Abstract
The main aim of the present chapter is to provide a systematic overview on the dialogical framework called Immanent Reasoning. Moreover, we would like to suggest that, if we follow the dialogical insight that reasoning and meaning are constituted during interaction, and we develop this insight in a dialogical framework for Martin-Löf’s Constructive Type Theory, a conception of knowledge emerges that has important links with Walter Young’s (2017) concept of Dialectical Forge in the context of Islamic Law. Moreover, both the dialogical approach and the Dialectical Forge seem to be close to Robert Brandom’s (1994, 2000) inferential pragmatism. The content of the present chapter is basically the same as in Rahman (2019).
In fact, the present chapter relies heavily on the main technical and philosophical results of Rahman/McConaugey/Klev/Clerbout (2018). However, some important modifications have been introduced, particularly in the conception of strategic objects. Many thanks to the reviewers, I owe the modifications to their suggestions
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- 1.
The relation between dialogical logic and the games of asking and giving reasons has already been pointed out by (Keiff, 2007) and (Marion, 2006, 2009, 2010). See for example:
My suggestion is simply that dialogical logic is perfectly suited for a precisification of these ‘assertion games’. This opens the way to a ‘game-semantical’ treatment of the ‘game of giving and asking for reasons’: ‘asking for reasons’ corresponds to ‘attacks’ in dialogical logic, while ‘giving reasons’ corresponds to ‘defences’. In the Erlangen School, attacks were indeed described as ‘rights’ and defences as ‘duties’, so we have the following equivalences:
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Right to attack ↔ asking for reasons
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Duty to defend ↔ giving reasons
The point of winning ‘assertion games ’, i.e., successfully defending one’s assertion against an opponent, is that one has thus provided a justification or reason for one’s assertion. Referring to the title of the book [Making it Explicit], one could say that playing games of ‘giving and asking for reasons’ implicitly presupposes abilities that are made explicit through the introduction of logical vocabulary . (Marion 2010, p. 490).
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- 2.
Ansten Klev’s transcription of Martin Löf (2017a, pp. 1-3, 7).
- 3.
In fact, the present paper relies heavily on the main technical and philosophical results of Rahman/McConaugey/Klev/Clerbout (2018). However, some important modifications have been introduced, particularly in the conception of strategic objects. Many thanks to the reviewers of the present paper, I owe the modifications to their suggestions.
- 4.
- 5.
Cf. Hintikka (1973).
- 6.
Lorenz (1970, p. 75), translated from the German by Shahid Rahman.
- 7.
Lorenz (1970, p. 109), translated from the German by Shahid Rahman.
- 8.
Lorenz (2001, p. 258).
- 9.
- 10.
Speaking of local reasons is a little premature at this stage, since only instructions are provided and not actual local reasons; but the purpose is here to give the general idea of local reasons, and instructions are meant to be resolved into proper local reasons, which requires only an extra step.
- 11.
- 12.
This rule is an expression at the level of plays of the rule for the substitution of variables in a hypothetical judgement. See Martin-Löf (1984, pp. 9-11).
- 13.
Note that P is allowed to make an elementary statement only as a thesis (Socratic rule); he will be able to respond to the challenge on an elementary statement only if O has provided the required local reason in her initial concessions.
- 14.
See, above point 3 of SR3. At the strategy level the move O! ⊥allows P to bring forward the strategic reason yougave up(n) in support for any statement that he has not defended before O stated ⊥ at move n.
- 15.
Krabbe (1985, p. 297).
- 16.
Here again we thank to the reviewers who urged us to sketch at least an example of material dialogues.
- 17.
See Martin-Löf (2014).
- 18.
Recall the distinction of language as the universal medium and as a calculus (van Heijenoort, 1967).
- 19.
Frege points out that within Boole’s approach there is no organic link between propositional and first-order logic: “In Boole the two parts run alongside one another; so that one is like the mirror image of the other, but for that very reason stands in no organic relation to it” (Frege G. , Boole’s Logical Calculus and the Concept Script [1880/81], 1979).
- 20.
For the interpretation of empirical propositions see (Martin-Löf, 2014).
- 21.
For a discussion on player dependence and the way this feature divides the Structural rules and the Particle rules, see above.
