It is widely agreed that Aristotle’s Prior Analytics, but not the Topics, marks the beginning of formal logic. There is less agreement as to why this is so. What are the distinctive features in virtue of which Aristotle’s discussion of deductions (syllogismoi) qualifies as formal logic in the one treatise but not in the other? To answer this question, I argue that in the Prior Analytics—unlike in the Topics—Aristotle is concerned to make fully explicit all the premisses that are necessary to derive the conclusion in a given deduction.
BrandisC.‘Über die Reihenfolge der Bücher des Aristotelischen Organons und ihre Griechischen Ausleger, nebst Beiträgen zur Geschichte des Textes jener Bücher des Aristoteles und ihrer Ausgaben’Hist.-Phil. Abhandlungen der königlichen Akademie der Wissenschaften zu Berlin (Jahr 1833)183524999
Alexanderin Top.ii.2 3.25-4.10 and 5.4-13 Wallies; Smith 1993 338-9; Code 1999 45. Aristotle holds that dialectic is ‘concerned with things which are in a way common for all to know not for any separate science’ (Rhet. 1.1 1354a1-3; similarly APo. 1.11 77a31). Accordingly Aristotle’s account of dialectical deductions in the Topics is sometimes called ‘formal’ on the grounds that its topoi are topic-neutral and provide general argument forms applicable to a large number of particular cases (Allen 2001 15-16 and 69-72; Smith 1997 pp. xxiv and xxvi; Wagner and Rapp 2004 8; Wagner 2011 356).
Striker2009194; see also Slomkowski 1997 24 27 and 134.
See Alexanderin Top. ii.2 158.31-160.3 Wallies; Primavesi 1996 152-4. Similarly Aristotle writes in the Categories: ‘If you will call the individual man grammatical it follows that you will call both man and animal [i.e. the species man and the genus animal] grammatical’ (Cat. 5 3a4-5; see Perin 2007 135).
See Whitaker199691-4; Weidemann 2002 206-7; Jones 2010 42-5.
Kneale and Kneale196237.
See Alexanderin Top. ii.2 288.12-289.31 Wallies; Maier 1900 79-80 n. 1; Brunschwig 1967 pp. lix-lxi and 163-4; 1968 16-18. This alternative sense of ‘indeterminate’ is also found in the Prior Analytics (APr. 1.4 26b14-16; 1.5 27b20-2 27b28; 1.6 28b28-30 29a6; 1.15 35b11; see Alexander in APr. ii.1 66.2-18 67.3-7 88.6-8 88.31-3 105.22-6 Wallies; Waitz 1844 383; Maier 1896 162-3; Brunschwig 1969 13 and 19; Crivelli 2004 245 n. 21; Striker 2009 98-9).
See Alexanderin APr.ii.1 266.32-267.5 Wallies; Philoponus in APr. xiii.2 252.31-5 Wallies; Pacius 1597b 155-6; Waitz 1844 434; Mendell 1998 185; Striker 2009 179. It seems clear that Aristotle regards the major premiss of A1 as indeterminate in the sense defined in Prior Analytics 1.1 (24a19-22). Aristotle describes this major premiss as being ‘without universality’ (ἄνευ τοῦ καθόλου 41b7); the same phrase (ἄνευ τοῦ καθόλου) is used in 1.1 to characterize indeterminate premisses (24a20). Also the major premiss of A1 is very similar to one of Aristotle’s examples of indeterminate premisses in 1.1 ‘Pleasure is not good’ (24a21-2).
See Alexanderin APr.ii.1 53.28-54.2 379.14-380.27 Wallies; Philoponus in APr. xiii.2 46.25-47.9 Wallies. Moreover the use of schematic letters helps Aristotle to abstract from speaker meaning since the speaker meaning of a sentence on a given occasion of use will typically depend on the literal meaning of its subject and predicate terms.
See Anagnostopoulos1994131-40. When some degree of inexactness is appropriate for the purposes of a given investigation Aristotle tends ‘to view exactness as something toilsome and as something that reflects the kind of pettiness or meanness that he elsewhere associates with the behavior of the illiberal person’ (Anagnostopoulos 1994 126).
See Alexanderin Top.ii.2 26.13-19 Wallies; similarly Smith 1997 51.
See Barnes198123-4n. 9; Rapp 2002 63 and 164. In Topics 8.11 (161b28-30) Aristotle takes the condition expressed by τῷ ταῦτα εἶναι to be part of the definition of deduction (cf. Rhet. 1.2 1356b17; se 6 168b24). This suggests that he takes this phrase to be equivalent to the one used in Topics 1.1 (διὰ τῶν κειμένων).
See Barnes198123-4n. 9; Bolton 1994 116; Primavesi 1996 59 n. 2; Rapp 2000 17-20; similarly Striker 2009 79-81.
See Alexanderin Top.ii.2 13.28-14.2 and 568.18-23 Wallies; Frede 1974a 22; Barnes 1980 168-9; Allen 1995 189; Smith 1997 143; Mignucci 2002 251; Ebert and Nortmann 2007 227-8; Striker 2009 81-2.
Mignucci2002254-6. The causal condition requires that the conclusion follow ‘through the things supposed’ (διὰ τῶν κειμένων Top. 1.1 100a26-7; se 1 165a2) whereas Aristotle denies that the conclusion of A3 has been deduced ‘through the things assumed’ (διὰ τῶν εἰλημμένων APr. 1.32 47a27-8).
Alexanderin APr.ii.1 347.5-7 Wallies. For alternative suggestions see Pacius 1597a 262; Ebert and Nortmann 2007 800-5; Striker 2009 214. Some of these commentators argue that in order to turn A3 into a deduction one must not only add a premiss but also transform the two premisses already present in A3.
Alexanderin Top.ii.2 568.13-18 Wallies. Similarly Aristotle states that arguments are subject to criticism if ‘the conclusion does not come about either when some premisses are taken away or some premisses are added’ (Top. 8.11 161b22-4). Again this implies that an argument in which premisses are missing is not subject to criticism as long as it can be turned into a deduction by adding suitable premisses; see Allen 1995 189; Rapp 2000 27-32.