INTEGRAL WORLD: EXPLORING THEORIES OF EVERYTHING
An independent forum for a critical discussion of the integral philosophy of Ken Wilber
Publication dates of essays (month/year) can be found under "Essays".
Reply to Smith
Dear Mr Smith
I was delighted to see that you've taken the time to write a review of The Mathematical Universe [Getting to the Point] by the group going by the pseudonym Mike Hockney. Having been an avid reader of these publications now for over two years, it is a pleasure to read your thoughts on the ideas concerning mathematical ontology and the apparent flaws in which it contains. I understand recently that you've been contacted by a certain individual by the name of Pedro Jesus [See: Razing with Reason], he is not as you might think an official Illuminatus, but he is part of a group which has grown around the aforementioned material. There are but a few of us who consider ourselves as dedicated students of Illuminism, our opinions concerning the validity of the arguments differ somewhat, and there's a scale shall we say of those who are in complete agreement with Hockney to those who take a much more skeptical approach. We do however share a certain appreciation for the sheer breadth and scale of the material, and are generally receptive to the main arguments that are made.
Your review in fact has caused some minor disagreements between us, and there has been some dispute over who should go about responding to your main criticism's. Pedro is a friend of mine, so I guess I am qualified to inform you that English is not his first language, hence the reason why sometimes his writing can seem a little disjointed and illegible. Perhaps this is why his communication is emotive rather than succinct and to the point - as an over compensation for a lacking in precise dialogue. That being said, he has done his best to convey what Hockney has said previously in response to your criticisms, and he has taken the initiative to write to you, but he doesn't represent the Movement as a whole, nor was he chosen by us to respond to you. Pedro is interested in publicity, and any publicity is good publicity as far as he's concerned, so in effect he has fulfilled his original purpose by provoking you into further debate. Whether or not this is beneficial to the rationalist cause is another question entirely, indeed there is split opinions in this regard. I myself am glad that this subject matter is being publicly debated, because it is serving as a platform for dialectical discourse, which ultimately means progress.
To that end I will endeavor to answer some but not all of the points you have made in your review. And I will do my utmost not to simply spout what Hockney has written, but you must understand that the theory of ontological mathematics has been presented in a series of books, sixty to be exact, plus a website which contains over two million words in total. So to come up with completely original answers is somewhat difficult as many of the points you've raised have been addressed previously, but like I said I will do my utmost to convey my understanding of the subject in my own way.
Firstly I'd like to reemphasize the fact that there have been many books in which this TOE has been presented, so my initial response to your review was that it is a little unfair to criticize the theory based upon your limited understanding of it. What you've read in the Mathematical universe is but the tip of the iceberg of an extensive and rigorous presentation of a theory. Perhaps it is the case that you are aware of this and do not have the time nor patience to read the whole theory, which is understandable. Allow me then to respond to your objections, not as an official spokesperson for the Illuminati, or the Movement that has been created around them, but as an individual who has been interested in these ideas of a while, and has gained the relevant knowledge to respond in a manner that hopefully you will find useful for further critique in this subject.
If I understand correctly your main criticism towards Hockney's argument is that there's an over emphasis on using the PSR in a negative way rather than as a positive. That is, there's a failure on Hockney's part to address the sufficient reason for why monads exist rather than do not exist. Firstly I'd like to say that fundamentally the rationalist tradition uses deductive reasoning to arrive at a priori conclusions, that has always been the method which rationalists prefer to use, and the reason being is one of epistemological concerns. Truths of reason are deductive, analytic and a priori; truths of fact i.e empirical evidence, is quintessentially inductive, synthetic and a posteriori. The epistemological claim is that the former is superior to the latter in terms of what we deem to be a sure foundation of knowledge. The two however are complementary and should express a certain harmony, but crucially the rationalist proclaims that all synthetic evidence should be used to support a priori truth, not the other way around. Epistemologically this is a valid approach to gaining knowledge, I see no reason why this should be subject to criticism. Granted, there have been a long line of rationalists who've been in error in regards to what a priori truth is, but what Hockney is arguing, is that's because we've strayed from Leibniz's position, that all truth is analytic - mathematical. The claim is being made that there has in fact existed such a group of rationalists who haven't strayed from this line of thought, but that said-group have been secretly developing this line of reasoning since Leibniz's death. Whether or not you believe that claim is down to your own discretion, I personally see no sufficient reason to place major doubt on this claim judging by the total works that have been put forth over the last 4 years.
