Here's my list. Feel free to add your own.
Axioms
A1. It's a zero-sum game:
Your gain is another's loss (or a group of others). Similarly, your loss is another's gain (or a group of others). In his book, Trading for a Living, Dr. Alexander Elder explains that it's actually a minus-sum game because of broker commissions. He considers "the game" to be played only between buyers and sellers, so money is constantly leaking out to the brokers as commission. Thus, it is actually a minus-sum game. However if you consider the brokers as participants in the game, then it's a zero-sum game.
A2. Banks and brokers are profitable in the long run.
If they weren't, they wouldn't keep doing it. They're businesses, not charities. In fact, the ones that aren't profitable (very rare) go out of business, so you're only dealing with the ones who know what they're doing.
A3. Banks have much better resources than individual traders.
Just to name a few:
- They can see the order flow (because they're the ones processing the orders): This is probably their biggest advantage.
- Deep pockets: Very deep!
- Talented, experienced, professional traders: I imagine they only keep the ones who are profitable. I assume the rest eventually get fired.
A4. (The Golden Axiom) Price moves in waves.
By "waves" I simply mean that it doesn't move in straight lines. It's always alternating between ups and downs. Ok, so this axiom only applies to liquid markets. I suppose there are certain times, viz. during news announcements, when this is not quite true either. However, looking at any chart reveals that this is true almost all of the time. I suppose the reason that price moves in waves is because as price goes up, some traders will take their profit. Their selling (and desire to get out) pushes prices slightly lower. Whatever the reason is, there is clearly strong empirical evidence that this is an inescapable truth. Price moves in waves.
Theorems (Implications)
T1. We can't all win.
Proof: This is a direct result of A1.
Implications: You must literally steal money from other traders! Trading is extremely competitive. It's not supposed to be easy.
T2. As an individual trader, the odds are stacked against you.
Proof: A1, A2, and A3 —> T2.
Implications: In order to succeed you need a very clever strategy. (Clever does not necessarily mean complicated.)
What about A4?
Axioms A1, A2, and A3 and Theorems T1 and T2 are pretty discouraging. Axiom A4 gives us hope. That's why I called it the golden axiom. The fact that price moves in waves is, well, a fact! It tells us something very important about the behaviour of price movements, and we can try to use that to be on the plus side of this zero-sum game. 
