This rule-of-thumb concords with more precise, modern analytical methods including Bayesian theory, in which every additional assumption needed to support a hypothesis reduces the probability of the issue. For instance, two marginally probable circumstances together are significantly less probable than either one on its own. This is why Conspiracy Theories become less and less reasonable for every element that must be added to get it to hold together.
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And as with all forms of Abductive Reasoning, the Law of Parsimony is not an infallible arbiter of Truth, but is more like a reverse-truth-detector that beeps more insistently the further from truth one strays. It is useful as a kind of triage for selecting which hypotheses may be more productively tested, whether through falsification or verification.
The situation is different today, and the open questions that once admitted supernatural agency as a possible explanation are now quite settled without any appeal to the supernatural and requiring no agency or intelligence whatsoever. Since then, new questions have been both asked and answered, again without need of any intervention by magic invisible wizards. The evidence points rather to no such intervention ever having occurred.
Yet on the other hand we might not forgive him this failure to apply his own fundamental rule of rationality. One may defend William of Ockham by pointing out that he was at least a monotheist, and thus walked his talk by not multiplying entities without necessity - just one invisible wizard accounted for all that could be seen. But was that really true? Was it though? Was he indeed a monotheist? And is one magic man really sufficient to account for the world he observed?
While christianity insists on the label "monotheistic," it does not walk the talk. To explain the entirety of observed reality, they have posited not just one but an entire pantheon of magical beings. To begin with, their wholly "good" god has to have a counterpart, Satan, to account for the existence of "evil" (the existence of which is more assumed than detected as substantive). This "enemy" actually cooperates with their main god to obediently torture all the souls who are not sufficiently in god's camp. Then, evidently lacking both the omnipotence and the goodness to forgive, their omnipotent and infinitely good god needs another god to act as an intercessory for us naughty imperfect creations that an infinitely wise and good god allegedly created to be like this. And even that being insufficient for ordinary daily needs, William of Ockham as a member of his church in good standing officially supported a long list of saints, angels, demons, spirits, and other beings (seraphim, cherubim, etc), all of which are indistinguishable from the kinds of entities that the acknowledged polytheistic pagan religions had in multiplicity.
This confused incoherent tangle of theology is a direct and demonstrable consequence of the syncretic origins of christianity - cobbled together from random bits of numerous previous religions, from zoroastrianism, caananite religions, egyptian cults, and the long lists of greek, roman, nordic, and vedic gods. Religion has evolved in a clearly Darwinian struggle for survival. Religious ideas have over the centuries accumulated through random permutations certain "sticky" adaptations that make them harder to get rid of and thus more likely to produce offshoots of ever-widening variety.
The divergence and proliferation of religions tells us two important things about it. 1) There is no underlying reality or truth towards which religion is converging, as can be observed in other pursuits such as the natural sciences. 2) Religion possesses no means of adjudicating its assertions. Whenever any two theologians disagree, they split and two new religions are born.
Occam's Razor properly applied is a useful way of avoiding such fruitless pursuits. In the first place, modern science does not have any need to appeal to magical agency for explanations for things, rendering any such appeal unnecessary and hence immediately excluded by Occam's Razor, which I remind us states that "Entities are not to be multiplied without necessity."
Secondly, we can see in countless instances that an invocation of even one magical agency is never enough, and leads to a never-ending cascade (or multiplication) of further invocations and assumptions; inventions, and speculations. Opening the door to even one absurdity invites a flood of absurdities to follow.
Analogously, just one Epicycle was never enough to explain the motions of planets in a geocentric cosmology: you needed either an infinity of epicycles lacking any explanation or mechanism (the nature of which only invited - demanded even - further speculation), or you could adopt just one heliocentric model that does not insist upon ideologically pure circular orbits to substantially solve the problem. Just one more idea - Relativity - gets you all the rest of the way to explaining everything about celestial mechanics. This is what is meant by an economy or parsimony of ideas.
When you are on the wrong track, sometimes a proliferation of necessary assumptions is the warning sign you need to turn back and try something else. This is the power of Occam's Razor: to shave away unproductive wild speculation of things we do not and cannot know anything about, and focus instead on a few things we can know and test.
The inventor of a thing is rarely its most accomplished practitioner (ref Adolphe Sax whom nobody remembers for his swingin' tunes and sick jams). William of Ockham was no exception. Had he applied his razor to his mind as diligently as he did to his face, he would have not wasted any time worrying about what gods were like.