I'd say, starting point is a fact that logical mind can't fully explain The Reality (name to describe some kind of eternal reality as opposed to our personal ‘unitary" reality). So we need to develop ability to somehow experience The Reality directly, without any intermediary filters.

Among other systems, aikido provides tools to develop, what I call ‘spiritual intuition' as a tool to realize such experience. Quite similar to some Buddhism teaching, aikido uses the whole range of paradoxes. These physical paradoxes (as i.e. successful execution of efficient martial technique while limiting as much as possible injury of attacker because of the compassion for living being) force us to abandon usual logical mind. The example of other tool can be a possibility to develop a strong personal discipline and commitment that is indispensable to any serious spiritual pursuit.

The lack of the competition as another characteristic of aikido practice allows us to direct attention to eternal values and concentrate what happen ‘inside' of us as opposed to pursuit artificial and transient goals. Any progress in development of intuition is immediately verified by physical practice on the tatami (i.e. am I able to reestablish a "World harmony" that was disturbed by attacker). The key is to create a martial situation where intuition can be verified by aikido techniques and practice of those techniques will push further spiritual development.