When asked in 1962 on what he was working Kazimierz Ajdukiewicz replied: Several years ago Polish Scientific Publishers suggested that I pre pare a new edition of The Logical Foundations of Teaching, which I wrote 1 before 1939 as a contribution to The Encyclopaedia of Education. It was a small booklet covering elementary information about logical semantics and scientific methodology, information which in my opinion was necessary as a foundation of teaching and as an element of the education of any (...) teacher. When I recently set to preparing the new edition, I rewrote practically everything, and a booklet of some 100 pages swelled into a bulky volume almost five times bigger. The issues have remained practically the same, but they are now analysed much more thoroughly and the threshold of difficulty is much higher now. The main stress has been laid on the methods used in the empirical sciences, and within that field, on the theory of measurement and the methods of statistical inference. I am now working on the last chapter of the book, concerned with explanation procedures and theory construction in the empirical sciences. When that book, which I intend to entitle Pragmatic Logic, is com pleted I intend to prepare for the press Vol. 2 of my minor writings, 2 Language and Cognition, which will cover some of my post-war pa pers. (shrink)

The present paper is devoted to present two pragmatic logics and their corresponding intended interpretations according to which an illocutionary act of hypothesis-making is justified by a scintilla of evidence. The paper first introduces a general pragmatic frame for assertions, expanded to hypotheses, ${\mathsf{AH}}$ and a hypothetical pragmatic logic for evidence ${\mathsf{HLP}}$. Both ${\mathsf{AH}}$ and ${\mathsf{HLP}}$ are extensions of the Logic for Pragmatics, $\mathcal{L}^P$. We compare ${\mathsf{AH}}$ and $\mathsf{HLP}$. Then, we underline the expressive and inferential (...) richness of both systems in dealing with hypothetical judgements, especially when based on different, sometimes conflicting, evidence. (shrink)

The purpose of this essay is to both discuss commands as a species of speech act and to discuss commands within the broader framework of how they are used and ...

This article aims to show that the incompatibility between the application of logic to norms and values and the expressive conception of these notions – basically summed up by the Frege–Geach problem – can be overcome. To this end, a logic is constructed for the expressive conception of norms and values which provides a solution to the Frege–Geach problem and is not affected by the limitations that occur in some previous attempts. More specifically, a pragmatic language LP (...) is introduced which is an extension of the language L of standard propositional logic, obtained by adding two categories of logical-pragmatic signs to the vocabulary of L: the signs of pragmatic mood (,,, standing for assertion, obligation and approval, respectively) and the pragmatic connectives (∼, ∩, ∪, ⊃, ≡, standing for pragmatic negation, conjunction, disjunction, implication and bi-implication, respectively). The notions of pragmatic validity, consistency (satisfiability), compatibility, equivalence and inference are then defined, and some criteria of pragmatic validity are given. It is thus possible to carry out in LP inferences on norms and values expressively understood, adequately formalizing Geach's problematic inferences. (shrink)

Kazimierz Twardowski was renowned as an outstanding philosopher, teacher, and organizer of academic life. No less famous was his style of work, depicted in many recollections of his students. In the paper, I present three aspects of good mental work: a) stoic inspiration for Kazimierz Twardowski’s style of work, b) the place of the techniques of mental work in the program of pragmatic logic according to the views of Kazimierz Ajdukiewicz and Tadeusz Kotarbiński, and c) selected contemporary approaches (...) consistent with the direction provided by the Lvov-Warsaw School. By exploring a new perspective in the study of good mental work by linking it to the ancient philosophy of life as well as to the most recent developments in the theory of good mental work, the paper reveals unexplored insights into the tradition of the Lvov-Warsaw School, demonstrating its significance, depth, and relevance to modern times. (shrink)

The article offers an analysis of Józef Bocheński's studies of the concept of nation. Bocheński acknowledges that there are difficulties in defining a nation. After that he claims that he will attempt to propose a definition of the Polish nation. Nation is a social group centered around some cultural ideal. The analysis shows that Bocheński did not avoid serious logical problems. First of all, he constantly falls into a circular reasoning. Furthermore, it is called into question if it makes sense (...) to refer to a cultural ideal or ideology while defining a nation. Is not such an attempt essentially bound to become circular? A doubt is also raised whether nowadays, in the face of constant migration of people and cultural ideals, one can continue to reasonably talk about nations. (shrink)

Second edition of the introductory guidebook to the basic principles of constructing sound arguments and criticising bad ones. Non-technical in approach, it is based on 186 examples, which Douglas Walton, a leading authority in the field of informal logic, discusses and evaluates in clear, illustrative detail. Walton explains how errors, fallacies, and other key failures of argument occur. He shows how correct uses of argument are based on sound strategies for reasoned persuasion and critical responses. This edition takes into (...) account many developments in the field of argumentation study that have occurred since 1989, many created by the author. Drawing on these developments, Walton includes and analyzes 36 new topical examples and also brings in work on argumentation schemes. Ideally suited for use in courses in informal logic and introduction to philosophy, this book will also be valuable to students of pragmatics, rhetoric, and speech communication. (shrink)

