Avicenna’s logical theory of negative judgement can be seen as a systematic development of the insights Aristotle had laid out in the De interpretatione. However, in order to grasp the full extent of his theory one must extend the examination from the logical works to the metaphysical and psychological bases of negative judgement. Avicenna himself often refrains from the explicit treatment of the connections between logic and metaphysics or psychology, or treats them in a rather oblique fashion. Time and again he is satisfied with noting that this or that question is not proper for a logician and should be dealt with in metaphysics or psychology—without bothering to refer his reader to the exact loci. The following is an attempt at a reconstruction of Avicenna’s theory of negative judgement in such a broad fashion. I will begin with his analysis of negative judgement as resulting from an operation of ‘removing’ the predicate term from the subject term. On this basis, I will move on to discuss how he conceives of the relation between negative judgements and affirmative judgements that contain privative or metathetic terms as well as the question of whether negative judgements can be reduced to affirmative ones. Having thus laid out his logical theory of negation, I move on to discuss the underlying metaphysics by looking at the relation between existence and non-existence, and existence and privation. Finally, I will address Avicenna’s scattered psychological remarks on how we can conceive of what does not exist.
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Shifāʾ: al-ʿIbāra I.6, 37–38 (in the following, all references by a solitary title are to Avicenna’s works); cf. the very similar account in Fārābī, in De int. 24–26. To be exact, in this model linguistic expressions are further subdivided to spoken and written utterances, the latter of which are conceived as expressions of the former. For a more detailed discussion of Avicenna’s semantic theory, see Inati (1984, 148–153), Black (1991, section II.2) and (2010, section II.A), Koutzarova (2009, 74–81) and Kaukua (2014b, 219–227). Bäck (2013) is an English translation of Shifāʾ: al-ʿIbāra.
Avicenna’s model is complicated by the possibility of mental causation, but this is not relevant for the purposes of the present paper. For a more detailed analysis of the model, see Kaukua (2014b).
Shifāʾ: al-ʿIbāra I.6, 37–39.
Shifāʾ: al-ʿIbāra I.6, 38–39; cf. Aristotle, De int. 5, 17a9-13; and Fārābī, in De int. 54–55.
Shifāʾ: al-ʿIbāra I.6, 41; cf. Najāt I, 51; and Ishārāt III, 23. The definition is discussed in Hodges (2012).
See Arisṭū, al-ʿIbāra 1, 59, where Iṣḥāq uses tarkīb and tafṣīl for synthesis and diairesis, respectively. Al-Fārābī uses Iṣḥāq’s terms in his uncomplicated discussion of the basic judgemental operations (see in De int. 26).
In this context, Avicenna mentions two ways of speaking about position and removal: either as restricted to predicative judgements or as encompassing the composite judgements as well (Shifāʾ: al-ʿIbāra I.6, 41–42). Although he does not state this explicitly, it seems plausible to understand the first way as referring to the reductive analysis and the second as reflecting the variety of logical forms encountered in basic kinds of judgement.
Shifāʾ: al-Qiyās V.5, 279–283. This is true in both of the cases that Avicenna distinguishes, namely in implications proper in which the constituent judgements are essentially related (fīhi ittibāʿun bi luzūm), and in chance connections of two unrelated judgements. Dasdemir (forthcoming) is a detailed analysis of the two types of conjunctive judgement.
Shifāʾ: al-Qiyās V.2, 246.
This complication is recognized already in the introduction of the concept of removal in Shifāʾ: al-ʿIbāra I.6, 41–42.
Shifāʾ: al-Qiyās V.5, 283–285.
Shifāʾ: al-ʿIbāra I.6, 43; my emphasis.
Shifāʾ: al-ʿIbāra I.6, 43–44.
See Zimmermann (1981, lxii–lxiv). According to Ammonius, this term derives from Theophrastus, though he is somewhat uncertain about the latter’s reason for introducing the term. It was either to refer to the placement of judgements in the table introduced in De interpretatione 10, 19b28-30, or to the replacement of the definite predicate by the indefinite in the same table. According to Stephanus, however, the term was designed to denote the transposition of the negative particle from the copula to the predicate.
Iṣḥāq translated aoriston as ghayr muḥaṣṣal (Arisṭū, al-ʿIbāra 3, 62); al-Fārābī follows him in the discussion of De int. 3 (in De int. 37–39) but introduces the term maʿdūl in his comments on De int. 10 (in De int. 101–103). For a subtle analysis of al-Fārābī’s theory, see Thom (2008). Following Zimmermann (1981) and Hodges (2012), I will henceforth speak of indefinite terms and judgements containing them as metathetic terms and judgements.
Shifāʾ: al-ʿIbāra II.1, 82. In all translations from this chapter, I have benefitted from Hodges (2012).
Al-Fārābī is explicit about this and notes further that certain features of the Arabic language, particularly the fact that the copula is normally not expressed explicitly, are prone to hide the distinction. Nevertheless, he also holds that the two propositions should be logically distinguished and makes the distinction along the same lines as Avicenna. (in De int. 101–103).
Cf. Ishārāt III, 27–28. Fārābī, in De int. 101, introduces the idea that the metathetic affirmation entails the positive existence of its subject as his own departure from some of the commentators. For a slightly different reconstruction of the difference between the metathetic affirmative and the negative judgement, see Hodges (2012).
Shifāʾ: al-ʿIbāra II.1, 82.
Shifāʾ: al-ʿIbāra II.1, 83.
For a useful analysis of this overlap, as well as an assessment of the Arabic discussion in the broader historical framework, see Wolfson (1947).
