The Recursive

Repetitive words or ideas are indeed one of a writer's and a philosopher's favourite toys. But why would you want to repeat what you have just said? There are many reasons:

1. To make clear
This is quite obvious. When someone you talk to don't understand, you will repeat your statement. On a related note, in literature there is something we call motifs, which are recurring elements in a literary work that help to develop themes. This is more intangible, since motifs can be anything from prop, setting, words, sentences, ideas, characters, etc. Human minds always look for patterns to make sense of a coherent whole. One of the reasons we can't stand randomness.
(Notably, the Hindus chant their mantras repetitively over and over. Since their purpose is to attain enlightenment, I see it as they savour the meaning of a statement over and over. Every possible meaning, every possible nuances, until every possible essence is considered and eventually the teachings become clear to them. So I put this under this section.)

2. To emphasise
Related to #1 but goes a step further. Rather than making unclear things clear, we are making things already clear clearer. A rather clear example is this very statement and the one before -- clear?

3. To deliver impact
Still related to #1 and #2. My favourite is a line from Churchill's speech:

We shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills, we shall never surrender.
-- Winston Churchill

Note the emphasis on we and fight. Try to remove the repetition and you will see that the impact is much lesser. By repeating the active voice, Churchill infused sense of belonging and raised the morale of the British in the war against the Germans.

Another example is by Wilfred Owen in Disabled:

Germans he scarcely thought of; all their guilt,
And Austria's, did not move him. And no fears
Of Fear came yet. He drought of jewelled hills
For daggers in plaid socks; of smart salutes;
And care of arms; and leave; and pay arrears;
Esprit de corps; and hints for young recruits.
And soon, he was drafted out with drums and cheers.
-- Wilfred Owen, Disabled, lines 30-36

Although the syntax is deceptively similar to #6 (later in the post), 'fears of Fear' doesn't indicate the superlative 'fear'. Rather, the repetition enhances the effect of the personification 'Fear'. Let me explain:
When the first letter of a word is capitalised, it is like a name of a person, so we say that the word is personified. Other notable examples would be 'Mother Nature' and 'Death'. Think of those two words carefully -- if you are imaginative maybe you will conjure images of benevolent mother and grim reaper. So you see, personification firstly changes the status of the intangible to the tangible. Fear, nature, death -- those are abstract concepts and are difficult to picture. What personification does is giving them bodies -- embodying them in real objects, bringing them from imaginary to real plane. What's more, they are not just tangible objects, but persons. With personalities, with emotions, with will, with mind; it's a Being. So, personification, when used appropriately (like what Owen did), is a very powerful tool.
Owen refers to the ultimate form of fear in the battlefield. This is perhaps one of the things that people who never experience war, including myself, understand. But if you read Owen, you would somewhat get a glimpse of it: the graphic enormity of war. The soldier in Disabled didn't understand this also, until it was too late. The ultimate Fear, which should be feared for your own good.

If in some smothering dreams, you too could pace
Behind the wagon that we flung him in,
And watch the white eyes writhing in his face,
His hanging face, like a devil's sick of sin,
If you could hear, at every jolt, the blood
Come gargling from the froth-corrupted lungs
Bitter as the cud
Of vile, incurable sores on innocent tongues, —
-- Wilfred Owen, Dulce et Decorum Est, lines 17-24

There is another way of making impact: make a monotony first so that a sudden break from it would be blatant. It is indeed a dualism paradox where something exciting requires something boring first.

4. To indicate recursive property
What do you call your grandfather's father? Great-grandfather? How about moving up a hundred generations? Easy: Great-(101x)grandfather.
What do you call a square of a number? A zenzic. What do you call a square of a square of a square of a number? Zenzizenzizenzic. I'm not pulling your leg -- it's the word which has the most z's in English.
On a similar note, speed is the rate of change of distance, acceleration is the rate of change of speed. So acceleration is the rate of change of rate of change of distance (one of my students was very amused by this). It's a pity the physicists didn't have the sense of humour like the mathematicians to coin a similarly recursive term for acceleration.