- 22.
By “internalization” we mean that the relevant content is made part of the setting of the game of giving and asking for reasons: any relevant content is the content displayed during the interaction. For a discussion on this conception of internalization – see Peregrin (2014, pp. 36-42).
- 23.
Among these variations can be counted cooperative games, non-monotony, the possibility of player errors or of limited knowledge or resources, to cite but a few options the play level offers, making the dialogical framework very well adapted for history and philosophy of logic.
- 24.
See Tractatus Logico-Philosophicus, 5.6.
- 25.
As observed by Marion (2006, p. 245), a lucid formulation of this point is the following remark of Hintikka (1996, p. 158) who shared this tenet (among others) with the dialogical framework:
[Finitism] was for Wittgenstein merely one way of defending the need of language-games as the sense that [sic] they had to be actually playable by human beings. […] Wittgenstein shunned infinity because it presupposed constructions that we human beings cannot actually carry out and which therefore cannot be incorporated in any realistic language-game. […] What was important for Wittgenstein was not just the finitude of the operations we perform in our calculi and other language-games, but the fact that we can actually perform them. Otherwise the entire idea of language-games as meaning mediators will lose its meaning. The language-games have to be humanly playable. And that is not possible if they involve infinitary elements. Thus it is the possibility of actually playing the meaning-conferring language-games that is the crucial issue for Wittgenstein, not finitism as such.
- 26.
The fact that these language-games must be finite does not rule out the possibility of a (potentially) infinite number of them.
- 27.
While establishing particle rules the development rules have not been fixed yet, so we might call those expressions propositional schemata.
- 28.
For such criticisms — see Trafford (2017, pp. 86-88).
- 29.
Lorenz identifies argumentation rules with rules at the strategy level and he would like to isolate the interaction displayed by the moves constituting the play level — see Lorenz (2010a, p.79). We deploy the term argumentation-rule for request-answer interaction as defined by the local and structural rules. It is true that nowadays argumentation-rules has even a broader scope including several kinds of communicative interaction and this might produce some confusion on the main goal of the dialogical framework which is in principle, to provide an argumentative understanding of logic rather than the logic of argumentation. However, once this distinction has been drawn nothing prevents to develop the interface dialogical-understanding of logic/logical structure of a dialogue. In fact, it is our claim that in order to study the logical structure of a dialogue, the dialogical conception of logic provides the right venue.
- 30.
With “ideal” we mean an interlocutor that always make the optimal choices in order to collaborate in the task of testing the thesis.
- 31.
In fact, when Trafford (2017) criticizes dialogical logic in his chapter 4, he surprisingly claims that this form of dialogical interaction does not include the case in which the plays would be open-ended in relation to the logical rules at stake, though it has already been suggested—see for instance in (Rahman & Keiff, 2005, pp. 394-403)—how to develop what we called Structure Seeking Dialogues (SSD). Moreover, Keiff’s (2007) PhD-dissertation is mainly about SSD. The idea behind SSD is roughly the following; let us take some inferential practice we would like to formulate as an action-schema, mainly in a teaching-learning situation; we then search for the rules allowing us to make these inferential practices to be put into a schema. For example: we take the third excluded to be in a given context a sound inferential practice; we then might ask what kind of moves P should be allowed to make if he states the third excluded as thesis. It is nonetheless true to say that SSD were studied only in the case of modal logic. Neither Trafford (2017) nor Duthil-Novaes (2015) nor Duthil-Novaes/French (2018) refer to previous and recent work on linear logic, dialogical paraconsistent logic and belief-revision – see, among others, Rahman/Carnielli (2000), Rahman (2001), Rahman (2002), Rahman/Keiff (2005), Keiff (2007), Keiff (2009), Rahman/Fiutek/Rückert (2010), Beirlaen/Fontaine (2016) and Barrio/Clerbout/Rahman (2018).
- 32.
To put it in her own words: “the majority of dialogical interactions involving humans appear to be essentially cooperative , i.e., the different speakers share common goals, including mutual understanding and possibly a given practical outcome to be achieved.” Duthil Novaes (2015, p. 602).
- 33.