You rightly pointed out that in fact Leibniz admitted that deductive reasoning can only take us so far in our search for knowledge. But that was hundreds of yeas ago when we didn't have the mathematical advances that we posses today. In Leibniz's original Monadology all monads are created by God. Moreover, all monads are programed by God to act in accordance with the law of pre-established harmony. Therefore, existence is entirely predetermined, and essentially there's no free will in this scheme. All monads are windowless and simply follow the inescapably laws of nature. Interestingly, Leibniz thought that somehow the human mind could eventually unlock this "God Program" through the creation of a charictaristica universalis. Through such a language humanity could essentially communicate with God. As genius as this is, it is no better an explanation of the sufficient reason for existence than the Abrahamic conception that God created the universe. The question instantly arises, "Who or what caused God?". According to the Monadology we cannot ascertain that reason until we develop the language to conceptualize it, but the fact that thing's *do* exist naturally implies that there is a cause, and it is perfectly rational to make that assumption, for if rationalism itself is irrational, then this throws serious doubt into mans search for knowledge and is completely at odds with mathematics. I think Gödel expressed this best when he said...
"If it were true [that there are mathematical problems undecidable by the human mind] it would mean that human reason is utterly irrational in asking questions it cannot answer, while asserting emphatically that only reason can answer them. Human reason would then be very imperfect and, in some sense, even inconsistent, in glaring contradiction to the fact that those parts of mathematics which have been systematically and completely developed show an amazing degree of beauty and perfection. In these fields, by entirely unexpected laws and procedures, means are provided not only for solving all relevant problems, but also solving them in a most beautiful and perfectly feasible manner."
The fact that Gödel was an ardent Platonist is almost entirely ignored by most people today. Gödel believed that existence itself was entirely consistent and complete, and that this is true a priori. What is often inconsistent and incomplete is our understanding of that reality, Gödel would've agreed with Hockney that the main reason for this is an over reliance on empirical evidence to probe truth. Another objection that Gödel shares with Hockney, is that mathematics itself has been perverted in order to fit empirical evidence, whereas mathematics is the sine qua non of deductive rationalism and in principal should reflect the PSR in that no number should be privileged over another number. Ontologically all numbers are on par, but scientific materialism insists that only real numbers have any ontological status in relation to reality. All other numbers are regarded as abstractions and merely useful fictions we use to make our equations work. Mathematics should be taken as a complete and consistent, immutable, platonic edifice upon which all other truths are measured and accounted just as Gödel envisioned. The difference between Gödel and Hockney is that Hockney claims to have discovered a complete monolithic system of mathematics which is free from the glaring inconsistencies rampant amongst the formalist approaches to mathematical truth. That system is based on Euler's formula, which according to Hockney fulfills the requirements of the PSR, precisely because it doesn't privilege any number over another. In fact Hockney goes so far as to say that Euler's formula IS the PSR expressed as a mathematical tautology.
