Abstract
The present volume develops a new way of linking Constructive Type Theory (CTT) with dialogical logic by following these three complementary paths, as mentioned in the preface:
-
A.
The path observing that Sundholm’s (1997) notion of epistemic assumption is closely linked to the Copy-cat and Socratic rules and that it provides the dialogical conception of definitional equality;
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B.
the path joining (in principle) Martin-Löf in his (2017a, 2017b) suggestions, according to which the new insights provided by the dialogical framework mainly amount to the following three interconnected points:
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B.1.
the introduction of rules of interaction rather than of rules of inference;
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B.2.
the challenge to the semantization of pragmatics and the claim of the deontic nature of logic;
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B.3.
the central role of the notion of execution in the rules of interaction: executions are responses to questions of knowing how.
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B.1.
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C.
The path stressing the importance of the play level and the associated notion of dialogue-definiteness.
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Notes
- 1.
- 2.
- 3.
In fact, as opposed to Martin-Löf’s understanding of dialogical logic, Lorenz’s dialogical constructivism does not only reject the semantization of pragmatics in which deontic features are formalized using specific propositional operators and indexes upon which depends the truth-value of the resulting proposition, but it also rejects the pragmatization of semantics in which a propositional kernel is complemented by moods yielding assertions, questions, commands, and so on. According to dialogical constructivism, pragmatic and semantic features are produced within one and the same act . See (Lorenzen, 1969), (Kamlah & Lorenzen, 1972), (Lorenzen & Schwemmer, 1975). It is precisely this tenet on the dual nature of actions in both their significative and communicative role, thoroughly worked out by Lorenz (2010a, pp. 71–80), that leads to this central claim that logic is part of ethics—see Sect. 11.5 for further details.
- 4.
See also Lorenz’s (2001) study of the origins of the dialogical approach to logic.
- 5.
(Schröder-Heister 2008). All the following quotations of this section, if not otherwise specified, will come from this same source.
- 6.
Nowadays, the notion of admissibility is a fundamental concept of proof-theory ; Schröder-Heister (2008, p. 218) pointed out that Lorenzen was the one to have coined this term.
- 7.
(Schröder-Heister, 2008, p. 217).
- 8.
(Schröder-Heister, 2008, p. 222).
- 9.
See also Marion (2006, p. 231) .
- 10.
Winning strategies in the first writings of Lorenzen and Lorenz (1978) were formulated in the form of sequent-calculus; thus the demonstration of “admissibility” amounts in this context to show that the sequence of plays determined by the local and structural rules for the logical constants yield those of the sequent calculus.
- 11.
Kuno Lorenz conveyed this information to S. Rahman by a personal email.
- 12.
- 13.
For a brief presentation of the philosophical tenets of Dialogical Constructivism see Sect. 11.7.
- 14.
- 15.
This is the main feature of dialogues for immanent reasoning, the dialogical framework which incorporates features of CTT. For a presentation of this framework, see Chaps. 6 and 7. The Socratic rule is the equivalent in immanent reasoning of the Copy-cat rule in the standard dialogical framework. For a presentation of the standard framework, see Chaps. 3, 4, and 5.
- 16.
- 17.
Jaroslav Peregrin (2014, pp. 3–5) calls the notion of use understood as following a rule “role”. Role distinguish linguistic uses from other uses such as using a hammer.
- 18.
See for instance (Brandom, 1994). To some extent only, for it seems like Brandom starts from the strategy level rather than from the play level as we do.
- 19.
As discussed in Sect. 10.5, Brandom’s approach only has the propositional level (i.e. his framework does not include the ontological level of the local reasons relevant for the backing of the proposition involved in the judgement). Perhaps because he fears that such a move would amount to incorporating into the framework an authority which would be external to the games that determine concepts. As far as we understand it, this is a serious limitation of Brandom’s approach since it fails to distinguish between the notations, or written forms, concerning the ontological level, and those concerning the propositional level: the present book, we hope, shows how to make the ontological level immanent to the dialogical process of reasoning. This suggests that the dialogical approach to CTT offers a way to integrate within one epistemological framework the two conflicting readings of Willfried Sellars’ (1991, pp. 129–194) notion of space of reasons brought forward by John McDowell (2009, pp. 221–238) on the one side, who insists in distinguishing world-direct thought and knowledge gathered by inference, and by Robert Brandom (1997) on the other side, who interprets Sellars’ work in a more radical anti-empiricist manner. The point is not only that we can deploy the CTT-distinction between reason as a premise and reason as the piece of evidence justifying a proposition, but it is also that the dialogical framework allows distinguishing between the objective justification (strategy) level targeted by Brandom (1997, p. 129) and the subjective (play) level stressed by McDowell —see also (Rahman, 2017).
- 20.
For more details on symmetry in the dialogical framework, see Sect. 4.3.
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Rahman, S., McConaughey, Z., Klev, A., Clerbout, N. (2018). Introduction: Some Brief Historical and Philosophical Remarks. In: Immanent Reasoning or Equality in Action. Logic, Argumentation & Reasoning, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-91149-6_1
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