Certainty, generally, is an illusion, and repose is not the destiny of man.” – Oliver Wendell Holmes



Last time after rejecting absolute certainty as both counterproductive as an aim and perilous when assumed, I suggested we consider a quasi-foundational approach to knowledge tailored to the five levels of reality. Briefly we end up with a matrix:

Level of Reality                        Informed by:

Internal Reality                         Subjectivity

Proximate Reality                   Subjectivity and science

Societal Reality                        Multiple authoritative sources

Cosmic Reality                          Science

Ultimate Reality                        Subjectivity and science

However principles justifying our greatest confidence seem to be more practically separated into four types: (1) metaphysical, (2) ethical, (3) empirical, and (4) ultimate. Metaphysical principles derive mostly from internal reality and subjectivity; ethical principles from a mix of internal and proximate reality and thus subjectivity and some science; empirical principles from understandings of cosmic reality and science; and ultimate reality and principles from subjectivity mixed with an element of science. The hope for any degree of certainty in societal reality is quite limited, a fact which reverberates as the peril of all forms of political dogmatism.

We also reviewed some useful tools for this scope of work including:

Author                          Tool

Santayana                   Reason (meaning and unity) and human ideals

Adler                               Common sense and intelligibility

Scruton                         Truth value and trust in language

Baggini                            Sincerity, accuracy, and objectivity

So now I hope to take these tools to task in creating a list of important principles within each group stratified on the degree of certainty of each. We begin with metaphysical principles next time.


The basis for this approach to a quasi-foundationalism is not entirely novel. In The Life of Reason, George Santayana explores reason as the vital impetus to meaning and unity. Reason allows man to distinguish between spirit and nature allowing him to understand his wants and needs and how to satisfy them. Instinct is transformed into human ideals that exceed simple survival needs as for example in the case of the highest human ends – goodness and art.2

Mortimer Adler makes the case for a common sense understanding of reality, particularly denying idealism (Kant’s thesis that reality for humans is a construct of the mind) and Heisenberg indeterminacy (the exact status of subatomic structure depends on an observer) . He specifically challenges the increasing tendency by physicists to assert that ‘what they cannot measure does not exist.’ Adler feels a genuine reality exists separately from human experience of it but is made intelligible by the human mind.3

Roger Scruton speaks of assigning a ‘truth value’ to a statement in a sense similar to that between an object and its name (for example Venus as both morning and evening star) as argued by Gottlob Frege.4 He also quotes Ludwig Wittgenstein:  “the world is the totality of facts, not of things.”5 And while the skeptic can challenge thought as depending on language and the imperfect meanings of words, Scruton thinks trust in thought is  justified since those words are human in origin and hence are correctly applied to human reality. Moreover the fact that language is shared by others  validates our belief that the mind is not completely private.6

Julian Baggini discusses the view of Bernard Williams that truth requires two virtuous features – sincerity and accuracy. Reasoned objectivity underlies legitimate beliefs even if others do not share those beliefs. Again the skeptic is undermined in blanket disbelief as he too relies on reason to challenge us, further confirming a rational approach as the means to justified belief.7

Before moving on to my hierarchy of most certain truths, it is worth remembering that much of what  impels doubt is based on our unavoidably particular experience of the world as a species and as individuals. The human experience is clearly different from that of a fish, a fly, or a bat; perhaps none of these is definitive, and it is chauvinistic for us to elevate the human picture above the others. However, since we are, after all, human and have only our own biologic equipment to inform us, it is difficult to imagine a better alternative from which to determine degrees of certainty or a plan for living.


1See Posts on this site 11/9/18, 11/12/18, 11/14/18, 11/16/18, 11/21/18, 11/23/18, 11/25/18, 11/26/18, 11/28/18, 11/30/18, and 12/2/18.

2Magill, Frank, Masterpieces of World Philosophy in Summary Form. Harper&Row Publishers, 1961, pages 761-767.

