ISSA Proceedings 2014 – Islamic Theological Arguments: An Epistemological Systematisation

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Abstract: This contribution starts a critical analysis and reconstruction of arguments in classical texts of Islamic theology (of the period AD 900-1100) from the viewpoint of the epistemological theory of argumentation. The main question of the analysis is whether these arguments can be reconstructed as being of one of the universal types of argument identified so far by the epistemological approach. The answer is: yes – though non-deductive arguments are not yet well elaborated.

Keywords: deductive arguments, epistemological theory of argumentation, Islamic theological argument, Koran, universality of argument types

1. Aim and structure of this article
Many classical texts of Islamic theology are heavily argumentative; and much of Islamic theology tries to base faith on valid and sound arguments. Some Islamic theologians even think that Islamic doctrines cannot be defended by revelation alone but have always to be justified by rational arguments. The rational approach in Islamic theology was significantly influenced by the Muʿtazila. But also the Māturīdiyya and the As̲h̲ʿariyya have dealt with kalām (Arabic for speculative theology) and applied rational methods in their theology (see e.g. van Ess 1966, pp. 17-33). This argumentative tradition has nearly not been studied in argumentation theory up to this day. This contribution starts to develop a critical analysis and reconstruction of the arguments in classical texts of Islamic theology from the viewpoint of the epistemological theory of argumentation. The theoretical aims of this study are threefold: First, we want to compile (the beginning of) a list of the most important types of arguments used in these texts, giving particular attention to non-deductive arguments. Second, we analyse them with the help of epistemological criteria in order to establish whether they can be captured in this way, in particular whether all of them are intended (in a broad sense) to be or can be reconstructed as being of one of the universal types of argument identified so far by the epistemological approach (deductive, probabilistic or practical arguments or combinations thereof) or whether there are e.g. specifically Islamic types of argument which should extend the present list of epistemologically valuable argument types or whether, on the other hand, there are (frequently used) argument types in Islamic theology which should be abandoned from an epistemological point of view. Third, we assess the examples with the help of the criteria developed in the epistemological theory of argumentation to gain an impression of the state of the art in classical Islamic theological argumentation. The arguments we will analyse in the following are taken from works by Abū Manṣūr Muḥammad ibn Muḥammad ibn Maḥmūd al-Māturīdī (about AD 870-944), by Abū al-Qāsim al-Ḥakīm al-Samarqandī (about AD 890-950) and by Abū Ḥāmid Muḥammad ibn Muḥammad, known as al-Ghazālī (AD 1058–1111), i.e. texts which were written roughly between AD 900 and 1100, i.e. in European terms at the end of the Early and the beginning of the High Middle Ages, before Thomas Aquinas or William of Ockham in Western Europe.

As just said, the argumentation theory which provides the background and criteria of our analysis is the epistemological approach to argumentation and, more specifically, the Practical Theory of Argumentation developed by one of us, because within the epistemological approach, apart from the profound theoretical justification, it provides the most elaborated and precise criteria for good argumentation, the broadest and deepest systematisation of argument types, and an elaborated theory as well as rules for interpreting arguments.[i]

2. Deductive arguments in medieval islamic theology
Islamic theologians of the period under consideration, of course, also use deductive arguments even of a rather sophisticated type. And since the erudite among them were familiar in particular with Aristotle’s logic they even had a theory of deductive arguments at their disposal.

Nice examples of rather good and sophisticated deductive theological arguments can be found e.g. in Māturīdī’s book Kitāb al-Tawhīd (“The Book of Divine Unity”, AD 944). In this book Māturīdī is arguing, among others, against Christian Christology and the doctrine of Trinity. In a long passage of this book he presents a wealth of independent arguments, which try to show that Christian Christology is self-refuting or contradicting well-known facts. An extract reads as follows:

1. [S1.1] The Christians are divided over Christ, [S1.2] for there are those among them who attribute two spirits to him, [S1.3] one of them temporal, the spirit of humanity which is like the spirits of people, [S1.4] and an eternal divine spirit, [S1.5] a part of God, [S1.6] and this came into the body. […]
[S4] Ibn Shabīb said: I heard one of their associates say that he [Christ] was son by adoption and not son by begetting, just as the wives of Muhammad […] are called mothers, and as a man says to another, ‘My little son’.
2. […] [S5] The Master […] said, Say to them: […] [S9.1] Further, it is well-known that a son is younger than a father, [S9.2] so [S9.3] how can they both be eternal? [S10.1] And if the whole is regarded as being in the body, [S10.2] say to him: [S10.3] Which thing in it is the Son? [S11.1] And if he says: The whole; [S11.2] he has made the whole Son and Father, [S11.3] in this making the Father a son to himself. (al-Māturīdī <944> 2008, pp. 97-99)

