The Newtonian universe is said to be mechanical. Briefly, why do people describe Newton's theory in these terms?

Answer 1

Newtonian mechanics refers to (and is valid for) the properties, behaviors, and interactions of large objects at low speeds. Newtonian mechanics is many times used synonymously with classical mechanics. The behaviors of billiard balls on a pool table is a classical example where the descriptions offered by Newtonian mechanics are applicable, and the evolution of the physical system is fully determined by initial conditions.

Rigid bodies, well-defined trajectories, and Euclidean space.

The word "mechanics" is used similarly for relativistic mechanics, wave mechanics, quantum mechanics, statistical mechanics, etc. It refers to the dynamics and interactions of the entities those theories are concerned with (e.g. the mechanics of waves), and also to the mathematical characterizations of the behaviors of those entities.

Einstein's relativistic mechanics has replaced Newtonian mechanics, although the way it would treat billiard balls on a table top is very similar to Newtonian mechanics. In fact, the physics effectively can be reduced to Newtonian mechanics, and therefore it may be more efficient for a physicist to simply use Newtonian mechanics as a very good approximation. In other circumstances, Newtonian mechanics will not provide good descriptions anymore, for example describing objects at high speeds.

For a very nice introduction to the philosophy of physics, I would recommend the book Philosophical Concepts in Physics, by James Cushing.

Also, there is more information on Newton in the following SEP article:

https://plato.stanford.edu/entries/newton-stm/