Abstract
The paper provides an interpretation of Aristotle’s view on scientific inquiry as problem solving. It tackles passages where Aristotle emphasises the role that the problem-solving activity has in science, and where he describes the history of humans’ problem-solving activity and the historical development of natural science as a problem-solving activity. Further, the paper examines Aristotle’s practice of raising, assessing and solving problems as well as the heuristic procedures he employs to move from ignorance to scientific knowledge. Finally, it raises a question about Aristotle’s view on the epistemic status of scientific definitions: does Aristotle conceive of the definitions, which are the results of scientific inquiries, as truths (known with certainty to be true, i.e. known with certainty to be principles) or rather as plausible hypotheses that may or may not be true?
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Notes
Phys. I 1, 184a10–14; Phys. I 8, 191a24–25; Phys. II 3, 194b17–20; Metaph. II 1, 993b19–24.
Apo II 1–2.
Here I translate with ‘problem’ two Greek words used by Aristotle: problema and aporia. These words do not have exactly the same meaning in Aristotle’s writings; an examination of their differences would certainly benefit our understanding of Aristotle’s ‘problematic’ approach. For reasons of space, however, I cannot provide this examination here. My present inquiry is based on the hypothesis that these words are often closely connected and sometimes even overlapping. Their connection is shown by Aristotle’s account of problema in Top. I 1, 104b1–17: problema is conceived of as something involving aporia. Their overlapping is suggested by the fact that sometimes Aristotle calls aporiai propositions that have the same linguistic formulation and epistemic content of a problema. For instance, according to Top. I 4, 101b32–33, a problema is a question of the form ‘is it the case that S is P or not?’; questions of this kind are labelled in Metaph. III as aporiai (e.g. 1001b26–28). All this, of course, does not imply that every problema is or involves necessarily an aporia. A mathematical problema, for instance, is simply a task to be performed. Aristotle seems to emply a sense of problema that is close to the mathematical one in the Analytics (see n. 35).
In APo II 14, 98a1, the word problema is used to refer to two kinds of zetoumena, i.e. the hoti- and the dioti-questions. I discuss the issue of whether and in what sense also the other zetoumena (i.e. ei esti- and ti esti-questions) and are problemata in Quarantotto (2017a), where I propose a positive answer.
Cf. also Apo II 19, 99b17–19.
Cf. also Rhet. I 11, 1371a31–34. The theme of wonder as generating philosophy goes back to Plato’s Theaetetus 155d.
On this passage, see also n. 20.
These activities include those concerning myths: according to 982b18–19, love of myth and philosophy have a common source in wonder.
The image of philosophy as free goes back to Republic VI 499a. The connection between the philosopher’s freedom with leisure goes back to Theaetetus 172d and 175e. Sophist 253c-d calls the true philosopher’s method ‘the knowledge that free people have’.
Aristotle provides this historical account in Metaph. I 1–2. His main aim is to emphasise the superiority of theoretical sciences over practical and productive sciences and arts (981b30–982a1), and to show that theoretical knowledge is present in some form or degree also in practical and productive sciences and arts (981a24–27). The reason why this account can also be read as a history of humans’ problem-solving activity is that theoretical knowledge is conceived as knowledge of the cause (981a28–30) and as deriving from the desire to escape ignorance—which is manifested in the psychological state of wonder and in the state of aporia (982b12–17). So, insofar as theoretical knowledge is present in some form or degree also in practical and productive sciences and arts, also these sciences and arts involve wonder, aporia and a problem-solving activity. In sum, the problem-solving activity is a common trait of the practical, productive and theoretical sciences insofar as all include the knowledge of the cause: they are aimed at solving causal problems (dioti); the practical and productive sciences address and solve problems for the sake of, respectively, action and production; the theoretical sciences for the sake of knowledge itself. Further also some non-scientific activities can be described as problem-solving activities: e.g. someone whose activity is guided by experience (rather than by art or science) would be able to solve factual (hoti) problems but not causal (dioti) problems (981a28–29); for instance, she would be able to cure somebody, without knowing why the cure works. On the problem-solving activity in science and art, see also the prologue to the Problemata Mechanica (987a11–848a37).
