As the diagram above shows in greater detail, positivist research takes the form of theoretical propositions, which can be stated mathematically or verbally. In either case, these propositions designate independent and dependent variables, and the relationships among them. The rules of mathematics, like the rules of algebra, or the rules of formal logic in general, pertain to how a researcher is allowed to relate the variables and the propositions to one another. This pertains, whether the research is quantitative or qualitative.
However, these propositions are only general statements. In a way, the propositions of a theory make up a schema. The form that this schema would take for a given experiment or a given case study would be an instanciation of them -- where these instanciations for an actual situation are called predictions. These are predictions of what should be observed to take place in the given experiment or case, if the theory were true. Where surveys fit into this research context, and what surveys are good for, is that they are useful for providing actual, observed values against which to compare the predicted values.
In this framework, what surveys are not good for include telling us what the theory or even the variables are in the first place. The theory, including the variables, has to be identified or otherwise prepared in the front end of the research process. Likewise, the experimental controls -- and for survey research, these typically include statistical controls in one or another statistical model, like multiple regression or PLS -- have to be established, again, in the front end of the research process, prior to designing the survey. In other words, what surveys are definitely NOT good for is to INITIATE the research process. The starting point is the theory, not the survey. Basically, this is the argument that surveys definitely have a valid place when we are testing a theory in a hypothetico-deductive research context.