Semicolons/Colons

I am sometimes quite unsure how I am supposed to deal with semicolons and colons. I have a decent understanding of when a semicolon should be used, but my confusion is about what I can do with the portion that comes after the semicolon. The sentence below illustrates my confusion because I am not sure if it is a grammatically correct sentence.

---The basis of Leibniz's charge is twofold; miracles need to remain special and sacred and predictions about the world have to be possible.---

The portion after the semicolon contains two sentences combined with a conjuction. I know this is usually wrong, but the word "twofold" implies that two clauses have to follow. Any feed back on semicolons in general would be appreciated. I also have questions about the colon use, and I will post sentences below.

---These are: Descartes' interactionism, Malebranche's occasionalism, and Leibniz's pre-established harmony.---

---The two events compliment each other through their relation in time, and this leads to correlation. This is what we mean by harmony: inter-substantially and intra-substantially.

Any help would be great.

Thanks,

Hal

[oregeezer]

I have always thought of them as pauses in a speech. Semi colon, short pause (join two thoughts together); Colon, full stop (beginning of a long list).
Your first example makes more sense when paraphrased:
The basis of Leibniz's charge is twofold;
a.) miracles need to remain special and sacred and
b.) predictions about the world have to be possible.