The idea of a sequence of problems is hinted at also in other passages: see for instance Metaph. I 10, 983a25–27; Metaph. III 1, 995a24–27. Cf. also DA I 1, 402a3, where Aristotle includes the knowledge of the soul among those that involve more wonder than others (thaumasioteron).
Phys. I 8, 191a23–33; Metaph. I 3, 984a18–b1.
Metaph. I 3, 984a18–b1.
Phys. I 3, 187a1–11; I 4, 187a26–31; I 9, 191b36–192a1; Metaph. XIV 2, 1088b35–1089a5; GC I 8, 324b35–325b5.
The path is a cognitive natural development, since it starts from how things appear to us (184a16), i.e. from how things are perceived by us (184a24–25), and since its course amounts to a transformation of our view on things: what was at first obscure to us becomes clear to us. The cognitive character of the path is also suggested by the fact that the path is compared to the ontogenetic development of linguistic abilities in human beings (184b3–5). Moreover, the path is objective, since it is sometimes engendered by truth (188b29–30) and the things themselves (191b31–34).
The metaphor of the path is used also in Metaph. I (cf. I 3, 984a18–19), where Aristotle describes his predecessors’ progressive discovery of the causes as a problem-solving activity (cf. I 3, 984a16–b1; b8–22).
Cf. also DA I 1–2: Aristotle starts his inquiry into the soul by formulating a series of questions and aporiai and by presenting this ‘problematic’ approach as necessary (anagkaion: 403b20–21).
Metaph. I 2, 983a11–23. Note, however, that it is not entirely clear whether, in this passage, the subject who feels wonder is a mathematician or someone who does not know mathematics. In the second case, the available knowledge, which makes the incommensurability of the diagonal unexpected, would not be mathematical knowledge.
Of course, the new knowledge that enables the solution of a problem can be a reformulation of the available knowledge itself, i.e. it does not consist necessarily of new data.
This includes the cases in which the available knowledge allows for different solutions of the same problem (cf. most of the problems collected in the Problemata physica).
In what follows, without aiming at completeness, I provide some paradigmatic examples of the way in which Aristotle formulates problems. On this issue, see Rossi (2017), who focuses on aporiai that consist of arguments for conflicting theses.
Cf. Topics I 11, 104b12–14; VI 6, 145b16–21.
This is clearly the case of the two examples from GA II 5 and GC II 1 3 tackled earlier.
Cf. Top. I 11, 104b14–16.
For instance, a certain proposition is a causal problem since on the basis of the available knowledge it can be solved in a variety of different ways (cf. the problems of the Problemata physica) or since the available knowledge is not sufficient to solve it (cf. Top. I 11, 104b14–16) or since the solution provided on the basis of the available knowledge involves unacceptable consequences (cf. Metaph. III 6, 1002b12–32). For an example of existential and definitorial problems, see Phys. IV 1 (and infra, Sect. 7), where Aristotle tackles the issue whether place exists and what place is.
In Sect. 8 I shall address the issue of whether Aristotle recognises the possibility of an end of scientific inquiry due to a complete and certain knowledge of things.
Metaph. I 1, 980a21.
This is clearly a Socratic legacy: see Meno 81d7–e1, 84a3–d1.
According to Laks (2009, pp. 39–41) and Rossi (2017), the formulation of a problem or aporia guides the inquiry also in a further way, i.e. by providing knowledge of the nature of the problem, conceived as a bond that blocks the inquirer. This hypothesis is based on a certain interpretation of Metaph. III 1, 995a29–30, where Aristotle says that ‘it is not possible to obtain release, agnoounta ton desmon’. This, in Laks’ and Rossi’s view, means that ‘it is not possible to obtain release, if you do not know what is binding you’, i.e. if you do not recognize the nature of what binds you. The knowledge of the nature of the bond bears on the aporetical material, the way it is structured and on its weak points. Therefore, it shows the way out from the impasse. Metaph. III 1, 995a29–30, however, can also be interpreted in a different way. The ignorance of the bond Aristotle refers to can be the ignorance of the mere existence of a bond, rather than the ignorance of its nature. This interpretation seems to fit better with Aristotle’s subsequent claim (at 995a30–31) that ‘the impasse experienced in thinking shows this [i.e. the bond] concerning the thing itself’. This suggests that, in Aristotle’s view, there are bonds in the things themselves (i.e. in reality and in the topics tackled by inquirers); the difference between those who inquire by formulating problems and those who inquire without doing so is the difference between those who recognise the existence of bonds and those who do not. On this interpretation, the knowledge of the bond does not include, by itself, any positive means for its solution (i.e. does not include the knowledge of the weak points of the arguments that comprise its formulation). This is why knowing the bond corresponds to experiencing an impasse, to being blocked and unable to move forward.
