We can witness the recent surge of interest in classifying different patterns or types of abduction. Many philosophers have suggested their own classifications emphasizing different aspects of abduction. Such a development is remarkable, in view of the fact that until quite recently the focus of the research on Peircean abduction was to identify its logical form. Another agenda in the recent attempts to classify abduction is whether to allow non-explanatory abductions. In order to resolve these two closely related issues, I propose to examine how Peirce would have responded to them. In particular, I suggest to do this in connection with Peirce's another life-long project, the classification of sciences. In this examination, it will be shown that Peirce struggled with the problem of conflating induction and abduction. I shall discuss how this problem influenced both Peirce's views on the interrelationship between abduction, deduction, and induction on the one hand, and his many classifications of sciences on the other. Also, the implication of the fundamental change in Peirce's views of abduction, deduction, and induction to the problem of the classification of sciences will be uncovered. Finally, I shall discuss whether inference to the best explanation is abduction. Insofar as this problem has bearing on the two controversial issues in classifying abduction, my negative answer will demonstrate that classifying abduction is yet to get off the ground. (C) 2015 Elsevier B.V. All rights reserved.