3Adler, Mortimer J., Intellect – Mind Over Matter. Macmillan Publishing Company, New York, 1990. ISBN 0-02-500350-X, page s 90-114.

4Scruton, Roger, An Intelligent Person’s Guide to Philosophy. Penguin Books. New York, 1999. ISBN 0 14 027516 9, page 29.

5Ibid., page 31.

6Ibid., pages 43-57.

7Baggini, Julian, The Edge of Reason. Yale University Press, New Haven, 2016. ISBN 9780300208238, pages 113 and 137-139.


“You cannot prove realism to a complete skeptic or idealist, but you can show an honest man that he is not a complete skeptic or idealist, but a realist at heart. So long as he is alive his sincere philosophy must fulfill the assumptions of his life and not destroy them.” – George Santayana.

The last twenty-four posts have considered and rejected various forms of certainty. First were Kant’s a priori statements or self-evident truths which we saw were limited in number and often mere tautologies. Second was the philosophical quest of foundationalism – wherein certain or near certain truths might be built into secure doctrine – a quest which eventually failed. Third and most successful came science which is, however, not only imperfect, but applies mainly to natural phenomena rather than the human existential problem.

We also examined the threats of lost opportunities in the futile search for certainty and the perils of unjustified certainty. But there is another danger overlapping these two – the danger of extreme skepticism and doubt as the eradication of all principles. Philosophical guidance in living requires us to pull ourselves out of this epistemological quagmire. Today I hope to outline a rational course for us to follow.

First we need to return to the levels of reality.1 It appears that science is sufficient for human needs when considering cosmic reality and some aspects of proximate and societal reality. Our knowledge of societal reality will always remain deficient, but the most accurate picture of the human world possible is attained by consulting the writings of a variety of reputable historians and journalists. Still caution must be observed however sure we think we are in the realm of societal reality.

On the other hand, the blueprint of a meaningful and flourishing life is more dependent on internal, proximate, and ultimate reality – none of which can be fully informed by science or outside authority. So we disembark in our journey at Kierkegaard’s great discovery – subjective truth. Using a mixture of individual intuition, experience, belief, and reason, each person must define fundamental principles in approaching life and the world which are validated by their coherence, instrumentality, and predictive efficacy. No principles thus derived are absolute, but with careful reflection and constant re-evaluation, we can structure them in degrees of certainty or justification for action. Once we stratify these principles, they can be deployed for priority in action. At that point science can be instrumental in effecting our priorities. Of course we also need to have fortitude to comply with our own stratified ‘certainties.’

(continued next post)


“I beseech you in the bowels of Christ think it possible you may be mistaken.” – Oliver Cromwell.



It turns out that not only is certainty elusive, but the seeking of certainty and the belief in one’s own certainty represent significant perils to humanity. Let’s start with John Dewey’s masterpiece The Quest for Certainty. Dewey’s thesis is simple – humans live in a world of hazards and thus seek security. In early civilization security was sought in two ways:  (1) superstitious belief and hope and (2) the development of simple technology. The first led to dogmatism which stifled human progress and became a cause of strife as societies attempted to impose their belief on others. The second depended on the study of nature, itself changing and inexact, pushing great minds of the past to defer its study to others as they sought absolute truth (e.g. Plato and Aristotle).  A dichotomy developed between theory and practice that delayed human advancement.

Philosophers receive the brunt of Dewey’s criticism and rightly so. His remedy is for philosophy to forsake “the quest for illusory certainty for discoverable paths to enjoyable goods.”1 In short, by abandoning certainty as its goal, philosophy paradoxically can improve the human condition.

J. Bronowski examines the obverse side of the coin – the danger of unwarranted certainty. In The Ascent of Man, he devotes a full chapter (or episode of the television series; available on YouTube) to this topic.2 He begins with science’s eventual recognition that material certainty is impossible referencing Carl Friedrich Gauss and his Gaussian curve with its ‘areas of uncertainty’ and Heisenberg’s uncertainty principle. He tells us: “All information is imperfect…There is no absolute knowledge and those who claim it whether they are scientists or dogmatists open the door to tragedy.”3 Bronowski thinks the acceptance of uncertainty translates culturally into ‘a range of tolerance as opposed to belief in unwarranted certainty which manifests as  intolerance. He concludes with a stop at the site of a former concentration camp where he argues the holocaust was the result of intolerance stemming from the ‘certainty’ of Nazism which ironically occurred at nearly the same time science was demonstrating certainty to be an illusion.

