On Not Knowing
By Bruce Barbour - May 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.”
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
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
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
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 problem1) it is a good starting
point. That Knowledge must be true is obvious2. 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 justification3. 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"
"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
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
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
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
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
billions if not 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
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 reasons4.
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
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 zero5).
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
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
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 above6.
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.
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.
* * * * * * * *
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
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 Mr 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.
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