See for instance her discussion of countermoves Duthil Novaes (2015, p. 602) : indefeasibility means that the Opponent has no available countermove: “A countermove in this case is the presentation of one single situation, no matter how far-fetched it is, where the premises are the case and the conclusion is not—a counterexample.“The question then would be to know how to show that the Opponent has no countermove available. The whole point of building winning strategies from plays is to actually construct the evidence that there is no possible move for the Opponent that will lead her to win: that is a winning strategy. But when the play level is neglected, the question remains: how does one know the Opponent has no countermove available? It can actually be argued that the mere notion of countermove tends to blur the distinction between the level of plays and of strategies: a countermove makes sense if it is ‘counter’ to a winning strategy, as if the players were playing at the strategy level, but that is something we explicitly reject. At the play level, there are only simple moves: these can be challenges, defences, counterattacks, but countermoves do not make any sense.
- 34.
See Rahman (2015), Rahman/Iqbal (2018) and strategies as recapitulations of cooperative moves in the chapter II of the present book.
- 35.
Notice however, that Duthil-Novaes/French (2018, pp. 138) seem to assume reflexivity when they bring up an example for the transitivity of implication.
- 36.
Notice that if the role of the Opponent in adversial dialogues is reduced to checking the achievement of logical truth, one would wonder what the role of the Opponent might be in more cooperation-featured dialogues: A soft interlocutor ready to accept weak arguments?
- 37.
- 38.
Cf. Rahman (2012, pp. 222-224).
- 39.
Klev (2017, p. 12 footnote 7) points out that the introduction rule of such kind of operator fails to be meaning-giving because the postulated canonical set Λ(A) occurs negatively in its premiss, and that the restriction avoiding such kind of operators have been already formulated by Martin-Löf (1971, pp. 182-183), and by Dybjer (1994).
- 40.
We could provide at the local level of meaning a set of player-independent rules, and add some special structural rule in order to force dialogue-definiteness—see Rahman (2012, p. 225); however, such kinds of rules would produce a mismatch in the formation of black-bullet: the formulation of the particle rule would have to assume that black-bullet is an operator, but the structural rule would have to assume it is an elementary proposition.
- 41.
This kind of criticism does not seem to have been aware of (Lorenz, 1970, 2009, 2010a, 2010b), carrying out a thorough discussion on predication from a dialogical perspective, which discusses the interaction between perceptual and conceptual knowledge. However, perhaps it is fair to say that this philosophical work has not been integrated into the dialogical logic—we will come back to this subject below.
- 42.
Transcription of Martin-Löf (2017a, pp. 1-3, 7).
- 43.
See Lorenz (1981, p. 120), who uses the expressions right to attack and duty to defend.
- 44.
- 45.
In the context of Operative Logik operations are expressed by means of arrows of the form “⇒”.
- 46.
See (Martin-Löf, 2017b, p. 9).
- 47.
- 48.
The bibliographic background of this section is based mainly on (Lorenz, 2010a, pp. 2017-2018) chapter Procedural Principles of the Erlangen School. On the Interrelation between the principles of method, of dialogue , and of reason.
- 49.
The act of executing must be distinguished from taking the action as an object: while executing an action, actor and execution are said to be indistinguishable.
- 50.
In the previous section we briefly present the discussion of the Cratylus found in (Lorenz & Mittelstrass, 1967).
- 51.
To use Peregrin’s 2014, pp.228–229 words.
- 52.
See Herder (1960 [1772], Part II).
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Acknowledgements
I would like to thank the Laboratory STL: UMR-CNRS 8163 and to Leone Gazziero (STL), Laurent Cesalli (Genève), and Claudio Majolino (STL), leaders of the ANR-Project SEMAINO, for fostering the research leading to the present study.
Many thanks to Christina Weiss for her superb editorial work. My thanks also to Zoe McConaughey (STL), Steephen Eckoubili (STL) Clément Lion (STL) and Mohammad Shafiei (U. Shahid Beheshti) for fruitful discussions, and to the reviewers who suggested important improvements.
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Rahman, S., Iqbal, M., Soufi, Y. (2019). Dialogues, Reasons and Endorsement. In: Inferences by Parallel Reasoning in Islamic Jurisprudence. Logic, Argumentation & Reasoning, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-030-22382-3_4
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