I am currently studying Classical Mechanics, 5th edition, by Kibble and Berkshire. Chapter 2.1 Newton's Laws says the following:

If we denote the force on the ith body due to the jth body by $\mathbf{F}_{ij}$, then

$$\mathbf{F}_i = \mathbf{F}_{i1} + \mathbf{F}_{i2} + \dots + \mathbf{F}_{iN} = \sum_{j = 1}^N \mathbf{F}_{ij}, \tag{1.2}$$

where of course $\mathbf{F}_{ii} = \mathbf{0}$, since there is no force on the $i$th body due to itself. Note that since the sum on the right side of (1.2) is a vector sum, this equation incorporates the 'parallelogram law' of composition of forces. The two-body forces $\mathbf{F}_{ij}$ must satisfy Newton's third law, which asserts that 'action' and 'reaction' are equal and opposite,

$$\mathbf{F}_{ji} = - \mathbf{F}_{ij}. \tag{1.3}$$

Moreover, $\mathbf{F}_{ij}$ is a function of the positions and velocities (and internal structure) of the $i$th and $j$th bodies, but is unaffected by the presence of other bodies. (It can be argued that this is an unnecessarily restrictive assumption. It would be perfectly possible to include also, say, three-body forces, which depend on the positions and velocities of three particles simultaneously. However, within the realm of validity of classical mechanics, no such forces are known, an deter inclusion would be an inessential complication.)

I found this last part confusing:

Moreover, $\mathbf{F}_{ij}$ is a function fo the positions and velocities (and internal structure) of the $i$th and $j$th bodies, but is unaffected by the presence of other bodies. (It can be argued that this is an unnecessarily restrictive assumption. It would be perfectly possible to include also, say, three-body forces, which depend on the positions and velocities of three particles simultaneously. However, within the realm of validity of classical mechanics, no such forces are known, an deter inclusion would be an inessential complication.)

I don't understand how it is reasonable to assume that, if three bodies are in close proximity, then only two 'affect' each other, and the other doesn't. This is clearly not an accurate generalization of the physical world.

I would greatly appreciate it if people would please take the time to clarify this.