Would you hyphenate "brought up," as in: "I was brought up to appreciate both creative and logical thinking." I'm thinking yes, but perhaps not necessarily.
I was going to use raised, but I used "raised" in the previous sentence, and wanted to avoid repeating it
No, you wouldn't use a hyphen. Here's an article about the proper usage of hyphens from the Purdue Online Writing Lab.
There should not be a hyphen in the case the OP described, as per the rules of the English language. "brought up" in this context is not an intuitively easily understandable construct, so confusion is understandable. However, the case is simply that this phrase is a metaphor: those who raise a child "bring them up" into the world, figuratively in that they teach them about the world and right from wrong and such, but also literally in that during this time children become taller, hence they literally are moving in an upwardly direction, being taken on this journey of sorts by those raising them.