The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of (...) pragmatic validity and pragmatic truth can be accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed. (shrink)

The reasoning process of analogy is characterized by a strict interdependence between a process of abstraction of a common feature and the transfer of an attribute of the Analogue to the Primary Subject. The first reasoning step is regarded as an abstraction of a generic characteristic that is relevant for the attribution of the predicate. The abstracted feature can be considered from a logic-semantic perspective as a functional genus, in the sense that it is contextually essential for the attribution (...) of the predicate, i.e. that is pragmatically fundamental (i.e. relevant) for the predica-tion, or rather the achievement of the communicative intention. While the transfer of the predicate from the Analogue to the analogical genus and from the genus to the Primary Subject is guaranteed by the maxims (or rules of inference) governing the genus-species relation, the connection between the genus and the predicate can be complex, characterized by various types of reasoning patterns. The relevance relation can hide implicit arguments, such as an implicit argument from classification , an evaluation based on values, consequences or rules, a causal relation, or an argument from practical reasoning. (shrink)

ABSTRACT My aim in this paper is to present a pluralist thesis about the inferential role of logical constants, which embraces classical, relevant, linear and ordered logic. That is, I defend that a logical constant c has more than one correct inferential role. The thesis depends on a particular interpretation of substructural logics' vocabulary, according to which classical logic captures the literal meaning of logical constants and substructural logics encode a pragmatically enriched sense of those connectives. The paper (...) is divided into four parts: first, I introduce the motivation for the pluralist thesis of the paper; second I introduce the calculus for the different logics endorsed in the pluralist thesis; third, I motivate how the different behaviors of the logical vocabulary of these logics can be pragmatically interpreted, and fourth, I motivate how the different inferential roles that each substructural logic attribute to logical constants can coexist, and how we should reason with a logical constant c given this plurality. (shrink)

The pragmatic notion of assertion has an important inferential role in logic. There are also many notational forms to express assertions in logical systems. This paper reviews, compares and analyses languages with signs for assertions, including explicit signs such as Frege’s and Dalla Pozza’s logical systems and implicit signs with no specific sign for assertion, such as Peirce’s algebraic and graphical logics and the recent modification of the latter termed Assertive Graphs. We identify and discuss the main ‘points’ (...) of these notations on the logical representation of assertions, and evaluate their systems from the perspective of the philosophy of logical notations. Pragmatic assertions turn out to be useful in providing intended interpretations of a variety of logical systems. (shrink)

We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value (...) defined classically, and everyaf is endowed with ajustification value, defined in terms of the intuitive notion of proof and depending on the truth values of its radical subformulas. In this framework, we define the notion ofpragmatic validity in P and yield a list of criteria of pragmatic validity which hold under the assumption that only classical metalinguistic procedures of proof be accepted. We translate the classical propositional calculus (CPC) and the intuitionistic propositional calculus (IPC) into the assertive part of P and show that this translation allows us to interpret Intuitionistic Logic as an axiomatic theory of the constructive proof concept rather than an alternative to Classical Logic. Finally, we show that our framework provides a suitable background for discussing classical problems in the philosophy of logic. (shrink)

We apply the recently elaborated notions of 'pragmatic truth' and 'pragmatic probability' to the problem of the construction of a logic of inductive inference. It is argued that the system outlined here is able to overcome many of the objections usually levelled against such attempts. We claim, furthermore, that our view captures the essentially cumulative nature of science and allows us to explain why it is indeed reasonable to accept and believe in the conclusions reached by inductive (...) inference. (shrink)

This paper presents a new view of logical pluralism. This pluralism takes into account how the logical connectives shift, depending on the context in which they occur. Using the Question-Under-Discussion Framework as formulated by Craige Roberts, I identify the contextual factor that is responsible for this shift. I then provide an account of the meanings of the logical connectives which can accommodate this factor. Finally, I suggest that this new pluralism has a certain Carnapian flavour. Questions about the meanings of (...) the connectives or the best logic outside of a specified context are not legitimate questions. (shrink)

We apply the recently elaborated notions of ‘pragmatic truth’ and ‘pragmatic probability’ to the problem of the construction of a logic of inductive inference. It is argued that the system outlined here is able to overcome many of the objections usually levelled against such attempts. We claim, furthermore, that our view captures the essentially cumulative nature of science and allows us to explain why it is indeed reasonable to accept and believe in the conclusions reached by inductive (...) inference. (shrink)

We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justi cations and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a (...) logic of assertions and conjectures: looking at the S4 modal translation, we give a de nition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is de ned and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, de ned as a hypothesis that in some situation the truth of p is epistemically necessary. (shrink)

This book presents a philosophical conception of logic -- "logical expressivism"-- according to which the role of logic is to make explicit reason relations, which are often neither monotonic nor transitive. It reveals new perspectives on inferential roles, sequent calculi, representation, truthmakers, and many extant logical theories.

