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On Not Knowing

By Bruce Barbour - May 2023 - Version 1.3 (October 2023)

“We need to enter the conversation willing to be wrong, willing to admit the limits of our own knowledge, willing to reconsider our evidence, sources, and premises. That is self-skepticism.”
― Patricia Roberts-Miller, Demagoguery and Democracy

"The only true wisdom is knowing you know nothing."
― attributed to Socrates

The Human Condition: We are born. And after an ever so brief time we die. And between those two points we either: (1) try to come to some conclusions, to gain knowledge, concerning what it's all about; or (2) to try not think about it at all by endless distraction.

Distraction is a choice - and I certainly indulge in it - but not endlessly. 

It is knowledge that interests me. What can be known for certain. This includes what is known to be true and what is known to be not true. And how can certainty be assured? That the "knowledge" is not mistaken. That the knowledge is true Knowledge.

There is a second class of held information that cannot be classed as true Knowledge. This is information held by a person that may be knowledge but there is a level of uncertainty in the truth of the knowledge. This information include beliefs and opinions that range from ideas that have no factual basis, to beliefs that have a good deal of evidence and/or reasoning behind them, but not sufficient to be conclusive.

Too many people unjustifiably claim to have true Knowledge on various subjects when really they are holding onto beliefs and opinions. People should be prepared to admit lack of Knowledge in an area or at least a lack of certainty, in preference to claiming certainty where certainty does not exist.

I have no issues with people having opinions and beliefs on what is true and what is not true, and expressing those opinions and beliefs, so long as they are acknowledged as just that - opinions or beliefs. In some cases a definitive claim to Knowledge may be able to be made. Later in this article I will discuss when and where this is appropriate.

There is a common definition of Knowledge as "Justified True Belief". While this has been disputed as not holding up in all situations (see Gettier problem(1)) it is a good starting point. That Knowledge must be true is obvious(2). The term "Belief" in this context simply means mental acceptance of the truth and validity of the information. In the definition it is the "Justified" term that is the most important. For Knowledge to be accepted as true it must have justification(3). This justification can be of various sorts depending on what type of information is being assessed.

Let's look at a famous case. In 1952 Bertrand Russell proposed his "teapot" analogy:

"Many orthodox people speak as though it were the business of sceptics to disprove received dogmas rather than of dogmatists to prove them. This is, of course, a mistake. If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense."

This analogy is supposed to show that the burden of proof lies on the person that is making an unfalsifiable claim. I support that assertion. However the "sceptics" are not entitled to definitively express the negative position, that the claim is not true, unless they have evidence or reasoning against the claim, as will be argued in this article. In some cases they may have valid evidence or reasoning but in some cases they don't. If they don't then all they can credibly claim is that they don't know or they can say that there is no evidence to support the claim and that their opinion is to the contrary.

Bertrand Russell also claims that the assertion that there is a god is analogous to the assertion that there is a china teapot between the Earth and Mars. I question whether this is a good analogy. It is a case of reductio ad absurdum in the extreme. To equate the concept of god (an omnipotent being capable of making the universe) to that of the concept of a orbiting china teapot (capable of making a nice cup of tea, with assistance) is absurd. However this article is not about god but about knowledge.

Also what falls out of the analogy is the seemingly common assumption, often in science and by others as well, that zero evidence equates to zero probability. This is also expressed in "Hitchens' razor", which states that "what may be asserted without evidence, may be dismissed without evidence."

To show that zero evidence does not necessarily equate to zero probability I will use a simple analogy of my own.

An astronaut, who shall remain nameless, was one of the very few men to walk on the moon (from 1969 to 1972). In his memoir he revealed that on the trip to the moon he had left his lucky coin on the moon surface. This was to ensure  safe lift off and also hoped for return to the surface in the future - which did not happen. He had carefully placed it away from the landing craft as he did not want it disturbed on lift off. Many people tried to get him to tell then whether it was heads up or heads down. He refused, saying it would be unlucky to reveal this. After his death a journalist said he had investigated this extensively and had concluded that the coin had been placed heads up. 