Phys. IV 4, 211a7–11.
Note that in Aristotle’s Prior and Posterior Analytics, the word problema refers generally to a proposition that must be proved by means of a deductive argument, i.e. a proposition that is the conclusion of a deductive argument whose premises must be provided (see, for instance, Apr. I 4, 26b31; I 26, 42b29, 43a18; II 12, 62a21; Apo I 31, 88a12). Hence, ‘grasping a problem’ means finding the kind of proposition that can be the conclusion of a scientific demonstration (whose premises must be provided).
Diogenes Laertius’s catalogue of Aristotle’s writings lists several titles that include the word problema: Problems from those of Democritus, Homeric Problems, On Problems, Reconsidered Problems.
According to the standard view, these treatises are not Aristotle’s but a Peripatetic compilation. Conceivably, however, Aristotle wrote treatises of this kind. This is suggested first of all by the fact that, in several passages of his writings, he refers to further discussion of issues in ‘the problems’ (De iuv. 5, 470a18; De somn. 2, 456a27–9; PA. III 15, 676a16–8; Meteor. II 6, 363a24; GA. II 8, 747b5; IV 4, 772b11; 7, 775b36–7). Another treatise of the corpus that can be considered relevant to a ‘problematic’ inquiry is De Mirabilibus auscultationibus, which deals with wonders.
In Quarantotto (2017a) I tackle this issue more extensively.
Arguably, this aspect of the textuality of Aristotle’s writings (the problema format) arises from the Socratic world of question and inquiry and from even more ancient forms of expression, like the Pythagorean akousmata (on this issue, see Quarantotto (2017a)). The Socratic legacy is clearly recognized by Aristotle himself: Metaph. I 2, 982b12–20, 983a11–21. On the history of the Problemata as a literary genre, see Flashar (1983, pp. 297–303). In Flashar’s view, the problematic inquiry was already rather common since the Sophistic; moreover, several Hippocratic treatises show an argumentative style that has a problematic character (e.g. On Regimen in Acute Diseases, Epidemics). However, the first whom is traditionally attributed a writing entitled Problemata, together with many books on the causes, is Democritus. Democritus’s Problemata, according to Diogenes’s catalogue of Aristotle’s writings, had been the object of two books by Aristotle (on the relation between Democritus’s Problemata and Aristotle’s, see Menn (2015)). Moreover, there is also evidence that supports the hypothesis that the problemata originated from geometry (Slomkowski 1997).
This text (and, in general, Aristotle’s writings) is not a document of Aristotle’s inquiry into place (i.e. of the heuristic procedures whereby he arrived at his definition of place), but a lecture directed to an audience of students and collaborators, aimed at explaining them what place is in Aristotle’s view and at persuading them that Aristotle’s account of place is correct or the most plausible. The way the text is structured, however, allows us to use it as a testimony of Aristotle’s heuristics (on the distinction between document and testimony, see Rossi 1979). This section of the paper is based on Quarantotto (2017b), where I examine Phys. IV 1–5 more extensively.
The question ‘how does x exist?’ is not included among the zetoumena/problemata in Apo II 1. This may be due to the fact that it concerns an aspect of the question ‘does x exists?’ and so can be viewed as a sub-question of the latter.
In Top. I 1, 104b1–17 a problema is conceived of as something involving aporia. On the relation between problema and aporia, see n. 3.
Aristotle considers and rules out the hypotheses that place is a body and that the located thing is a body (209a3–7), that place is a limit and that the located thing is a limit (209a7–13), that place is a kind of incorporeal entity, i.e. something intelligible (209a13–18), and that place is a cause (209a18–23). These are the first four aporiai. The latter two (209a23–29) are Zeno’s aporia (which concerns the existence of place conceived merely as something that exists) and an aporia (connected to Zeno’s one) about the growth of place.
