The “Different Types Of Knowing” argument is a simple rebranding of the scientism accusation, that is so common in religion vs science debates. It basically holds that there are different and non overlapping types of knowing - namely, the scientific type and the spiritual/religious type - and that in order for a person to be both rational and mentally balanced, both types of knowing are essential. This common argument goes on to claim that one kind of knowing cannot infringe on, analyze, or judge the other, and that each must govern its own magisteria.
The fastest way to cut through this nonsense argument is to simply ask your counterpart what type of “knowing” he/she has employed in order to make this argument in the first place. Let this question sink in for a few moments as your counterpart reluctantly realizes that they just made a self refuting claim.
The difficulty the religious tend to have, as usual, is with distinguishing between objective and subjective claims. The issue is not between different types of “knowing” but between objective reality and subjective feelings and opinions. All of us: religious believers, atheists, agnostics, etc, have subjective feelings and opinions - some of which happen to be very important feelings and opinions, about love, friendship, passion, etc - but this does not mean these feelings can be used to support objective truth claims about the universe. This is why we invented the concept of objectivity, and invented the scientific process to establish what is or isn't objective.
It might, for all I know, turn out that science will not be the only way to discover objective facts about the universe, but up till now, it is by far the best way we have found for doing this. In fact, science is not even a way of “knowing”, it is a process of getting to objective truth by screening out subjectivity and bias - not because subjectivity and bias are necessarily bad, but because subjectivity and bias are not objective.
There really is no mystery as to the different types of “knowing” because there really is only one type of “knowing”. The differences are not in the “knowing” part but in that some facts are objective - the earth really does orbit the sun, for example - and some facts are subjective - I really love my wife, you have faith in Jesus, etc. The problems only begin when people use subjective opinions to support objective truth claims.
Whenever one of my religious friends uses subjective feelings about Allah/Yahweh/Lord Brahma to support an objective claim about the universe, and then claims that this comes out of a different type of “knowing” that cannot be disputed, I politely inform my friend that this “knowing” they speak of is nothing more than their own subjective feeling. And since we all possess subjective feelings, their “knowing” is in no way more powerful or profound than mine. Anything that can be subjectively asserted (or “known”, if you insist) can also be subjectively dismissed or asserted in any other way. This is why we developed the concept of objectivity in the first place - in order to find a common ground that is not mired in personal biases.
Isn’t it a bit odd, therefore, that the only people who babble about other types of “knowing”; insisting on supporting their objective truth claims with subjective feelings, are the ones that are never able to support their objective truth claims in any other way?