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Absence of proof is not proof of absence
January 3rd, 2013 (November 21st, 2013)
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Absence of proof is not proof of absence
 
During 2012, I wrote several times about the notion of origin and about the fact that Buddhism leaves the question unanswered, for logical valid reasons (cf. e.g. gplus.wallez.name/g7achUU7wci). In several conversations (in relation to my posts or to others'), irrational atheists made the claim that absence of proof of the existence of God is equivalent to a proof of absence of existence of God. Finally, I mentioned a few times during 2012 that Gödel and Tarski had made clear that, within formal systems, there could be undecidable propositions (which can be logically true but without us being able to prove so). So let's go back to logic and to reality checks, for if we want to use reason in a spiritual context, it might be relevant to know how to reason correctly.
 
Logic
 
If A and B are two logical propositions, A 'proves' B, i.e. A ⇒ B, when "if A is true, then B has to be true. If A is false, then we gain no information about B."
 
A critical point is that, when A is false, A ⇒ B tells us nothing about B. This is important because this is how we can make assumptions and know what the consequences would be without necessarily making the assumptions true, i.e. this is important because this is how we can plan! For example, the relation "I jump from a plane at high altitude without parachute" ⇒ "I die" is true even without me jumping out of a plane! However, the relation "I jump from a plane at high altitude" ⇒ "I die" is false, because "I jump from a plane at high altitude" may be true without the "I die" turning into a necessary consequence (should I have the good sense of strapping a parachute on prior to jumping). I can plan… and if I favour survival, I can pay attention to strapping a parachute before jumping, regardless of how much risk there is in trying to do so.
 
An absence of proof merely leads to a lack of information regarding any consequence. So if one assumes the relation "miracles ⇒ God," then a lack of miracle does not prove the non-existence of God, but merely a lack of miracle so far.
 
 
The whole notion becomes even funnier when one considers that several propositions could independently prove a given consequence. Are there multiple independent propositions which might imply "I die"? To consider one or a few of the possible 'causes' does not prove in itself that I have exhaustively listed all possible causes: indeed, I may die even though all the listed causes were absent. Would that make the implication "I jump from a plane at high altitude without parachute" ⇒ "I die" any less valid? Not at all. Would that make my death less real? Not at all.
 
Similarly, a lack of miracle does not make the implication miracles ⇒ God invalid. Nor does it prove that no other cause could prove the existence of God.
 
 
Reality check
 
That the world has existed for a long time without a particular proof manifesting itself does not make the proof irrelevant, the relation wrong, and it does not provide any information regarding the consequence. Virtually any event–context pair occurred only once in history, so any miracle would be a unique event, like any other event. Maybe the lack of proof merely indicates a lack of observation! Missing proofs forever would not mean the proofs are inexistent, it would only mean the observer is dumb or blind.
 
Even stripping the context out of the conversation —an assumption which nothing justifies,— some events are extremely rare because of the conditions required to make them arise: until recently in the history of planet Earth, nuclear explosions were totally non-existent on the planet. Did this prove they were impossible in any way? Did this long absence prove that no specie on Earth would ever create an unsafe technology?
 
Bacterias were wholly invisible for most of human and scientific history. Does this prove they were non-existent prior to their discovery? Electromagnetic waves were wholly invisible for most of human and scientific history. Does this prove they did not exist prior to their discovery?
 
Last but not least, there is no situation in which we can safely discard the context: for example, "I jump from a plane at high altitude without parachute" ⇒ "I die" might seem quite ascertained, however what if someone else has a parachute and we can catch one another during the free fall, secure ourselves together, then open the parachute? There are of course 'regularities' which allow us to ignore the context on a frequent basis and be wrong only on rare occasions… but 'rare' does not mean impossible and "not seen until now" does not mean impossible. Conditions might change, of which we were not even aware of the criticality or importance: space-time seemed pretty docile until some considerations involved speeds close enough to the speed of light to make General Relativity relevant. The speed of light was simply not considered, let alone considered relevant to moving solid objects (and not light itself): we cannot even know which traits might be relevant to a context, prior to mis-predicting some consequence!


Does this mean God exists?
 
An absence of proof is not a proof of absence: there is no generally-accepted proof of the existence of God, but this is no proof of non-existence. So does God exist? Obviously, an absence of "proof of non-existence" is not a proof of "absence of non-existence," i.e. is not a proof of existence!
 
 
Wrap up
 
The above applies to proofs (which deal in certainties) and there are major differences between 'proofs' and 'signs' or 'indications':
• Absence of sign–indication is a sign–indication of absence.
• Absence of proof is not proof of absence.
For statistical-aware readers, 'signs' refer to P[B | A] > P[B | ¬A] which is indeed equivalent to P(¬B | ¬A) > P(¬B | A), while 'proofs' are dissymmetrical (implication is not equivalence). This is regularly mentioned in relation to the "burden of proof" (often-misnamed when it addresses more a burden of observation than a burden of reasoning).
 
Signs and indications may naïvely appear a lot more scientific —and are regularly presented as such by atheists,— however it should be well-known by most that "correlation is not causation": signs and indications poorly explain causality and they would never answer the question of the Origin easily. Moreover, rigorously establishing the inequality P[B | A] > P[B | ¬A] may be far from trivial (outside of simplistic paper models). Even picking the right conditioning is without warranty (cf. nuclear, bacterias, electromagnetic waves, speed of light… or "black swans" which were long considered to be less likely than unicorns and dragons, based on up-to-date knowledge based on 'observations' (by explorers)): the choice of the conditioning (in probabilities) is very human and has historically been fragile to the extreme.
 
What's the point of all this? Stop clinging to certainties! Most certainties are not established by rigorous reasoning (because of the arbitrariness in conditioning — a 'karmic' arbitrariness, since based on habits and mental fabrications of what we consider 'normal' at that point).
Keep looking!


#Buddhism   #buddhistcircle   #logic  
[ image from http://www.shmabstracts.com/abstract.asp?MeetingID=783&id=97764 ]