Forms of Carroll’s Paradox in Post-Classical Arabic Logic

Abstract

Arabic logicians in the thirteenth century discussed a set of arguments raised by the theologian Fakhr al-Dīn al-Rāzī (d. 1210) that in some respects closely resembles Carroll’s paradox. Roughly, the paradox states that we can never reach a conclusion from a set of premises without incurring an infinite regress. The present article presents and discusses Rāzī’s formulation of the problem with syllogistic deduction, his own solutions to the problem, and the contributions of Afḍal al-Dīn al-Khūnajī (d. 1248) and Najm al-Dīn al-Kātibī (d. 1276). It is argued that the proposed solutions developed by these authors are best understood as tending in the direction of Gilbert Ryle’s distinction between knowing-that and knowing-how.

KEYWORDS:

• Arabic logic
• inference
• entailment
• Carroll’s paradox
• Fakhr al-Dīn al-Rāzī
• Afḍal al-Dīn al-Khūnajī
• Najm al-Dīn al-Kātibī

Acknowledgements

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) as part of the research project ‘The Heirs of Avicenna: Philosophy in the Islamic East from the 12th to the 13th Century’ under Grant number 273594864, directed by Prof. Dr. Peter Adamson, Lehrstuhl VI für spätantike und arabische Philosophie, Ludwig-Maximilians-Universität München. I would like to thank the participants at the April 22, 2022 meeting of the KU Leuven Colloquia in Medieval Philosophy – especially Stephen Read – and the participants of the LMU-Berkeley Conference on Arabic Logic, held on June 3, 2022 at Ludwig-Maximilians-Universität in Munich, for their valuable feedback on earlier versions of this paper.

Disclosure statement

The author reports that there are no competing interests to declare.

Notes

1 See especially the introduction in El-Rouayheb 2019.

2 For a study of consequence in medieval Latin logic, see Read forthcoming.

3 Moore 1902–3, p. 81; Russell 1903, p. 35; Quine 1936, p. 121, 1960, p. 357.

4 A recent special double issue of the Lewis Carroll Journal dedicated exclusively to ‘What the Tortoise Said to Achilles’ gives an impression of the development of philosophical discussions around Carroll’s paradox, and relevant recent issues elicited by it (Moktefi & Abeles 2016).

5 Ryle 1945–6, p. 6.

6 Ryle 1946, p. 223.

7 In-text references in this section are to Qarāmalikī’s edition of the logic part of the Mulakhkhaṣ: Rāzī 2002–3 [1381]. Two recent editions of the entire work are Rāzī 2021a and Rāzī 2021b.

8 Rāzī uses the same word, ‘ḍarūrī’, which means ‘necessary’, but we must understand by ‘knowledge of the premises’ being ‘necessary’ not that it is a necessary condition for knowledge of the conclusion (because this is being assumed for this horn of the dilemma). Rather, it must mean that the premises are necessarily known, presumably because they are necessarily true. This is contrasted with knowledge of the premises being ‘the product of reasoning’, that is: derived from other premises. For a fourteenth century explanation of the terms ‘necessary’ (ḍarūrī) as opposed to ‘produced by reasoning’ (naarī) which are both distinct from ‘intuitive’ (badīhī), see Taftāzānī 2011, pp. 103.4-10.

9 For Urmawī’s and Quṭb al-Dīn’s discussions, see the latter’s commentary on the former’s Maṭāliʿ al-anwār: Tatānī 2014, pp. III 17-21; and illī 2017, pp. 238.5-242.3; Samarqandī 2014, pp. 319.8-323.7.

10 Rāzī 2002–3 [1381], pp. 247.13-248.4.

11 Rāzī 2021a, pp. 379.9-380.2/Rāzī 2021b, pp. 295.12-296.8: ‘On the possibility of jointly grasping several objects at a single stroke. Concerning conceptions, [this is possible] because if it weren’t, then no assent would ever come about. For the relation (nisba) between one thing and another is only possible if both things are grasped. The falsity of the consequent here indicates the falsity of the antecedent. Moreover, one may conceptualize a compound by means of its definition, and this is only possible when all its parts are conceptualized at once. Concerning assents, [this is possible] because if it weren’t, then only a single premise could ever occur in the mind. If this were the case, no conclusion would ever occur, for we know by necessity that no single premise is ever productive of a conclusion. The falsity of the consequent here indicates the falsity of the antecedent. Anyone who says that when we turn our mind to an object of knowledge, it is impossible for us to turn to another object of knowledge [at the same time], must be referring to our imagination (khayāl), not to our intellect with which we may well [do these things]’.

12 Rāzī 2002–3 [1381], pp. 248.5-7.

13 Khūnajī 2010, pp. 241.10-242.3.

14 Khūnajī 2010, pp. 242.6-14.

15 Khūnajī 2010, pp. 243.1-11.

16 Kātibī 1293 [692], fol. 51r18-21.

17 Kātibī 1293 [692], fol. 51r21-24.

18 On hypotheticals, Kātibī earlier in his commentary says: ‘They said: this is because when the consequent is true in actual fact (fī nafs al-amr), then it is true jointly with every fact stipulated. And it is necessary that it is so in relation to whatever is not incompatible with its truth. Its truth is not known on account of stipulating it. Know this! And in this sense, it is more general than the first [sense] because its truth is only the truth of the consequent without the first [sense in which] it is not true except when both antecedent and consequent are jointly true’ (Kātibī 1293 [692], fol. 43v9-11).

19 Kātibī 1293 [692], fol. 51r24-26.

20 Kātibī 1293 [692], fol. 51r28-31.

21 Kātibī 1293 [692], fol. 51r33-37.

Additional information

Funding

This work was supported by the Deutsche Forschungsgemeinschaft.