Reinventing Philosophy

 

© 2008 Aleksandar Kandić

 

Abstract: Modern era (particularly the 20th century), brought an increase in number of philosophical and scientific disciplines, an increase whoose intensity is constantly increasing itself. At first, the natural sciences declared their independence from the philosophy of nature. Later, the ramification of natural sciences lead to foundation of many new scientific disciplines. Analogical developments might be observed in philosophy. What has been a simple division of philosophical disciplines into physics, logic and ethics turned into a labyrinth of disciplines. This makes the comprehension of unity of philosophy an extremely difficult task. These disciplines have to share certain common form: it is in the objects of enquiry, as well as terminology and methods of investigation where the differences emerge. We claim here that the unity of philosophy, as well as science, consists in the mathematical organization of disciplines and acquired knowledge. In all philosophical disciplines, such as metaphysics, ontology, epistemology, or even ethics and aesthetics, as well as all theoretical and practical disciplines aiming to acquire systematic, justified knowledge, we tend to sort our facts in such a manner that principles and axioms (which represent the universal, absolute and self-evident) constitute a foundation of our factual material. Any discipline which lacks this characteristic cannot properly be called a discipline, but a pile of unsorted facts, opinions and notions. The current tendencies in science and philosophy are almost anti-intellectual: multiplicity is being described, not explained. What we need to do is reinvent philosophy.

 

Key words: unity of philosophy, mathematics, discipline

 

        Modern era (particularly the 20th century), brought an increase in number of philosophical and scientific disciplines, an increase whoose intensity is constantly increasing itself. At first, the natural sciences declared their independence from the philosophy of nature. Later, the ramification of natural sciences lead to foundation of many new scientific disciplines, some of which seem to be quite exotic - even for a hard science-fiction fan. Exobiology, or astrobiology, we are told, is the interdisciplinary study of life in space, combining aspects of astronomy, biology and geology[1]. Also, there exist a tendency to study each type of empirical phenomena within the terminological and methodological framework of particular scientific discipline. For example, limnology  (in brief) is the study of inland waters, both fresh and saline, such as lakes, rivers, wetlands, etc[2]. The bigger the number of –ologies, the more difficult is for a man to grasp the interconnectedness of these disciplines, the common form reappearing through all of them. Providing they really are scientific disciplines, they have to share certain common form: it is in the objects of enquiry, as well as terminology and methods of investigation where the differences emerge.

        Analogical developments might be observed in philosophy, or, should we say, in what is understood by “philosophy” today. What has been a simple division of philosophical disciplines into physics, logic (sometimes identified with epistemology) and, of course, ethics – a division prominent since the ancient times - turned into a labyrinth of disciplines, some of which sprung from the need to resolve problems in already established branches of philosophy, and some of which are spontaneously created in order to provide necessary criticism as well as terminological and methodological framework to many new-born scientific disciplines. So, not only that we have philosophy of science, philosophy of mathematics, physics, language, history, art, etc, but we also have philosophy of biology, anthropology, psychology, education, we have bioethics, metaethics, and even philosophy of philosophy, or metaphilosophy[3]. It seems that the emergence of “philosophy of exobiology” would not make such a great surprise anymore. I think this very much answers the provocative question “Why still philosophy?”, since philosophy is proved to be needed more than ever. Proportionally, the amount of publications in philosophy has to be the highest ever: papers, books, studies, they occupy tons of paper. A few centuries back, it was possible to get hold of any significant publication, today it’s difficult to follow even those in the branch which is your main field of interest.

        However, quantity does not imply quality! As I have already pointed out in the first paragraph, such a great number of disciplines and publications makes the comprehension of unity of philosophy an extremely difficult task. A professional philosopher is expected to be updated with publications in his branch, which, on the other hand, usually prevents him to satisfy his interests in other fields of philosophy, or science. Simply, he’s short of time. As a consequence, the system produces a narrow-minded thinker (an oxymoron, that is): while he has gained a respectable level of understanding and information within his own branch, or discipline, he is not able to correlate this information to the findings of other disciplines. Inevitably, he becomes a link in the chain, without grasping the meaning of the whole chain.

        And this problem of unity of philosophy is what concerns me most. If we all inhabit the same world, there has to be a principle by which all individuals and their subjective perspectives are correlated. How could there be two or more first principles? How could there be two or more true explanations, two or more true philosophies? For example, Descartes strongly believed that there could be only one true philosophy. Naturally, there could be infinite ways to express and formulate such fundamental principles, but it is erroneous to think of such formulations as principles themselves. This, I believe, is the source of all confusion. It appears that there could be many solutions to one problem, as well as that many existing philosophies and philosophical disciplines provide conflicted and opposed solutions to the same problem. However, in reality, the problem doesn’t know it is a problem. It is only in our minds, in our subjective, limited perspectives that simple becomes complicated, and unity becomes multiplicity. Today’s conception of philosophy is very much different from the genuine: instead to look for some kind of unifying, a priori principle, it merely describes and arbitrarily systematizes our numerous experiences. More and more, philosophy tends to work in the service of empirical, natural sciences, and - as a consequence - we end up with a growing number of terms, notions, disciplines, publications etc. This is the situation we have previously discussed. Everything is problematized, nothing is solved.

