For that matter, how can I be sure that the concepts in my head, which I am here rendering into words, correspond to the concepts that form in your head when you read these words? How do I know that what I mean when I write, say, "concept" is the same thing that you understand when you read the word "concept"?
I want you to clear your mind for a moment. Close your eyes. Take a deep breath. Then look at the following pictures and their associated captions.
Was I right? If so, how did I do it? Here are some possibilities:
1. I got lucky.
2. I have a magical ability to predict or control your actions.
3. God told me.
Now, I am going to tell you that none of those are the right answer. Of course, just because I tell you that doesn't mean that I'm right. I could be mistaken, or I could be lying. But here is what I believe to be the right answer: I have a model of you that allows me to predict some (but not all) of your behavior. That model is (to a first order approximation): you are a human. Because you are a human, your brain is hard-wired to pay attention to certain visual stimuli. Among those visual stimuli that your brain is hard-wired to detect are the creatures known as "cats" in English, "gatos" in Spanish, "katzen" in German, "chatulim" in Hebrew, and "paka" in Swahili. The reason your brain is hard-wired to detect cats is that this ability conferred a relative advantage in reproductive fitness to some of your distant ancestors, probably because their feline neighbors were more kubwa than your typical modern nyumba paka. (And how you know how to say "house" in Swahili.)
Of course, none of this guarantees that you and I mean the same thing when we say or hear the word "cat". It's possible that the features of cat-ness that my brain cues in on are different than yours, and that some time in the future we will discover that what you mean by "cat" corresponds more to what I mean by, say, "furry". But that's not likely. Why? Because in the little experiment above I not only associated the word "paka" with images of (what I think of when I say the word) cats but also with numbers, and numbers are concepts that go with nouns like "cat" and not adjectives like "furry". It just doesn't make sense (to me) to say, "one furry, two furries..." Maybe "paka" means "furry thing". But that doesn't make sense either because then the last image should have been labelled paka moja too and it's not, it's mbwa moja. (And now you know how to say "dog" in Swahili.)
Why do I believe that my explanation of my (limited) ability to predict your actions is the correct one? Because it explains more than the other possibilities. Consider theory #1, for example. The odds of my predicting your actions with as much precision as I can by pure luck are indistinguishable from zero. It's not impossible, but it's extremely unlikely. And every time I do it it -- every time I interact with (the things that I perceive to be) my fellow humans and get responses from them that make sense out of the myriad possible responses they could produce if they were simply choosing responses at random, it becomes more unlikely.
Theory #2 is not so easily ruled out. In fact, I cannot prove to you that it's false . So why do I reject it? Because it lacks explanatory power. My ability to predict your actions is limited. I can predict that you will be able to figure out that "paka" means "cat" from examples, but I cannot predict what your favorite flavor of ice cream is. Again, it's possible that I am lying about this, that I really can predict (or control!) your ice cream choice. But that just begs the question: are there any limits to my prophetic abilities? If so, what are they? If not, why do I not use my omniscience to work my will on people more often?
The fundamental problem with theory #2 is that "magic" is nothing more than a synonym for "mysterious unknown process." So theory #2 is not really a theory at all, it's an oblique way of punting on trying to come up with a theory. The whole point of this exercise is to get a handle on my ability to predict the future, and invoking "magic" is essentially saying, "I don't know." Magic is not a valid theory, not because it's necessarily incorrect (remember, I already conceded that I can't prove that my abilities are not magical), but because it cannot possibly represent progress. Invoking magic is not an explanation, it's giving up on all hope of finding an explanation.
Theory 3 is even harder to dispense with. God is not quite the same as magic because God is knowable, at least partially. So how can I convince you that I am telling the truth when I say that my ability to predict the future is not a revelation from God?
One possibility is to make another prediction: I probably don't have to convince you that I'm telling the truth. You almost certainly believe me. In fact, you probably believed that I was not having revelations from God even before I told you. Your belief was probably so strong that my positing divine revelation as an explanation for the results of the cat experiment seemed like pedantry.
Am I right? If so, how did I manage that trick?
Why, the same way I managed the first one, of course: I have a model of you. I have a model of you even though I have no idea who you are! How did I come by that model? Through a life-long and on-going process of generating hypotheses, testing them, and discarding the ones that don't fit the facts. This goes all the way down to hypotheses about what words mean, and which words I can rely on to have the same meaning in your brain as it does in mine (like "cat") and which ones I can't (like "God").
Rationality grounds out in having everything hang together in a way that grants me the gift of prophecy that I demonstrated at the beginning of this post. No other mental process has that property. Prayer might grant you inner peace and harmony, but it does not help you build bridges or restore sight to the blind or increase crop yields. This is not to say that prayer is without value. Inner peace and harmony are much to be desired. There is not much value in being able to build an iPhone if your life is a continuous nightmare of existential angst, though improving crop yields and inventing vaccines should not be lightly dismissed either. It's a lot harder to achieve inner peace if you are sick or hungry than if you are not.
The point is: the apparent infinite regress of rationality bottoms out in its effectiveness, in its ability to confer the gift of prophecy and hence the power to change the world according to one's desires. That still leaves open the very thorny problem of identifying or selecting those desires. The hardest part of getting what you want is, very often, figuring out what it is, and in this rationality offers less help, though it does offer some. I'll explore that in a subsequent post.
 In the middle ages thousands of people died painful deaths because of the impossibility of proving theory 2 to be false.