Let's take a detour and see about other languages:
5. To express plurality
Certain languages, instead of modifying their nouns, prefer to repeat them to indicate amount of more than one. For example, in the Malay/Indonesian language, the word 'person' would be translated 'orang' while 'people' would be 'orang-orang'. A very regularised modification, unlike a certain language in which the modification follows a rule but not always consistent.

6. To indicate the superlative
This should be quite a known fact to Christians. In the Hebrew language, it is one way to express superlative as such: X of Xs. So for instance 'the wine of wines' means the wine superior to any other wines. This syntax may seem logical when we say 'king of kings' and 'lord of lords' but befuddling when we say 'people of peoples'. This is because nouns like 'king' and 'lord' already imply superlativity in their meanings, so this Hebrew syntax works when such nouns are used but otherwise sounds strange in English.

Now, for the reasons less obvious:
7. To confuse
'Huh? Isn't this contrary to #1?' you ask. Actually to be more exact, it is to prompt people to ponder about things but sometimes if you think too much you get confused. A fine line between philosophical musings and clueless rants indeed.

Since this is an area of philosophy, let's have Plato:

Quis custodiet ipsos custodes?
-- Juvenal

Plato questioned Socrates "who will watch the watchmen?" in The Republic. This is a very common question when we are talking about society structure, morality and laws. This invites us to think: those who ensure adherence to the law -- who will make sure they themselves adhere to the law?

Moving on to epistemology. Look at the following dialogue:

A: Some people don't know what they don't know.
B: But if something is unknown, how can you possibly know it?
A: What I mean is, you know certain things -- those form the body of your knowledge, correct? You should realise that there are gaps missing here and there in your body of knowledge. Those are those that, when you learn of them, you would know that they will fit the gaps.
It is like a game of jigsaw puzzle. When you almost finish it, you don't know what the missing pieces look like, but at least you know their shapes. And when the pieces fit snugly in the gaps, you know that those are the missing pieces.
B: Ah, so you mean that there are people don't even realise that there are gaps in their understanding?
A: Precisely. That's why the quest for knowledge is neverending. The gaps are always there, getting finer and finer, too microscopic to the untrained eyes. But I hope someday our understanding will be complete, not even a sliver of truth excluded.

Makes you think twice, doesn't it? Perhaps another one?

In the above dialogue, B knows that A knows that B knows that A knows...that B already knows what A means.

Confused enough?
There's a poem titled 'thinking I think I think' by Charles Bernstein. Before you click the link, brace yourselves, for the poem is discombobulating as the title is ungrammatical.
Bordering on that delicate tipsy tightrope walk between, how about:

And the biggest self of self is, indeed, self; that sin is, in fact, grounded in this notion of what is it that I want as opposed to somebody else?
-- Gov. Mark Sanford of South Carolina, addressing his extramarital affair on June 24, 2009, as transcribed by Federal News Service. (Source)

And what is that supposed to mean? I'm as clueless as the next guy.
Next, reverse psychology. In one passage I read, a villain is having a monologue: "What can you do to make a person doubt a truth?" He answered himself, "Simply tell the truth."
Essentially, this is reverse psychology. The villain is perceived as someone who is not likely to tell the truth, thus his words are doubted. But this kind of assumption is utilised by the villain.
To complicate matters, there is reverse-reverse psychology, where the hero is as clever as the villain and expects the villain to use reverse psychology. In this case the villain may try to speak as such that he sounds like using reverse psychology, while in fact he is not. He simply lies.
Taking the mind game further -- the pattern should be clear by now -- there is reverse-reverse-reverse psychology and so on, but alas, I'm getting recursive.
8. To entertain
While repetition is a proper rhetoric device, linguists are wary of redundancy. To what extent is a repetition redundant? I'm not answering that question, instead I will mention repetitions that are clearly redundant but funny.
Put up your hands: Who among you are guilty of using redundant 'ATM machine' and 'PIN number' in daily conversations? Oh my, we are all suffering from RAS syndrome. As you can read in the Wikipedia article, RAS syndrome is a mockingly funny, yet most suitable, name for the phenomenon.

9. To make a pun
Homonymic pun is a perfect excuse for repetition; words that don't mean the same thing but look the same or at least similar. So at the heart of it, it's not really repetition per se, since the meanings of the words are different. See comment section for example.

Finally, if you're still not clear on recursiveness, click here.