In a scientific context, the word proof is used to indicate a demonstration of the veracity of an affirmation. It is important to highlight the difference between proof and evidence, which is my intention in the present article.
On one side evidence is the name for the observation of facts that support explanations that have been given or that match forecasts that have been made according to a certain model. The apparition of new evidence could reinforce an idea or give room for a reformulation of such, honoring the systematic doubt that characterizes critical and skeptical thinking. On the other hand, a proof (or demonstration) has a more permanent character (at least apparently) meaning than when something is proved it is considered to be "true", an adjective that we must be really careful to use in the scientific and skeptic world.
Then how is it understood that in a scientific context in which one is always willing to verify the validity of observations, there would be something of permanent character? Could that be considered science? Of course it can, one just has to understand in which areas one is working, and under which conditions for this apparent inconsistency vanishes.
When a scientist refers to something as a demonstration, instead of speaking of evidence, it is because he is working in an axiomatic context; so, what is that? Easy, it is a context in which people have agreed that certain premises are satisfied, and we work using the laws of logic. It is of course more than clear that whatever is proven there is only valid when the used premises are satisfied.
In such a context it can be demonstrated that the sum of the inner angles of a triangle is 180 sexagesimal degrees or that a certain phenomenon conditioned to fitting into some given restrictions behaves in an asymptotically stable way, for example. Such demonstrations are valid only if we assume that the axioms in which they are based are in fact satisfied, in the example above they would be the axioms of Euclidean geometry or the ones relative to proposed model for the phenomenon being studied. In such a context definitions and theorems are proposed and the knowledge is built. Knowledge that will be useful as long as the axioms are satisfied, or in some cases it will provide a good approximation if axioms are partially met.
I feel that the idea of a demonstration is not well understood, mostly as used in everyday speech; for instance, skeptics and atheist are constantly required by
theist to provide a demonstration of the non-existence of god in order for them to consider agreeing with us on the matter. this is in many cases the argument that is drawn after having shown the clear arbitrary nature of supernatural belief of this kind, or any actually.
I address this subject because I believe that the most frequent explanations on the matter have not engaged properly the nature of the request we are constantly asked to meet. The arbitrariness of the belief has been more than well displayed by the idea of the orbital tea pot, or simply the explanation that the lack of falsifiability of an affirmation turns it useless. It has been put more than clearly that a demonstration of non-existence makes no sense in this case (or in any alike), what I believe has been left behind is to explain that the actual idea of demonstration makes no sense, and than in order for it to make sense we need to set some axioms.
Something can only be proven when we have axioms that condition such demonstration, otherwise it would be no more than an expression of stubbornness. So, which would be the adequate axioms to analyze the existence of god, and in that way, once and for all meet our interlocutor's ancient claim? Let's leave them to propose them, meaning, let us ask them; what properties does your god have? Such properties can be analyzed in order to see if we achieve a conclusion on its existence. We could end up analyzing the case of some classical properties such as almightiness and infinite compassion, for example.
Reasoning would probably go like this: If it exists then it has these properties, let's see if that let's us come to some conclusion. For example with the premises above mentioned it is absurd that tragedies and catastrophes take place. Then we would conclude that a being with such properties can't exist, because it would be absurd that it did so. It is important to clarify here that the only method than can give us a demonstration of non-existence y reducing something to absurdity, on the other hand if we were trying to prove that something does exist it would be enough to show an example. Of course this example shown is way to simple, but my objective is to get my point across by simplifying the explanation.
Generally one of two things comes up in these cases, one would be the popping up of the phrase "Aha.. but god has mysterious ways", which simply has nothing to do with the reasoning made, properties defined are inconsistent with the observations
made (assuming that one of the axioms is that what we both observe is real). The second most common situation is really the one I am more interested in addressing, and it is the use of the idea that one is analyzing from a logical system's point of view something that is outside of its scope.
This last idea is in itself a logical fallacy, it makes no sense, first the idea of a proof only applies to a logical analysis, and also if it weren't through logic with what strategies could we work?, and what would be the validation of such strategies?
Yes, I know my skeptical friend it is exhausting to go back on these things; it's just like verifying one more perpetual motion machine, to see if the second law of thermodynamics holds. It's just that when the need for a demonstration is drawn to attention by someone it would be important for people to know what they are asking for and I believe that we have to explain what a demonstration is to whoever is asking for one.
The very idea of a demonstration makes no sense what-so-ever in a context that is not axiomatic as the case of reality, in other words, in real life we shift axioms according to observations a demonstration would die along when the axioms were left behind (still meanwhile they are really useful). There it only makes sense to analyze the evidence running away from arbitrariness.
One simple example of the fall into arbitrariness is simply the claim made by theist that they feel there is a god when they pray. A not arbitrary attitude on the subject would claim that something happens when they pray, that makes them feel in a certain way, in other words, it's logical to suspect that something is happening, and if we would like to put down the existence of a superior being that is communicating with them as one of the possible explanations, let's go ahead and do it! But let us not give preference to this possibility before other possible explanation, that would be intellectually dishonest and arbitrary, unless there is evidence that supports such idea strongly than the others. If that is not the case the intellectually honest hypothesis is simply equiprobability of the causes, not to mention the opening to other possible causes that haven't been considered, in every day speech a plain "I don't know"
Another classical example would be the existence of an universe and the explanation of its origins, that could (in the most possible open minded sense of the word) perhaps be due to the existence of a creator, just like it could be due to other things whether they are understood or not. The honest attitude is in all cases is running away from the argument from ignorance (argumentum ad ignorantiam, pero ac queda mal decir en latn en serio) and a plain "I don't know", unless there is evidence that pushes in someway (which there is, but doesn't actually push in THAT way).
Summarizing, if we go into demonstrations we must agree on some axioms, and we submit to logic, which isn't probably the most adequate strategy in this case. The alternative is the objective analysis of evidence running away from arbitrariness. In this context nothing can be considered true (contrary to what happens in the axiomatic context), and the suspicion that a candidate to be a cause is responsible for the phenomenon observed has to at least come out of an observation that is, as a minimal requirement, coherent with a preference of this before other possible causes.
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