In the mechanist vision, the non-living world does not possess its own intentionality or agency. Even in the living world, natural intentionality or teleology is ideally reduced to some version of efficient cause. There is no place in the mechanist vision for intentionality in nature at large. Modern science continues to view inanimate matter as passively obedient to externally imposed laws—like a computer obeys its program. It is not seen as imbued with its own powers of self-organization like organisms are. Living things provide our model for self-organizing systems, but our model for intentionality remains largely our own consciousness. According to scientific understanding, consciousness is now recognized as a product of natural self-organization. However, owing perhaps to the profound human desire to be separate from nature and above it, we still seem unwilling to admit either consciousness or intentionality as broad natural categories. (Similarly—if indeed it exists—the broad role of self-organization in inanimate matter is not yet recognized.) Nevertheless, intentionality might be a useful concept outside its human context. It is only a matter of convenient habit, evolutionary conditioning, and historical circumstance that we regard the world fundamentally from a third-person point of view: as a passive it incapable of responding on an equal footing to our interventions. In science this means a certain kind of description, which I call first-order science. Characteristically it describes the world as it is supposed to be “in itself” without reference to the describer. The fact that consciousness is only reluctantly an object of scientific investigation mirrors the exclusion of the scientist’s consciousness from her accounts. The scientific interaction with nature (as in experiment) may be described in third-person terms, insofar as it might affect the data. But the scientist’s intentionality is excluded from the description as irrelevant. To include intentionality in nature as an object for scientific study would imply including the human intentionality behind science. And that would be to open, as they say, a can of worms.