This is LONG, so....
There is a difference between thinking and contemplating. Both have their useses for different things. Thinking involves your active mind using all of its past experience and knowledge to solve a problem/find a solution. This is an active endeavor. Thinking comes in handy indeed. Contemplating, on the other hand, requires the nage to remove all past assumptions, expectations, hearsay, and emotional attachments involved with a particular problem so that only the problem itself is in mind for reflection. Essentially remove the clutter. With practice, you can contemplate to the extent that only the crux of the issue remains. This is less active. Reflecting doesn't really require probing.
Thinking about the argument, "Stop The Murder of Children" is indeed compelling. An equally compelling statement is "Women's Bodies Are They're Own."
If fact, most people on the planet would agree with both of these statements. A complete newcomer to the issue would most likely be swayed (at least initially) by the first person with an opinion that he/she encountered. I'm sure that many of you have heard the argument of an ardent supporter of either side. It sounds reasonable doesn't it? It should, they believe it so they try to pass that belief(for better or for worse) on to you.
Unfortunately, thinking about the issue of abortion will only get you confused. Why? Because there is no problem to be solved. Crux; Either you believe a fetus is "alive" or you don't. (Let's leave out Trimesters ok?) This line of thinking will/can only lead you to try to convince others that your way is correct (some choose violence as their means) This question is not for us to answer. Unfortunately, I know of no ultimate source that comments on this subject. Although someone's book may, another's' book may not.
By contemplating on the problem however, not only the crux of this issue can be seen, but also that it itself has a source. Then and only then does the true problem reveal itself; that people, for whatever reason, are forced/opt into a position where this "procedure" is necessary/"necessary." If all the money/effort spent on either side of the abortion cause were used to improve the society, less abortions and more happy families would result.
Essentially contemplating involves emptying the mind to see things in their "true light." Essentially remove all preconceived notions/assumptions. This is not easy, but with practice gains will be made.
What does this have to do with Aikido?
Firstly, most of the concepts, as I have encountered them, require as much contemplating as thinking. Thinking helps remember the look of a technique. Contemplating will help connections to be made. How many things have you learned in Aikido go against what you "thought?" Spend less time thinking about your training, and more time contemplating (i.e. worrying about replicating a technique exactly instead of looking for what the technique teaches.)
Also, for Art to occur (not renditions/replicas), the mind should enter a state of "no-mind," essentially empty of conscious thought. Then the mind is free to create, flow by its own devices. "Good" art feels very natural. "Bad" art feels contrived. Though there is nothing definitive here there are tendencies.
How can Aikido be used martially? Remember, your brain can do amazing things (i.e. calculate trajectory of moving baseball) by emptying your mind, you can begin to utilize this power. Attack comes, appropriate response happens. Remember, Aikido can look like anything. When you learn the principles, and can enter "no-mind" at will, you will no longer fear anyone.