All three lines are grammatically correct. This is because the end of the sentence can be cut off with the punctuation of lines one and three and still be correct. To clarify, "One of the oldest philosophical debates known to man is the question of which has greater influence upon an individual," is a sentence in its own right; and thus the last part is merely extra baggage.
The reason line two is still in the running for being correct is because the colon is describing "the question of which has greater influence upon an individual." Given that that is what I believe you are trying to accomplish with this sentence (describing what the debate is) line two would be the most correct for your situation.
The majority of people here are choosing the first line, but that's because semi-colons are difficult to comprehend; even for the most adept English users. I have a couple of sources that can be utilized to help you, and anyone else here, out in the future for grammar issues:
How to use semi-colons: http://theoatmeal.com/comics/semicolon
This comic is how I learned how to use semi-colons correctly; it's quite entertaining too! There are more grammar comics on that site as well if anyone is interested in looking at them.
GrammarBase: http://www.grammarbase.com/
This will check anything that you type for grammatical errors and provide suggestions, all for free; though there are some things that should be noted when using it.
First off the checker won't ever say that the use of 'you' is correct or incorrect in a sentence; it will assume that there is some context to the sentence that makes 'you' a proper subject. Papers shouldn't contain the word 'you'; the reader shouldn't ever feel targeted.
Second, it'll say whether or not you're using complex words; the phrasing is correct, it's just suggesting for you to tone it down.
Third, passive voice (was, were, generally any use of the verb be) is frowned upon. This is not to say that you shouldn't ever use passive voice, but if you can find a way to use active voice that will clarify your meaning to the reader (and not sound like nonsense) then you should.
Grammarly: http://www.grammarly.com
This is a much more advanced version of GrammarBase, and may be more preferable to you if you find yourself writing collegiate level papers frequently. The problem with it is that it isn't free like GrammarBase. It will tell you whether or not you have errors, but not where in the sentence. It will also cut you off if you use the free portion a bit too much in a single day. I don't use Grammarly because I'm cheap, but if you want to pay for it I definitely would say the price is worth it, based off of my limited use of it.
Hope this helps!