1 I am grateful to Eric Lewis for very helpful comments on a draft of this review.

2 That a demonstration takes the form of a syllogism is debatable, as we will see below.

3 Barnes, Jonathan ‘Aristotle’s Theory of Demonstration,’ Phronesis 14 (1969) 123-52CrossRefGoogle Scholar; reprinted in Barnes, J. Schofield, M. and Sorabji, R. eds., Articles on Aristotle, vol. 1 (London: Duckworth 1975)Google Scholar

4 Ferejohn is here (141) quoting Burnyeat, M. ‘Aristotle on Understanding Knowledge,’ in Berti, E. ed., Aristotle on Science: The Posterior Analytics. Proceedings of the Eighth Symposium Aristotelicum (Padua and New York: Antenore 1981) 118Google Scholar.

5 See Barnes. An axiomatic science, on Ferejohn’s account, is based on a few simple principles which are assumed to be the primary truths of the discipline. From these basic truths (which are not constructed through empirical investigation, but somehow a priori) all the theorems of the discipline are derived by deduction (17).

6 Ferejohn cites Ross and Hintikka as proponents of strict syllogisticism, and Barnes and Smith as proponents of anti-syllogisticism. These positions are intertwined with positions on the relative chronology of the Prior and Posterior Analytics.

7 Ferejohn points out, ‘In the logic of quantifiers, existential import is always conveyed by means of existentially quantified statements of general existence (that is, nonemptiness of predicate extensions), such as “There are men.” On the other hand, in Aristotelian logic, it is always carried by singular existential presuppositions generated by the fundamental idea that general subjects like “Every man,” no less than singular subjects like “Socrates,” actually make reference to the individuals to which they apply’(44).

8 Ferejohn seems to want to say that Platonistic universals might refer to kinds, but not to individuals. I take it this is what he means when he says that Platonistic universals express necessary relations between kinds. Aristotle’s view that universals cannot exist separately from individuals (Meta. 7.13) would seem to conflict with any view that one could refer to kinds without referring to individuals. But Ferejohn wants to leave aside the Metaphysics, and so perhaps this passage is irrelevant to his argument.

9 I do not understand Ferejohn’s reluctance to allow that what he calls ‘definitional premises’ are definitions. Perhaps he is relying on the passages (at 72a18-21; 76b35-7) where Aristotle says that definitions do not say that anything is or is not (I will discuss these at some length below). But he neglects the evidence of An. Post. 2.10, where Aristotle enumerates several different types of definition, and in the summary does not even mention the kind of definition which Ferejohn thinks is ‘primary’ (94all-14). Although he does not say so, Ferejohn may think there is a significant distinction between horos and horismos (both translated as ‘definition’) in Aristotle’s usage. Again, the evidence of 2.10 tells against this; Aristotle calls the same kind of definition both horos and horismos (93b38-9; 94all-12).

10 There is a problem here. If he thinks that the axioms of mathematical sciences are ‘mere’ analytic truths, then he must think that the mathematical sciences cannot use demonstration, if demonstration must begin with premises which are not ‘ merely’ analytic. But Aristotle uses so many mathematical examples that it is difficult to believe that he did not mean demonstration to be of use to the mathematical sciences among others (Ferejohn says as much himself [117]). Perhaps Ferejohn does not mean to identify axioms with ‘mere’ analytic truths, but to grant them the same status as the definitional premises of other sciences which combine analytic and essentialistic necessity.

11 In favor of Ferejohn’s reading, it is possible, since Aristotle here uses the word ‘deiknumi’ (to show or to prove) rather than the more technical term ‘apodeiknumi’ (to demonstrate) that he does not mean to say that the attributes must be proved in demonstration, but only that they must be shown to belong to the genus in some way or other.

12 See Bolton, Robert ‘Essentialism and Semantic Theory in Aristotle: Posterior Analytics, II, 7-10,’ The Philosophical Review 85 (1976), 521CrossRefGoogle Scholar. I do not in my account agree in every respect with Bolton.

13 It does not help that in this section Ferejohn refers to the archai which are horoi as ‘immediate definitional first principles’ and allows that Aristotle refers to them as amesoi, both terms which he has elsewhere reserved for the referential universals which, on his view, can function as premises in demonstration.

14 See Richard Sorabji, ‘Definitions: Why Necessary and in What Way?’ in E. Berti, ed., Aristotle on Science.

15 Ferejohn thinks that type 3 is not a type of per se predication, but a type of per accidens predication, which Aristotle wishes to exclude from consideration. So it is types 1, 2, and 4 which are of interest in his project of establishing which sorts of sentences can be the immediate premises of demonstration.

16 Ferejohn’s examples here are misleading. Sentences of this form cannot enter into demonstration, simply because they are not universal in form. More likely examples are, ‘Dormice are mammals,’ and ‘Dormice are fish.’

17 Aristotle’s Categories and On Interpretation, J.L. Ackrill, trans. (Oxford: Clarendon 1963)

18 It is not clear what Ferejohn thinks would follow if Aristotle were using ‘what-is-it’ in a sense limited to substance. One obvious implication would be that per se predications of type 1 would have to have as their subject term the name of some substance, rather than of something in any other category.

19 Are the hierarchies established by the single-question method different from the hierarchies established by the division of a genus? They start from different ends, but they can hardly have different results. On Ferejohn’ s account they both have to yield immediate predications.

20 Aristotle does, it is true, suggest a way in which they can be made to satisfy the condition by turning adjectival forms into nominal forms, but Ferejohn points out that that is equally true of all predications expressing inherence relations.

21 There are other problems about the predication of differentiae of species, which Ferejohn allows are not solved in the An. Post., but in the Metaphysics, with the doctrine of the unity of definition. These problems are 1. ‘the semantical problem of providing an adequate explanation of their truth conditions,’ and 2. ‘the ontological problem of saying where differentiae fit into the classifictory metaphysical scheme of the Categories’ (94).

22 Genera and species are of course relative terms, but genuinely distinct in this context, because genera are divided by differentiae while species are constituted or determined by differentiae. So the predication of differentiae of genera is very different from the predication of differentiae of species.

23 It is worth noting that most commentators have supposed that Aristotle introduces types 3 and 4 per se predication only to complete the list, and not because he thinks that predications of these types have any role to play in demonstrative science. Ferejohn’s claims here are non-standard.

24 As a kind of appendix to his argument, Ferejohn argues in the last chapter of the book that the same hierarchical conception of the categories which Aristotle used to explicate per se predication of type 1 was used to immunize his theory of scientific predication against the danger of what Ferejohn calls ‘semantic fragmentation,’ namely the association of a common term with a group of disparate items (137). Aristotle is most worried about this as it occurs with negative predication (people are not horses). His solution to the problem, which allows him to introduce negative predication into demonstrative science without thereby introducing semantic fragmentation, is to specify that every demonstration must pertain to a single underlying genus. Aristotle does not decide independently how specific a scientific genus must be; rather he fixes the line of maximum generality allowable in a legitimate scientific genus as that past which the application of negative predicates precipitates semantic fragmentation (138).