From Polonius' conversation with Laertes in Act 1 Scene 3 what kind of a life philosophy does Polonius seem to have?
If you look at the totality of Polonius's advice to Laertes, it is pretty clear that Polonius is very concerned with outward appearances and maintaining one's reputation. Most of his advice is in reference to the appropriate actions a man must take to keep himself from damaging his reputation.
1.The first few pieces of advice are specifically about behavior. He tells Laertes to "give thy thoughts no tongue." He is telling Laertes to keep his opinions and thoughts to himself so as not to offend anyone or be misinterpreted by anyone. He follows that up with, "nor any unproportion'd thought his act." He is telling him not to overreact to what others say. He follows this theme a few lines later when he counsels Laertes to listen to everyone, but reserve his comments and judgements. He wants Leartes to be friendly, but not overly so, until Laertes knows for sure they can be trusted -- only then should hold them "with hoops of steel."
2. He warns him not be hot-headed and then enter into quarrels, and be careful of what he might reveal if he is in a fight.
3. He next goes on about Laertes' outward physical appearance, telling him to look nice, but not gaudy -- afterall, the clothes are a first impression.
4. His last piece of advice is to be careful with money -- lending to others often comes with more strife than it is worth -- thus could create conflict.
Polonius sums up all of this advice with a final thought: "This above all to thine own self be true." If you only look at that one line, then it could be regarded as a contradiction to everything he says before it, but if you consider the complete sentence, he makes a logical point. The rest of thought is "And it must follow, as the night the day, thou canst not then be false to any man." What he means is that if you keep in mind all of the advice, and think about your actions first, then you will not likely offend anyone else in the process -- therefore you will be able to maintain you yourself and you reputation.
In the end, the speech reveals a bit of Polonius's skepticism about the nature of humanity -- assuming the negative about other people's natures and motives, but Polonius has his position in the court by playing the game correctly, so he is probably speaking from some truth of experience.