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Papers by shahid rahman

PREFACE Prof. Goran Sundholm of Leiden University inspired the group of Logic at Lille and Valpar... more PREFACE Prof. Goran Sundholm of Leiden University inspired the group of Logic at Lille and Valparaiso to start a fundamental review of the dialogical conception of logic by linking it to constructive type logic. One of Sundholm's insights was that inference can be seen as involving an implicit interlocutor. This led to several investigations aimed at exploring the consequences of joining winning strategies to the proof-theoretical conception of meaning. The leading idea is, roughly, that while introduction rules lay down the conditions under which a winning strategy for the Proponent may be built, the elimination rules lay down those elements of the Opponent's assertions that the Proponent has the right to use for building winning strategy. It is the pragmatic and ethical features of obligations and rights that naturally lead to the dialogical interpretation of natural deduction. During the Visiting Professorship of Prof. Sundholm at Lille in (2012) the group of Lille starte...

Inferences by Parallel Reasoning in Islamic Jurisprudence, 2019

The main aim of the present paper is to show that, if we follow the dialogical insight that reaso... more The main aim of the present paper is to show 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 Robert Brandom's (1994, 2000) inferential pragmatism. However, there are also some significant differences that are at center of the dialogical approach to meaning. The present paper does not discuss explicitly phenomenology, however, one might see our proposal as setting the basis for a further study linking phenomenology and the dialogical conception of meaningthe development of such a link is part of several ongoing researches.

The aim of the paper is to develop a new constructivist approach to the game theoretical interpre... more The aim of the paper is to develop a new constructivist approach to the game theoretical interpretation of AC based on the CTT-proof of Per Martin-Löf (1980). More precisely, Clerbout and Rahman showed that the CTTunderstanding of AC, that stresses the type dependence involved by the function that constitutes the proof-object of the antecedent, can be seen as the result of both an “outside-inside” approach to meaning. It is this approach to meaning, so we claim, that provides a natural dialogical interpretation to AC, where the (intensional) function involved — understood as rules of correspondence produced by the players’ interaction — constitutes a play object for the (first-order) universal quantifier that occurs in the antecedent of the formal expression of this axiom.

While discussing his notion of objective knowledge Popper introduces the idea of dispensability o... more While discussing his notion of objective knowledge Popper introduces the idea of dispensability of knowing subjects, the autonomy of knowledge and the argumentative function of language. The main claim of our paper is that, on our view, objective knowledge produced by argumentative interaction is not achieved by dispensing knowing subjects but by differentiating between the play and the strategic levels of argumentation, where a distinction should be drawn between a particular concrete knowing subject engaged in that interaction, say Karl, and an arbitrary one. Moreover, the theory of meaning deployed at the level of plays, the so-called local meaning, provides already some kind of objective knowledge, since it is player-independent and it does not reduce to the purely logical one of the strategy level. In fact, despite our criticism we think that Popper's discussion of the notion objective knowledge still deserves to be reflected on, particularly so in view of new results conce...

One of the epistemological results emerging from this initial study, is that the different forms ... more One of the epistemological results emerging from this initial study, is that the different forms of co-relational inference, known in the Islamic jurisprudence as qiyās represent an innovative and sophisticated form of reasoning that not only provide new epistemological insights of legal reasoning in general but they also furnish a fine-grained pattern for parallel reasoning that can be deployed in a wide range of problem-solving contexts and that does not seem to reduce to the standard forms of analogical argumentation studied in contemporary philosophy of science. More specifically the main claim is that a dialectical framework provides the right instrument to stress three of the most salient features of this form of inference: (1) the interaction of heuristic with logical steps, (2) the dynamics underlying the meaning-explanation of the terms involved (3) the unfolding of parallel reasoning as similarity in action. They display what we take to be the main epistemological idea beh...

Logic, Argumentation & Reasoning, 2018

Arabic Sciences and Philosophy, 2018

One of the epistemological results emerging from this initial study is that the different forms o... more One of the epistemological results emerging from this initial study is that the different forms of co-relational inference, known in the Islamic jurisprudence as qiyās, represent an innovative and sophisticated form of reasoning that not only provides new epistemological insights into legal reasoning in general but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical argumentation studied in contemporary philosophy of science. However, in the present paper we will only discuss the case of so-called co-relational inferences of the occasioning factor and only in the context of Islamic jurisprudence.

