  But the point is more than that, because these are also the properties of -existence- itself.  Hence:

The greatest challenge facing science isn’t to define and understand the universe, but to define and understand math.