        At this point, it would be useful to remind ourselves of what philosophy is. In my opinion, if one wants to learn about specific concept, the best way to begin is to look for the earliest evidence, particularly before the subsequent and contemporary developments take effect on one's understanding of given concept. Among the first thinkers who begun to value proof and the powers of reasoning, who disregarded mythical thinking, were Thales, Heraclitus, Zeno of Elea, and the most influential of all, Pyhtagoras. Therefore, if one wants to learn about philosophy, one should try to dig out as much evidence as possible on the thinkers mentioned: that includes their own writings, if available, and the writings of their criticists, commentators, biographers, etc. Philosophy is what Pythagoras thought it to be, not an empty word which may be given any meaning that pleases us mostly, in particular moment. Etymologically, philosophy is love for wisdom. But, to say that philosophy is love for wisdom seems very implausible and insufficient. If by wisdom we understand the highest kind of knowledge, what could be the methods of acquiring such knowledge, and even more important, what could be its objects? In certain manner, the word philosophy denies that philosophers can achieve such kind of knowledge: they are nothing but the lovers (or friends) of wisdom, they do not actually posses it. Still, their reasoning should imitate – in higher or lesser degree – the structure of true, divine knowledge. This structure is entirely mathematical. In this sense, the philosophical method is nothing else but mathematical method applied to the study of things, and Nature.

        What does this mean? One of the most important concepts in philosophy, mathematics, and generally, science, is the concept of axiom. The word axiom comes from the Greek word axioma, which means “that which is deemed worthy”, or “that which is considered self-evident”. In Republic VI, Plato used the term archen anupotheton to denote such unhypothetical first principle[4]. Axiom is a proposition which is accepted without any proof. In contemporary mathematics, the concept of axiom is very loose. Any proposition might be considered an axiom, as long as it’s properly defined in terms of the formal language we employ, and integrated into the formal system through the rules of derivation. On the other hand, in ancient mathematics, axiomatic propositions represent certain universal principles, things which are abstracted from experience and aren’t a mere product of human imagination. They are real. They could be utilized as starting points in explanation. However, is it really appropriate to speak of axioms, of plurality of principles? Whenever we deal with a plurality of things which are of the same kind, we feel the need to postulate one thing by which they become what they are. A plurality of principles would require an explanation of a higher order, a principle by which these principles are principles. So, instead of inferring from particular towards universal, we should rather infer from universal towards particular. We should descend from the first principle. It is the goal of metaphysician to discover the first principle of reality.

        In all philosophical disciplines, such as metaphysics, ontology, epistemology, or even ethics and aesthetics, as well as all theoretical and practical disciplines aiming to acquire systematic, justified knowledge, we tend to sort facts in such a manner that principles and axioms (which represent the universal, absolute and self-evident) constitute a foundation of our factual material. Thus, relative, contingent facts become deducible from the first principles. Aristotle thought that each science has its own principles, or archai[5]. Our knowledge, then - providing it is systematic - might be represented in the form of the chain of deductions:

 

A -> A’ -> A’’ -> A’’’ -> A’’’’ -> A’’’’’ -> ...

 

“A“ stands for axiom, the self-evident truth or unhypothetical first principle which constitutes the foundation of our knowledge. If the causal relations established between the first principle and all subsequent conclusions are considered necessary, then it is natural to assume that absolute certainty may be attributed to all of the premises in the chain, and not only to the first one. And if absolute certainty is transferable through implication, then any of the subsequent premises might be taken as starting points in explanation. This is, basically, the idea which distinguishes philosophical knowledge from ordinary knowledge, dependant on the (highly unreliable) testimony of the senses.

        Historically, this thesis is supported very well. It is generally accepted that Pythagoras and his followers invented not only the word “philosophy”, but also the word “mathematics”, which is derived from the Greek word mathema, and primarily means learning, study, science. The Pythagoreans also conceived methods, goals and procedures of the mathematical discipline. They were divided into mathematicians (in ancient Greek, mathematikoi), or those who posses true, systematic knowledge, and listeners - as we could translate the Greek word akusmatikoi - who only transmit information without proper understanding. Furthermore, Aristotle (in his Metaphysics) stated that the Pythagoreans thought the principles of mathematics were the principles of all things[6], and often compared philosophy to mathematics. And, of course, the great Plato claimed that “geometry is the knowledge of that which always is, and not of a something which at some time comes into being and passes away”[7]. As we all know, for ancient Greeks, mathematics was primarily geometry. They didn’t use algebra, or symbolic representation. Instead, they literally draw their proofs, they represented them visually. Euclid’s Elements set a perfect example. Of course, this had some disadvantages of purely practical nature, but in my opinion, it made a much more immediate, much more efficient approach to both mathematical and philosophical studies. In modern era, Descartes’ earliest philosophical writing Regulae, though unfinished, has to be one of the most ambitious, and most systematic attempts to revive this ancient conception of “mathematical philosophy”.

Having all this in mind, I conclude that the unity of philosophy, as well as science, consists in the mathematical organization of disciplines and acquired knowledge. This is the common form reappearing through all disciplines. Any discipline which lacks this characteristic cannot properly be called a discipline, but a pile of unsorted facts, opinions and notions. The current tendencies in science and philosophy are almost anti-intellectual: multiplicity is being described, not explained. If there exists a unique principle, or at least several universal laws necessary and sufficient to explain the governing of our world, then these laws seem natural to be rediscovered over and over again by thinkers and great minds of all times. True knowledge is of that which is unchangeable, timeless, constant, that which is real in the most rigorous sense of the word.

What we need to do is reinvent philosophy.

 

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[4] Plato: The Republic, 510b

[5] Aristotle: Posterior Analytics, 76a-b and Metaphysics, 1005a

[6] Ibid, 985b

[7] Plato: op. cit, 527b