Revista de Humanidades de Valparaíso, 2013

el que debía proporcionar un nuevo comienzo a una teoría general del lenguaje y de la ciencia. En... more el que debía proporcionar un nuevo comienzo a una teoría general del lenguaje y de la ciencia. En lo referente a teoría general del lenguaje, la Escuela de Erlangen afirma que el lenguaje no es un hecho que descubrimos, sino una realización cultural humana cuya construcción puede y debe ser controlada. El proyecto de un desarrollo constructivo de un lenguaje científico fue llamado Orthosprache. Desafortunadamente, este proyecto no fue continuado y de alguna manera parecía desvanecerse. Quizás podríamos decir que una de las razones es que los lazos semánticos entre lógica dialógica, que se restringió a la semántica de la constantes lógicas y las aspiraciones lingüísticas más generales de la Orthosprache, no fueron desarrollados suficientemente y, entonces, la nueva teoría del significado de la lógica dialógica parecía haber sido separada del proyecto de establecer una teoría general del significado. En este artículo nos proponemos presentar una forma posible en la cual una teoría dialógica general del significado podría estar relacionada con lógica dialógica. Más precisamente, el objetivo principal del artículo es establecer las bases para el significado de las frases elementales en el contexto de la interacción dialógica.

Logic, Epistemology, and the Unity of Science, 2016

It is our main claim that the time is ripe to link the dynamic turn launched by game-theoretical ... more It is our main claim that the time is ripe to link the dynamic turn launched by game-theoretical approaches to meaning with P. Martin-Löf's Constructive Type Theory (CTT). Furthermore, we also claim that the dialogical framework provides the appropriate means to develop such a link. We will restrict our study to the discussion of two paradigmatic cases of dependences triggered by quantifiers, namely the case of the Axiom of Choice and the study of anaphora, that are by the way two of the most cherished examples of Hintikka.

Filosofia Unisinos, 2015

Recent work on the development of a dialogical approach to the logic of fi ction stresses the not... more Recent work on the development of a dialogical approach to the logic of fi ction stresses the notion of existence as choice. Moreover, this approach to existence has been combined with the notion of ontological dependence as deployed by A. Thomasson's artifactual theory of fi ction. In order to implement such a combination within the dialogical frame several predicates of ontological dependence have been defi ned. However, the defi nition of such predicates seems to lean on a model-theoretic semantics for modal logic after all. The main aim of the present paper is to set a dialogical frame for the study of fi ctions in the context of the dialogical approach of CTT recently developed by S. Rahman and N. Clerbout where a fully-interpreted language is unfolded. We will herewith develop the idea that in such a setting fi ctional entities are understood as hypothetical objects, that is, objects (functions) the existence of which is dependent upon one or more hypotheses that restrict the scope of choices available. We will fi nish the paper by suggesting that this provides both a natural and genuinely dialogical way to understand R. Frigg's take on scientifi c models as fi ctions and a new perspective on Thomasson's notion of generic ontological dependence.

Baltic International Yearbook of Cognition, Logic and Communication, 2013

In its origins Dialogical logic constituted one part of a new movement called the Erlangen School... more In its origins Dialogical logic constituted one part of a new movement called the Erlangen School or Erlangen Constructivism. Its goal was to provide a new start to a general theory of language and of science. According to the Erlangen-School, language is not just a fact that we discover, but a human cultural accomplishment whose construction reason can and should control. The resulting project of intentionally constructing a scientific language was called the Orthosprache-project. Unfortunately, the Orthosprache-project was not further developed and seemed to fade away. It is possible that one of the reasons for this fading away is that the link between dialogical logic and Orthosprache was not sufficiently developed-in particular, the new theory of meaning to be found in dialogical logic seemed to be cut off from both the project of establishing the basis for scientific language and also from a general theory of meaning. We would like to contribute to clarifying one possible way in which a general dialogical theory of meaning could be linked to dialogical logic. The idea behind the proposal is to make use of constructive type theory in which logical inferences are preceded by the description of a fully interpreted language. The latter, we think, provides the means for a new start not only for the project of Orthosprache, but also for a general dialogical theory of meaning. 1

