In order to problem-solve, do we`need a record of all previous attempts at problem solution.?

Do we then try to extrapolate to the real problem ?

What if a rogue developer in your organization has systematically
trashed all records (mainly to cover up for their mistakes) ? Is meaningful software development still possible ?

Not necessarily. But it depends on your opinion really. If you're not familiar with the source code, it could take a while to break it down so you do. Or would it be faster to just start over? Depends on the software and what stage the dev cycle is in.

in general term if we need to solve any problem, we need to know what happen and what was going on so we can better understand how that problem occur or what that problem was. And in another term if there was a explaination to what and how that problem occured, the solving time could be minimized.

It is good if you record each and every steps that carried out to solve a particular task. The advantage is you people can track back the effort involved in such a task.

I don't think if it is a centralized log keeping system then it is possible for any employee to destruct anything.

You can use a groupware tool like Lotus Notes so that a communication loop will start when a new task starts. It is very simple to maintain and it is flexible too.