Attentionality
Attentionality happens at a stage prior to "intentionality". Attentionality (specifically, 3rd order intentionality, which is unique to human beings) is the result of Joint-Shared-Attention. It is a "we-space" instead of an "I-space". Thinking in terms of “attentionality” rather than “intentionality” emphasizes the constitutively social form of our thought and action and allows us to ground the declarative order in the ostensive-imperative world.
Types of Intentionality
1st order Attentionality – I see X: Being able to direct your attention toward something.
2nd order Attentionality – I see you see X: Being able to understand that others can/are directing their attention toward something. This is also referred to as ‘sociality’ and encompasses all social animals.
3rd order Attentionality – I see you see me see X: Being able to understand that others know that you are directing your attention toward something, and they know that you know that they are directing their attention toward something. This is also referred to as ‘abstracting’ and it is this triadic relationship between people and object that enables language, which is unique to humans.
References:
https://en.wikipedia.org/wiki/Joint_attention#Levels_of_joint_attention