Dedicated to Nicholas MaxwellIt is indeed a fact that the title of my latest article, From Knowledge to Wisdom, is literally the same as Nicolas Maxwell’s work. And as we know, there isn’t, spiritually speaking, any coincidences. And that’s why we are now reading his work to find, eventually, actual connections between the Portuguese and British philosophies.
Concerning European thought, it is perfectly known that both philosophies have a distinct role compared to the French and German ones. Firstly because the former seem especially related and traditionally “confronted” with the Continental culture. Secondly because both spiritual traditions have a unique interpretation of Aristotle’s philosophy, chiefly regarding on practical fulfilments based on living and spontaneous experience (1). Moreover, it is known that the Aristotelian notion of experience was not inspired on mechanical or technological procedures, those barely practiced in Antiquity and increasingly developed in the Modern Age. Besides, the works of Baron of Verulam, namely the Novum Organum, were most useful in pointing out why the induction problem needed to be solved beyond syllogistic exercises practiced by medieval scholars in a purely formal registry.
We don’t think, like many western academics do, that the British thought is simply reduced to empiricism, pragmatism and materialism. In Bacon’s scientific methodology, the crooked mirror and the theory of the idols are, for example, true philosophical resources to understand how the human mind can wrongly judge, while distorting, the immanent forms of nature itself. And that is why the induction process, going from sensible experience to lower axioms or propositions, is fundamental to guarantee new and general axioms based on intermediary ones. So, the “living axioms” or the middle ones were meanwhile considered, not according to a syllogistic method stemming from abstract propositions, words and notions, but under the light of a natural history, made of particular facts gradually and carefully inducted to perform the knowledge of forms (2).
This same process was, curiously enough, analogical to the Socratic induction, in which the crucial aim was to extract concept definitions, especially regarding the negative cases, under the method of exclusion, in order to conclude for the positive ones (3). So, as Socrates was always ready to persecute dialectically the divine world of Ideas, Francis Bacon was trying to implement aninduction methodology capable of perceiving the interplay of matter, forms and motion in nature, mostly invisible to human senses. Moreover, the mathematics application on Bacon’s operative induction was just an auxiliary one, scarcely coming after the process in which the multiple would give its place to the simple (4), the incommensurable to what was susceptible ofmeasure, the insensible to what could be calculable, vagueness or confusion to what offered certainty, as we can similarly experience or testify before the alphabet letters and note music itself.
On the other hand, Galileo Galilei was not the founder of the experimental method, according to some academic manuals of philosophic history. The true one was indeed Francis Bacon, whose experimentation methodology was an admirable model of investigation of causes about the elastic, fluid and ethereal elements. An example of this can be found in his work, Novun Organum, where he makes the famous investigation of the form of heat.
It is possible that some historians of science could see or detected in Bacon a forerunner of Karl Popper in respect of the method of falsification. Despite of everything, we think that Bacon’s natural philosophy should be investigated further into the limits and the possibilities of classical knowledge, principally enunciated by John Locke, David Hume and by the German philosopher, Emmanuel Kant. Subsequently, the problem is to know how the empirical facts and the formal sciences expressed by logical and mathematical propositions work.
In other words, the problem emerges as a remote one. So, Francis Bacon needs, perhaps, to be strongly reconsidered in order to weigh how Aristotle’s physical, logical and metaphysical thought was eradicated in the Modern Age. Therefore, a new scholastic system was born based on mechanical science and, naturally, more and more dependent on mathematical logic and analytical thought.
Crucial it is as well to see how John Locke had, effectively, recognized mathematics as an independent knowledge domain facing the empirical one. And how, in turn, David Hume conceived the same thing with one single exception: the mathematical concepts would have their origin in sensitive or perceptual experience. And last but not least, how Bertrand Russell reduced mathematics into formal logic (5).
So, at this point supervenes, according to our perspective, the philosophical problem of the present Anglo-Saxon culture: a specific form of positivism due to a contemporary deviation from the philosophia perenis, mostly represented by Aristotle’s logic. In fact, the Greek philosopher did not conceive a mathematical logic.
Aristotle´s induction is indeed the first logical inference by which the human spirit operates the transition of the multiple towards the unit. Philosophy, by considering images (fantasmata) originated in senses, begins with audacity of inferences just to transcend time and space determinations. In fact, the process of conception can be no more reduced to mathematical abstraction, as currently demonstrated in geometric postulates or paradoxical notions (6) which, by itself, are in contradiction with natural experience.
Fractional, negative, irrational, imaginary numbers are just mathematical fictions, like when we define a point without dimensions, or even a line without breadth. Mathematical fiction can also include the tendency of the polygon to the circumference and, most of all, the non-distinction between straight lines and curves. We must recognize that similar fiction represents a different world outside nature and life, a world in which industrial and machinery activity are solidly dependent.
