Q: Is there a "forwards" and "backwards" in one dimension? Take a displacement in three dimensions and reduce the number of dimensions by one. The original displacement loses one degree of freedom; giving it two parameters to specify a magnitude and an orientation. Now reduce the number of dimensions to just one, leaving just a magnitude... or does it?
For a displacement in just one dimension, does this mean there is no sense of direction and therefore a "forwards" and "backwards"?

A: You're confusing the definition of a vector. A vector always has magnitude and orientation regardless of the dimensionality and they are not independent. In typical physics applications, the magnitude is the Euclidean norm of the vector. 
So in 3D, you have 3 components defined by scalars multiplied by the unit, or basis, vectors. In 2D, you have 2 components defined by scalars multiplied by the basis vectors. And in 1D, you have 1 component defined by scalars multiplied by the basis vectors. In some sense, a true scalar (magnitude only, no basis vector) could be thought of as a 0D vector. 
Yes, in 1D there is still a direction and it is either in the $+\hat{i}$ or $-\hat{i}$ direction. 

A: Of course there are forward and backward.

Now reduce the number of dimensions to just one, leaving just a magnitude

Note that it is a magnitude, not an absolute magnitude.

a direction paramaterized by two discrete symbols +,- has been added.

No. There is only one value there which is a member of $\mathbb{R}$. The sign is part of the value.

Frankly this smacks of a philosopher's approach: playing word games instead of paying attention to the actual situation. The words that we use to describe things are important, but you have to give the meaning that corresponds to reality.
