What can be asserted without evidence can be dismissed without evidence?

Much of what we are taught in our formative years we just absorb and accept uncritically. Take, for example, how we are taught to divide one fraction into another. Consider solving 1/3 ÷ 1/9. To solve this at school, we were instructed to flip the second fraction (swap the numerator and the denominator) and multiply the two resulting fractions together. So 1/3 ÷ 1/9 becomes 1/3 x 9/1 or 1/3 x 9, which equals 9/3, or 3. However, being familiar with this procedure for solving the division of fractions doesn’t provide us with an understanding of why the answer is 3. Indeed, in the past, I have asked people if they can work out what 1/3 ÷ 1/9 is. Most just say 1/27, but some apply the aforementioned procedure of flipping the second fraction and derive the correct answer of 3. But, of course, if we understand what fractions are and understand what divide means, we can simply see that the answer is 3 without having to apply this procedure. 

Let's consider another example, the extremely widespread stance that the burden of proof rests with the one making the positive assertion. Or, to coin a statement made by Christopher Hitchens, "what can be asserted without evidence can also be dismissed without evidence". In the context of whether there’s a transcendent God, an afterlife, or even free will, many people of a materialist persuasion repeat this ad nauseam. They say that our default position ought to be that none of these things exist and that this is because the burden of proof always resides on those who make the positive assertion. I ask them why this is so. Thus far, I have never got any type of meaningful answer. I’m either met by a deafening silence, or some non-sequitur. So, we can surmise that they do not know why someone who asserts that something exists bears the burden of proof.

I imagine that it's due to the following. In our observations of the world, we note that the Universe exhibits predictable regularities. We capture such regularities by physical laws. Further, it seems that these laws have universal applicability: that is, the very same laws apply throughout the Universe. Hence, by extrapolation, we know what entities to expect and what not to expect. Thus, for example, our expectation is that stars will have planets orbiting them and not flying teapots. It is reasonable therefore to demand that if someone asserts that x exists, but x would be unexpected given our knowledge of physical laws as we currently understand them, then the burden of proof ought to be on that person who is making the assertion.

But this general rule is problematic when we are talking about the possible existence of any type of entity that one cannot measure or detect. A transcendent God or Creator, souls, and it seems even consciousness, do not have any physical properties such as mass, or charge, nor any other detectable attribute. Since physical laws can only apply to that which we can measure or detect in some manner, it appears that the aforementioned justification for the burden of proof is not applicable in these cases.

In response to this, it is often objected that anything that cannot be detected is no different to saying that it doesn't exist. And, in the case of consciousness whose existence they generally do not deny, they might stipulate that it is identical to, or is nothing more, than a physical process or processes occurring in the brain. Regardless of the merit of such assertions, it simply assumes upfront some type of materialism or physicalism. Which is question-begging since from the outset it is the very metaphysical position that rules out any transcendent creator, souls or nonphysical consciousnesses. Hence, even though there may be a lack of empirical evidence for such things, they could no longer regard their position as being the default; they would need to actually present arguments for supposing some type of materialism is correct.

It seems, therefore, that the idea that the burden of proof rests with the one making the positive assertion only applies to the material or physical realm. In other words, to objects and processes that occupy a position in space-time. In order for this positive assertion dictum to be universal, one would have to assume some type of materialism or physicalism. An assumption that rules out any Gods, souls, and arguably even free will, from the very off. 

Regardless of the topic, the general problem here that I'm trying to get at is that applying something learnt by rote, but without an underlying understanding of why it is applicable, can frequently lead people astray. It can stifle debate, which in turn acts as a barrier to understanding. People all too often uncritically soak up what they are taught without really understanding the reasons why something is held to be true. Yes, when dividing one fraction into another, applying the procedure of flipping the second fraction then multiplying the two fractions together will generate the correct answer. But this is surely of limited use if one is failing to understand why the answer is what it is.

It is more pernicious in other cases, such as for the alleged universality of the burden of proof demand. For this is fooling people into believing that in the absence of any empirical evidence, the hypothesis that there is no God or souls is the a priori more reasonable one. It may be that there is no God or souls. And it might be able to be argued that their non-existence is more likely than their existence. However, this needs to be established, which in turn requires arguments. The non-existence of God or souls can't just simply be assumed to be the default reasonable position, nor should we question-beg the whole issue by assuming some type of materialism from the outset. Doing either of those won't persuade anyone disposed to believe in a God or souls since they are highly unlikely to either agree that their non-existence should be the default position or that materialism is likely correct. Those who think the existence of any Gods or souls is unlikely due to their prior conviction to materialism are required to argue for materialism.