PIL, to open one's eyes, be attentive, to contemplate. O, an intensifier particle. SOU, to shuffle, to untangle. IA, a hard or difficult thing.
So, voilà, we have that, according to this "faketymology" φιλοσοφία means something like 'to untangle something difficult in order to assert it strongly by contemplating it' (sic). What a wonderful fantasy has been concocted.
Back to the Real World
Not only should we forget that a Grimm's Law should occur to make pil into phil, but also we are lacking a ph in 'pil-o-sou-ia'. Not only that, but the intensifier is given a whole morphosemantic concept as "to assert strongly"! No, this is not how an intensifier particle works, and even if we were to blindly accept all this... SOU doesn't mean 'untangle' but 'to tangle, to tie a knot' just the opposite. All in all, a complete mess of a fantasy.
And this is even disregarding the fact that in greek 'philos' is a word and 'phil' is not. Also note that Mayan never used this word, and is not a valid word in any Mayan dictionary, also I think it breaks several Mayan rules.
But how? How can a language so dissimilar as Mayan be equated to Greek? This is actually a very interesting question, is it a misreading of Mayan dictionaries and Greek ones? Or is it a purposefully evil attempt at creating fake etymologies and fantasies to sicken real linguists and discredit Mayan studies?
When this doesn't work some equate it to other languages. I've read Mayan is a 70% Mesopotamian (sic), which makes no sense, since there were more than one language in use in the Mesopotamia at any time. Even that it is 70% Aramaic, which really startles me since Mayan prefers bi-consonantal roots and Semitic languages favor tri-consonantal ones, even when, by way of suffixes, Mayan can seem to have tri-consonantal roots, like for example hanal, akbal, both use the suffix -(V)l, but roots are han and kab respectively.
The most incredible? Someone wrote Yucatec Mayans and Japanese people can speak "fluently with no need of an interpreter". Really? Let's put this statement to the test, shall we? Let's write some common phrases in both languages to see how much they can understand each other;
Anata no namae wa nani? Your name is what?
Mayan (Yucatec): Bix a k’aaba’ ?
What your name?
Hum... I really don't think they would understand what the hell they are talking about. Certainly I wouldn't recommend you to speak Mayan to a Japanese. Let's see the answers to this, maybe they can glean the meaning from the similarity of the words for that;
Watashi no namae wa Alex. My name is Alex
Mayan (Yucatec): In k’aaba’e’ Alex.
My name (is) Alex.
Hum... again, I don't think they would understand a word. Specially not if one speaks of "namae" and the other of "k'aaba'/k'aaba'e", or, for that case, "watashi" vs. "in", or "anata" vs. "a". So we can say for sure that this is not the case, then how come so many people on the Internet go by this theory? We sure love a good conspiracy or secret knowledge story no matter how wild it is.