Math Circle 4 -- Jaki Musings
Amplifying the works of James Duane Nickel’s Math Circles.
Why Jaki?
EN: Your essay brings together a wide range of Stanley Jaki’s writings into a single thread. What first drew you to Jaki, and what convinced you his ideas were worth revisiting today?
JDN: In early 1986, while living in Australia, I first read about Stanley L. Jaki in an appendix to a commentary on Genesis. Everything that was said about him intrigued me. I somehow found a book catalog that listed many of his publications, all from Edinburgh—Scottish Academic Press. Before the days of the Internet, ordering book catalogues was the way for me to find books and then buy ones of interest. (The other way was through physical bookstores, and I had to make a three-hour automobile journey of about 150 miles to browse the nearest one, a Scripture Union bookshop in Adelaide, South Australia. There were other bookstores and two university libraries in the city—these also were recipients of my footprints.) After converting Australian dollars to English pounds at our local bank, I placed a mail order with a certified check. In a month or two, several of his books arrived via Australia Post: Science & Creation, Cosmos and Creator, The Origin of Science and the Science of Its Origins, and The Road of Science and the Ways to God.
My initial reading of Jaki was like entering another world. His scholarship was breathtaking, i.e., he had done his homework with copious footnotes to prove it. I have often remarked that dwelling within his writings is equivalent to earning two Ph.Ds.
The primary focus of Jaki’s writings regarding the history of science was to bring to the English-speaking world the massive research revealed by Pierre Duhem’s (1861-1916) ten-volume French publication Le Système du monde: Histoire des doctrines cosmologiques de Platon à Copernic (shortened in English as The System of the World or The World System—these volumes have not yet been translated into English). Duhem’s meticulous findings regarding the medieval origins of modern science are without parallel, and Jaki has displayed his quintessential ability to both indwell Duhem’s thoughts and articulate them.
Jaki remains the gold-standard for his analysis of science in the development of Western thought, known now as the Jaki-Duhem thesis. Others have built on his work, but no one has yet reached the heights of his intense research and profound expression.
The Origin of Science and the Science of Its Origin
EN: You emphasize Jaki’s argument that modern science had ‘only one viable birth’ within a Christian worldview. What do you see as the strongest evidence for that claim?
JDN: Let’s briefly investigate the Greeks. Euclid’s work was a monument to Greek “science.” By that time, though (ca. 300 BC), Greek thought had trapped itself, and there was no escape route from the blockage built by Plato and Aristotle. (See the answer to Question 3.) The work of Archimedes also failed to provide a breakthrough even though his work was read widely during the High Middle Ages, such a widespread reading that French philosopher of science Alexander Koyré (1892-1964) in Études galiléennes (1939) gave midwifery status to Archimedes as he posthumously attended Galileo’s viable birthing of modern operational science.
Until the High Middle Ages (12th to 14th centuries), European scientific thought had not differed significantly from its Greek heritage. There was one major difference, though. Both Plato and Aristotle imputed final causes to nature to such a degree that any reference to a transcendent deity was expunged, especially nature’s true purpose and identity found in the revelation of the Incarnate Son of the Father, the One in whom all things co-inhere. Medieval scholastics engaged Aristotelian science but not to the extent of accepting his pantheism because their Christian faith required in them not only a need for God, but that this God could have created things contrary to Aristotelian a priori (from what is before) dictums of necessity, a view of nature that required a posteriori (from what comes after) investigation. This contingent view of creation, a view natural to the Christian faith during those times, was the reason Christianity in its European expression became, as Jaki states, “a broadly shared cultural matrix.” It was that matrix that formed the womb for the viable birth of modern science. This birth was grounded in investigations of nature, the development of mechanical tools like the clock, and an understanding of the astronomical “harmony of the spheres” simpler in both elegance and brevity than the complexity of Ptolemy’s (ca. 150 AD) planetary epicycles. Thus, the thoughts, empirical findings, and mathematics of men like Copernicus, Galileo, Kepler, and Newton traveled on the road built by their Medieval ancestors, a road traceable to the reality that lay behind the opening statement of the Apostles’ Creed, “I believe in God the Father Almighty, Maker of heaven and earth and of all things seen and unseen.”
Jaki thoroughly adjudicates the ancient Egyptian, Babylonian, Chinese, Indian, Arabic and Mayan cultures using the same theological rubric.
Addendum: In the 1990s, there arose an educational emphasis in Christian circles that has now become known as Classical Christian education. “Classical” is the preface to this model because of its pedagogical reliance on Classical Greeks, i.e., on the Greek Trivium (three roads): grammar, logic, and rhetoric and the subsequent Pythagorean Quadrivium (four roads): Arithmetic, Music, Geometry, and Astronomy. This curriculum formed the basis of medieval education, with the target being Christian theology, known then as the “Queen of the sciences” (aka. knowledge). My issue with this model is not necessarily with its pedagogy or its goal, but with what it does with the way of thinking engaged by Plato (ca. 425-ca. 348 BC) and Aristotle (384-322 BC). For example, in 2005, I visited a highly regarded Classical Christian school in Tennessee. During my stay, I visited the secondary curriculum coordinator. His thrilling exuberance was on display as he explained a way to teach rhetorical science in coordination with Aristotle’s methods. This regrettable situation happens when a school hires curriculum designers and science educators who have not been thoroughly trained in the historical flow of scientific thought. No matter what degree you hold, if you approach science with no knowledge of Jaki’s work, you will hamstring your teaching.
