[thdc]

If by "thinking" you mean strictly your own thoughts, I don't think public or private should have much, if any, effect.

The difference between publicizing your thoughts or keeping them private is what discourse is attracted - the ability to gather other people's thoughts and views on the topic... hopefully constructive ones - which you may then think about.

It's possible to come across these other thoughts without going public with varying degrees of difficulty, but anticipating that you are going public can influence how you present your own thoughts in various ways.

The above sentences are my thoughts which I've shared publicly. I tend to weaken my claims when thinking publicly with words like think, believe, probably, etc. to invite alternate ideas if someone would disagree or reinforcement if one agrees. Does it work? I have no clue.

In general, I only think publicly when I'm interested to know what other people think of a topic (usually things more opinion based); otherwise I stay private. I also try to avoid anything that invites non-constructive discussions.