Doubt and Certainty

Philosophical Reflections VII

The world is objectively real, so we can learn about it by using reason to integrate sensory input, memory and experiment. I have examined and refuted a number of attacks on the inherent validity of reason and science. In addition, in passing I have touched upon certain fundamental questions about the limits of human knowledge. We now return for a more detailed analysis of these.


The two Absolutes form the bedrock of our beliefs. Each of us knows beyond any possibility of doubt that our consciousness exists, and that some kind of reality external to our consciousness exists. All the rest of our knowledge consists of our understanding of the nature of these two existents. As the reality we perceive is hard, it is possible to test our ideas against it, and thus to learn.

However, it is impossible for such derived knowledge to be absolutely sure: some element of doubt always remains. For example, the world we know might dissolve tomorrow, and be revealed as a complex illusion (and so on, ad infinitum).

This most fundamental of doubts is not based on any evidence, however: it is simply an inescapable logical consequence of the fact that external reality is external. The very reasons by which we know there is an external reality – we didn’t create it, don’t control it, and know it only by means of how it impinges on us – mean our understanding of its nature can never be an Absolute.

The same goes for all the tools of our consciousness, both fundamental (reason, senses, memory and physical action) and incidental (intuition and feelings): all are beyond absolute validation. For example, reason is the primary tool of our conscious mind, but is not designed by it (although by the use of reason we can work out explicit rules of valid & invalid reasoning). It is a “given” of consciousness, its basis rooted in external reality: therefore its reliability cannot be an Absolute. However, note that everyone must use the fundamental tools and thus assume their basic validity, even in the act of disputing them!

Doubt such as this, inherently beyond disproof but with no basis in evidence, I call “empty doubt”.

Empty Doubt and Real Doubt

Empty doubt is essentially meaningless. By definition, there is no evidence for it. By its nature, we can’t do a thing about it. Yet it is brandished by those who would destroy the human mind as if it were some sort of invincible weapon. “How can you know that our view of reality is true?”, they ask. I ask: “How can you know that our view of reality is not true?” In the realm of logical certainty and logical doubt, these two questions are equal.

Yet, we do know that some sort of reality exists; we do know that it can get exceedingly unpleasant, if not fatal: it is, therefore, impossible for us simply to wallow mindlessly in the limbo of two equal and opposite empty doubts. By their nature, empty doubts are undecidable: therefore they are not tools of cognition, and have no value to a conscious mind in its necessary (Prime Principle) pursuit of knowledge. We must attempt to decide between propositions. We are thus forced into the realm of “real doubt”.

“Real doubt” is doubt based on actual evidence. Since empty doubt is in principle undecidable, the only response open to a rational mind is to base its decisions and actions on its evaluation of real doubt: its evaluation of evidence. By this measure, there is no doubt that the external world is objectively real, and crushing doubt that it is illusory. By this means, we can learn about the world.

The hypocrisy of those who trumpet empty doubt has been noted before. Now we see why they are necessarily hypocritical: as conscious life, in reality they can survive only by operating in the realm of real doubt, whatever else they wish were true.

Empty Claims

An empty or “arbitrary” claim is a positive claim made without any appeal to evidence. The converse of empty doubt, it has the same logical status.

Clearly, empty claims are as meaningless as empty doubts. An equally “possible” contradictory claim or doubt can be made, forcing us into the realm of evidence. A simple example illustrates this. Someone may say: “I believe in God. I can’t prove it, but you can’t disprove it either! So your atheism is no more valid than my faith.” Such a claim is easily deflated by a simple claim contrary to its central tenet: “I agree, God exists. But actually, He hates irrationality and will send all believers to hell, saving only those who live by reason. Prove me wrong!” This issue, like all others, must be decided on the basis of evidence.

A new hypothesis also may be unsupported, but there is a vital difference between it and an empty claim. The former seeks to explain something and predicts testable consequences; the proposer accepts the onus of proof. The latter might seek to “explain” something, but is not proposed in order to be tested and thus expand knowledge, but purely to cling to an irrational (unprovable) belief in the face of contrary evidence. Even a valid hypothesis, however, can also be an empty claim if it is misused, e.g., proclaimed to be true or used as the basis for ethical or other prescriptions.

The Onus of Proof

As empty claims are cognitively meaningless, the only subjects open to discussion are those where there is real evidence. In that case, the task facing any rational mind is to determine the best explanation of the evidence. There is no other basis for a decision. Therefore, the question of the onus of proof does not arise: the onus of proof is always on the evidence. But if the evidence is inconclusive, which explanation should you decide on (assuming you must make a decision)?