In our own time, zealots such as Islamic extremists and white supremacists echo similar intolerance and danger informed by their dogmatic certainty. Other examples will likely occur to readers. Dogmatism it turns out is not only the enemy of truth, but also of our species. The more rational  alternative is a mixture of approaches and attention to degrees of subjective truth which is  the subject of our next post.

1 Magill, Frank. Masterpieces of World Philosophy. HarperCollins Publishers.  1990. ISBN 0-06-270051-0. Pages 552.

2Bronowski, J., The Ascent of Man. Little, Brown, and Company, Boston, 1973. Page 353-375.



“‘If you thought that science was certain – well that is just an error on your part.” – Richard Feynman, Nobel Laureate, 1965, Physics.



The last eight blogs delved into science as certainty. It appears science is the best model of certainty for the theological agnostic and the philosophical skeptic. We identified science as a modern form of foundationalism, set on a base of 10 very reasonable, if not absolute, axioms: trust in empiricism, material monism, mathematics and statistics, a uniformity in nature that permits induction, causality, universal applicability, the validity of human reasoning and the scientific method, transferability between fields, refinement into a limited number of underlying laws, and the non-existence of the supernatural.

Science’s weaknesses as a presumptive expression of certainty include: issues of verification and falsification, the limits of the absoluteness of mathematics and its usage in scientific theorizing, and issues of internal connection between its branches, and correspondence with the human experience of reality. Nonetheless, science represents an amazingly consistent picture of nature and the cosmos, proven by the reliability of its predictions and the technology it informs. Theologians and philosophers may legitimately speculate on or impose other principles on to the world, but it appears foolish to purchase this with a denial of scientific explanation.

Perhaps it is better for the philosopher to point out difficulties in the methods of science, seek more integration of its branches, refine its interoperability with the human experience, and focus on arenas where science offers limited illumination: ethics, politics, aesthetics and the liberal arts, history, metaphysics, and theology. It is also incumbent on the doubtful to concede that where science cannot offer certainty, no certainty is possible (excluding possibly logic and mathematics). We will come back to this alternative in the section synopsis.


“All science is either physics or stamp collecting.” – Ernest Rutherford, Nobel Laureate, 1908, Chemistry.



“I now regard my former belief in the superiority of science over other forms of human thought and behavior as a deception…” – Max Born, Nobel Laureate, 1954, Physics.


The last area we explore in the quest to determine whether science offers us the route to certainty is the issue of connection. Here there are two levels at issue – connectivity within branches of science and correlation with the human experience of the world.

One of the most stunning aspects of the history of science is the separate development of its branches. After Aristotle, most thinkers restricted their work to one field: for example physics, chemistry, or biology. Advances in each field occur in a silo and the tools, methods, and language are different enough that no one scientist, can pull together all the pieces. Subatomic physics, biology, and meteorology are probabilistic while higher level physics and chemistry are mechanical. Reality is revealed in pieces that do not coalesce into a single matrix. The chemist, cellular biologist, geneticist, botanist, zoologist, paleontologist, geologist, and meteorologist do not present a comprehensive picture of planetary life. It is as if each feels a complete explanation within their field is the final goal.

This fragmentary model of science leads to significant breaking points. String theory, the standard model, atomic theory, and chemistry are wonderful until we arrive at an explanation of life. The second law of thermodynamics fits cosmology well, but not biology. It is as if there is a brick wall, science cannot hurdle. Similar arguments can be made for consciousness and human behavior. It is unclear if this is merely inadequate time for a definitive correlation, a defect in the scientific establishment, or something forever impenetrable. The latter would be a powerful argument against science as the ultimate tool of certainty.