I hope you agree that this assertion is no sillier than Bertrand Russell's teapot analogy.

The coin can't be viewed from Earth, no-one is going to go back to the site anytime soon. There is zero evidence as to which side is up. So a person who believes that zero evidence equates to zero probability would say the journalist is wrong - there is no evidence that the coin is heads up. But clearly despite this lack of evidence simple probability tells us that there is a 50% chance of it being a head.

What if it was a lucky playing card instead of a coin. Someone claims it is a king, in fact a king of clubs. Again no evidence. Would someone on that basis be able to claim definitively that it was not a king? Clearly no. There is a one in thirteen (7.7%) chance that it is a king and a one in 52 (1.9%) chance that it is the king of clubs.

This shows that:

Zero Evidence does not always equal Zero Probability.

Note that I say "not always". Because sometimes zero evidence does mean that it most likely has zero probability. The two scenarios need to be differentiated.

If a scientific experiment is performed and the experiment did not find any evidence for the hypothesis then this is reasonable evidence of zero probability - provided the test was properly set up, is repeatable and the current state of technology was sufficient to be able confirm or deny the hypothesis. This is verified zero evidence. In this case - zero evidence does equal zero probability.

If no scientific experiment is performed - due to impossibility or other reason - and there is zero evidence then nothing is known scientifically. This is non-verified zero evidence. However, as per the analogy, non-verified zero evidence does not necessarily mean zero probability.

How then can a probability, or a possible probability, be determined? The answer to this is straight forward: reason needs to be used to best determine a possible probability.  In many cases this will be a subjective probability - a probability based on a person's individual reasoning processes. It may not be objective or definitive, except in specific cases, such as the lucky coin analogy, which will be far fewer than other situations.

A real world example: 50 and more years ago there was zero evidence that there were exoplanets, that is planets orbiting suns outside of our solar system. The technology of telescopes had not developed sufficiently to be able to discover them even if the astronomers of the time had scanned the skies with their best telescopes. What is it reasonable to conclude?

If someone of the time concluded that because there was zero evidence of exoplanets there were no exoplanets they would have been wrong. The number of confirmed exoplanets is currently (2023) over 5000. The number could end up in the hundreds of billions in our galaxy alone.

Let's once again visit Russell's Teapot. There is zero evidence for the teapot. But that does not by necessity equate to zero probability.

If a government was stupid enough it could spend many millions of dollars searching the space between Earth and Mars for china teapots. Our technology may be able to do this now while it wasn't able to in 1952 when Russell proposed the analogy. If not now then maybe in the future. If that search was thorough and found nothing teapot like this would still be zero evidence of the teapot. However this is a different form of zero evidence, zero evidence after searching or after a properly performed scientific test. This form of verified zero evidence is significant and can be used to conclude that there is no teapot without needing to consider further reasons(4). This is why it is "Zero Evidence does not always equal Zero Probability". Sometimes zero evidence does equate to zero probability, as in this case.

Hopefully the government is not going to spend millions of dollars on a teapot search. Back to the original analogy - there is zero verified evidence. The approach to the teapot problem now should be reason.

The reasoning might go: very few Earth space craft have entered the space between the Earth and Mars. Those that have have been unmanned. Space flight is very expensive. The worth of every gram of space cargo is considered. It is unlikely that a china teapot would be considered worthy of transportation. The system of launching a teapot from an unmanned space craft would also be complex, again not worth doing. From this reasoning we can conclude that the teapot is very unlikely. Its probability is zero (or close to zero(5)).

Bertrand Russell was right in inferring that there is no china teapot between the Earth and Mars in 1952. However it is not solely because there was zero evidence but because reason supports this conclusion.

If the people 50 years and more ago had of applied reason to the existence of exoplanets they would have said "Our sun has planets orbiting. And some of those planets have moons. As far we can determine there is little to indicate that our solar system is in anyway strange or unique in this respect. Given this there is a significant probability that other suns have planets orbiting them as well."

