Prior’s Turn to Medieval Logic

The peculiar aspect of medieval logic, that the truth-value of propositions changes with time, gradually disappeared as Europe exited the Renaissance. In modern logic, it was assumed by W.V.O. Quine that one cannot appreciate modern symbolic logic if one does not take it to be tenseless. A.N. Prior’s invention of tense-logic challenged Quine’s view and can be seen as a turn to medieval logic. However, Prior’s discussion of the philosophical problems related to quantified tense-logic led him to reject essential aspects of medieval logic. This invites an evaluation of Prior’s formalisation of tense-logic as, in part, an argument in favour of the medieval view of propositions. This article argues that Prior’s turn to medieval logic is hampered by his unwillingness to accept essential medieval assumptions regarding facts about objects that do not exist. Furthermore, it is argued that presentists should learn an important lesson from Prior’s struggle with accepting the implications of quantified tense-logic and reject theories that purport to be presentism as unorthodox if they also affirm Quine’s view on ontic commitment. In the widest sense: philosophers who, like Prior, turn to the medieval view of propositions must accept a worldview with facts about individuals that, in principle, do not supervene (present tense) on being, for they do not yet exist.

Some Characteristics of the Referential and Inferential Predication in Classical Logic

In the article we consider the relationship of traditional provisions of basic logical concepts and confront them with new and modern approaches to the same concepts. Logic is characterized in different ways when it is associated with syllogistics (referential – semantical model of logic) or with symbolic logic (inferential – syntactical model of logic). This is not only a difference in the logical calculation of (1) concepts, (2) statements, and (3) predicates, but this difference also appears in the treatment of the calculative abilities of logical forms, the ontological-referential status of conceptual content and the inferential-categorical status of logical forms. The basic markers or basic ideas that separate ontologically oriented logic from categorically oriented logic are the (1) concept of truth, the (2) concept of meaning, the (3) concept of identity, and the (4) concept of predication. Here, this differences are explicitly demonstrated by the introduction of differential terminology. From this differential methodology follows a new set of characterizations of logic.

Mythologisms in Novel Interpretations

This article discusses mythologisms in Roman interpretations. Attempts were also made to show the philosophical essence of the mythological interpretations in Ulugbek Hamdam’s novel “Isyon va Itoat” (Rebellion and obedience), to analyze the work with a complex structure, symbolic logic.

Interactive Computation and Artificial Epistemologies

What is algorithmic thought? It is not possible to address this question without first reflecting on how the Universal Turing Machine transformed symbolic logic and brought to a halt the universality of mathematical formalism and the biocentric speciation of thought. The article draws on Sylvia Wynter’s discussion of the sociogenic principle to argue that both neurocognitive and formal models of automated cognition constitute the epistemological explanations of the origin of the human and of human sapience. Wynter’s argument will be related to Gilbert Simondon’s reflections on ‘technical mentality’ to consider how socio-techno-genic assemblages can challenge the biocentricism and the formalism of modern epistemology. This article turns to ludic logic as one possible example of techno-semiotic languages as a speculative overturning of sociogenic programming. Algorithmic rules become technique-signs coinciding not with classic formalism but with interactive localities without re-originating the universality of colonial and patriarchal cosmogony.

Semiotic analysis of symbolic logic using tagmemic theory: with implications for analytic philosophy

This article uses tagmemic theory as a semiotic framework to analyze symbolic logic. It attends particularly to the issue of context for meaning and the role of personal observer/participants. It focuses on formal languages, which employ no ordinary words and from one point of view have “no meaning.” Attention to the context and the theorists who deploy these languages shows that formal languages have meanings at a higher level, colored by the purposes of the analysts. In fact, there is an indefinitely ascending hierarchy of theories of theories, each of which analyzes and evaluates the theories at a lower level. By analogy with Kurt Gödel’s incompleteness theory, no level of the hierarchy can capture within formalism everything in a sufficiently complex system. The personal analysts always have to make judgments about how a formalized system is analogous to the world outside the system. Arguments in analytic philosophy can be useful in clarification, but neither clarification of terms nor clarification of the structure of arguments can eliminate the need for personal judgment.

Interoperability and standardization: lessons from the fruit-bowl

PurposeThis study hypothesizes the limitations of standardization as an interoperability development tool within emergency management.Design/methodology/approachPragmatism and Morgan's seminal organizational metaphors inform the conceptualization of the Interoperability Orange metaphor using symbolic logic and visual imagery.FindingsThe essence of standardization is homogeneity. Within emergency management, it is commonplace to develop legislation to standardize policies, procedures, training, equipment and terminology to engender interoperability among first responder and associated organizations. Standardization is achievable with similar or a small number of organizations. However, it is unlikely, if not impossible, in the context of disasters and catastrophes, given the broad range of organizations, groups and individuals typically involved. This diversity of cultures, subcultures, norms, values and indigenous and technical languages intimates that standardization is counterintuitive, particularly in disasters and catastrophes. The posited Interoperability Orange metaphor demonstrates that standardization as a policy, though desired, is theoretically unobtainable in enlarging multiorganizational environments. Thus, new perspectives, policies and solutions for interoperability are needed.Originality/valueThe posited theory builds on the growing body of metaphor-based emergency management research. The Interoperability Orange provides an accessible and easy-to-use communicative tool that aids theoretical cognition – notably within multicultural English as a Second Language environments – as it enables a deeper more critical and explicit understanding of the limits of standardization expressed via metaphor, symbolic logic and imagery.

Metainferential Reasoning on Strong Kleene Models

Barrio et al. (Journal of Philosophical Logic, 49(1), 93–120, 2020) and Pailos (Review of Symbolic Logic, 2020(2), 249–268, 2020) develop an approach to define various metainferential hierarchies on strong Kleene models by transferring the idea of distinct standards for premises and conclusions from inferences to metainferences. In particular, they focus on a hierarchy named the $\mathbb {S}\mathbb {T}$ S T -hierarchy where the inferential logic at the bottom of the hierarchy is the non-transitive logic ST but where each subsequent metainferential logic ‘says’ about the former logic that it is transitive. While Barrio et al. (2020) suggests that this hierarchy is such that each subsequent level ‘in some intuitive sense, more classical than’ the previous level, Pailos (2020) proposes an extension of the hierarchy through which a ‘fully classical’ metainferential logic can be defined. Both Barrio et al. (2020) and Pailos (2020) explore the hierarchy in terms of semantic definitions and every proof proceeds by a rather cumbersome reasoning about those semantic definitions. The aim of this paper is to present and illustrate the virtues of a proof-theoretic tool for reasoning about the $\mathbb {S}\mathbb {T}$ S T -hierarchy and the other metainferential hierarchies definable on strong Kleene models. Using the tool, this paper argues that each level in the $\mathbb {S}\mathbb {T}$ S T -hierarchy is non-classical to an equal extent and that the ‘fully classical’ metainferential logic is actually just the original non-transitive logic ST ‘in disguise’. The paper concludes with some remarks about how the various results about the $\mathbb {S}\mathbb {T}$ S T -hierarchy could be seen as a guide to help us imagine what a non-transitive metalogic for ST would tell us about ST. In particular, it teaches us that ST is from the perspective of ST as metatheory not only non-transitive but also transitive.

Remark on Relevant Arithmetic

This is a brief note about the history of the analysis of the collection of theories, RM3modn, in Meyer and Mortensen "Inconsistent Models for Relevant Arithmetics" Journal of Symbolic Logic 49 (1984).