Why dedicating my career to D. Lekkas did not involve a “leap of faith”.

D. Lekkas is –among other things– a mathematician. He reintroduced music as a formal branch of mathematics, something you couldn’t possibly know as his dissertation has not been published yet due to a series of unfortunate coincidences. However, his contributions in many epistemic1 (“scientific”) disciplines have been equally spectacular, something you could have known but don’t, partly because high impact peer-reviewed journals do not publish his articles. However, the latter is not the issue here, and I will not get into the discussion of why this happens, nor who is responsible, how and if. After repeatedly and exhaustingly discussing the matter with many friends, colleagues and members of the working group I have created for the study of the work of D. Lekkas, I just want to support that identifying a person as at least one of the most important personalities in arts and episteme ever, includes no leap of faith, but rather a very clear and consistent mechanism.

Episteme (known as science in the west) is largely like a sport (one reason it is not episteme). Federer and his fans do not need to announce him a top tennis player. He has been No. 1 in the rankings for quite some time, and this is enough. Similarly, any scientist’s caliber is (mainly) measured as a product of his / her publishing achievements in high impact journals and big publishing houses. Institutions such as the Nobel Prize etc. ensure that some scientists are crème de la crème. A question, however, should be whether such institutions ensure that someone who is not scoring high on their lists is not noteworthy —let alone top-class. I think you should agree that not being on such prestigious lists is not exclusive of your capacity to be such an extraordinary person, even though it may be somewhat unusual.

The benefit of the doubt. Let us take an extreme case. Suppose you had a conversation with someone you knew nothing about, and he told you that all science is ill-based, physics is junk and he held the key to all major (scientific) questions. What would you do? What did I do? For example, should I suppose he is mad? Is he the genius of our century? Something in between?

OK, I have heard similar stuff before, i.e. there are some problems with science etc. Admittedly never that far-fetched. The person making such a statement (science is witchcraft2) should either be mad or the supreme genius. So, at least I am in a position to recognize the importance of the statement. Case 1: he is mad, which is the most likely. No harm done. Case 2: He is both mad and right at some points; indeed many people see problems in contemporary sciences or even in the politics contemporary science includes. It should be no big deal for him to have discovered some faults –but again, going from that to such an overstatement about the status of science as a whole and about well-established disciplines such as physics (not parts of physics; the whole thing called physics) is too much. Anyway, case 2, in general, is the most probable according to my personal experience.

And we come to case 3: he is totally right. If this is the case then there is no room for errors. Even if I heard 10 great stuff and one bullshit, then it would be a total failure. What I had to judge was something that required infinite accuracy and consistency. No room for mistakes. If case 3 holds –quite improbable I gathered– then the importance and the impact should be huge for everyone, everywhere. Harvard, Yale, MIT and Oxford (among other top educational organizations)should close or change their curricula, a big part of Nobel Prizes are about to lose their value and basic textbooks in sciences should change. All this mean that no matter how improbable it may have been for him to be completely right, were he right, the impact would be unimaginably huge. So huge, that were he right, no-one would admit he is right –no-one inside the system, that is. Still, quite impossible but the weighted cost in case he is right is huge. So what do I do given I cannot yet refute his claims?

I gave him the benefit of the doubt. Now, giving someone the benefit of the doubt is not making any leap of faith. It is not like I accepted or adopted his stance. It only meant, and it only means, that I will try not to be prejudiced, but listen to what he says and judge accordingly.

Judge what? What I had to decide was not only whether he was right or wrong, but whether the whole scientific edifice is fundamentally problematic and whether he could possibly be the biggest personality in modern history –to say the least. I mean, when I, as a tennis trainer, have to evaluate some new player who comes supporting he is better than anyone I’ve seen, my mission is not to just see if he plays tennis –even well– but if he is what he says, even though I’ve never heard of him and he is not on the rankings. Is there a way to judge that player? Indeed there is, if, for example, I just let him show me his skills and he manages to serve in a row 50 serves >200 km/h on the side-line, then yes, I could take his claims very seriously and evaluate him further.

But even if Lekkas could do something as impressive as serving those 50 serves, what would that be in terms of science or whatever else? And am I eligible to understand such a feat in science even if I saw it?