Basically, the damaging consequences of modern science is certainly the centre of the Portuguese philosophy inquiry, especially regarding the calculating progress based on extensive and disqualified abstraction. Mathematics cannot hence explain phenomenal motion in spite of the possibilities of non-superficial and volumetric operations of arithmetic – multiplication and division -, whose respective incognita is foremost implicated in generation and corruption phenomena. But, of course, there also exists the Pythagorean point of view, a deeply one dependent at least on a minimum of divine revelation, or, more precisely, on a speculative process beyond all kinds of quantitative applications confined to extensive observation, construction and experimentation.
It is out of question that William Hamilton’s studies about the “quantification of the predicate” are useful to modern logic, namely those ones regarding Morgan and Boole’s studies. But it is also true that Aristotle’s logic is not a particular case of the theory of classes as is commonly presented in academic institutions. Aristotle’s logic surpasses the conversion of combined propositions, useful for lawyers and judges, as celebrated in the classical period of Roman rhetoric, but, in the end, not capable of realizing a philosophical speculation or a wisdom inquiry.
Therefore, if the process of academic culture expands and communicates human knowledge, the art of invention increases much more and infinitely the living world of metaphysical wisdom. The British thinkers, logicians, psychologists, epistemologists, can meanwhile recognize that even Sherlock Homes, a fictitious character created by Sir Arthur Conan Doyle, used an investigative method in many senses beyond the positivism of the Nineteenth Century. Deduction, induction (7), abduction (8), all this can be undoubtedly found in Sherlock Holmes mystery stories. Nevertheless, we shall carefully listen to the man who was, fictitiously speaking, an experimentalist in “Baritsu” (9) and, more surprisingly, unacquainted with something referred to Philosophy: «imagination is often the mother of truth».
(1) Aristotelian experience is not a locked up process. In fact, it is not possible to reach the universal by just knowing partial, regular or cyclical accidents extracted from induction reasoning. Empirical process demands also deduction reasoning for conclusive universal science. In this sense, the Portuguese discoveries were consequently inspired in the empirical “revolution” of Aristotle’s cosmology, particularly represented in the realistic vision of Henry, the Navigator, or even more through the classification of zoological, botanic and mineralogical phenomena.
(2) The following passage is a specific expression of Bacon’s non-Aristotelian Aristotelianism: «There are and can be only two ways of searching into and discovering truth. The one flies from the senses and particulars to the most general axioms, and from these principles, the truth of which it takes for settled and immovable, proceeds to judgment and to the discovery of the middle axioms. And this way is now in fashion. The other derives axioms from the senses and particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms at last. This is the true way, but as yet untried» (Novum Organum, I, Aph. XIX, Bacon, IV, 1901, 50).
(3) This induction method goes beyond the remit of induction by simple enumeration. By that it means that Bacon’s induction is especially founded on collection, comparison and exclusion of factual qualities in things and their hidden structure.
(4) Bacon’s natural philosophy is concerned with simple natures or the ultimate ingredients of things, as, for instance, heat, light and weight. In this particular sense, Bacon´s interpretation concerning the basic structure of matter is not identical with natural law.
(5) Two main things overtop Russell’s objective in his way to logicism: 1. Mathematical truths can be translated into logical truths; 2. All mathematical proofs can be recast as logical proofs, or more properly, theorems of mathematics can constitute a proper subset of the theorems of logic, like numbers can be identified with classes.
(6) Worth of memory is Nicholas of Cusa’s coincidentia oppositorum, in which method does not enter Aristotle´s third term. And that is why dialectics are especially important in this paradoxical method, where God Himself is presented like a sphere whose centre is everywhere and its circumference nowhere. In short, Nicholas of Cusa conceived God as a non- physical centre of all beings and all things.
(7) Despite Holmes’s deductive proceeding, inductive reasoning is often valorized: «It is a capital mistake to theorize before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts».
(8) Abduction, originally formulated by Aristotle, is a syllogism in which the second premise has only the character of probability.
(9) “Baritsu”, or more correctly Bartitsu, was an eclectic martial art and self-defence method created by Edward William Barton-Wright, a British engineer who lived for three years in the Empire of Japan. Bartitsu was developed in England in the years 1898-1902 and became somehow immortalized as “Baritsu” by Sir Arthur Conan Doyle. The “New Art of Self-Defence” combined several fighting styles like fencing, boxing, wrestling, savate, jujitsu and a walking stick as a means of self-defense. At the present, it is known as the martial art of Sherlock Holmes.