SpringerBriefs in Philosophy, 2015

A brief examination of the most recent literature in logic shows that a host of research in this ... more A brief examination of the most recent literature in logic shows that a host of research in this area studies the interface between games, logic and epistemology. These studies provide the basis for ongoing enquiries in the history and philosophy of logic, going from the Indian, the Greek, the Arabic, the Obligationes of the Middle Ages to the most contemporary developments in the fields of theoretical computer science, computational linguistics, artificial intelligence, social sciences and legal reasoning. In fact, a dynamic turn, as Johan van Benthem puts it, is taking place where the epistemic aspects of inference are linked with game theoretical approaches to meaning. 1 This turn came about in the 1960's when Paul Lorenzen and Kuno Lorenz developed dialogical logic-inspired by Wittgenstein's language games and mathematical game theory-and when some time later Jaakko Hintikka combined gametheoretical semantics with epistemic (modal) logic. If we had to pinpoint a date, it would be 1958 with Lorenzen's talk 2 "Logik und Agon". However, these two approaches to logic-the dialogical one and the one based on Hintikka's GTS-springing from a dynamic reading of the epistemic conception of logic, disregarded a major advance precisely in the epistemic approach to logic, namely, the development by Per Martin-Löf of Constructive Type Theory (CTT)with the sole exception of the pioneering paper of Aarne Ranta [1988]. 3 This framework, providing a type theoretical development of the Curry-Howard-isomorphism 1 New results in linear logic by J.-Y. Girard at the interface between mathematical game theory and proof theory on the one hand and argumentation theory and logic on the other resulted in the work of, among others, S.

Journal of Philosophical Logic, 2010

In classical India, Jain philosophers developed a theory of viewpoints (naya-vāda) according to w... more In classical India, Jain philosophers developed a theory of viewpoints (naya-vāda) according to which any statement is always performed within and dependent upon a given epistemic perspective or viewpoint. The Jainas furnished this epistemology with an (epistemic) theory of disputation that takes into account the viewpoint in which the main thesis has been stated. The main aim of our paper is to delve into the Jain notion of viewpoint-contextualisation and to develop the elements of a suitable logical system that should offer a reconstruction of the Jainas' epistemic theory of disputation. A crucial step of our project is to approach the Jain theory of disputation with the help of a theory of meaning for logical constants based on argumentative practices called dialogical logic. Since in the dialogical framework the meaning of the logical constants is given by the norms or rules for their use in a debate, it provides a meaning theory closer to the Jain context-sensitive disputation theory than the mainstream formal model-theoretic semantics.

Advances in Logic, 2001

In this paper I present a dialogical formulation of free logic which allows a straightforward com... more In this paper I present a dialogical formulation of free logic which allows a straightforward combination of paraconsistent and intuitionistic logic-I call this combination Frege's Nightmare. The ideas behind this combination can be expressed in few words: in an argumentation, it sometimes makes sense to restrict the use and introduction of singular terms in the context of quantification to a formal use of those terms. That is, the Proponent is allowed to use a constant for a defence (of an existential quantifier) or an attack (on a universal quantifier) iff this constant has been explicitly conceded by the Opponent. When the Opponent concedes any constant occurring in an atomic formula he concedes tertium non-datur (for this formula) to. This yield a free-logic which combines classical (for propositions with singular terms for realities) with intuitionistic logic (for propositions with singular terms for fictions). This extended free-logic can be also combined with paraconsistent logic in such a way that contradictory objects can be included in the domain of fictions. The idea is here to combine the concept of formal use of constants in free logics and that of the formal use of elementary negations in paraconsistent logics.

HUGH MACCOLL AND THE TRADITION OF LOGIC, 1998

Shahid Rahman WAYS OF UNDERSTANDING HUGH MACCOLL'S CONCEPT OF SYMBOLIC EXISTENCE Hugh MacCol... more Shahid Rahman WAYS OF UNDERSTANDING HUGH MACCOLL'S CONCEPT OF SYMBOLIC EXISTENCE Hugh MacColl (18371909) proposed, in several papers, a non-standard way of understanding the ontology underlying what we today call quantified propositions. His ...