Inductivism is the method upon which the DSM's atheoretical approach to classification is predicated. Therefore, it will be worthwhile to consider why inductivism is a lost cause. This will involve drawing Reichenbach's distinction between the context of discovery (how theories are dreamed up) and the context of justification (how theories are tested), because inductivism has appeared in both contexts.
In the context of discovery, inductivism is a psychological theory of the way theories are arrived at--namely, theories come about (one might even say they are caused) by perceiving the similarity in a set of observations. On this view, empirical (sensory) observations form the building blocks of scientific theories.
Inductivism might be right as a psychological theory and wrong as an epistemological method. In the context of justification, Bacon and Mill have claimed that science progresses through the accumulation of facts. However, inductivism can be shown to be methodologically wrongheaded by reconstructing inductivism as the following logical argument.
(1) IF Theory, THEN Observation.
(3) THEREFORE, Theory.
This argument is an example of the well-known fallacy of affirming the consequent. The truth of the conclusion does not follow with logical necessity from the truth of the premises, as can be seen if the Theory is, "All swans are white," and the Observation is, "My swan is white." An example more close at hand would be if the Theory is, "Schizophrenia is a disturbance that last for at least 6 months and includes at least 1 month of active-phase symptoms" (American Psychiatric Association, 1994, p. 273), and the Observation is "This schizophrenic individual has had symptoms for more than six months." The logical loophole in these examples is the case in which a black swan is discovered and a schizophrenic individual turns up who has been symptomatic for two months.
The latter case does not exist. Why? Because if someone experiences delusions for less than six months, then that person is not schizophrenic by definition. Many authors rightly find the arbitrariness and artificiality of this state of affairs annoying (e.g., Carson, 1991; Carson and Sanislow, 1993). In philosophical circles, the practice of eliminating exceptions to the rule by fiat is known as "monster barring." Heavy doses of monster barring are known to cause methodolgical blindness--they prevent scientific discovery and arrest the growth of knowledge.
Inductivism has been treated here in such detail because inductivism underwrites the operationism that is indemic to the DSM.