An analogy. If I were a professional conductor, would Ι –or indeed should Ι– be capable of recognizing that some pianist, composer or even violinist is the best I have ever heard? I believe I should; it is part of the job. Why, to take another example, am I expected to concur that, say, Aristotle was one of the greatest philosophers? Or, even MORE so, when I say “Aristotle was one of the greatest philosophers ever”, why doesn’t anybody ask me, “How the heck do you know”? Is there really a way to know? Did anyone read everything and fully to be able to understand all philosophers from the naturalists (before Aristotle) till, say, Heidegger to have an opinion? Maybe five or ten geniuses but certainly not me. Others say it is common knowledge. Why is it “common knowledge” that Aristotle is great? As in Münchausen’s trilemma, when I try to justify this opinion, how far back should I go to find someone who is expert enough to ensure me this to be the case? Or is it just a consensus? Among whom? If a person living now is to become as famous as Aristotle in 1000 years, should I wait till then? Are is there NO systemic criteria NOW? Were I a contemporary of Aristotle, would there be no way to understand his magnitude? Is magnitude then due to the consensus of others, only?

But if I were a scholar specialized on Aristotle? Then I could say “Aristotle was the greatest philosopher ever”, and, while many people might wish to know how I arrived at such a conclusion, no-one would say I am mad! But how could I have known that he was the best even if I were an Aristotelian scholar? Am I the genius he was to judge him? Besides, have I read everyone else to really know? In the end, we shouldn’t even dare to say anything about how great Aristotle was (or wasn’t)! Or should we? Aren’ t there qualitative criteria in science? Can I not make systemic evaluations? If not, why do I do science I the first place? I could just do statistics and evaluate scientific claims according to votes (but oh, wait, science —not episteme!— is based on statistics… damn!).

Then we have science. Arguably, any physicist should have a say over (e.g.) relativity or quantum mechanics. How come? He is an expert. In what? Physics. All physics? No, only his particular domain. Even though it feels more natural for a physicist to be able to evaluate any domain in physics, physicists are specialized. Why are they eligible to have an opinion about as diverse physical domains as supernovas and microchips? We seem to understand that the mechanisms are common or similar. It would be somewhat far-fetched to declare that Einstein was too great for anyone less than him to be able to understand him. Any physicist can or indeed must understand physics owing to the way he is educated: they have not learned isolated “facts” but rather mechanisms.

What about science in general –or even more so episteme? Let us try to answer a simple question. Suppose there are two “scientific” conferences, one about food chemistry and one about phonetics in ancient Greek language. Quite irrelevant, right? Then how come they are both “scientific”? What do they have in common and in what way? Can we call two fields “scientific” for NO systemic reason at all? Is it just a matter of tradition? Even in this case, there should have been some systemic reasons some time in the past somewhere.

You see, science has not one coherent definition to make things clear. But episteme has one, which makes thing clearer in science as well. Episteme is a system of knowledge logically structured. Therefore, anything that is a knowledge system, structured logically (consistently, non-redundantly etc), is episteme. Phonetics and chemistry may be called epistemes exactly for this reason.

So why can a physicist have a say over all physics justified by the mere fact that he is knowledgeable of the underlying common mechanisms, and not a scientist (or, even more an epistemon), for the same reason? Logic, i.e. mathematics, is the necessary condition to have a saying about all episteme (and of course its empiristic counterpart, science). But is it a sufficient condition?

The sufficient condition ( ~ telic cause) is to know the particulars of each field. Is this even possible? Is contemporary science not so vast that one may not even be able to become specialized in one domain during a lifetime? As I will argue next, this popular belief is the gravestone of contemporary science increasing the need for a shift from science to episteme. (This may not be the purpose of this article, but still needs to be addressed in order to answer the initial question).

Should one examines tendencies, it is quite clear that the contemporary tendency is to create absolute experts who know everything about nothing and interdisciplinary committees knowing everything, without any single member being able to question anything outside his specialization. However, this is not how episteme started, and it definitely is not a healthy development. It is in principio opposite to the fundamendal doctrines of episteme, and if someone thinks science is better, then OK, this is another discussion, but whatever science is, it may not be an evolution of episteme. Fundamentally, episteme seeks broad surveillance, unity and interdisciplinarity inside each and every person –despite the particular interests every person has— and should have. The deviation of specialized science from general episteme is the basic reason for the host of hidden fallacies tormenting science that will eventually lead to its collapse. But how could anyone have such a general overview of the immense edifice of modern science to be able to make such judgments? I could just say I am an epistemologist –or philosopher of science if you prefer– but then again this doesn’t reveal the reason I can know. How can Lekkas, I or you know?