The Classical Christian education world must engage with questions like these: Has Platonic and Aristotelian thinking become the foundation instead of Christ? Is your school inculcating a retrofitted version of Christian Platonism? Are you using Classical learning to lead a student to Christ, or is Christ the true and only foundation of thinking/learning? Does the living Logos ground your approach to teaching logic?
I am not opposed to reading Plato, Aristotle, Pythagoras, or the Greek corpus of thought. We must, however, learn to read them with a critical eye; Jaki leads the way.
Undermining Science
EN: Your essay suggests that certain philosophical movements—empiricism, idealism, positivism—actually undermine science rather than support it. How does that work?
JDN: Remember, when we attach -ism to a word, it means we absolutize its meaning. When we say “absolute,” we mean a perspective unconditioned by qualifications or limitations; a concept not modifiable by factors such as culture, individual psychology, or circumstances, but which is perfect, unchangeable, self-existent, self-sufficient. The antithesis of absolutism is relativism.
We can locate the origin of the philosophical movements you mentioned in the Greek philosophers Plato and his student Aristotle. Between 1509 and 1511, the Italian artist Raphael (1483-1520) painted “The School of Athens” in which he portrayed Plato with his right index finger pointing up and Aristotle reaching his right hand forward, palm down, five fingers extended. These actions reflect their respective philosophies: Plato’s theory of forms pointed up to the “vault of the heavens,” concepts that unfolded into idealism. Aristotle, in contrast, directed his attention horizontally toward the earthly realm, ideas that evolved into empiricism.
School of Athens by Raphael (detail)
We first define our terms. We note the close connection of empiricism with positivism.
Idealism: Ideational means “of, pertaining to, or involving ideas or constructs.” Idealism, therefore, is the view that fundamental reality is mind-dependent, a “stop and think” approach to knowledge. Subjective idealism holds as a pre-commitment that existence is in human perception. Objective idealism maintains that there is no categorical distinction between the knower and what he knows—that both are part of absolute thought. Idealism a priori absolutized.
Empiricism is a view that emphasizes the study of real-world operations, a “look and see” approach to knowledge. If we do not see empiricism as a tool but as absolute, i.e., the view that all knowledge is a posteriori or derived by experience alone, the result is Logical Positivism. For anything to be meaningful and true, it must be verifiable either scientifically, i.e., empirically, or logically, e.g., in Euclid’s Elements (ca. 300 BC), he logically derived geometric propositions. A synonym for Logical Positivism is Scientism.
We trace the line of Idealism from Plato to Descartes to Kant to Hegel to Nietzsche. In a nutshell, it is the gospel of unadulterated subjectivism.
To the idealist, the absolute center of the universe, i.e., that which is the ground of true existence, is the cogitations of the human mind. This viewpoint is illusory because the doctrine of the contingency of creation forces the human mind to face creation’s objectiveness, a realism that exists outside the human mind, a realism that doggedly interferes with any attempt by the human mind to play god.
Galileo’s (1564-1642) scientific work refuted Descartes’ (1596-1650) tilt to rationalism (cogito, ergo sum, “I think, therefore I am”) by realizing that his ideas about free-fall motion had to be put into the cauldron of experimental testing for them to be formulated as law.
The discoveries of the founders of the Scientific Revolution, Copernicus, Galileo, Kepler, Newton, et al., occurred in a sui generis context. In their findings, they saw a lawfulness in the physical world, not merely as impressions on their minds, but as reflections of the Creator’s mind of wisdom and sustaining power of faithfulness.
What we learn from the Scientific Revolution is that its founders grounded scientific law on the interpenetration of mind with matter. Both facets are complementary; neither is absolute. They inhere in one another because of a common Creator and Sustainer.
The history of the Post-Scientific Revolution reflects the tragic instability of a host of gifted thinkers either neglecting or denouncing the bedrock out of which science arose. Every instance of neglect or attack was detrimental to the scientific enterprise.
In contrast, we detect the line of thinking invoking Empiricism/Logical Positivism from Aristotle to Francis Bacon to Locke to Hume to Comte to John Stuart Mill to Mach.
To the empiricist, truth is dependent only upon rigorous observation, an observation that is measurable. Science consists in the economy of its empirically validated sensations.
The multifaceted success of scientific experimentation in the 16th to 18th centuries resulted in the absolutization of the experiment. If experimental differences arose, the scientists focused so much on reconciling the results that they lost sight of the underlying reality that exists behind those experiments. A belief in metaphysics, in the efficacy of recognizing that which is behind the experiments, took a hit.