The logical constants are technical terms, invented and precisely defined by logicians for the purpose of producing rigorous formal proofs. Mathematics virtually exhausts the domain of deductive reasoning of any complexity, and it is there that the benefits of this refined form of language are felt. Pragmatic issues may arise — issues concerning the point of making a certain statement — for there will be more or less perspicuous and illuminating ways of presenting proofs in this language, and we (...) may be puzzled or misled when we wonder why the mathematician is taking some particular step. But this is hardly a compulsory topic in the philosophy of language. (shrink)

Robyn Carston and I share a general methodological position which I call ‘Truth-Conditional Pragmatics' (TCP). TCP is the view that the effects of context on truth-conditional content need not be traceable to the linguistic material in the uttered sentence. Some effects of context on truth-conditional content are due to the linguistic material (e.g. to context-sensitive words or morphemes which trigger the search for contextual values), but others result from ‘free' pragmatic processes. Free pragmatic processes take place not because (...) the linguistic material demands it, but because the utterance's content is not faithfully or wholly encoded in the uttered sentence, whose meaning requires adjustment or elaboration in order to determine an admissible content for the speaker's utterance. To make room for these processes, I will argue, we need to distinguish the logical form of an utterance, in the standard sense, and its modified logical form, affected by free pragmatic processes. This distinction will be elaborated and I will show that it can be interpreted in three different ways. (shrink)

There are two fundamental questions concerning the choice and presence of objects in various formal systems: Where do these objects come from? What do we know about them? To answer these questions I introduce the notion of a proto-ontology as the pre-theoretic realm of entities from which the basic objects – individuals – of the formal system S are postulated. The pragmatic aspects of such choices are investigated with regard to first-order logic, both pure and applied, set theory (...) and mereology. It is claimed that the postulated objects enter the formal system S with a package of properties and relationships, the recognition of which depends on the interpretation and application of the available predicates of S. If these properties and relationships are not made explicit, a possible clash may arise between them and the properties and relationships “assigned” to the individuals of S by the interpreted predicates of S. As regards the relationship between logic and metaphysics, I contend that logic can perhaps be viewed as the articulation of the fundamental features of proto-ontological objects without which no discourse or theory would be possible. In this sense logic could also be viewed as a theory and method of the construction of a well-articulated metaphysical theory. (shrink)

Topics in Cognitive Science, Volume 14, Issue 3, Page 574-601, July 2022.

A number of statements of the form 'x asserts p', Often described as pragmatically inconsistent, Are examined. By applying the predicate calculus and descriptive axioms to these sentences it is shown that if it is assumed that p is true a formal inconsistency is deducible from them. From the results of this analysis partial definitions of both assertion and pragmatic inconsistency are formulated.

This paper responds to the generous comments by Alexander Klein and Cheryl Misak on my “American Pragmatism and the Vienna Circle: The Early Years”. First, besides offering some clarification of my original thesis, I argue that Jerusalem was not liable to the anti-Spencerian criticisms by James that Klein adduces in the course of defending James against the charge of psychologism. Then I investigate the impact of Wittgenstein’s Ramsey-derived pragmatism, importantly foregrounded by Misak, on the Vienna Circle and argue that it (...) was mainly limited to Schlick but not recognized as pragmatist, also leaving unaffected the impact of James’s pragmatism on Frank, Hahn and Neurath specified in my original paper. That said, Klein’s and Misak’s comments add significantly to our understanding of long-neglected transatlantic philosophical connections in the early twentieth century. (shrink)

Solves what is sometimes, but not always, referred to as the third paradox of material implication. Readers downloading this piece should please also download the corrigendum. Note that "pragmatic" is here used in its original sense of context-sensitive, that is, adjacency. (This comment is made in response to an article in a student journal published in the western U.S. which claimed that I said that because something involves translation it must be pragmatic; that is so, in the original (...) sense; only grammaticality can ever be context-free; all meaning is context-sensitive, as "lawful" cannot meaningfully modify "whale."). (shrink)

In "Abstracts from Logical Form I/II," it was stated in the abstract that it remained necessary to put the pilot experiments into a "comprehensive theory." It is suggested here that the comprehensive theory is nothing other than classical logic modestly extended to include higher-order predicates, functions, and epistemic predicates, as well as a quantitative quantifier to deal with cases other than "all" (taken literally) or "some" in the sense of at least one. It is further suggested that up to (...) a point the theory should generalize across languages, and that logical form is very powerful. (shrink)