ALLAN AND KARBOWSKI ON THE QUASI-MATHEMATICAL METHOD IN THE EUDEMIAN ETHICS

This paper’s aim is to consider the I 6 methodological prescription and its relationship with Allan’s quasi-mathematical method theory, which aims at bringing Aristotle closer to an Euclidean model. I will also consider Karbowski’s objections to Allan and his own thesis, which holds that it is possible to treat book II in accordance with prescription I 6, always going through the vaguest opinions and definitions first only then to the most accurate.


Introduction
This paper's goal is to regard the methodological prescription of the Eudemian Ethics 1 I 6 and its relationship with Allan's quasi-mathematical thesis -which draws Aristotle nearer to Euclid's methodwhile also presenting Karbowski's objections to Allan.Moreover, I will also expound Karbowski's theory, which holds that it is possible to read book II in the light of prescription I 6, always going through the vaguest opinions and definitions first only then to the most precise.
Let us observe here how Aristotle prescribes his method in the sixth chapter of the first book of the Eudemian Ethics: [1] We must try, by argument, to reach a convincing conclusion on all these questions, using, as testimony [marturios] and by way of example [paradeigmasi], what appears to be the case [phainomenois].
[2] For it would be best if everyone should to turn out to agree with what we are going to say; if not that, that they should all agree in a way and will agree after a change of mind; [3] for each man has something of his own to contribute to the finding of truth, and it is from such [starting points] that we must demonstrate: [4] beginning with things that are correctly said, but not clearly, as we proceed we shall come to express them clearly, with what is more perspicuous at each stage superseding what is customarily expressed in a confused fashion. 2 The philosopher tries to define in the first sentence how one should precisely guide oneself in order to get to the truth on moral matters or, at least, to clearer concepts.Employing indications is using the endoxa as a starting point, which will be cleared up, in order to have premises or hypotheses used as "models" of the investigation.The second assertion then seems to justify the first, for "it would be best if everyone should to turn out to agree", meaning that it will be easier to establish the endoxa (which are the reputed opinions) as models, making the first reputed opinions survey already seen as a group itself.If that isn't the case, Aristotle goes on: since all men cling to truthassertion which seems to be the basis of his argument -, one only needs to then prove whatever it is that each one of us can contribute: that is, reputed opinions.In a way, these opinions would already be indications but not models, since they would not have been clarified yet.That is the point when, once more, one has the need to go through the aporiai so as to establish a consistent group and to finally prove what is that something each person has to "contribute to the finding of truth".This should be conforming the initial indications from which one has begun, the nonclarified endoxa, to the established models or paradigms through the enlightenment of the endoxa.One must observe and reach out for patters within the indications as to only then be able to confront them and to clarify one's opinions.Mansion3 proposes an important distinction for the forth assertion: a distinction between the investigation's starting point and knowledge stricto sensu.The first would be the "more understandable to us" (that is, to the observer) whereas the latter would be "more understandable in itself" (that is, due to the nature of the object's knowledgeability).The interpreter highlights an aspect of this distinction in the process of understanding by asserting that "an immediate evidence that imposes itself is more understandable for us, but which doesn't fully satisfy our spirit in such a way that it excited us to proceed investigating" (1979, p. 213-4) Following this interpretation, the endoxa might be taken as to be indications because they are the most understandable for us and, since they are so, they become the starting points of our investigation, which usually goes through the particulars first and then to the universal.

The Endoxa Method
If book I does in fact confirm itself as a preamble to what will be investigated and if the "endoxa method" is a correct procedure that Aristotle recommends at the beginning of the treatise, one may hold Barnes' thesis, which presents the endoxa as the components of the Eudemian Ethics' method from the beginning until the end of its definitional quest.Let us now take a look at what such procedure consists of.