The answer to these questions is more simple than one would expect. It is a matter of logic, and logic, not statistics is the first thing one learns when one learns episteme (see Aristotle’s Organon). Logic, in contrast to, say, statistics, is a method of prooving. Unfortunately students are taught much more statistics than logic (if any). Fortunately I, as a philosophy of science student, had the opportunity to study logic (and set theory) in more depth before focusing even more under the guidance of Lekkas. Therefore I know that if two things are in principio inconsistent, they remain inconsistent at any other level –thus no need to know everything about every science. Moreover, if two things are inconsistent and one shows that the first of the two is correct, then, automatically, the second is false. This is the simple case of contradiction studied as early as in Aristotle’s De Interpretatione.

Whatever Lekkas says is inconsistent with the basic methodological premises of science. I don’t care what a field unknown to me supports; if its conclusions are based on a wrong methodology, even if they happen to be correct, I reject the field in principio. I have logic as a tool to evaluate judgments; indeed it happens to be the only tool available for this job!

So, I started listening to D. Lekkas. Carefully. Every day for about three months. Each day motivated me to listen to him one more day. I had many doubts. I had many questions. I also had many unclear things in my epistemology (things I did not even know I had to clarify before he asked me). Not only did he give me sufficient grounds to doubt about the very foundations of science, but he went too many steps ahead: he offered me the alternative theory: episteme. Becoming a lekkasian scholar changed my approach to many things –none of which is to be mentioned here; I must be particularly cautious not to deviate from this article’s main purpose and refer to the content of his system here because then it will be inevitable to expand too much. This will be done when I publish a book I am preparing about the foundations of his epistemology.

In a nutshell then, I know logic and I can evaluate all theories in principio otherwise I’d better go home and stop pretending being an epistemologist, as a conductor should do were he unable to discriminate between the various characteristics of instruments, genres and musicians (in spite his inability to perform in all and every instruments all and every genre). Lekkas showed me unbelievable inconsistencies in science from his original inter-disciplinary perspective. He also presented me the contradictions-free alternative. I have not become himself, nor can I reproduce everything by heart exactly the same way he expresses everything –but I am fully capable of following the arguments.

I have to address one very common (pseudo-) argument sounding convincing enough to many. “OK, you can’t find any mistake to his arguments. What if someone else comes to you who will successfully support other stuff that are incompatible to what Lekkas supports?”.

He/she would be welcome. As a matter of fact, I am looking for anyone who could successfully argue with Lekkas. However, there are some consistency issues in regard to this claim. In episteme, when one has a working hypothesis, he is to drop it iff one presents a counter-argument or (equally) one presents a clearly better working hypothesis. A better working hypothesis could be a more consistent one, a more concise one or a more theoretically productive one (or, of course, a combination of the former). If not, one can’t live his life waiting for that to happen. Mathematics, being the archetypical episteme, offer us the best example: they are completely based on axioms. An axiomatic system can be evaluated based on its consistency, productivity, non-redudancy and elegance. One could conceive of the possibility to be offered better mathematics –evaluated exactly by the former criteria. So what? Should we stop using mathematics because someone could someday improve or change mathematics?

Yes and no: indeed, if we had reasons to believe that someone could or would present a system that would overthrow the totality of mathematics (or even a big part of them), then yes, we might as well wait before keep on using them. But if we just suspected that someone could someday just make minor corrections at some specific, marginal cases, then no, we should keep using mathematics as the best tool there is. By the way, the most thorough and consistent reform about mathematics I have ever heard of, has been announced by Lekkas. Still we both (I and Lekkas) consider mathematics as by far the best tool we have.

Of course, the former argument wasn’t made for me to admit that “look guys, Lekkas is super, but might be wrong somewhere, I don’t know!”. On the contrary, the former argument’s lesson for our case is that when Lekkas’ system is so BIG, including so many domains, so coherent, consistent, productive, so much more than any other known to me system, then yes, I will admit, beyond any doubt, that he is by far the biggest personality of our cultural system, ever. But what if someone presents something better, even at some specific points?

If that someone brings “something better with minor changes”, then that would be what Lekkas says with some minor changes. Science is still overthrown, Lekkas wins and is hugely right. The real question is what if someone brings something completely different –or manages to show that science is correct.

The second is impossible: Lekkas has already shown too many inconsistencies. The first is a logical impossibility as well. One should first change mathematical logic! Let us see why.