The reduction of all knowledge to the scientific form, i.e., the scientific method (empiricism), is Scientism. Since religion, or belief in a transcendent reality behind the experiments, is not science, then Scientism dumps religion into the realm of the nonsensical. Scientism, by definition, does not allow the “Divine Footprint” in the door. As Jaki notes (A Mind’s Matter, p. 4.), “Scientism is the general ideology of those who define science as the art of eliminating God from the ultimate equation.”
Some questions rarely asked in this milieu are: How is scientism justified? Is it empirically verifiable? If we ground knowledge of truth upon information gained only through the five senses, where is the empirical evidence, the experiment, that proves this relationship?
We learn from history that information gained by the scientific method is, borrowing a phrase from C. S. Lewis, always “in the dock.” History tells us we should never enthrone Science as the absolute adjudicator of knowledge.
Science progresses only when it recognizes the equal ultimacy of a priori and a posteriori. It negates its purpose when it absolutizes either approach. Ideas and experiments work together to develop effective models of the world, models that explain and predict. Logical analysis, i.e., deduction, and the search for patterns, i.e., induction, work as a team. Empirical and theoretical factors are inseparably integrated. All creative science is an integration of praxis and theory.
What Scientism and Idealism lose by not allowing the “Divine Footprint” in the door is acknowledging the ramifications of seeing humanity as the imago dei. Humans are not just fact-based or idea-based creatures formed by blind chance. The Triune God gifts humans with the ability to intuit, to gain insight, to touch and handle things in a way that the Hungarian-British scientist/philosopher Michael Polyani (1891-1976) described in The Tacit Dimension ([1966] 2009) as tacit knowledge.
I can best explain tacit knowledge by my experience with my father. He was a farmer. By the experience of decades, he knew when to water, when to plow, when to fertilize, what to plant, and when to plant. He knew the conditions of the soil by feeling dirt in his hands and by intuiting from that sense what to do. Likewise, a factory worker perceives the existence of quality issues through experience. A shop owner grows to understand customer patterns through daily interaction. Tacit knowledge is not just the gathering of information from reports, surveys, or even scientific experiments.
In Science and the Gospel (p. 38), Victor H. Fiddes spoke to both Logical Positivism and its next of kin Scientism, “Essential to scientific discovery is a kind of intuitive grasp of reality, an inner apprehension [i.e., tacit knowledge], which, far from being inimical to the exactitude which science requires gives it its needed conceptual support. If science were to lose this disinterestedness, as appears to be happening, the ultimate consequences for scientific discovery would be disastrous. ‘Pure logic could never lead us to anything but tautologies,’ wrote the French physicist Henri Poincaré. ‘It would create nothing new; not from it alone can any science issue.’”
In the next paragraph, Fiddes addresses the place of mathematics in this equation: “The fact that modern science is linked inextricably with mathematics does not change this basic orientation. Mathematics itself cannot be isolated form the intuitive apprehension of reality.” I could say much more about mathematics and intuition, but that discussion is not the focus of the answer to this question.
Underlying Assumptions
EN: Do modern scientists still depend on the same underlying assumptions Jaki describes—a rational universe and a mind capable of knowing it—even if they no longer frame those beliefs theologically?
JDN: If there is no rationality both outside us, the workings of the physical universe, and inside us, our capability to intuit and reason, science would not exist. There are modern scientists who no longer frame their beliefs in the context of their founding fathers. Some think these scientists are in the majority; others think their number is dwindling. It is difficult to tie statistics to this situation.
For those who either reject or ignore their heritage, their deeds belie their pre-commitment. Science is only possible in a rational universe with a mind capable of knowing it. They live, therefore, in a schizophrenic world of their own making.
On Meaning and Purpose
EN: Jaki argues that science intentionally sets aside questions of meaning and purpose. What happens to a culture when those questions are left entirely outside its most respected form of knowledge?
JDN: This answer builds on the answer to Question 4.
Is it not a wonder that so many followers of Darwinism devote their entire careers to the purpose of proving that there is no purpose to anything?
That they use their rational capabilities to prove their existence to be a probabilistic impossibility, a mere accident arising from the cosmic crap-game of time, chance, and matter?
Or that they engage all their intellectual powers to demonstrate that no intellect is the sine qua non of the origin and design of the universe?
A culture cannot be built, exist, or thrive without meaning and purpose. Our present Western culture was built on meaning and purpose, the purpose that gives meaning to life revealed through the incarnate life, death, resurrection, and ascension of the Son of the Father. We are now trying to exist in rejection of that foundation, and the world of science is not helping matters. It needs to stimulate reform in the humanities by seeking to reframe its development of high tech by stimulating a similar development of the high touch of robust human flourishing.
We do well to heed the warning of Whittaker Chambers (Witness, p. 17), “... history is cluttered with the wreckage of nations that became indifferent to God, and died.” … and act appropriately.