but the mental experiences, which these directly symbolize, are the same for all, as also are those things of which our experiences are the images.
I believe that in general mental phenomena like thinking and loving are similar from person to person, although there will be defining qualities for this or that persons thought, love etc.
Also there is a broadly similar experience of outer phenomena - for example the cat one the mat will look similar to most who see it. But it may have overlayed meanings, like being mine, or being a symbol of good luck, or having escaped from the ship etc which are more personal interpretations.
I think that many people are idealistic about certain interpretations, and for instance want to universalise their religious beliefs or lack there of, so that all humanity can be as well grounded as they are. I think that is possibly a bit of a pipe dream as things stand, as the world is so vast, complex and dynamic. As such, the idea of uniformity in interpretation (cf Habermas*?) would take more effort/work than any of us - even collectives - can give. It would be like trying to tame the weather. So we will have to get used to a fair degree of diversity (cf Lyotard*?), whether we like it or not.
*IIRC the philosopher Habermas things communities can progress towards a shared consensus through rational engagement, where as Lyotard thinks more about hetrogeneity and local meanings.