If we were exclusively 3 dimensional beings, then we would not be able to experience a 3 dimensional world. Why? Below is the reason:

Construction:

1. Circle is a geometrical construct that needs two dimensions for its construction.
2. The construction of a circle is possible only in a 2-D space.
3. Two dimensional space is a necessary and sufficient condition for the construction of a circle.
4. When we say that a certain geometrical or topological construct is N dimensional we mean that an N dimensional space is the necessary and sufficient condition for its construction.

Perception:

1. Circle as a 2-D construct can be perceived fully only from above, from above the 2-D space in which it is constructed.
2. To fully perceive a circle one needs to transcend the circle’s space.
3. One has to be transcendent to the circle in order to perceive the circle, or else the circle itself will be transcendent to one’s perception.
4. Circle in its entirety is always a transcendent shape to the immanent
5. In order to perceive a circle in its entirety, the shape of the circle, one has to step into the third dimension, a dimension that is transcendent to the dimensions of the circle and yet contains the space of the circle.
6. The condition for a perception of the 2-D totality of a circle is being in a space that is both transcendent to the space of the circle and yet contains the space of the circle as immanent.
7. To perceive an N dimensional shape in its entirety one has to be placed in the N+1th

Conclusion:

1. To perceive (experience) the N dimensionality of a space, rather than deducing and inferring it, one has to be transcendent to it, being located in an N+1 dimensional space.
2. For an N dimensional space to be perceived (experienced) it has to be immanent to the observer’s consciousness, but this immanence is possible only if the observer is transcendent to the observed, hence enjoying a higher dimension than the observed.
3. The dimensionality of an N dimensional space is always transcendent to the observer located in the same space.
4. The dimensionality of a space becomes immanent only and only for an observer that is transcendent to that space.
5. Our experience of 3-D space is immanent: We intuit the 3 dimensional character of our space immediately and don’t need to deduce or infer it by examination and investigation.
6. The 3-d character of our space is given to us immediately; it is immanent.
7. Since our experience of the world is already 3 dimensional and immanent, therefore we have to be transcendent to it and located outside of it.

QED.

***To experience two dimensionality directly one has to be in the third dimension. Therefore to experience three dimensionality one has to be in the fourth dimension.