There exists a general attitude among some of those who fancy themselves educated that they will not believe in what they cannot empirically establish. Such people tend to hold science in the highest esteem as a means of understanding nature and acquiring knowledge (under the assumption that nature is the extent of reality) and use their empirical standards to discredit and even scoff at the idea of miracles and the religious. But closer analysis reveals that there is a disconnect here. Using inductive means alone, it is not possible to come to reasonably justifiable belief in laws of nature, let alone laws of nature that necessarily exclude miracles.
In his Enquiry Concerning Human Understanding, Hume draws a distinction between two general kinds of knowledge: relations of ideas and matters of fact. Relations of ideas are things such as geometry which consist entirely of concepts in the mind that can lead to some degree of certainty. Matters of fact are the kind of knowledge in question.
This kind of knowledge will never lead to the same degree of certainty as relations of ideas because there is no matter of fact that cannot necessarily be a different way. For example, it is a commonly accepted idea that the sun will rise every day. But, for some reason or another, it is perfectly possible that the sun will not rise tomorrow. There is nothing that necessitates the sun rising. We merely believe the sun will rise because of our experience of it rising.
Consider billiard balls hitting each-other on a pool table. With no prior experience of what happens when they hit each-other, there is no logical necessity of what must happen. Upon contact they could both combust, remain at rest, or turn into magical flying dragons. It is experience that tells us that they will interact the way they do when the balls hit each-other. Hume uses this analogy to demonstrate that we do not come into this world establishing our knowledge by way of reason, we simply observe causes and effects.
The reduction of everything to some sort of cause and effect is fundamental for Hume. No man deduces that billiard balls will interact a certain way, he observes it and learns from it. No man deduces that bread will nourish him, he simply eats it and observes that it benefits him without fully knowing why beforehand.
But in observation of these causes and effects, we never have a logical connection between the cause and effect. We simply observe that the causes and effects tend to go together, and are prone to assuming it will be the same way in the future. In establishing a foundation for why these causes and effects must necessarily go together, we may turn to science, but science simply gives us more insight into the causes surrounding an effect. Science can give us further insight into the causes that gave bread a nourishing effect in a certain instance, but there is nothing necessary about the causes and effects that necessitates that it will be the same in every instance.
This leads to the conclusion that our inductive knowledge is imperfect. We observe causes and effects, but we can assign no necessary link between the two. It may run contrary to our common sense, but for all we know bread could be poisonous tomorrow even though the same bread nourished us today. When we observe causes and effects, the only knowledge that we have is that in a certain instance, certain effects correlated with certain causes. Our experience leads to no necessity that the same perceived causes will lead to the same perceived effects in the future.
It then follows that inductive knowledge is very imperfect for two reasons. We can never be omniscient of all causes in every instance, and there is no necessity that the same causes will always have the same effects. Our experience simply suggests it.
We could perhaps appeal to probabilities. But, as Hume points out, this leads to circularity. Probability has shown itself to behave in a certain way in the past, therefore we are inclined to find it reliable. But just as any cause does not necessarily lead to a certain effect, probability does not necessarily guarantee certain results. We have experience that flipping a quarter 100 times will likely lead to 50 heads and 50 tails. Despite what we may find intuitive, it very well could be the case that our experiences with probabilities will no-longer apply in the future.
Furthermore, if we try to force mathematical truths upon matters of fact, we are assuming before the fact what we would like to prove which is that nature will always behave in the same way. Therefore, even probability fails at giving a definite reason to trust our experience because it is experience that has given us trust in probabilities.
Why do we then assume that the same causes will always lead to the same effects (if we could even have perfect knowledge of causes)? Hume concludes (rightly within this epistemic framework) that it is nothing more than custom. We have a natural inclination to expect that things will follow in the same way even though such an assumption has no real epistemological foundation through induction.
At this point, we are left with two options. One option is that we fall on our own inductive sword and acknowledge that our experience of certain causes in a certain instance can never lead to any kind of knowledge of a law of nature that must always hold true. We are therefore left with much uncertainty and epistemic humility as we recognize that most of our knowledge of matters of fact are based on the natural human tendency towards the idea of custom even though such an idea is not founded in any kind of certain epistemic way. Or we must introduce some sort of thing which allows us to believe that there are indeed reasons to believe that causes will always have the same effect. What that thing is is an entirely different subject, but we must acknowledge that our experience is insufficient to do so.
If we wish to maintain that we will believe nothing more than what our experience tells us, then we must acknowledge that we cannot come to know inviolable, necessarily true laws of nature. Our own narrow, imperfect experience of perceived causes leaves us with uncertainty solely in the fact that there could be innumerable causes of which we have no empirical knowledge that actually lead to the effects we perceive and attribute to other causes. Furthermore, we have no reason to believe that the causes we do perceive will always lead to the same effects.
Therefore somebody who founds their entire body of knowledge upon experience has absolutely no epistemic ground from which they may fundamentally discredit miracles or other effects which they have not experienced. A reported miracle or strange phenomenon could be the result of causes of which a person has no knowledge and therefore has no reason to discount. Such was the case when peasants in the fields of Europe reported rocks falling from the sky and were the object of derision for believing in such a thing by the scientific elite. We now know, however, that there are indeed perceived causes for what we call meteorites, and it is now those who scoffed at such an idea who are the object of derision.
But we could just as easily assume a scenario in which meteorites simply started falling from the sky because causes which had previously never yielded such an effect suddenly for no known reason produced an entirely different effect. Such a possibility cannot be excluded solely on experience.
This applies to miracles in that someone reporting a violation of the previously assumed laws of nature cannot be discounted because there is no reason to necessarily believe that our experience of certain causes yielding certain effects disqualifies the same causes yielding entirely different effects. The only grounds by which such a scenario could be certainly discounted is a flimsy reliance on custom.
The possibility of miracles is further opened up by the fact that the reported strange effects which go against prior experience of certain causes could be the result of causes which a person relying solely on induction has no reason to exclude. There is nothing in our experience of dead people remaining dead that necessarily excludes the possibility that there is a God who was the cause of a dead person coming back to life.
To necessarily exclude such a probability based solely on a purely inductive epistemology is wildly inconsistent with the consequences of that same epistemic view.
Therefore, the delusions of grandeur amongst those who wish to presume that their experience of certain phenomena necessarily exclude the possibility of other events is exactly that, a delusion. If a person is to base the entirety of their beliefs on experience of certain causes and effects, they must acknowledge the full limitations and frailty of such an epistemology that can never consistently lead to knowledge of certain laws of nature by which certain things must happen and certain other things are necessarily impossible. Inductive epistemology is limited by the unfathomably modest experience that one truly has with certain causes and the reality that there is no necessity that those causes will always yield the same effects.
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