This passage does not contain a classical argument indicator; however, sentence S5: “The Master said, Say to them” serves this function. It means: the following are proposals how to argue against assertions of the Christian doctrines summarised in S1[-S4], whose negations, of course, are Māturīdī’s theses. The negation exactly of which thesis entailed in S1 is the thesis sustained by S9 is not made explicit; only the content of S9 allows us to infer that S1.4 is the claim under attack, hence the thesis could be: ‘(The divine spirit in) Christ is not eternal.’ That parts of the formulation of the thesis show up only in the reasons is an indicator for a deductive argument. (In the following reconstructions, “S” indicates a sentence from the argument’s original text; “P” indicates a premise; “A” indicates a hypothetical assumption, which is not used as a premise taken to be true; “L” designates a lemma; “T” is the name for a thesis; “e” as well as “<…>” (angle brackets) indicate insertions included in the spirit of the argument and meant to be acceptable for the arguer; “[…]” (square brackets) indicate insertions, comments etc. made by us, the authors.) The argument can be reconstructed as follows:

<eA1 (= part of S6) assumption (not premise) of a part of the Christian doctrine: The divine spirit in Christ is the son of God (the Father).>
P1 (= S9.1): All sons are younger than their fathers. [This can be formalised as follows: For all x and y holds: if x is son of y, then there is a moment tz, for which holds: y subsists at tz, and all moments tw, at which x subsists, are later than tz.]
<eP2 For all x holds: If there is a moment ty, at which x does not subsist, then x is not eternal.>
P3 (= S9.2): ‚So‘: description of an inferential relation: From S9.1 (= P1) [and eA1 and eP2] follows the implicature of S9.3 (= T1): ‘The divine spirit in Christ and God (the Father) are not both eternal.’ [Māturīdī formulates this assertion as a rhetorical question, which implicates the negation of the main propositional content of S9.3.]
∴ —————————————————————————————————
T1(= S9.3): God the Father and the divine spirit in Christ are not both eternal. [Māturīdī has formulated this conclusion as a rhetorical question, which however implicates a negative answer.]

Here the explicit argument terminates. It suffers from two defects, which, however, can be repaired easily. First, the thesis T1 does not follow. Since one of the premises of the inferential relation described in P3, namely eA1, i.e. ‘The divine spirit in Christ is the son of God (the Father)’, for Māturīdī and Islamic theology is just a hypothetical assumption, only a weaker, conditional thesis follows: eT1*:

<eT1* If (eA1:) the divine spirit in Christ is God’s son, then God (the Father) and the divine spirit in Christ are not both eternal.>

(This implication is logically equivalent to the disjunction:

<eT1.1* (¬eA1): The divine spirit in Christ is not God’s son, or God (the Father) and the divine spirit in Christ are not both eternal.>)

Second, for Māturīdī’s overall aim already T1 is too weak because he does not negate God’s eternity and only wants to attack the assumption of Christ’s divinity. With a further implicit premise the result can easily be strengthened in the spirit of Māturīdī’s argument:

<eT1* If (eA1:) the divine spirit in Christ is God’s son, then God (the Father) and the divine spirit in Christ are not both eternal.>
<eP4 God (the Father) is eternal.>
∴ —————————————————————————————————
<eT2 (¬eA1): The divine spirit in Christ is not God’s son, or (the divine spirit in) Christ is not eternal.>

The second horn of this Christian dilemma is in contrast to S1.4, i.e. to one of the Christian doctrines described in the introduction of Māturīdī’s argument.