The only way we can learn about reality is by the way it impinges on us. Something that does not exist cannot affect us, so an absence of evidence is already a prima facie case for denial. Therefore, the onus of proof lies on the side which proposes the existence of something, not on the side which denies it. To earn the right to be taken seriously, the proposer must indicate how the thing will impinge on us: thus allowing the idea to be tested, bringing it into the realm of evidence. This is also why the simplest hypothesis is to be preferred, other evidence being equal (“Occam’s Razor”).

The Best Explanation

A valid theory of knowledge must be based on reality. External reality is hard: it impinges on us consistently in ways determined by its nature, therefore by using reason we can discover that nature. Human reality is that we are conscious, rational beings who have no instinctive knowledge of facts. By our nature, we can learn only extrinsically: from our senses, from the way reality impinges on us.

Therefore the only way a human being can gain knowledge about reality, and have any confidence in it, is by using his or her reason to determine the best explanation of all the facts available. As reality cannot be self-contradictory (A is A), true knowledge can’t be either: thus a rational mind must strive for an integration of all its knowledge without internal contradictions. But can reaching the best explanation allow us to reach the truth?

The Truth

Our knowledge of reality has two overlapping parts: our knowledge of facts and our understanding of why they are so. The former is the observed nature of things that exist. The latter consists of theories and statements of natural laws.

Our knowledge of the facts of reality may be incomplete, but what we know, we know (to “know” requires due diligence in research and adherence to the laws of logic and evidence.) There may be further details to discover, but as reality itself is hard and cannot be self-contradictory, further probing of reality cannot invalidate earlier knowledge. Thus if we discover an inconsistency, we know we have come across some previously unknown factor.

We cannot know every single fact of reality: only something the size of the universe can hold all the information in the universe! Our power to understand the universe consists of our ability firstly to abstract the concretes of reality into concepts, and secondly to use logic to arrive at testable theories about it. The first allows us to think about innumerable concretes as a single unit, and the second allows us to discover the laws and principles which explain the facts of reality. The latter enables extreme compression of information: to describe the exact atomic structure of a single grain of sand would require a vast library; to describe the laws which govern the structure of all grains of sand requires a pamphlet.

Our understanding of natural laws is more prone to error than the simple collection of facts and their abstraction into concepts: as our theories explain rather than describe, they can’t be verified as directly by reference to primary perceptions. However, the accumulation of successful precise predictions, and the building of further successful theories and technologies on their foundations, eventually proves them: in that no real doubt remains. Then one might still have grounds to seek to improve them, or find limits to them: but not to doubt their basic truth.

The ABO blood groups are a good illustration. Their existence and the resulting rules of blood mixing were established. Inconsistencies (clotting between supposedly compatible groups) showed up further blood factors such as Rh, thus extending the earlier knowledge without invalidating it. Further research then explained the blood groups by reference to surface molecules and the workings of the immune system. Much still remains to be learnt about the immune system, but the wealth of consistent data and successful applications proves the basic theory beyond all real doubt.

More Truth

Knowledge builds on knowledge. Almost a truism, this is the cause of the exponential growth in scientific knowledge. New theories suggest new avenues for investigation. The arduous life’s work of one person becomes the starting point for another. New knowledge leads to new technology, which itself increases the rate at which further new knowledge can be gained, and so on in an ever-increasing spiral.

The result is the virtual disappearance of many former scourges of mankind; a massive increase in human productivity; everyday technologies and luxuries beyond the imagination of previous generations; the ability to fly around the world and to reach the planets. There can be no real doubt that knowledge builds on knowledge. But for this process to work, the knowledge being built upon must be fundamentally valid. The process works, with spectacular success. Therefore the knowledge is valid. It is true.

There are many pathetic things about modern philosophy, but one of the most pathetic is the moaning that we can’t be sure of anything. We can be sure of what we know, with only empty doubt remaining: and empty doubt is cognitively meaningless. When a theory precisely accounts for a wide range of things and contradicts nothing known, then either it is basically true or it is an amazing coincidence. By definition, the latter is very unlikely. When we can make computers on a chip; when we can genetically engineer microbes as we like; when we can make tons of metal fly us through the sky at our command: we don’t think, “Wow, what a bit of luck!” We know: “Such is the power of our minds to know reality and by knowing it, to turn it to our use.”

