There was, therefore, always a "fact to the matter" about which concepts and universals exist in the world. In the late Middle Ages (perhaps beginning with Occam, although Porphyry also makes a much earlier remark indicating a certain discomfort with the status quo), however, the certainty that existed on this issue began to erode, and it became acceptable among the so-called nominalists and empiricists to consider concepts and universals as strictly mental entities or conventions of language. On this view of concepts—that they are purely representational constructs—a new question then comes to the fore: "Why do we possess one set of concepts rather than another?" What makes one set of concepts "good" and another set of concepts "bad"? This is a question that modern philosophers, and subsequently machine learning theorists and cognitive scientists, have struggled with for many decades. One approach to answering such questions is to investigate the "role" or "purpose" of concepts in cognition. Thus the answer to "What are concepts good for in the first place?" by and many others is that classification (conception) is a precursor to "induction": By imposing a particular categorization on the universe, an organism gains the ability to deal with physically non-identical objects or situations in an identical fashion, thereby gaining substantial predictive leverage (; ). As J.S. Mill puts it ,  From this base, Mill reaches the following conclusion, which foreshadows much subsequent thinking about category goodness, including the notion of category utility:  One may compare this to the "category utility hypothesis" proposed by : "A category is useful to the extent that it can be expected to improve the ability of a person to accurately predict the features of instances of that category." Mill here seems to be suggesting that the best category structure is one in which object features (properties) are maximally informative about the object's class, and, simultaneously, the object class is maximally informative about the object's features. In other words, a useful classification scheme is one in which category knowledge can be used to accurately infer object properties, and property knowledge can be used to accurately infer object classes. One may also compare this idea to Aristotle's criterion of "counter-predication" for definitional predicates, as well as to the notion of concepts described in formal concept analysis. A variety of different measures have been suggested with an aim of formally capturing this notion of "category goodness," the best known of which is probably the "cue validity". Cue validity of a feature formula_8 with respect to category formula_13 is defined as the conditional probability of the category given the feature (;;), formula_81, or as the deviation of the conditional probability from the category base rate (;), formula_82.