Substructural logics, pragmatic enrichment, and the inferential role of logical constants

Inquiry ◽  
2018 ◽  
Vol 63 (6) ◽  
pp. 628-654
Author(s):  
Pilar Terrés Villalonga
Author(s):  
Denis Bonnay ◽  
Benjamin Simmenauer

What is a logical constant? In which terms should we characterize the meaning of logical words like “and”, “or”, “implies”? An attractive answer is: in terms of their inferential roles, i.e. in terms of the role they play in building inferences. More precisely, we favor an approach, going back to Dosen and Sambin, in which the inferential role of a logical constant is captured by a double line rule which introduces it as reflecting structural links (for example, multiplicative conjunction reflects comma on the right of the turnstyle). Rule-based characterizations of logical constants are subject to the well known objection of Prior’s fake connective, tonk. We show that some double line rules also give rise to such pseudo logical constants. But then, we are able to find a property of a double line rules which guarantee that it defines a genuine logical constant. Thus we provide an alternative answer to Belnap’s requirement of conservatity in terms of a local requirement on double line rules.


Author(s):  
Ned Block

Mental (or semantic) holism is the doctrine that the identity of a belief content (or the meaning of a sentence that expresses it) is determined by its place in the web of beliefs or sentences comprising a whole theory or group of theories. It can be contrasted with two other views: atomism and molecularism. Molecularism characterizes meaning and content in terms of relatively small parts of the web in a way that allows many different theories to share those parts. For example, the meaning of ‘chase’ might be said by a molecularist to be ‘try to catch’. Atomism characterizes meaning and content in terms of none of the web; it says that sentences and beliefs have meaning or content independently of their relations to other sentences or beliefs. One major motivation for holism has come from reflections on the natures of confirmation and learning. As Quine observed, claims about the world are confirmed not individually but only in conjunction with theories of which they are a part. And, typically, one cannot come to understand scientific claims without understanding a significant chunk of the theory of which they are a part. For example, in learning the Newtonian concepts of ‘force’, ‘mass’, ‘kinetic energy’ and ‘momentum’, one does not learn any definitions of these terms in terms that are understood beforehand, for there are no such definitions. Rather, these theoretical terms are all learned together in conjunction with procedures for solving problems. The major problem with holism is that it threatens to make generalization in psychology virtually impossible. If the content of any state depends on all others, it would be extremely unlikely that any two believers would ever share a state with the same content. Moreover, holism would appear to conflict with our ordinary conception of reasoning. What sentences one accepts influences what one infers. If I accept a sentence and then later reject it, I thereby change the inferential role of that sentence, so the meaning of what I accept would not be the same as the meaning of what I later reject. But then it would be difficult to understand on this view how one could rationally – or even irrationally! – change one’s mind. And agreement and translation are also problematic for much the same reason. Holists have responded (1) by proposing that we should think not in terms of ‘same/different’ meaning but in terms of a gradient of similarity of meaning, (2) by proposing ‘two-factor’ theories, or (3) by simply accepting the consequence that there is no real difference between changing meanings and changing beliefs.


2018 ◽  
Vol 4 (3) ◽  
Author(s):  
Lynne Tirrell

The very rules of our language games contain mechanisms of disregard. Philosophy of language tends to treat speakers as peers with equal discursive authority, but this is rare in real, lived speech situations. This paper explores the mechanisms of discursive inclusion and exclusion governing our speech practices, with a special focus on the role of gender attribution in undermining women’s authority as speakers. Taking seriously the metaphor of language games, we must ask who gets in the game and whose moves can score. To do this, I develop an eclectic analysis of language games using basic inferential role theory and the concept of a semantic index, and develop the distinction between positional authority and expertise authority, which often conflict for members of oppressed groups. Introducing the concepts of master switches and sub-switches that attach to the index and change scorekeeping practices, I argue that women’s gender status conflicts with our status as authoritative speakers because sex marking in semantics functions as a master switch—“the F-switch”—on the semantic index, which, once thrown, changes the very game. An advantage of using inferentialism for understanding disregard of women’s discursive authority is that it locates the problem in the sanctioned moves, in the deontic structure of norms and practices of scorekeeping, and not primarily in the individual intentions of particular people.


