Following your hypothesis, it's impossible to have a rational conversation about anything. Look at solipsism for goodness sake. We can't even know that anything outside our own mind really exists.
If someone chooses to define a purpose for their life, then can be perfectly rational in doing so. Inasmuch as we accept that there is a reality (which we can't definitely prove btw), we can accept any number of truths based on our experience in that reality.
You can have a rational conversation about anything as long as you don't use irrational arguments.
Solipsism proposes that the world is just a creation of the mind.
However the only way to define the mind is in the context of the world outside of it.
So no, the world isn't just imagination, and the imagination isn't just an artefact of the world. You can only define each one of them in function of the other.
Just like you can't define good without bad.
No one I know has been able to define a rational purpose for their life. You can't have purpose to yourself, just to others. Either way it's an infinite purpose chain.
Find me anything in our universe that isn't, in effet, an infinite chain of purpose (or cause, if you will).
Just because the "purpose" of the cosmos is irreconcilable with the purpose that one being defines for themselves, doesn't mean that purpose is nonsensical.
I use the word nonsensical over the word irrational, because there are many things in the world which you would term irrational. One of them is the emergence of intelligence (yes, you can rationalize this as an evolutionary adaption, but the basis of everything is irrational, so who cares?). Irrational though it is, we are still, to some extent, rational minds trapped in this irrational world. To dispose of any presupposition as irrational, simply for the sake of logical consistency, is an irresponsible way to live.
It is neither rational nor irrational to live as a solipsist. It is simply an axiom on which you base the rest of your rationalizations. Choose your axioms wisely, and the world will unfold accordingly.
I think you mean't "To dispose of any presupposition as irrational, simply for the sake of logical consistency, is an responsible way to live." Not to, is irresponsible.
If someone chooses to define a purpose for their life, then can be perfectly rational in doing so. Inasmuch as we accept that there is a reality (which we can't definitely prove btw), we can accept any number of truths based on our experience in that reality.