Replace God with Euler's formula in Leibniz's Monadology and essentially you have arrived at ontological mathematics as the true charictaristica universalis. Nothing creates Euler's formula, it is eternal and unchanging, it is unequivocally the only contender for the status of an immutable Platonic form. All of this can be worked out with deductive reasoning, and without formal proof. It is true but unprovable, and accessible only to intuition and reason. You've objected that this perhaps might be the case, but it is of no use if we cannot set out and apply that knowledge to the world of phenomena around us. To this point i shall return later on, I have my own ideas about how we can utilize this knowledge, but for now I will say that it seems a little short sighted to make such a criticism, as this is literally the first time in history anyone has suggested that Euler's formula is the fundamental principal of nature; it is an untapped resource, so to speak. Your other objection is that mathematical knowledge such as Euler's formula could just be a product of our mental processes, as could be reason. Therefore, reason is no different to empirical evidence in this regard and shouldn't be elevated above it. Again, if we take into account Gödel's incompleteness theorem we can deduce that you're wrong. If one asserts that no knowledge is possible then that violates the law of non contradiction. Then if one say's that knowledge is purely justified using axioms and formal logic then there will always be a statement within that system that is true but unprovable, ergo knowledge must be innate and platonic. There must be a foundation of knowledge, a priori, otherwise nothing is true. Just because we discover mathematical truths, doesn't mean that that knowledge is not innate.
Due to the fact that our minds are able of deducing such things as statements that are true but unprovable, implies that the mind is *not* just a mechanism following inescapable laws of cause and effect. The philosopher John Lucas has argued precisely that, and although it cannot be taken as a definitive argument against strong A.I, if we take into account the free will theorem by John Conway we can see that it's not so redundant to talk about the mind and brain as a holistic system capable of exhibiting free will after all; it is entirely justified in fact.
"The brain is a computing machine connected with a spirit"
There's no definitive empirical proof of the nonexistence of free will, so really it is in our own best interest to hold that there is free will. Otherwise, there's simply no objective justification for law and ethics, and we inexorably arrive at a position of extreme nihilism. I think there has been some confusion on your part Mr Smith equating Hockney's rhetorical passion over free will with an irrational argument. While it is true that Hockney certainly is forthright in his opinions on this matter I think his philosophical position is still valid non the less, and one has to consider what Hockney is trying to overcome - nihilism. It makes perfect sense to say that the fundamental units of existence are uncreated and eternal, dependent on nothing else for their existence, as there cannot be an infinite regress of causes. This cosmological argument is far superior to any theological explanation to why things exist, and infinitely more satisfying than materialism which remains mute on the matter. There is no better explanation to existence than mathematical monism at present, the closest I have seen is Max Tegmark's ultimate ensemble mathematical universe, which has its fair share of inconsistencies. Hockney's position is one of "if you haven't got a better explanation then shut the fuck up", which to his credit is entirely valid.
Although there can be no formal and rigorous proof of the ontology of monads, calculus itself is a justification for the ontological existence of monads. Modern calculus is based on the limit, an arbitrary small dimensional value. But was not how Leibniz intended it to be. Using monads in calculus means that no information is lost in differential equations, same as if we were to throw an apple into a black hole, it doesn't simply disappear into nothing, the information of that apple still exists at the boundary of the black hole. Monadic calculus is algebraically complete, just as ontologically mathematics is complete. There's no loss of information in the universe, the amount of information is continually increasing. This is a fundamental constant, and preserves the overall net value of energy in the universe. Mind follows a process of neg-entropy, going from a low energy state to a high energy state, and matter, entropy; from a high energy state to a low energy state. The two are directly correlated and in opposition to one another. So in answer to your objection that Hockney doesn't give a sufficient reason for the total energy of the universe you are also wrong. This has been extensively explained throughout the God Series publications, and I implore you to read more into it, save me the trouble of having to point you in the right direction.
I am aware that there are some other points throughout your review that haven't been addressed here. Unfortunately I lack the necessary time to go into those further. But I will let you know that your critique has been forwarded to the authors of the Mathematical Universe so it's possible that you might get a reply from them in the future.
lastly I would just like to share with you what kind of practical uses we can take advantage of with ontological mathematics. Besides making a metamathematical argument for the existence of free will, which has many implications to our ethical and political systems, I think that perhaps Euler's formula has some interesting things to show us in regards to electromagnetism. Such insights we're currently lacking, and who knows, perhaps they could one day open up new avenues of science and understanding. I will not go into any details here but it suffices to say that I am thoroughly exited about the implications.
Many thanks for taking the time to read my reply to your review, I hope to hear more from you in the future.