The argument is a proof of a contradiction:[ii] from some assumptions of Christian Christology and some trivially true premises follows the opposite of one of these assumptions; hence at least one of these assumptions must be false. The argument in its reconstructed form is deductively valid. Furthermore, the premises P1, eP2 and P3 as such are true; we can leave it open whether eP4 (eternity of God the Father) is true; in particular premise P1, i.e. ‘All sons are younger than their fathers’, is true for natural sons. However, a critical point of the argument is whether ‘son’ in the assumption eA1, i.e. ‘Christ is the son of God (the Father)’, can be interpreted as meaning natural sonship. If in Christian Christology not a natural sonship is meant – which probably is the case – we would have two different meanings of ‘son’ in eA1 and P1; this would make the argument invalid. More precisely this would be a fallacy of missing fit, namely of fallacious ambiguity (Lumer 2000, pp. 415-416). By the way, Māturīdī himself in sentence S4 mentions that in Christian Christology at least sometimes the expression ‘son’ is not interpreted in the usual way, but he ignores this critical point in his argument. He could have restricted his result to Christian doctrines which assume a natural sonship and could have objected to other versions that their use of ‘son’ is more than unclear – which for Māturīdī’s critical purposes would be sufficiently strong. Finally, apart from being true, the argument’s premises are also accepted by Māturīdī’s (Muslim and Christian) addressees – which makes the argument adequate in this respect for convincing rationally. – So, altogether the analysed argument of Māturīdī is quite a good deductive argument though in the end it is fallacious.

This was only one example of a deductive argument in medieval Islamic theology. Of course, there are many more of them. Given this wealth of deductive arguments, the theoretical question is no longer whether there are deductive arguments but whether there are non-deductive arguments in medieval Islamic theology.

A particular important kind is practical arguments, i.e. arguments consisting of listings of advantages and disadvantages of an object which justify a specific evaluation of this object. Practical arguments, though perhaps not of a very explicit form, must have been present in daily life of Muslims of the period under consideration, simply because they reflect the basic way of human decision-making. The search for and analysis of respective examples so far is only the topic of further research.

3. Specifically islamic argument types? – authority arguments from the Koran
One of our theoretically central questions is whether there are specifically Islamic argument types, in particular argument types which could be recognised by the epistemological approach to argumentation as being effective in the sense of leading to true or acceptable (e.g. near to truth) beliefs (i.e. whether they are based on effective epistemological principles (cf. Lumer 2005a, pp. 221-222; 231-234) which have not yet been recognised in epistemological argumentation theory). The most obvious candidates are authority arguments from Holy Scriptures, which are present in Islamic theological texts as well as in theological texts from other revealed religions.

Good and instructive kinds of such authority arguments from Holy Scriptures can be found e.g. in Abū al-Qāsim al-Hakīm al-Samarqandī’s screed against the fatalists who think believers do not need to care for subsistence, since Allah already cares for them. At one point e.g. Samarqandī argues with the help of an authority argument from Holy Scriptures that sometimes believers are obliged to strive for their subsistence – though Allah generally cares for the subsistence of human beings. The translated argument is this:

[S1] At certain times it is a duty to strive for living, [S2.1] because [S2.2] the Koran says: [S2.3] ‘And shake the palm tree’s stem by pulling it towards you! [S2.4] Then it lets plunge juicy and fresh dates on you’ [Koran 19:25], [S3.1] and the Koran says: [S3.2] ‘We have created the day for you in order that you gain your livelihood’ [Koran 78:11]. (al-Samarqandī <950> 1838, p. 40)

The argument indicator in S2.1 tells us that the preceding sentence, S1, is the thesis – whose content is sufficient for refuting the fatalists – and that the following sentences, i.e. S2.2 to S3, are the arguments. Sentence S2.4, i.e. one part of the Koran citation, is not necessary for Samarqandī’s argumentative purposes. The rest is a complex argument with two convergent (i.e. each of them sufficient) reasons for the thesis that sometimes it is a duty to strive for one’s living. Both reasons are – independent and correct – citations of Koran verses about doing something for gaining one’s livelihood.

The explicit argument is rather frugal. The transition from the two explicit reasons to the thesis presupposes two groups of implicit reasons. The first group of implicit premises deals with a general problem to be expected in such arguments from authority of Holy Scriptures, e.g. from the authority of the Koran, and, more specifically, how to get from an invitation expressed in the Koran to an effective obligation. This problem can be resolved by inserting some fairly general premises which can be used in most arguments from the authority of the Koran. These general premises are:

E1 – Principle of revelation: Everything written in the Koran is the word of Allah, i.e. a communication by Allah.
E2 – Principle of divine truth: The propositions of all judgements stated by Allah are true.
E3 – Principle of divine duty: All invitations by Allah constitute a respective divine duty (i.e. a duty enforced by Allah).