Paradigm Shifts

(Part 2 of original publication)

A paradigm is a basic model of an aspect of reality. The philosopher Thomas Kuhn proposed that knowledge evolves by new paradigms replacing old ones, as evidence accumulates which makes the old ones unsustainable. How does this relate to the “truth” of theories proposed in the previous section?

Firstly, as with much philosophy, the theory of paradigm shifts is partly correct, but is not the rule. Most science proceeds by happy accumulation. Theories are modified but not invalidated at the root.

Secondly, a paradigm, though generally accepted as the best working hypothesis and most fruitful line of inquiry, is not necessarily regarded as “the truth”. A theory may be the best explanation of the available facts, but if there are too few facts, or too little precision, or other possible explanations, then its truth remains uncertain. So a “shift” would not invalidate “truth”.

Thirdly, new paradigms cannot keep coming forever. Eventually we reach the right one. A new paradigm, by definition, must be a better description of reality than the old one: as reality stays where it is, we thus get closer and closer to the truth. The phenomenon of paradigm shifts is a result of testing theories against a hard reality. A paradigm can only shift if it is wrong (not fully consistent with reality): and if it is wrong, it will shift, as reality eventually will prove inconsistent with it. A paradigm which is fundamentally right cannot be shifted, only refined, as reality cannot fundamentally contradict it. Proponents of paradigm shifts must agree that at least one paradigm is indeed true: the paradigm of paradigm shifts!

Finally, it is instructive to examine two famous paradigm shifts: Einstein’s relativity versus Newton’s laws, and the discovery of continental drift.

Newton vs Einstein

Newton developed laws of motion and gravitation which dominated physics for 200 years because of their explanatory and predictive power. Then slight discrepancies were discovered, which Einstein’s theory of relativity explained perfectly. The end result was a paradigm shift from Newton’s force of gravity in a flat, infinite universe to Einstein’s curved space-time.

However, Newtonian physics remains a close approximation of the truth. Space is not flat, and gravity affects time: ideas inconceivable to Newton. Yet Newton’s equations are so accurate in the absence of very strong gravity that they are still used: apples still fall, and the moon still orbits, by the equations of universal gravitation. Einsteinian physics is a deeper theory, with greater predictive power, from which Newton’s laws are seen to be simplified approximations.

This is an example of an important type of paradigm shift: the new paradigm explains more things, and from it the old one can be derived as either a consequence, a special case, or an approximation. Such new truths do not invalidate old truths, but subsume them.

This case also illustrates the importance of precision. Discrepancies can be hidden in imprecise measurements: as technology improves and precision increases, the room for error shrinks and our confidence in our theories rises greatly. Pre-Newtonian celestial mechanics was quite inaccurate, but so were the measurements; Newtonian physics was close to the truth, but increasingly precise data showed up its limitations; now the confirmation of Einsteinian physics is very precise indeed.

Continental Drift

The continents used to be considered static, maybe rising and falling but certainly staying where they belong. Early this century, certain evidence led to the proposal that the continents move. In the absence of a credible mechanism, geologists rejected this theory.

Then evidence accumulated that the continents do move, carried on moving crustal plates. This evidence became overwhelming, and there is now no real doubt that continental drift is true. Of course, many details remain to be worked out.

This is an interesting case, as geologists were right to demand the onus of proof from the proponents of such a strange theory (they were wrong, however, to fail to integrate the evidence for it that did exist). However, there was no compelling evidence for the static earth either: this was just “common sense”. Thus the prevailing paradigm, though the “best explanation” of the available evidence, never qualified by the rules of evidence as “true”. What was true one day was not false the next: it was never true.

Three Modern Paradigms

The above is not merely knowledge after the fact. The status of a paradigm does not await hindsight, but is readily determined from the status of the evidence, at any time. To prove the point (and stick my neck out!), here is how I would judge three modern paradigms, based on my knowledge of the evidence.

  1. Quantum Mechanics: the extent and precision of confirmed predictions proves the basic theory (though “cutting edge” hypotheses are still up in the air, and the loonier interpretations are demonstrably false). Ultimately it will be derivable, as exact or approximate, from a deeper theory.
  2. Big Bang Theory of the origin of the universe: the best explanation of available facts, but not enough facts to prove it. May be confirmed and refined, or may suffer a complete paradigm shift.
  3. Evolution of living things: the fact of evolution and the important mechanisms of mutation and natural selection are true, but further as yet unknown mechanisms cannot be ruled out.

