I latched onto the logical side of Law Of Attraction and explored it that way after reading As a Man Thinketh, later renamed to As You Think.
It explored the idea that your thoughts that you think all the time are the source of the actions in your life including the small decisions you make in day to day life and the things you talk about with people. These actions then leads to results which end up being a direct result of your thoughts. I had no doubt with this, it just makes sense. If you think about being wealthy, you will do those things that will make you wealthy and avoid those that don't for example.
The book also created the concept of being able to use your awareness to "weed out the bad thoughts" by actively picking which things you think about. This is probably the most important lesson in the book, that by listening to your thoughts and honouring only those that will help, you guide your thoughts into helpful patterns that influence and improve the actions you take.
The tricky part however is when you start experiencing aligning syncronicities that can't be explained by coincidence. Things you think about appear as if you willed them into existance. Yes, there's always a reason why behind it, but as far as your view goes it's like it was just magical. It's from there you can start to experiment experientially with thought patterns and it's influence on this so called "real world" of ours.
I say if you are highly logical, instead of looking for what is illogical about LoA, look at what makes sense, and try out what you do believe in about it. Much of it is common sense, ie: thoughts to action to results, but just as much of it is not logical. It's only when your logical mind has been tricked into enough falsities that it starts letting down the barriers of being right about things enough to experience what the world is really like.
To get the book:
As A Man Thinketh -- FREE eBook -- timeless classic by James Allen
I hope you see something new for yourself out of this. Parthon.
ps. Supposedly you can get Think and Grow Rich from there for free too now.