This type of reasoning does not provide an objective probability. Rather the probability is subjective - different people may come up with different probabilities based on how they see the reasoning. And they are unlikely to assign a numeric probability at all unless specifically asked and then they could guess a figure or a range that conforms to the results of their reasoning and how confident they are in their reasoning.

On some subjects two people might come to diametrically opposed conclusions. There may be no hard science to back up either view conclusively. One person may conclude that one or more of the reasons held by another person are not correct or are unimportant. And they may conclude that other reasons are more persuasive. Another person may hold contrary or opposite views, giving weight to a reason that was rejected by the other. It is the nature of human reason and opinions in some areas.

Problems may come when a person believes that his or her position is backed by science. This may be despite there not having been definitive repeatable experiments undertaken using the scientific method to prove their hypothesis.  Nor extensive repeatable observations. Regardless of this they may think the position is totally justified and is therefore true Knowledge. They may also claim true Knowledge on the basis that there is zero evidence (not scientifically tested). As I have argued in this article this is not warranted as a sole justification for true Knowledge.

The same problem occurs if a person justifies their information on religious grounds and claim it is true Knowledge. There is no scientific evidence. And the arguments from reason, such as they are, are never definitive. Many religious people justify their "knowledge" by a "leap of faith" which basically means they acknowledge the uncertainty, the less than 100% probability, and claim and believe their "knowledge" as true regardless. As humans they are entitled to believe and have whatever opinions they like or that mean something to them.

One further question to be considered is: If there is zero verified evidence and if the issue is then considered on the basis of reason and subjective probability, is a person ever justified in claiming they have Knowledge?

In the example of Russell's teapot there was zero verified evidence. However the reasoning was such that 100% certainty could be claimed in 1952. I am happy to accept this as true Knowledge - Justified True Belief. But what if the reasoning is not so clear cut, which will happen in a large number of situations.

Say a person is using reason to assess the likely subjective probability of a subject. If a person is of the opinion that the subject has a high probability of being true perhaps they can still express a view with certainty. But what is that probability?

Often statisticians define an experimental result as statistically significant at the 95% level of confidence. This level of confidence is often used in scientific experiments - e.g. drug efficacy tests - to determine whether the hypothesis is proven or not. At this level of confidence there is a one in twenty chance of being wrong.

However this is not a sufficient level of certainty to be able to claim Knowledge when there is no evidence and the claim is only based on reasoned argument. The probability assessment is based on a person's subjective assessment of the reasoning. Consequently there are higher bands of uncertainty on the probability because of this subjectivity when compared to a probability determined empirically in a scientific experiment.

For Knowledge claims based on reasoning and subjective probability the level for significance should usually be 98% and above(6). The reasoning against the orbiting extraterrestrial teapot would in my opinion reach this bar. Much will not. In which case these claims should be expressed as opinion, which can be expressed and argued for by the holder of the opinion as fervently as they want.

What about atheism? An atheist would say there is no god. It is much more definitive than the agnostic position which is that they are relatively certain (the degree of certainty varies with the agnostic) that there is no god but acknowledge that this position is not 100% certain. They say - there is no proof at present but show me proof and then I may change my position. The atheist would say that they are certain that such proof is not possible - because god doesn't exist. Atheists would base their opinion on their reasoning and also the absence of proof. As I have shown in this article the use of reasoned argument is fine but basing the opinion on absence of proof is logically suspect in certain instances(7). Atheists would state their position as 100% certain and if not 100% then certainly above the 98% threshold. So are they entitled to claim Knowledge? Perhaps when they though the use of reason get to the same level of certainty as a person might have against orbiting teapots, then perhaps they are justified. Especially if they are not alone in coming to this conclusion. And regardless I also have no issue with people claiming personal (small k) knowledge just as I have no issue with people making a similar claim for their belief in god. Whatever makes them happy, to get them through this thing called life. I just hope they both step back before slapping down people with a different view to them.

Below that 98% subjective probability and down to a, say, 70% level a person should not be claiming true Knowledge. They can however still say that it is their opinion if that is their wish, while acknowledging the uncertainty. Between 70% and 30% they are in the area of being undecided or agnostic.

