That should not be the definition of purpose - if we are trying to be scientific. Martian scientists should come to the same conclusions.

Do you mean that a Martian scientist would not conclude that when a human being uses that word, they are referring to a particular part of their brain that is being stimulated?

What I'm saying is that the notion of "purpose" is an interpretation we project onto the world: it is a characteristic of the map, not of the territory.

To put it another way, there are no purposeful things, only things that "look purposeful to humans".

Another mind with different purpose-detecting circuitry could just as easily come to different conclusions -- which means that the Martians will be led astray if they have different purpose-recognition circuits, following which we will have all sorts of arguments on the boundary conditions where human and Martian intuitions disagree on whether something should be called "purposeful".

tl;dr: if it's part of the map, the description needs to include whose map it is.

"Purpose" - in this kind of context - could mean "goal directed" - or it could mean pursuing a goal with a mind that predicts the future.

Now you have to define "mind" as well. It doesn't seem to me that that's actually reducing anything here. ;-)