Absolutely certain knowledge cannot be shown to exist



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Both the antique Greeks and philosophers during the Enlightenment divided arguments (reasoning) into two types: Probability arguments and demonstrative arguments.



Probability arguments

Probability arguments may also be called reasoning about matter of fact, arguments from observations, inductive arguments, causual reasoning and inference of not observed objects from observed (including induction), are based on what we can observe.

The name comes from that they do not represent "truths", they are only indicating probabilities of "truth".

The contrary to every probability argument is logically possible, even if it is not in accordance with our observations:

  The proposition "A stone floats on water" not possible to demonstrate as false using logic only, its incorrectness must be demonstrated aided by observations.

Probable arguments may appear to be certain

When we have dropped a heavy stone and seen it fall, as anything heavy on the earth has done through all our life, we believe that everything we experience as heavy will fall when we drop it. Everybody have noted this. The probability for the heavy stone to fall is hence extremely high, and it is in everyday speech possible to say that it is certain that it will fall when we drop it.

But within philosophy it is noted that it is not possible to prove with logic that it will fall, and hence this is called a probability argument.

Of course, it also exist probability arguments that are less certain then the above mentioned.

A probability argument about our world is not demonstratively certain

A common feature of all probability arguments is that they are not based on logical premises, but are based on observations. They are hence not logically established, but are within philosophy regarded as only probable, regardless of how probable they are.

All information about our world are based on probability arguments

All that we know about our world and all our experience has reached us through our senses, either directly or indirectly through accounts of somebody else's observations and experiences. Sence experiences and conclusions from these represent probability arguments.


  Probability is the very guide of life

Joseph Butler in the Introduction of Analogy of Religion (1736)



Deductive and demonstrative arguments

A deductive argument is shaped as a logical reasoning. This type of argument may also be called demonstrative argument or demonstration (when the premises are "absolutely true", see below), rational argument, logic operation or relations of ideas. Deductions were analyzed in detail by Aristotle and his basic example was the syllogism:


If F is larger than E and E is larger than D, then F is larger than D

The two first parts of the argument are called premises and the last part is the conclusion. The opposite of the conclusion in every deductive argument is logically impossible:


The opposite of the conclusion in "If a woman always got darker voice than a man, and Eve is a woman and Carl is a man, then Eve got darker voice than Carl" is logically impossible.

In this case, one of the premises in the logical argument was not in accordance with what we use to observe, but that does not matter for the logical structure.

A demonstration is a deduction where the premises represent "absolute truth". The term "demonstrative" is not denoting a practical demonstration, but is used for something that can be demonstrated using logic only.

Demonstrative arguments are e.g. abstract logic operations like equality and inequality and mathematical relations. The demand of the premises to be "absolutely true", and not to consist of probability arguments (see above), results in that no demonstrative argument concerning our world can exist.

Examples of demonstrations: Syllogisms (If F is larger than..., see above) or tautologies like "A is equal to A" or "If 12 is defined as when 1 is added to 11, then 12 is more than 11".

In a deduction (that is not a demonstration) the letters or numbers mentioned in the previous paragraph denote objects or phenomena that are basically founded on observations of our perceived world.



Nothing in our perceived reality is demonstratively certain

As both probability arguments and demonstrative arguments are ultimately based on observations, a conclusion is that we never can reach a demonstratively certain understanding of anything in our perceived reality.

This has been known for long and is clearly expressed e.g. by Nicolaus of Autrecourt
(about 1300 - about 1350) and David Hume (1711 - 1776).

A demonstrative argument about our world is not demonstratively certain

Within philosophy, what is demonstrative certain (absolutely certain, eternally true) is separated from what is only probable.

As our ideas ultimately are based on our observations, and therefore basically are founded on probability arguments, relations between ideas (demonstrative arguments) can never become more trustworthy than the observations that provide their basis. This may also be expressed like that a demonstrative argument never can provide more information about the world than is given by its premises, and the premises are always derived, although sometimes indirectly, from probability arguments.

This must be regarded as commonly known, but is still something that many philosophers with rational inclination easily forget.



Conclusion: "Absolutely certain knowledge"
cannot be shown to exist

The discussion above shows that no proposition about our perceived world can be said to be "demonstratively demonstrated", "eternally true", "logically demonstrated" or known with "absolutely certain knowledge" or just with "knowledge"

In everyday language we express matters as being certain. We believe that the world we observe really exists. We can, and have to, trust many of them, because they are the basis of our survival.

As "absolutely certain knowledge" concerning our perceived reality cannot be said to exist, they cannot be reached by any method, neither by induction, deduction, mathematical models nor by any other method whatsoever.

This is also the case for terms related to "absolutely certain knowledge" like "know", "fact", "true" and "truth". In everyday speech we use such terms when we express "extremely high probability", but if a pretentious philosopher should use them without proper definitions, this sounds the alarm for bad philosophy.



A reasonable suggestion

David Hume is sometimes considered, and then according to me erroneously, to be a hardcore skeptic. He suggested that we should divide arguments into three classes, where one class considers information about reality when we repeatedly have observed information to be consistent. At page 56 in his Enquiry he writes:


Mr. Locke divides all arguments into demonstrative and probable.

In this view, we must say, that it is only probable all men must die,
or that the sun will rise tomorrow.

But to conform our language more to common use, we ought
to divide arguments into demonstrations, proofs, and probabilities.
By proofs meaning such arguments from experience
as leave no room for doubt or opposition.

This suggestion leads to interesting questions concerning methods, where the answers are likely to be divided into two views: Dogmatic views - that a jury decides what should be considered as proofs, and dynamic views - that the background to a proposition should carefully be accounted for and be possible to criticize (scientific method).

The suggestion appears to be ignored by philosophers within epistemology.


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