The other issue of connection in science is its correspondence with human experience. Relativity, quantum uncertainty, and multidimensional string theory are abstruse to the common person. Science focuses on the how while the human wants to know more of the why. Physics can explain the optics of the color of flowers, and botany can explain their function and structure, but no science can explain their aesthetic quality. Astronomers can explain the phases of the moon, and biologists the working of the human eye, but the experience of the wonder of a full moon is outside the realm of science. Science can tell us the origin and structure of most of the components of the sky, but not why or even how humans come to experience the concept of a cosmos. Most importantly, science offers no explanation as to why we are here and what we should do while here, the vital questions of life itself.

For science to be absolute, it must unite the fields of study within a rubric of human meaning; otherwise it comes across as insightful observations with practical uses, but not the comprehensive certainty so many seek.


Last time we looked at the imprecise pairing of chaoplexity with scientific modeling and dubious use of quantum mechanics to explain a spontaneously appearing universe. My final example of suspect mathematics in science is even more metaphysical, string theory.

In the first half of the 20th century it must have appeared that the fundamental nature of matter was finally elucidated with Niels Bohr’s model of the atom with three readily understandable subatomic particles: electrons, protons, and neutrons. Unfortunately, that hope was brief since astronomers were already finding other particles in cosmic radiation. Later research using particle accelerators led to the unsightly Standard Model of Particle physics wherein subatomic particles like the proton are made up of still smaller particles called quarks of which there are dozens with odd names like the down quark or the charmed antiquark; coming in ‘flavors’ arbitrarily called red, green, and blue; and with spin of 0, 1, or 2.3

Such a disconcertingly complex outcome led many physicists to seek a still ‘smaller’ and simpler explanation underlying this particle ‘zoo.’ At that point string theory comes on the scene. The general theory is simple enough – particles are not points, but “string-like” and can be (1) stretched like rubber bands; more energy when stretched and less when contracted, and (2) vibrate like rubber bands. With work physicists and mathematicians were able to make string theory work by joining it to supersymmetry leading to the more coherent superstring theory. Here at last was a theory that could unify physics, a theory of everything; explaining  all of the particles, the forces, and the laws of motion, and accommodating special relativity and quantum theory.4

However there are problems. First superstring theory is actually many equally coherent theories, each requiring more than the commonly accepted  four dimensions – in fact 10 in all (the remaining six being tiny curled up dimensions). String theory depends on only one constant, but requires many additional seemingly arbitrary constants to explain the standard model. The theory is contingent on supersymmetry which is not visible in the natural world. The theory itself appears to be untestable. Last is the question of how the differences between unified particles and forces is to be explained.5

Some physicists are dubious of superstring theory. Richard Fenyman dislikes the tendency to explain or discount anything inconsistent with the theory. Sheldon Glashow scoffs that it cannot be demonstrated and has not led to a single experimental prediction.6 Lee Smolin bemoans the incredible resources diverted to this theory to the exclusion of other research based on the scientific community’s rigid belief in the theory or ‘groupthink’, referencing Kuhn’s book on scientific paradigms at one point. Others believe string theory’s greatest strength is its beauty, suggesting it qualifies as aesthetics.7

None of this is intended to diminish science which for the most part is the best system for identifying “truth” known to humanity. However my goal is to remind readers that the mathematics underpinning science and some resulting theories are not certain, some not even in an empirical context. Next time we look at one more concern with science as certainty, issues of connection.


1Horgan, John, The End of Science, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1996. ISBN 0-201-62679-9, page 191.

2Ibid. Page 202.

3Hawking, Stephen, A Brief History of Time, Bantam Books, New York, 2009. ISBN: 978-0-307-29117-2, pages 86-89.

4Smolin, Lee, The Trouble with Physics, Houghton Mifflin Company, Boston, 2007. ISBN: 978-0-618-91868-3, pages 103-112.

