To consider whether all problems are soluble (strong version), it's important to consider:
- what is a problem?
- what is a solution?
Notice that I did not include the qualifier, "unless it violates the laws of physics" anymore than one about time limits or having enough knowledge. Why not?
Consider the problem of an asteroid going twice as fast as a photon. How can that be solved?
Answer: It is not a problem. Asteroids do not have problems.
Only persons have problems.
Here is what my dictionary has for problem: "a matter or situation regarded as unwelcome or harmful and needing to be dealt with and overcome". Notice that "regarded as" implies a mind doing some thinking.
Situations like an asteroid moving at speed S slower than a photon are not inherently problematic. Whether they are a problem or not is a matter of interpretation (how it's regarded). That requires a person to interpret.
Note: the word "problem" is routinely used in more than one way. For example we will say, "Yesterday I worked on a fun math problem. I haven't solved it yet." The "math problem" is *welcome*, not unwelcome, but is called a "problem". With this use of the word problem, *no solution is even needed* since no one minds the problem. My dictionary tries to cover this use with "a thing that is difficult to achieve or accomplish" which is decent but I think imperfect.
This type of problem is not the one we're talking about with "all problems are soluble". But these can turn into the other kind of problem -- the type regarded as unwelcome -- and if that happens then we are talking about it.
So, problem 2: a *person* wants to make an asteroid move at twice as fast as the speed of light.
How can he solve that? Doesn't solving it violate the laws of physics?
(Note: we could actually turn out to be mistaken about the laws of physics, but that's not important to our discussion.)
To solve this one, we need a more nuanced conception of what a solution is. Not all problems are solved in the straightforward way.
This problem can be solved by the person changing his preference. If he no longer wants to make the asteroid go twice as fast as the speed of light, it will no longer be "regarded as unwelcome", and so there is no more problem.
So, you may be wondering: can we solve all problems by changing our preferences? Wouldn't that be vacuous? Or does this technique have limits?
There are objective truths about which preferences are good or bad.
Bad is stuff like: unobtainable, counter productive, doesn't solve the problem it intends to solve, or aimed at a bad problem.
People cannot arbitrarily change their preferences by an act of will. They can only change them, in short, when they are persuaded that the new preference is better. This limits preference changing only to objectively better preferences. (As a complicating factor, which I won't explore here, they can also change preferences when they think a new one is better but are mistaken, but don't know they are mistaken.)
This allows for changing preferences as a solution (or part of a solution) to the extent it's objectively needed -- because bad preferences themselves cause problems -- but limits it from being arbitrarily used for everything.