Paradigm Shifts and Reality

It is notable that paradigm shifts are only possible in an objective universe. No version of subjectivism, of the subjugation of reality to individual or collective whim, can account for such advances in knowledge.

What causes a paradigm shift? A generally accepted theory, usually with emotionally committed adherents, is forced to change by the pressure of new evidence. Whence such evidence? The facts of reality are inconsistent with the theory. In the memorable words of T.H. Huxley, it is:

“The great tragedy of science – the slaying of a beautiful theory by an ugly fact.”

This is only possible if reality is unaffected by our beliefs, no matter how strong: reality can only be inconsistent with our cherished theories if it is independent of our consciousness. This is especially telling in the two cases analysed above, where the new paradigm is, by the “common sense” of collective humanity, bizarre nonsense.

Far from weakening the case that the universe is objective and therefore knowable, paradigm shifts prove it.

The Epistemology of Doubt

Empty doubt cannot influence our conclusions, but it does remain in the background as a reminder that we are not omniscient. The only valid conclusion from it is that one must always keep an open mind. An open mind is not one which believes nothing and exists in grey agnosticism, or which whines that it can’t be sure: that is a mindless mind. An open mind is one which is always open to fresh evidence.

This is an inescapable consequence of the contextual nature of knowledge: if knowledge is the consistent integration of all known facts, then any new fact must be integrated with it. If a new fact is inconsistent with past knowledge, then this inconsistency must be handled: either the “fact” is wrong, or the previous explanation of the facts must be modified to incorporate it. It is as irrational to refuse to integrate new knowledge as it is to reject the integration of past knowledge.

The Three Laws of Doubt

From this discussion we can distil three laws of doubt for a rational mind (with apologies and change in order to Newton’s laws of motion):

  1. First law: For every empty doubt, there is an equal and opposite empty doubt. These cancel each other out, forcing us to base our arguments and beliefs on an evaluation of evidence.
  2. Second law: A rational mind will continue in a belief until acted on by external reality. Rationality requires that you come to the best explanation of the facts available to you. Having done so, only new evidence can justifiably change your mind, and such new evidence must be integrated with the sum of your previous knowledge and opinions. This is a rational, open mind.
  3. Third law: The change in belief is proportional to the strength of new evidence, and inversely proportional to the strength of previously integrated evidence. That is, one may modify not at all, modify somewhat, or totally reject one’s theories, depending on how the new evidence fits in with the old. The reasons are the same as for the Second Law. The mental equivalent of friction in this case is an irrational resistance to change: the desire to cling to a belief rather than to know reality. Sadly this is all too common!

The Ethics of Doubt

People, both individually and collectively, are not omniscient, and are capable of error in fact and logic. The implication for ethics is that the initiation of force between rational beings, to coerce thought or action in accordance with any belief, is morally evil. Each of us must act according to our understanding of reality, our values, and our judgements. To force another to act according to your judgements rather than his (where his actions are not demonstrably dangerous to others, i.e., themselves involving physical force), or to harm another simply because he won’t accept your beliefs, is the most fundamental of crimes. By what right can a finite being force another against his judgement? You might be wrong. (Even if you did know everything, you would still have no such right, but that is another issue. To do it when there is real doubt, as with religion and politics, is unspeakable). If you cannot prove to a man’s mind that he is wrong, then the rational and moral response is to let him be. Reality is the arbiter of truth and falsehood: it is against reality that our ideas succeed or fail, that we prosper or die.

Curiously, it is the very people who most preach doubt and uncertainty – mystics and subjectivists of all kinds – who most favour the use of force as the tool of ideology. Their ideology, the only one free from doubt! These preach statism in all its forms, proclaiming the right of governments to control individuals’ actions and to seize their property according to the demands of the ruling ideology. This apparent contradiction is actually perfectly consistent with their philosophy: when you start from the premise that reality is what you want or what you vote, and not what it is, then the enslavement of men is your friend, and the rational judgement of free minds is your enemy. So then no matter what ideals you may start with, it is force and violence you will end with.

Thus we see the inevitable ethical consequence of evading reality: of bad metaphysics and bad epistemology. Human beings must live by reason and by understanding reality. If they refuse to do so themselves, then ultimately their only recourse is to enslave the men and women who do.

© 1993, 1996 Robin Craig: first published (in two parts) in TableAus.