5Ibid., page 117-123.

6Ibid., page 125.

7Horgan, John, The End of Science, Addison-Wesley Publishing Company, Inc., Reading, Massachusetts, 1996. ISBN 0-201-62679-9, page 70.


“God used beautiful mathematics in creating the world.”– Paul Dirac, Nobel Laureate in Physics, 1933.      “



In the last post I noted that mathematics developed independently of science over thousands of years until the Age of Reason when several great minds yoked them initiating a revolution in science. However, by the early 20th century, cracks began to show both in the proposition that mathematics is absolute and in the application of increasingly abstract mathematics to empirical reality. The doubts inherent in these mathematical speculations and modeling is the subject of this post.

Our first example is the area of chaos theory and complex system analysis which John Horgan labels chaoplexity.1 While basic science depends on the assumption of the uniformity of simple systems in generating scientific laws, most of reality is complex. So while we can predict the product of the mixing of two chemicals in a test tube it is unclear what this tells of about chemical reactions occurring in Earth’s primordial soup. On the face of it, chaos theory’s central tenant that highly complex systems inevitably lead to unpredictability appears to be logically inconsistent with predictive modeling.

In addition scientific models are prone to structural problems including speculative assumptions and bias in the choice of inputs. Nancy Cartwright, a philosopher of science, considers numerical models nothing more than “a work of fiction.”2 Nonetheless experts constantly forecast future events based on this method including portentous phenomena such as climate change and the course of pandemics.

A second example is quantum mechanics and uncertainty, which is inscrutable at best and irrational at worst. Still some physicists use the probabilistic nature of matter in space-time implied by this theory to argue that even if nothing at all existed before the big bang, there was an infinitesimal chance that a singularity would appear spontaneously. Since there was an infinite period in which this could occur, the appearance of the universe from naught is a reasonable explanation (everything just came from nothing!). This too seems illogical since there would have been no time and no environment in which a spontaneous event could occur.

This theory does not appear empirical at all, rather a mathematical labyrinth requiring assumptions and contortions which are of course beyond non-mathematicians. In fact, this theory seems closer to metaphysics than strict science,and lay persons are expected to accept its “truth” on faith in the knowledge of the experts, a circumstance hauntingly reminiscent of the assertion of priests in early religions.

(continued next post)


“If all the arts aspire to the condition of music, all the sciences aspire to the condition of mathematics.”– George Santayana.                `               `



Last time we looked at whether mathematics corresponds to absolute truth; today we investigate mathematics as a tool of science particularly as the substructure of scientific certainty. Nowadays we see math as so integral to science that we might think they developed in lockstep, but that is not the case. Mathematics likely started as counting possessions such as fingers, children, goats, or coins; followed by the geometry necessary for land measurement and construction. At that time, science was predominantly observational – e.g. identification of the constellations and planets and the four ancient elements of earth, water, air, and fire – or speculative as in the case of Democritus’ atomism.

Some ancient geniuses transposed common mathematics onto the mystery of nature most famously in an increasing understanding of the motion of the planets and sun (Thales predicted an eclipse in the sixth century B.C.E.) and on the harmonics of stringed instruments (Pythagoras; also the sixth century B.C.E.). But successors failed to follow up on their insights, so in fact the greatest scientist of the ancient world, Aristotle, studied zoology and botany only by observation and description; while its greatest mathematician, Archimedes, took mathematics much further, but mostly for technology rather than for the analysis of nature.

Successive cultures in Rome, Arabia, India, and even medieval Europe advanced in pure and applied mathematics, but failed to identify its utility in elucidating nature. That seems to appear suddenly in the works of Copernicus, Kepler, and particularly Galileo who rejected scholastic views of knowledge and subjected observational and experimental data to mathematical analysis in formulating theories. Arguably their insight that mathematics can explain data was their greatest contribution to science and one of the great feats of humanity. Newton, Pascal, Lavoisier, Faraday, Einstein and countless others followed, all using mathematics as the knife by which to dissect out the hidden structure of reality.