The other problems which have to be resolved by a second group of implicit premises regard the transition from what is written explicitly in the Koran to the type of invitation or duty formulated in Samarqandī’s thesis, i.e. a duty to strive for living. The first citation expresses a very concrete invitation, namely to shake the palm tree’s stem, whereas the thesis speaks of an abstract duty to strive for living. The context of the Koran citation makes clear that the addressee, i.e. Mary who is in a desperate situation, by shaking the palm tree will contribute to her livelihood. However, commands and duties are intensional texts; and they do not allow for abstractions. I.e. we can say that by shaking the palm tree etc. she contributes to her livelihood, but this does not imply that if Mary has the duty to shake the palm tree, she necessarily also has a duty to contribute to her livelihood (in this situation). The problem is that from one and the same concrete duty enormously many abstractions could be generated, which in other situations will lead to contradicting duties; and we have no formal principle to choose the normatively correct abstraction. (Of course, in the other direction, from the abstract to the concrete, there are no comparable problems: If we have got an abstract duty we can easily classify more concretely described acts as instances of fulfilling that abstract duty.) Hence such abstractions without further substantial premises are not epistemically justified. Since Samarqandī does not provide such substantial premises we do not see any epistemically and interpretively justified reason to proceed from the concrete to the general in Samarqandī’s first argument; its inference is invalid.

The second argument contains smaller technical problems. In the following reconstruction they are resolved by introducing acceptable premises, which in the end make the argument deductively valid. First, the Koran citation in S3.2 speaks only of Allah’s intention to provide a functional commodity, not of a duty. This gap can be bridged by a general normative teleological principle, i.e. that such natural functions (created by Allah) constitute duties to embrace them. (Such normative teleological thinking is also present e.g. in ancient Greek philosophy.[iii]) Second, the Koran quotation in S3.2 simply speaks of gaining one’s livelihood, whereas the thesis S1 speaks of striving for living. Here a premise is needed which says that the duty to do something implies the duty to strive for doing so.

On the basis of these explanations, Samarqandī’s argument can be reconstructed as follows:

Reconstruction of Samarqandī’s sub-argument 1:

P1 – (= S2.2-S2.3): The Koran says: ‘<Mary,> shake the palm tree’s stem by pulling it towards you’ [Koran 19:25].
<eP2 – (= E1) Principle of revelation: Everything written in the Koran is a communication by Allah.>
<eP3 – (= E3) Principle of divine duty: All invitations by Allah constitute a respective divine duty (i.e. a duty enforced by Allah).>
<eP4 – ‘<Mary,> shake the palm tree’s stem by pulling it towards you’ is an invitation.>
∴ —————————————————————————————————
<eL1 – Mary (in the respective situation) has the divine duty to shake the palm tree’s stem by pulling it towards her.>
<eP5 – Mary’s shaking the palm tree’s stem by pulling it towards her is an instance of striving for her living.>
∴ —————————————————————————————————
T1 – (= S1) At certain times it is a duty to strive for living.

Premises P1, eP4 and eP5 are true; the two principles will be discussed in a moment. The first inference is deductively valid, whereas the second is not because of the intensionality problem.

Reconstruction of Samarqandī’s sub-argument 2:

P6 -(= S3): The Koran says: ‘[reformulated:] Allah has created the day for men in order that they gain their livelihood’ [Koran 78:11].
<eP2 – (= E1) Principle of revelation: Everything written in the Koran is a communication by Allah.>
<eP7 – (= E2) Principle of divine truth: The propositions of all judgements stated by Allah are true.>
<eP8 ‘Allah has created the day for men in order that they gain their livelihood’ is a judgement with the proposition that Allah has created the day for men in order that they gain their livelihood.>
∴—————————————————————————————————
<L2 – Allah has created the day for men in order that they gain their livelihood.>
<eP9 – Normative teleological principle: If Allah creates something in order that a human being can do a certain action (and if He communicates this), then to strive for this action is a divine duty.>
∴—————————————————————————————————
<L3 – Human beings have a divine duty to strive for gaining their livelihood.>
∴—————————————————————————————————
T1- (= S1): At certain times it is a duty to strive for living.

The premises P6 and eP8 are true, and the three inferences are deductively valid; and all this is easily recognisable to be so. (The three inferences, of course, can be contracted to one inference only, thereby omitting the two lemmas.)
These four principles are accepted by Muslims but not e.g. by Christians. We can leave open the question whether the principles are true. In any case they rely on strong metaphysical and empirical presuppositions: that Allah exists; that He communicates with human beings; etc. If (some of) these principles are false, the argument is not argumentatively valid and, according to the epistemological theory of argumentation, a fortiori not adequate for rationally convincing. On the other hand, if these principles are true the argument is argumentatively valid and situationally adequate for rationally convincing Muslims; however, the argument is not adequate for convincing other addressees. This reflects the fact that arguments from the authority of the Koran are, of course, addressed to a specific audience, namely Muslims, who believe in the Koran.