* * * * * * * *


1. Gettier problem - In most of these scenarios it seems that people are mistaken in their justification for various reason. It was not correct justification. The problem seems to be fixed by saying or inferring that indeed the justification itself has to be true. Obviously. Some think "warranted" is a better term than "justified". But information can be wrongly warranted as easily as it can be wrongly justified.
2. "What is truth?" is an interesting and complex question. Some people, let's call them the "skeptics", say their is no absolute truth and Knowledge. An example of this would be the claim that we actually live in a simulation - think "The Matrix" without the red pill. Or we are all dreaming our lives. Or, as Descartes suggested as a possibility, we are being continually deceived by a demon. In which case everything which we think we know is wrong. These arguments could be used to counter anything. There are other less extreme, but often far fetched, arguments that can also be used to punch holes in any justification. Ultimately this type of argument is a dead end. If you want to progress a discussion on knowledge you have to accept that some form of Knowledge is indeed possible. Then you need to decide what that is.
Scientific experiments are often accepted as valid if they reach the 95% level of certainty. Meaning that there is still a one in twenty chance of being wrong. Is an experimental result with a 95% level of certainty "Truth"? Science calls confirmed outcomes of experiments "Theory" because they could be - and sometimes are - overturned by subsequent experiments. Therefore is scientific "Theory" the "Truth"? It is "Justified" but not always at the 100% level. If we don't accept some level of uncertainty as tolerable then the scope of accepted "Knowledge" would decrease significantly. And indeed that is the view of some people.
3. Information can be true and can be believed to be true without justification. In this instance your belief in the information may be just lucky. It does not reach the standard of Knowledge. For other so called information you may be unlucky. Luck is no way to build a reliable system of Knowledge.
4. Though someone can always claim that the only reason a teapot was not found is that search was in someway defective. In certain circumstances it can be difficult to empirically prove a non-existence.
5. Elon Musk launched a car into space a while back. It went in the direction of Mars. There is a small chance he could have also had a teapot on the front seat - I have seen no reportage to suggest that. And I can't imagine Elon Musk would keep it quiet. It would have been interesting if Bertrand Russell had used a car instead of a teapot in his analogy. The conclusion based on the analogy might have had to be different. It is also possible that in say 50 or 100 years (if our civilisation has survived) when space flight between Earth and Mars colonies maybe routine that someone could launch a teapot out of a spaceship's garbage chute. Just for laughs! However at the moment I am happy to agree with Bertrand Russell that there is no teapot between the Earth and Mars.
6. In some situations it may be able to be a lower probability bar if there are a lot of well qualified people expressing a 95% plus level of subjective probability. In this case the band of subjective probability uncertainty could well be less.
At 98% there is still a 2% probability - one in 50 chance - of being wrong. As discussed in Notes point 2 some level of uncertainty may need to be accepted for practical reasons.
7. I am sure some atheists would claim that there has been sufficient wide spread scientific study while not actually aimed at testing the god hypothesis has nevertheless failed to show any signs that there is a god behind the creation of the Universe and humanity. And this is sufficient proof for them that god does not exist. An interesting argument but certainly not 100% definitive. Some scientists have also looked at the Universe and observed that the universe is very finely tuned to be near perfect for life and the evolution of humanity, a Goldilocks Universe, and question why this is so. Even some well known people that seem to be totally atheistic when pressed may acknowledge that in the final analysis they are agnostic because absolute proof is not possible at present. For example Richard Dawkins - author of "The God Delusion" and "The Selfish Gene". It is interesting that Richard Dawkins said he was also agnostic about fairies. I would put fairies into the same class as orbiting china teapots. No scientific proof but the reasoning against the proposition is such that I would accept there are no fairies. The arguments for a god (as a class - not any specific god) are more substantive than for fairies so are in a different category that require a higher level of proof. As another example - Graham Oppy, an Australian philosophy professor and an author of a number of books on atheism and describes himself as an atheist, says there are no definitive arguments against god but justifies atheism by saying the arguments against god are better than the ones for god. These are arguments from reason and this shows that arguments from reason without any substantive proof are very rarely definitive.

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