Thereafter  for centuries, mathematics and science grew in parallel without impediment until coming up against two fundamental challenges. First, mathematics itself showed defects as outlined in the last blog. Second, in the desire for solid foundations for scientific theories, mathematics was overstretched to fit some theories, and increasingly modified or invented merely to permit models of nature that transcend any experience of reality at all. It is this latter trend in the relationship of science to mathematics that is most disconcerting with respect to its certainty. Next time we will look at some important examples including (1) chaos theory and complex systems, (2) quantum mechanics, uncertainty, and the spontaneous appearance of matter, and (3) string theory.


“As far as the laws of mathematics refer to reality they are not certain; and as far as they are certain, they do not refer to reality.”– Albert Einstein.

In our investigation of science as certainty, we arrive now at the complementary discipline of mathematics. If we accept the definition of science as “a branch of knowledge or study dealing with a body of facts or truths systematically arranged and showing the operation of general laws,”1 then mathematics appears to be the first science methodically uncovered by the ancients. This seems confirmed by the Webster definition of mathematics as “the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities…”2 Alfred North Whitehead goes somewhat further in defining mathematics as “the science concerned with the logical deduction of consequences from the general premises of all reasoning,”3 though for our purposes we will use the use the stricter Webster definition.

In today’s blog we examine the certainty of mathematics while next time we will look at mathematics as a scientific tool. Grade school mathematics particularly addition and subtraction appear to be the pinnacle of unquestionable truth, but remain difficult to prove philosophically. The analytic philosophers in the early 19th century worked tirelessly at demonstrating that mathematics could be validated using only rigorous logic. However this  effort proved hopeless once Kurt Godel developed his ‘incompleteness theorem’ showing that any system that proves all true statements, also permits paradoxes that make no sense (such as “this sentence is false”), whereas any tinkering to the system to eliminate paradoxes results in some true statements no longer being demonstrable.

Meanwhile Gregor Cantor demonstrated that rules of infinity broke basic rules of mathematics, effectively proving that two unequal numbers can be equal. By mapping infinite series such as all integers, against all even numbers, he showed that while there are clearly more integers than even numbers, there are in fact an infinite number in each series. .

Other fields in mathematics also show areas of concern. Euclidean geometry looks ironclad, but  late 19th century mathematicians discovered non-Euclidean forms of geometry that were equally coherent, but gave different results (consider a triangle projected on a sphere versus a plane). Worse yet, some  scientists argue Euclidean geometry is not verifiable in the real world at all.

Chaos theory shows that unpredictable results or non-linearity occur in complex mathematical systems, thus undermining the presumption that all mathematic relations are absolute. In fact unpredictability is predictable in such systems, which appears inconsistent with our usual understanding of mathematics.

Also troublesome is meta-mathematics; which questions what numbers are (Platonic, self-existing, ideas vs. formalistic or logic-based entities) and the sublime question of whether mathematics is discovered or invented by the human mind (Einstein believed the latter). Such fundamental questions do not diminish the practical nature of mathematics, but do subvert our trust in its absolute certainty. As Morris Kline wrote in The Loss of Certainty in 1980, “It behooves us therefore to learn why, despite its uncertain foundations and despite the conflicting theories of mathematicians, mathematics has proved to be so incredibly effective.”4


1Webster’s New Universal Unabridged Dictionary, Barnes & Noble, Inc. 2003. ISBN 0-7607-4975-2, p. 1716 – definition 1.

2Webster’s New Universal Unabridged Dictionary, Barnes & Noble, Inc. 2003. ISBN 0-7607-4975-2, p. 1186 – definition 1.

3Fadiman, Clifton, Editor, The Treasury of the Encyclopaedia Britannica.Viking Penguin, New York, 1992. ISBN 0-670-83568-4, page 659.

4Ferris, Timothy, Editor, The World Treasury of Physics, Astronomy, and Mathematics. Little, Brown, and Co., Boston, 1991. Page 525.