This result leads to the question whether these audience-specific arguments constitute a distinctive, sui generis type of Islamic argument. One could for instance reinterpret the principles – in a Toulminian way – as inference rules. As the reconstruction has shown there is no need to do so; authority arguments from the Koran can as well be reconstructed as deductive arguments with particular premises, namely the principles. Therefore the question is which theoretical conceptualisation is generally more appropriate. From an epistemological viewpoint the reconstruction as a deductive argument with particular premises is better in many respects and worse in none than the alternative systematisation. First, it reveals the epistemological foundations, i.e. logically valid inferences and materially true premises with their different respective procedures of validation, which, in addition, are theoretically well established. Furthermore, core questions of argumentation theory regarding the epistemological effectiveness of argument types are thus separated from argumentation theoretically irrelevant questions about the truth of particular material premises; the potential falsity of a (material) premise then does not affect argumentation theory. The alternative approach has nothing to offer in all these respects. Moreover, the deductive reconstruction is parsimonious in providing only one type of argument with many sub-forms constituted by the deductively valid inferences. The alternative approach instead considers every material principle as the basis of a new argument type without any possibility of systematisation.

4. Hermeneutic arguments in islamic theology
Some Islamic theologians of the period under consideration already use a variety of rather sophisticated hermeneutic arguments.

A good source with a wealth of hermeneutic arguments of various types is Ghazālī’s book Against the divinity of Jesus because Ghazālī accepts the authority of the Bible but attacks its Christian interpretation; in particular he advocates a figurative interpretation of many passages which Christians take literally. One part of his argument is this:

[S1] It is well known that this group [the Christians] uses the word ‘God’ for the Messiah […]. [S2.1] If only I knew whether [S2.2] this is just an honorary title because everything mighty is called ‘God’ [S2.3] or whether they really want to say that he [Christ] is God. [S3] If the latter is intended, then this group is more unreasonable than all the others.
[S4.1] They get into such trouble because they hold to the literal sense, [S4.2] even though certainty is given to the clear understanding that the literal sense is not meant. [S5] However, in every law there is text whose literal sense is contrary to reason. [S6] But then the teachers of the respective law have interpreted the texts.
[S7] A group of significant men has been led to similar things. [S8] One of them said: ‘I am sublime.’
[S9] Another said: ‘How mighty I am!’
[S10] And Hallādj said: ‘I am God. And in this cowl is nothing except God!’ […]
[S13] This is a question of reason, because the literal sense cannot be meant. […] (al-Ghazālī 1966, p. 92)

What is interesting in this text from an argumentation theoretical point of view is that Ghazālī uses a simple version of a hermeneutic Principle of Charity, sketched in S4.2 to S6 and S16.2, by which to seemingly nonsensical texts a reasonable figurative meaning can be attributed:

Principle of Charity (= S4.2–S6; S16.2): If in a [holy text or in the text of an authority or of a significant man or in a] law the literal meaning is contrary to reason (S5), <in particular if it is obviously false,> then the text has to be interpreted (S6): then i. the literal sense is not meant (S4.2); ii. instead, to the <text or> word <that leads to the nonsense> a reasonable meaning has to be attributed (S16.2) <i.e. a meaning which makes the utterance reasonable, in particular one that makes it true>.

This Principle of Charity is formulated in such a way as to make Ghazālī’s argument deductively valid. The principle goes in the direction of present-day principles of charity in rationalising interpretations; it is a big progress for hermeneutics because it provides a methodological way to reveal figurative meaning. Nonetheless, in its present form the Principle of Charity is too simplistic and strict for being true. Taken as an empirical hypothesis about the author’s intention, Ghazālī’s Principle of Charity is false: even authorities believe false propositions and sometimes talk nonsense. The relations expressed in the principle hold only frequently. Weakening the principle in this respect to a statistical truth with high frequency would alter the argument entirely, namely make it a defeasible argument – which, however, probably is an argument structure beyond Ghazālī’s theoretical horizon. Furthermore, the Principle of Charity, apart from presupposing the falsity of the literal meaning, does not use at all further evidences (like the context) which could reveal what the author really meant; thereby it does not take seriously the communicative meaning of utterances. This problem leads to some kind of circularity: the reader of the holy text must already know the truth; he cannot use the text to find out what the truth is, in particular the revealed truth about the divinity of Christ. This makes the holy text worthless as evidence.