Let me elaborate at this point on the issue of logic a bit more. What does logic do? Logic does one thing, JUST ONE. It establishes identities. It tells us when proposition A is identical to proposition B –or not identical. Logic is the anatomy of tautology, nothing more, nothing less. One very interesting consequence is that logic may be used as a generator of possible scenarios. “It either rained on May the 12th 1983 in Oxford or it did not rain on May the 12th 1983 in Oxford”. No other logical possibilities exist. In every phenomenon, every issue or subject, logic may be used as the generator of all possible cases and scenarios. Can there be more scenarios? No, as long as we accept mathematics the way they are! There may be only a specific number of scenarios, more would be either tautologies, or contradictions.

The great thing about logic as a scenario generator is that it may produce all and every possibility without any need for empirical data: no matter what data are offered, the number of ALL possible scenarios is limited —language has no way to express other scenarios even if they existed; but then they would be unintelligible scenarios! We would need to meditate or something to grasp them –much like Germans need to meditate to grasp scenarios their language doesn’t allow them to have. Statistics is irrelevant, or, it just measures the probabilities of the scenarios predicted by logic; statistics CANNOT produce scenarios!

D. Lekkas is able to a) point out the inconsistencies of the scenarios and doctrines of many accepted, fundamental and mainstream theories. b) point out what is wrong with theories that are popular among alternative theories (by alternative I mean non-mainstream, as they are often presented in, say, TED conferences) and c) go as far as to produce and propose new theories to replace the defective ones. All this is done through the strict usage of logic. His strictness in mathematics is infinite. Please note that the logical possibilities he is able to detect in the fundamentals of basic sciences are (unfortunately) not common ground since if they were, they would have been mentioned or addressed in all major textbooks, or these major textbooks would not contain such fundamental flaws. Please do not ask me how do I know they are flaws. While I was in junior high school I learned how to follow (and make) mathematical proofs. In the meantime, there have been 2 bachelors, one Msc and one Phd (among others). “Science” is my job –as is the job of others who I am sure will agree with me as soon as they have the chance to talk to Lekkas. Many, many people, scientists, academics and professors have discussed with Lekkas in my presence. Not a single one of them rejected what he said, while many of them consider him a genius. I am not using this as a proof for anything, inductive reasoning may not be used to prove anything. It is just a token of my personal experience. How do I know this to be the case? This is exactly the meaning of logic; to know who is inconsistent! But please, do not ask me how do I understand an inconsistency when I see it. This is stuff for cognitive science or the philosophy of mind to answer, similar to questions such us “why do we find it intuitively correct that 3-1=2?”

But I can’t stress this enough because its importance is fundamental: I do not need more logical tools than a junior high school pupil has to evaluate simple logical inferences. Nothing more than what is needed to draw conclusions and make proofs in euclidean geometry taught to a 13 year old boy. This is exactly the reason my case is so powerful. I repeat, the content of Lekkas’ epistemology will be presented elsewhere, while there is (elsewhere) papers written by him on several issues. Α 13 y.o. (as much as any professor) knows that the sum of the angles of a triangle in an euclidean space equals 180 degrees. As long as the maths we know apply this will not change. Will it ever change? Even though this is sort of an analytic truth, i.e. an obvious, a priori truth, I will grant you the benefit of the doubt and agree that it might change –even though I cannot see how. So what? Should I stop considering the sum to be 180 degrees because it might change? Why not? Do I have any empirical proof that triangles will always behave this way? … see where this line of thought takes us?

Now, there are many other people who have dedicated their career to, say, the study of a historical person. People do have careers, their careers often involve specialization of some sort, and specializing on another person’s work and life is common. Maybe I and such people should found a club or something. Understandably, many would like to consider the persons they focus on to be unique, special and noteworthy. Why not me? Indeed, belonging to the animal kingdom I would share many traits with others of my particular species. And I do. I cannot claim I am not biased after dedicating my career to D. Lekkas to consider him extraordinary. However, it should be clear that the reason I decided to do this was exactly because I realized he was extraordinary and he, alone, could change the route of science for ever. From this point on, it is your responsibility as well to evaluate the matter.

1Epistēmē refers to επιστήμη, not knowledge (as in gnōsesγνώσις), being inaccurately translated as science which is its opposite. Some differences: Episteme relies on the classical Greek tradition; science in the tradition of logical positivism. Science is based on experience, episteme on surveillance.

2In case this rings a bell, Feyerabend did not say science is witchcraft, he merely said that as a knowledge system, the “truths” of science may be compared to the “truths” of witchcraft.

Leave a Reply

Page optimized by WP Minify WordPress Plugin