At the beginning of the akrasia discussion in the Ethica Nicomachea VII 1 (=EE VI 1), Aristotle prescribes the following: We must, as in all other cases, set the apparent facts before us and, after first discussing the difficulties, go on to prove, if possible, the truth of all common opinions about these affections of the mind, or, failing this, of the greater number and the most authoritative (...).4 I will presuppose his analysis on the interchangeability between the phainomena and the endoxa in such a way that one may read "set the apparent facts" as an opinion survey on the matter.It is also advisable to bear in mind Barnes' comment5 which states that if phainomena and endoxa refer to the same things in some passages, that still doesn't authorize us to think that they necessarily are synonymous for Aristotle -Barnes owes this qualification to the fact that in other contexts they may refer to different objects, as the phainomena in De Caelo make reference to sensory objects, for instance.Barnes6 distinguishes three important steps established by the following prescription: (1)   establishing (tithenai) what seems to be the case, (2) going through (diaporein) the aporias or challenges, (3) proving (deiknynai) the reputed opinions as much as possible.Steps (1) e (2) are practically inseparable, for the doxographical survey itself brings the aporiai forward.According to Barnes, there shall be two moments in which one grasps the reputed opinions: the first would be when one gathers these opinions, which I will here name as "preliminary endoxa" due to the fact that they may present inconsistencies in such a way that they could not all form a group, since a group must be consistent.
Secundo, after going through the aporiai, one shall have enlightened endoxa, meaning that they form a group which indicates to the investigator how to proceed next.This preliminary survey of reputed opinions (which dispute the status of truth and are usually in contradiction) will generally take one to a confusing and puzzling path meant to be gone through.With that said, the process of going through aporias mentioned in the passage above becomes clearer and reveals itself as aspiring to preserve the most compatible endoxa as possible, thus forming a consistent group.This will be accomplished through the analyses of the preliminary endoxa and the incompatibilities that show upfor example, in the akrasia discussion in the Ethica Nicomachea, Aristotle points out inconsistencies that derive from Socrates' opinions only to later establish which opinions he can keep or modify.Now I pass on to step three, (3) "proving the opinions as much as possible".This is the result which came from "going through the aporiai" and reformulating the reputed opinions so as to finally obtaining a consistent group.Barnes7 identifies that the notion of "proof" is a kind of problem solving that the initial endoxa survey produced.He stresses that truth is exclusive and exhaustively found in the remain group of reputed opinions.It seems that it is an exhaustive process because the endoxa form a maximally consistent group, meaning that adding any other opinion would make them inconsistentthus no longer a group.Nonetheless, how can we understand Barnes when he states that truth must be found exclusively through the remaining group of reputed opinions?I am convinced that an Eudemian Ethics passage can be useful to make the procedure's last step comprehensible.
Looking back at the EE I 6 prescription, we can better understand how what was taken as being the investigation's starting point actually works within the "endoxa method".In 1216b28, Aristotle says that "for each man has something of his own to contribute to the finding of truth".As previously exposed, this "thing" everyone can contribute to truth and that needs to be proved is the reputed opinions.In the Ethica Nicomachea VII 1 (EE = VI 1), this is also required.What is proven is not that the truth is the end of the definitional quest, nor that it is a definitive proof given to an argument, but that it is a proof that one

Book II -Allan's thesis on the "quasi-mathematical" method
After having endorsed that the procedure in I 6 is based on the refinement and the conformity of the endoxa, which serves as the Eudemian Ethics' prescription throughout, which this paper's hypothesis, one begins to read book II with an odd impression.
In II 1, Aristotle first says that what he shall present comes from reputed opinions ("For wisdom, virtue and pleasure are either in the soul or outside it, and it is those in the soul that are more worthy of choice" 1218b35) and by inductions alike ("Let this be assumed; and about excellence, that it is the best disposition, state, or capacity of anything that has some employment or function."1219a1-20).
