"it would be unphilosophical to deny the phenomena solely because they are inexplicable in the present state of our knowledge"

We are so far from recognizing all the agents of nature and their divers modes of action that it would be unphilosophical to deny the phenomena solely because they are inexplicable in the present state of our knowledge. But we ought to examine them with an attention as much the more scrupulous as it appears the more difficult to admit them; and it is here that the calculation of probabilities becomes indispensable in determining to just what point it is necessary to multiply the observations or the experiences in order to obtain in favor of the agents which they indicate, a probability superior to the reasons which can be obtained elsewhere for not admitting them.  Laplace 

This statement starts out with a rather obvious truth that fits in rather well with what North Whitehead has been pointing out, that rejecting ideas that don't fit into your current models of reality can't account for as obviously not existing is "unphilosophical".  Then he goes on to say something that was popularly dumbed down in the slogan Carl Sagan cribbed from better thinkers, "we ought to examine them with an attention as much the more scrupulous as it appears the more difficult to admit them."  

Among other things that could be said about this, it empowers the certainly, often self-interested assertion that some things are properly considered "more difficult to admit them."  That can assert self-interest, ideological preference directly into would-be objective science.  Atheist do that all the time with total success - until their conclusions fall as time catches up with some of them.   Ironically, it is the social sciences that are the most rampant vehicle of that cycle of rise and crashing fall of scientific ideas.

Having read that this morning while looking at Laplace's essay on probability, I can't resist pointing this out.

In the dumbed-down atheism of today, as can be seen in the phenomenon of pseudo-skepticism, even Laplace's proposal to test such ideas with rigorous applications of mathematical probability is rejected as a means of achieving what he proposed, finding out if they are true or not.   That rejection has been explicit in pseudo-skepticism since J. B. Rhine started what even Ray Hyman has had to admit is some of the most rigorous scientific examination of human behavior ever conducted and mathematicians who examined his work declared that his use of statistical analysis was flawless. 

Faced with decades of such rigorous testing and the most rigorous of statistical analysis of the results, it is the very atheists who will drop that, perhaps, apocryphal comment of Laplace to Napoleon who reject his standard of doing exactly the things that made him worth name-dropping.  Of the validity of "a probability superior to the reasons which can be obtained elsewhere for not admitting,"  taboo ideas.  

Here's one of America's foremost experts in statistics, Jessica Utts on one of those things that pisses atheists off mightily.