One aim of phonological theory is to characterize the set of "possible words". For examples, speakers of English know that "blick" is a possible word, though it is not an actual word. But "kahvi" is not possible in English (though it is in Finnish). Under these assumptions, the "possible English" in which "blick" is a real work and "brick" is unattested has the same phonological grammar as real English. It differs only in which words happened to be selected as lexical entries from amongst the outputs of this phonological grammar. A corollary of this approach is that phonological theory accomodates only a single probability (namely, the probability that an arbitrary possible word is attested as an actual word). This probability is located outside of the grammar.

This paper will provide an overview of evidence that probabilities are located inside the grammar. Probabilities pertain to pieces of phonological descriptions. They are reflected both in the likelihood that complex forms will exist as a function of the frequencies of their subparts, and in well-formedness judgments. Well-formedness judgments may in general be viewed as reflecting perception of likelihood. Evidence will be provided from a range of experimental and computational studies, looking both at internal evidence and at experiments in which well-formedness judgments are gathered systematically.

Details of the results from these studies substantially constrain the class of feasible phonological models. Evidence for sigmoidal warping of perceived likelihoods suggests that likelihoods are categorized in the mind, . Probabilities are the same for both perception and production, supporting models in which they arise directly in all domains from actual experience with words. Lastly, that probabilities are horizontally organized (as in a Markov model) rather than vertically organized (as in a stochastic context-free grammar). As a result, longer words are worse than shorter ones, and temporal separation tends to engender statistical independence.