2020 ◽  
Author(s):  
Franc Marušič ◽  
Rok Žaucer ◽  
Amanda Saksida ◽  
Jess Sullivan ◽  
Dimitrios Skordos ◽  
...  

Number words allow us to describe exact quantities like sixty-three and (exactly) one. How do we derive exact interpretations? By some views, these words are lexically exact, and are therefore unlike other grammatical forms in language. Other theories, however, argue that numbers are not special and that their exact interpretation arises from pragmatic enrichment, rather than lexically. For example, the word one may gain its exact interpretation because the presence of the immediate successor two licenses the pragmatic inference that one implies “one, and not two”. To investigate the possible role of pragmatic enrichment in the development of exact representations, we looked outside the test case of number to grammatical morphological markers of quantity. In particular, we asked whether children can derive an exact interpretation of singular noun phrases (e.g., “a button”) when their language features an immediate “successor” that encodes sets of two. To do this, we used a series of tasks to compare English speaking children who have only singular and plural morphology to Slovenian-speaking children who have singular and plural forms, but also dual morphology, that is used when describing sets of two. Replicating previous work, we found that English-speaking preschoolers failed to enrich their interpretation of the singular and did not treat it as exact. New to the present study, we found that 4- and 5-year-old Slovenian-speakers who comprehended the dual treated the singular form as exact, while younger Slovenian children who were still learning the dual did not, providing evidence that young children may derive exact meanings pragmatically.


2000 ◽  
Vol 65 (3) ◽  
pp. 1076-1114 ◽  
Author(s):  
Jonathan P. Seldin

AbstractEvidence is given that implication (and its special case, negation) carry the logical strength of a system of formal logic. This is done by proving normalization and cut elimination for a system based on combinatory logic or λ-calculus with logical constants for and, or, all, and exists, but with none for either implication or negation. The proof is strictly finitary, showing that this system is very weak. The results can be extended to a “classical” version of the system. They can also be extended to a system with a restricted set of rules for implication: the result is a system of intuitionistic higher-order BCK logic with unrestricted comprehension and without restriction on the rules for disjunction elimination and existential elimination. The result does not extend to the classical version of the BCK logic.


2020 ◽  
Vol 19 (1) ◽  
pp. 1-25
Author(s):  
Chiara Fedriani

AbstractThis paper analyzes uses, functions, and literary distribution of the negative politeness formula si placet ‘(lit.) if it pleases (you)’ in a corpus of Late Latin texts (third–sixth century CE). Drawing on both qualitative and quantitative observations, it is suggested that the pragmatic enrichment undergone by this conditional parenthetical clause is due to a conspiracy of factors, namely a process of semantic and pragmatic change fostered by a “politeness-induced invited inference” (Beeching 2005), which was triggered by a general process of literary imitation within the very specific discourse tradition of philosophical dialogues. The analysis shows, indeed, that si placet is very rarely used in the history of Latin and it is circumscribed to this specific literary genre. This suggests that this politeness formula developed as a genre-specific stylistic feature and as such it was replicated over centuries through the circulation of textual models and the propagation of genre-related practices, as a valuable linguistic device to render the idea of an urbane conversation among educated peers and, ultimately, as a marker of socio-cultural identity.


2018 ◽  
Vol 15 (2) ◽  
pp. 476 ◽  
Author(s):  
Heinrich Wansing ◽  
Daniel Skurt

In this paper, we shall consider the so-called cancellation view of negation and the inferential role of contradictions. We will discuss some of the problematic aspects of negation as cancellation, such as its original presentation by Richard and Valery Routley and its role in motivating connexive logic. Furthermore, we will show that the idea of inferential ineffectiveness of contradictions can be conceptually separated from the cancellation model of negation by developing a system we call qLPm, a combination of Graham Priest’s minimally inconsistent Logic of Paradox with q-entailment (quasi-entailment) as introduced by Grzegorz Malinowski.


2003 ◽  
Vol 26 (6) ◽  
pp. 691-692
Author(s):  
Alice G. B. ter Meulen

In designing stratified models of human language, understanding notions of logical consequence and validity of inference require separating the aspects of meaning that vary between models from logical constants. Modelling meaning requires choices regarding the primitives, where the Fregean program is still offering us the fundamental insights on the role of truth, judgement, and grasping or sharing of thoughts.


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