In the ensuing part of his argument Ghazālī interprets a passage from Paul’s first letter to the Corinthians with the aim to show that even Paul does not affirm the divinity of Jesus and implicitly even denies it. The passage is hermeneutically rich in using a variety of hermeneutical means: text quotes, references for them, references for assertions about word meanings, a disambiguating argument and the hint to an argument which works out an implicature in the Gricean sense. The disambiguating argument and the argument working out an implicature are very interesting from an argumentation theoretical point of view. Ghazālī has a quite good intuition about the structure of these arguments in bringing together many necessary minor premises. But he does not formulate the major premise, i.e. a principle of disambiguation and a principle for revealing implicatures. In our reconstruction we have formulated such principles on the basis of what is said in the minor premises, adding to this some plausible necessary conditions. However, it would be illusory to strive for an argumentatively useful strict principle; all the viable principles are only frequentist or probabilistic, e.g. the principle of disambiguation:

<eP5 Hermeneutic Principle of Contextual Disambiguation: 1. If a speaker s ascribes a quality called “F” to an object a (cf. P1), 2. where “F” has the meanings ‘F1’ and ‘F2’ (cf. eP2), 3. if, furthermore, s in the respective context attributes the qualities ‘F11’, …, ‘F1n’ to a, which are implied by ‘F1a’ (cf. P3, P4), 4. if in the respective context s does not attribute any quality ‘F21’ to a which is implied by ‘F2a’ (cf. eP6) and 5. if no other (in particular opposite) evidences regarding the meaning of “Fa” are present in s (cf. eP7), then s with “Fa” mostly means ‘F1a’.>

This Principle of Contextual Disambiguation is probably true and makes the inference of the first argument (inductively) valid. However, with such a frequentist premise the argument becomes a defeasible statistical argument with a probabilistically qualified thesis. Such arguments are based on a best-evidence principle, according to which the best evidence has to be included in the argument. All this bursts the structure of deductive arguments. Though Ghazālī is at the edge of defeasible argumentation, probably he could neither formulate such a Disambiguation Principle nor did he see the new quality of this kind of arguing and the technical requirements it brings with it. As a consequence, in his arguments he violates in particular the best-evidence principle. Though he has rather good hermeneutic intuitions these technical gaps are impediments for further formally elaborating his hermeneutical arguments.

5. Conclusion
The preceding analyses have shown that Islamic theological texts of the period between AD 900 and 1100 use a wealth of argument types. Apart from deductive arguments in general, we have identified deductive arguments from the authority of the Koran and a remarkable variety of hermeneutic arguments. None of these argument types requires enlarging the list of good argument types recognised as such by the epistemological approach to argumentation. We have found and analysed deductive arguments, but Ghazālī’s arguments in part can be reconstructed as defeasible, statistical arguments. The latter case is particularly interesting because Ghazālī probably did not know or recognise them on a theoretical level. As a consequence his respective arguments are rather rudimentary and, what is more, he could not avoid several risks of these arguments, in particular that they always need to fulfil the best-evidence condition. This argumentation theoretical limitation probably was one obstacle for further developing theological hermeneutics.

NOTES
i. General overview of the epistemological theory of argumentation: Lumer 2005b. Practical Theory of Argumentation: The general approach is developed and justified in: Lumer 1990; 2005a. A systematisation of existing argument types is developed in: Lumer 2011a. Criteria for particular argument types are developed in: deductive arguments: Lumer 1990, pp. 180-209; probabilistic arguments: Lumer 2011b; 1990, pp. 221-260; practical arguments: Lumer 1990, pp. 319-433; Lumer 2014. For theory and rules of interpreting arguments, see: Lumer 2003; for fallacy theory: Lumer 2000.
ii. The argument evaluation in this paragraph uses the criteria exposed in: Lumer 1990, pp. 187-189; abridged criteria: Lumer 2011, p. 14.
iii. Aristotle, e.g., uses the (empirical) fact that something is a unique function of human beings as a reason for a normative (in a broad sense) claim that fulfilling this function is the supreme good for which human beings should strive (NE 1097b-1098a). Thereby he seems to assume a normative implication of supposed “teleological” facts.

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