The 4th is still a state or possible state of 3D matters. Just like a 2D paper when raised up and down can be considered as 3D object. 4D is the same. When you classified it as time, you are limiting the scope of the possibility of the state.
I do agree on that. I just disagree that time is not allowed to be a dimension because time is also a factor that affects the location of the object. In fact, displacement in location due to time is the most common 4D that we see every day. A car that is in front of you will not be there in t= +10s. So t is a factor that affects the 3D of an object. I prefer that you call it dimension of matter though because "state" of matter is a totally different thing which tends to refer to the phase of matter rather than the physical dimensions of it. i.e the 4th state of matter is ionized plasma.
First off, a dimension is a simply a measurable quantity. Examples of this would be a length in a single direction, the mass of an object, or a duration of time. More complex quantities can be composed from simpler ones such as, N=kg*m/s^2. Understanding the relationship between such units is the basis of physics, and the most common application being dimensional analysis. Now some objects have multiple dimensions in the same unit. For instance an object we observe everyday has 3 length dimensions (depth, width, height). All of with remain independent of each other (if you change one, it doesn't change the others). This one has been so commonly encountered, it is dubbed as 3D. But to be clear, naming the order of a dimension is not standardized in the scientific community because of the near infinite number of applications and/or configurations there are. Thus it must be specified which dimensions your are examining. To understand this more, take the mathematical quantity known as a vector. In principle, the vector has 3 independent values v=(xi+yj+zk) or v=<x,y,z>. Vectors are commonly used to store the position of an object (unit of length), the velocity of an object (unit of length/time), and the acceleration of an object (length/time^2). Note how each of these 3D vectors have to specify which dimensions they are describing. This proves that there is no single correct ordering of dimensions. So a 4th dimension is literally what ever quantity you want that does effect the previously describe ones. For example, lets say we choose the first 3 dimensions as lengths (in a Euclidean space), then the next dimension we could choose could be time, mass, electric charge, magnetic charge, temperature, density, etc. Edit: if you start looking at quantities at the atomic level, after a point, it becomes probability waves of energy... at least in the math.