Nonetheless, the hypotheses introduced throughout the chapter look more like postulations, for they are not previously examined as endoxa should and they aren't introduced as being the opinions of the wise or of the majority.Allan8 also notices that in this passage he seems to use an Euclidean method in which "references assumptions or vague initial definitions".According to the Euclidean or deductive method, each proposition gives out reasons or assures the following proposition so that one can deduce by the hypotheses a definition.Allan also identifies the same argumentative pattern throughout book II when defining kûrios (II 6, 1222b21), eph'autōi (II 6, 1223a4), phrohairesis (II 10, 1226b 16-21) and areté etiké (1227b5-10).Before these examples, Allan holds that definitions are taken by following this method and also that at least the second book advances in an Euclidian manner, with one definition securing the next, connected by a deductive method: "(...) the Eudemian version, carrying out its avowed principle of steady advance from the vague to the clear, arrives in order at a series of connected definitions." 9.
Besides shedding an Euclidian strategy upon Aristotle, Allan also finds similarities between the way Aristotle uses terms that introduce hypotheses and definitional derivations, as hupokeisthō and estō 10 , which he presumes were terms of the mathematical context.These similarities are not conclusive though.
Karbowski 11 takes advantage of this non-conclusive fact and asserts that these terms were already broadly used by philosophers of Aristotle's time and before, including himself.Nonetheless, this is not enough to give up on Allan's theory: Aristotle may have well made use of mathematics' technicality and methodological strategy in his works, thus formulating a deductive structure alongside its closest terms: that is, the mathematical terms.

Karbowski's Critique of Allan
Karbowski does not identify the passage in which Allan does not rebuild differently than I 6 prescribes (thus subsidized by Barnes' thesis on the compatibility of the endoxa).2. Good/ends in the soul are best among human goods.
3. Therefore, happiness must be a good (the best good) in the soul.
4. Goods in the soul are either states or activities.
5. Activities are better than states, and the best activity is correlated with the best state.
6. Therefore, happiness must be the best activity in the soul, the one correlated with the best state.
7. The best state of the soul is its excellence.
8. Therefore, happiness is the activity of the good, i.e.: excellent, soul. 13s reconstruction presents as its first premise a clarification of what is generally taken as being happiness 14 ; the second premise takes profit of what is the general opinion, or endoxa; the forth deals with theses that Aristotle regards as irrevocable 15well, Allan could have here said that there is merely a hypothesis and nothing else -; the fifth premise comes from the already mentioned connection between telos and ergon 16 ; finally, the seventh premise comes from an induction (épagogé) 17 .One can tell that almost every premise emerges previously in the text and that more refined notions, that were not at present in the text before, are derived from them until a conclusion is made, which is the aspired definition.In this scenario it is very unlikely that one can take Aristotle's argument as a rebuilt hypotheses aspiring an Euclidian kind of deduction.
There is yet another objection to make: in themselves).
In order to conclude, I shan't try to restrain the use of the quasi-mathematical term in the Eudemian Ethics, but only try to show that Allan's interpretation looks only towards one direction and is thus liable to not address important aspects of the method, as the I 6 prescription and the idea of passing from the vaguest to the most precise when dealing with definitions.Aristotle uses postulates, but one must keep in mind that they were broadly used as archai or logos in Aristotle's historical context and that one should so delimitate its use.Karbowski holds that this use was associated to the necessity of dissociating postulates from first principles of moral's dominium, apart from following the criteria of the I 6 prescription.
By following the prescription's criteria, Karbowski refers to the continuity of the I 6 passage that was not here quoted, which consists on deepening the previous prescriptions: For that way of proceeding is the philosopher's, in every discipline,; but great care is needed here.For, it appears to be the mark of the philosopher never to speak in an unconsidered fashion, but always with reason, there are some that go undetected when they produce arguments that are foreign to the inquiry and idle.(They do this sometimes because of ignorance, sometimes because of charlatans.)By such arguments are caught even by those who are experienced and of practical ability at the hands of men who neither have or are capable of architectonic or practical thought.This happens to them through lack of training; for it is a lack of training to be unable to distinguish, in regard to each subject, between those arguments which are appropriate to it and those which are foreign.
