There are two essential arguments that make this a good question; assuming that the existence of physical objects is a fundamental truth, which is not, but just for now:
-  According to the empiricists, existence is subjective. That means that an object exists only if I can perceive it. If I cannot perceive it, it doesn't exist. For example, my wife perceives a stain on the wall. For she, the stain exists. I cannot perceive it. Moreover, it has a physical effect on our existence: she performs actions intended to remove the stain on the wall; I don't. Such example implies the existence of a 2-dimensional object, and some level of density. 3-dimensional objects are equivalent: she sees a cloud I can't see. That makes clear that the existence of clouds is subjective. You will say that clouds are completely different from rocks, so the existence of rocks cannot be subjective. That's false: rocks are exactly like clouds, have the exact same properties of a cloud, except on a different scale. Constituent particles are closer, they exert forces between them capable of keeping integrity for x time, etc. So, existence is subjective.
-  Better yet, time and space are subjective forms of knowledge. The empiricists, and mainly Immanuel Kant, argumented that time or space are not physically real; that they are some type of subjective knowledge created inside our mind in order to process the objects of our perception. Kant calls this type of knowledge syntethic a priori: in simple words, knowledge that is independent on other knowledge (synthetic), and previous to experience (a priori). Space and time are just forms of knowledge we develop in order to organize our perceptions. Then, space and time are not real facts, but mental features that perception-related knowledge depends on. Kant makes a clear difference between what we perceive (phenomena) and those manifestations, out there, that cause the phenomena, but that we don't have access to (noumena).
Such preamble was mandatory in order to address your question: do forces (phenomenal manifestations) exist in reality (noumena)? This, because a force is an effect of a phenomenal perception, the interaction between two physical objects, causing a spatio-temporal effect on both: attraction or rejection.
Such elements sets the problem into this context: According to proposition , if space and time are subjective, then forces might not be real, but just a phenomenal manifestation. Moreover, according to , the existence of forces, as any other phenomenal manifestation, is subjective. Until this point, the physical, real existence of forces would be already in serious problems.
Yes, you might state, but without realizing the enormous implicances of such assertion: if forces, space and time don't really exist, all Newton postulates or Einstein theories and most scientific disciplines would be in serious trouble! Well, my friend, that could really be the case. Einstein or Newton didn't uncovered the issues of the noumenal reality: they've just formalized the rules of the objects of our perception. Forces, a small part of such body of knowledge -- science --, are just some form of subjective perceptions.
Now, let's address problem : objects are not real. There's no formal definition of matter, and even worst, of physical objects. Objects are just ideal representations of groups of perceptions (e.g. an apple is a mix of tastes, colors, smells, textures, etc.). Our mind is able to add apples, like 1+1=2 but that ideal has no physical meaning... at all. Apples can only exists as ideas, but there's no way that ideas could exist outside any mind. Our of our minds, there are just physical interactions, chains of hydrocarbons, whatever. John Locke (another empiricist) was at the origin of such idea.
Then, if  objects are just ideas,  existence is subjective, and  time and space are just forms of synthetic a priori knowledge, then, it would be clear that forces exist only as ideas.
The book I'm currently working on suggests precisely such idea, but within a different approach: physical things being ideal entities, interactions between physical objects also become ideal manifestations, an idea that John Locke and David Hume already suggested long time ago. Hume focus specifically on causality; the effect of forces in interacting objects can be considered a form of causation.
At this point, it is important to remark the features of the quantum theory, which by considering the issues of subjectivity has become our most successful scientific discipline. Features that would be absolute truths in relativity or thermodynamics, like the existence of objects, are accepted, although having weak basis. For example, classical thermodynamics rely on the existence of particles. If the existence of particles would not be an absolute truth, thermodynamics would not be possible to be formulated. How could we possibly account for Boltzmann entropy without relying on the existence of particles as a fundamental truth? Here, we have the same problem as the one implying addition, e.g. 1+1=2 apples.