Aristotle shows that, besides being unable to explain the role of place within the locomotion of a body, Plato’s account of place is ineffective with respect to its own explanandum, i.e. generation (209b21–210a11). The general opinion on place according to which everything that is occupies a place is shown to be false since it implies an infinite regress (i.e. Zeno’s aporia). Aristotle argues for the view that only bodies—and only insofar as they move per se and are in contact with a different body that contains them—occupy a place (211a12–b1).
Further, there are reasons to suppose that this hypothesis is ruled out also because it is incompatible with one of the relevant data: it cannot explain the motions of the simple bodies towards their appropriate places and their rest in their appropriate places (cf. Sedley 2012, Quarantotto 2017b, p. 40).
To arrive at this conclusion, Aristotle also employs an analogical reasoning: he employs as heuristic tool the analogy between place and vessel (aggeion). This analogy is introduced right from the start of the inquiry (208b3); it is used to rule out the hypothesis that place is the form of the located body and the hypothesis that it is the matter of the located body (209b28–33); it is progressively elaborated to distinguish between Aristotle’s hypothesis and the hypothesis that place is an extension external to the located body (212a9–14). The final result of this analogical procedure is that place is described as the analogue of the limits of an immobile vessel (212a13–16).
On this requirement, see also DA I 1, 402b25–403a2: the definitions that are unable to account for the accidents of the defined thing (i.e. by means of which it is impossible to demonstrate these accidents) are labelled as ‘dialectical’ and ‘void’.
There is an exception, though: the motions of the simple bodies towards their appropriate places and their rest in their appropriate places (211a4–6). At 212b29–213a10 Aristotle provides an explanation of this phenomenon on the basis of his definition of place (although he presents this explanation as insufficient: 213a4–6). The reason why he provides this explanation is that the phenomenon at issue has not been used to construct the definition of place and so it is not obvious that the definition is able to explain it (on this issue, see Quarantotto 2017b, pp. 247–258).
Trans. Barnes.
Apo I 22. I take it that also the procedures tackled in Apo II 13, 19 and in Top. VII 5 are not heuristic procedures by applying which we can be sure that a given definition is a principle.
I leave aside the question of whether nous is a faculty or a disposition (hexis). If it is a disposition, then a fortiori it seems impossible to conceive of it as a kind of intellectual insight that shows us that a given definition is true.
Top. VII 5, 154a23–24, 155 a17–18; DA I 1, 402a10–11.
DA I 1, 402a11–22.
This question concerns definitions, not axioms (like the principle of non contradiction). I leave aside the issue of whether, in Aristotle’s view, the arguments he employs to show that the principle of non contradiction is true are such that, on their basis, we know with certainty that it is true.
In Metaph. IX 10, 1051b17–1052a11, Aristotle tackles the knowledge of what he there calls asuntheta and ti esti, which arguably are or include principles/definitions. He claims that knowing them (i.e. having a true grasp of them) amounts to touching them (thigein) and thinking them (noein), whereas ignoring them amounts to not touching them, and that ‘it is impossible to be in error regarding the question what a thing is’ (1051b25–26). So, the passage suggests that the knowledge of principles/definitions is a matter of ‘all or nothing’, but does not seem to say anything about the means whereby we know that something is a principle (i.e. a definition that expresses the essence or ti esti of a thing): it leaves open the possibility that someone knows a principle/definition, without knowing (with certainty) that it is a principle/definition.
It can be argued that, in Aristotle’s view, knowing that a definition is a principle does not require certainty. For instance, knowing that a definition is a principle may amount to having good reasons to believe that a definition is a principle. One may object, however, that this knowledge (having good reasons that a definition is a principle), since it is not certain, is still an hypothesis.
See, for instance, Kosman (1973).
On this requirement, see for instance Apr. I 30, DC II 13, 294b7 ff.
I am grateful to Francesco Ademollo, David Charles, Paolo Fait, Emiliano Ippoliti, Giulia Mingucci, Monica Ugaglia and Diego Zucca for discussing with me a previous draft of the last section.
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Quarantotto, D. Aristotle on Science as Problem Solving. Topoi 39, 857–868 (2020). https://doi.org/10.1007/s11245-018-9548-2
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DOI: https://doi.org/10.1007/s11245-018-9548-2