Shifāʾ: al-ʿIbāra II.5, 124. The concern over the transgression of the limit between logic and metaphysics is frequent in both al-Fārābī and Avicenna.
Shifāʾ: al-ʿIbāra II.5, 125; my emphasis.
Shifāʾ: al-ʿIbāra II.5, 125–126; cf. Aristotle, De int. 14, 23b21-32.
Shifāʾ: al-ʿIbāra II.5, 129; cf. Fārābī, in De int. 209–210.
Shifāʾ: al-ʿIbāra II.5, 126; cf. 127.
Shifāʾ: al-ʿIbāra II.5, 127; cf. Aristotle, De int. 14, 23b15-20.
Shifāʾ: al-ʿIbāra II.5, 128.
Frege (1918–1919, 147–148).
This argument from the unity of judgement or thought is not the only one Frege introduces. He also argues that the dissolution model fails to account for double negation and that a model that treats affirmation and negation as two kinds of assertion is more economical and hence preferable (Frege 1918–1919, 148–149, 154). I believe that Avicenna’s model can be developed to deal with double negation, since his account of the truth conditions of affirmation and negation is quite straightforward: a negation is true iff the corresponding affirmation is false, and by the same token, a double negation is true iff the corresponding single negation is false. But since such an extrapolation is rather far removed from what Avicenna explicitly considers, I refrain from further analysis here. By the same token, the question of the explanatory economy of the two theories cannot be addressed here.
There is a peculiar feature of the Arabic which may have contributed to this conclusion, for the negative copula laysa is syntactically independent of its positive counterparts—and every bit as productive of judgemental unity.
Shifāʾ: al-ʿIbāra I.6, 43; see Sect. 1 above.
For a discussion of these notions in terms of the mediaeval transcendentals, see Koutzarova (2009, 339–350).
Shifāʾ: al-Ilāhīyāt I.5.12, 25; my emphasis.
Shifāʾ: al-Ilāhīyāt I.5.13, 25.
Shifāʾ: al-Ilāhīyāt I.5.16, 26.
For a reconstruction of an Avicennian theory of intentionality along these lines, see Kaukua (2014b). In brief, the idea is that while acts of taṣawwur produce mental content, the intentional relation between that content and the external world is first produced through an act of taṣdīq. It is important to note that there are different kinds of taṣdīq; in some cases we give our assent after careful conscious consideration (for instance, when deciding whether or not to believe another person’s report) whereas in other cases, such as perception, we do this almost automatically. From the point of view of the production of the intentional relation, however, the cases are similar.
Shifāʾ: al-Ilāhīyāt I.5.24, 28; cf. I.5.18, 26–27; VII.1.9, 238; as well as the remarks on thoughts about the past and the future in III.10.22-23, 122–123.
One must be cautious when distinguishing between non-existence and privation in Avicennian texts, because the two are normally glossed over by a single term, ʿadam. While one could perhaps press the case of translating all instances as ‘non-existence’, this would obscure the natural connection in many contexts to Aristotelian discussions of sterēsis. I have therefore decided to use both ‘non-existence’ and ‘privation’ as translations of the Arabic term, each choice depending on the context.
See Shifāʾ al-ʿIbāra II.5, 124; and Sect. 2 above. Cf. Shifāʾ: al-Ilāhīyāt VII.1.5, 237–238.
Privation is also said to provide the reference for our negative judgements; see Shifāʾ: al-Ilāhīyāt III.6.10, 98 [‘facing the affirmative (utterance) is permanence (al-thubūt), and facing the negative (utterance) is privation’]; VII.1.5, 238; and VII.1.9, 238.
Shifāʾ: al-Samāʿ al-ṭabīʿī I.2.14, 19.
Shifāʾ: al-Samāʿ al-ṭabīʿī I.3.10, 32.
Shifāʾ: al-Samāʿ al-ṭabīʿī I.2.13, 19; I.3.8, 30–31; and Shifāʾ: al-Ilāhīyāt III.6.7, 97–98. In Shifāʾ: al-Ilāhīyāt VII.1.6-8, 238, Avicenna lists six different ways in which we can speak of privation, dependence on the corresponding positive attribute being common to them all.
Cp. Shifāʾ: al-Ilāhīyāt VII.1.10-11, 239 and IX.6.3, 340 with VII.1.9, 238. The two cases are also different in that the opposition of a privation and the corresponding form has no mean, whereas the opposition of two positive contraries has a mean and allows a gradual transformation from one contrary to the other (VII.1.20, 242).
Shifāʾ: al-Nafs V.5, 238.
Shifāʾ: al-Nafs I.5, 48–50.
Shifāʾ: al-Nafs V.6, 239–241.
Shifāʾ: al-Nafs V.2, 220–221; V.6, 241, 247–248.
Shifāʾ: al-Nafs V.3, 222.
Cf. the remarks on the perception of pain in Shifāʾ: al-Ilāhīyāt IX.6.2, 340.
Avicenna subscribes firmly to the Aristotelian idea that in this life thinking always requires a phantasm (see Aristotle, De an. III.7, 431a15-17); see, for instance, his refutation of an intellectual memory in Shifāʾ: al-Nafs V.6, 244–248.
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This paper has benefitted from the perspicacious comments of Yusuf Dasdemir, Sonja Schierbaum, Mika Perälä and the anonymous referees of Topoi. My sincere thanks are due to them all. The research has been funded by the Academy of Finland.
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Kaukua, J. Avicenna on Negative Judgement. Topoi (2016). https://doi.org/10.1007/s11245-016-9380-5
- Negative judgement