It is also a good thing to appraise separately the account of the reason and what is being demonstrated, first because of what has just been said, that we should not in all cases pay attention to what emerges from arguments but often rather to what appears to be the case (as things are, whenever they cannot solve a problem, they are forced to accept what has been said), and secondly because what seems to have been demonstrated by argument is true, but not for the reason that the argument claims. 25rbowski briefly suggests that we all follow this hypothesis, finding conditions that justify Aristotle's use of postulates.First, the properly philosophical argument must be appropriate (oikeion) for its goal26 ; maintain the causal principals separate from the derived facts that they establish27 ; be in accordance to how things appear to us (phainomenois) 28 ; have valid arguments29 ; have true premises30 .
Karbowski argues that Aristotle's chief motivation in his arguments is to follow these criteria, that, on the other hand, lead him to using postulates.The challenge remains to understand how these criteria interrelate themselves with the postulates of book II.Having true premises and being a valid arguments I will use the abreviation of Ethica Eudemia as EE and Ethica Nicomachea as NE.All the translations of Ethica Eudemia are from the book ARISTOTLE.Eudemian Ethics.Translated and edited by Brad Inwood and Raphael Woolf.Cambridge: Cambridge University Press, 2013.
endoxon or more can build an investigation when they are refined, thus working as a premise.This shows how one should treat the notion of proof and truth as having a very wide-ranging pallet of meaning within Barnes' endoxa method itself, since what is really being proved is the reminisce of the preliminary endoxon.This is precisely what Aristotle prescribed as the EN VII 1 procedure's first step, yet now already in a consistent a properly philosophical group; by properly philosophical I mean that the endoxa can now be properly used for the definitional quest: the endoxa are thus both the investigation's own elements and its starting point.
That soul has a function has already been agreed; let it now be assumed that this function is to instil life.6.Hence (by the proposition secured in [5]), the function of human soulexcellence is good human life: and by the preceding proposition such life is the chief good attainable by man.(ALLAN, 1980, pp.309-10).
Allangives away examples that corroborate to his assertion by briefly rebuilding Aristotle's definitional investigation on eudaimoniagoing through areté (hypothesis 2, 1218b37) and ergon's definitions first -, even after it had already been identified as being the highest of goods achievable to men in book I. Allan only presents what he believes to be the hypotheses and their consequence for the final definition of eudaimonia: (II 1, 1219a40): practicing complete virtue in a complete human life.4. Let end be equivalent to function, and let its definition be: highest or ultimate good, for whose sake all else is done.
12e author rebuilds the same passage that Allan did, exposing that what he had believed to be hypotheses and postulates had actually already came from Aristotle's text itself, in order to show that it was only a definitional derivation of what is more understandable in itself (by its nature) from the more understandable to us, which are closer to what we morally know:12 Karbowski presents another argumentative structure as a contrast to the derivation of happiness presented by Allan, aspiring to show that EE II has other argumentative strategies.The author presents a different version of EE II, which in the light of EE I 6, reveals that Aristotle goes through the what is vague and "more understandable for us" to the more precise and "more understandable in itself" when Aristotle derives a clear definition of virtue through an unclear definition of virtue.Let's now take a look at how the author rebuilds the passage on the virtue of 18EE II 5, 1222a6-12.Virtue is set down (hupokeitm) to be the sort of state that enables people to perform the best actions and which best orients them towards what is best; and the best and most excellent is what accords with correct reasoning.And this is the mean relative to us between excess and deficiency.lt is necessary, then, that virtue of character in each case in a mean point and has to do with certain means in pleasures and pains and in pleasant and painfu1 things.(EE 11.5 1222a6-U, tr.Inwood and Woolf).