This article examines the role of the logician Francesco Storella (active ca. 1550–1575) in contributing to the intellectual and social legitimation of alchemy in mid sixteenth-century Naples. Storella achieved this by leveraging the tradition of the “Hermetic Aristotle,” focusing on his 1555 edition and commentary of the Secretum secretorum. The study first analyses Storella’s philological strategies, including the historicisation of the text and the use of the Tabula smaragdina, to firmly link Aristotle’s authority to the Hermetic foundation of alchemy. Second, it demonstrates how Storella mobilised his philosophical logic to defend the ars alchemica as a rational and demonstrable discipline, compatible with a physico-astrological framework (Albertine tradition) necessary for achieving genuine metallic transmutation. Finally, the study reconstructs the Neapolitan intellectual network linking Storella with the philologist Domenico Pizzimenti and the young naturalist Giambattista della Porta. This confluence, unified by a commitment to the rational justification of singularia and an Albertine-influenced physics, highlights Naples as an exceptional point of convergence where academic theory, philological rigour, and experimental practice merged. This robust synthesis conferred a decisive epistemological and social status upon alchemy within Renaissance Aristotelianism, providing the essential cosmological and rational justification for the transmutation of metals.

In this article, I will discuss logic within the framework of Wittgenstein’s Tractatus Logico-Philosophicus. More specifically, I will focus on a topic that belongs to the domain of Tractarian philosophy of logic. Strictly speaking, the idea is to address, based on Wittgenstein’s own approach, the notion of tautology as an instrument for designating logical propositions. For this reason, I will examine certain elements discussed by the philosopher, particularly those found between aphorisms 6.1 and 6.4 of the aforementioned work. One of the most significant implications of this discussion is that the properties of logical propositions and logical concepts are made explicit in the corresponding logical symbols and, for this reason, can never be expressed linguistically. From this arises the distinction between “saying” and “showing” within the context of Tractarian philosophy.

ABSTRACT In his Reply to Gaunilo , Anselm presented two additional arguments for the existence of God beyond those that appear in the Proslogion . In “The Logical Structure of Anselm's Argument,” Robert M. Adams isolates each. One, he develops into a modal ontological argument along the lines of other 20th century ontological arguments (e.g., those of Malcolm, Hartshorne, and Plantinga). The other he sets aside with the following remark: “[this argument] turns on the philosophy of time, not the philosophy of logic.” Now the argument's time has come. In this paper, I show the following: (i) this argument is valid in system K, and so requires fewer logical resources than other modal ontological arguments; (ii) its axiological premise is plausible, requiring only the judgment that a perfect being cannot begin to exist, and can be defended; (iii) its metaphysical premise follows from David Lewis's recombination approach to modal plenitude; (iv) unlike other modal ontological arguments, it requires as a premise only that a perfect being is possible, not that one is necessarily possible; and (v) while it avoids parodies and the charge of begging the question, it does face a symmetry counterargument, although one that is more complicated than standard symmetry objections.

The ERC Advanced Grant project ConLog is nearing successful completion ConLog investigates non-trivial logical systems in which certain contradictions are provable. The aim is to develop a clear comprehension of the contradictoriness of these logics and to study the consequences of this understanding within the philosophy of logic. Thereby, the project will yield a paradigm shift in our conception of what a respectable logical system and an acceptable scientific theory are.

The object of this study is the Thomistic concept of rational-theological knowledge. The subject matter is the philosophical logic and methodology of Thomas Aquinas's five arguments for the existence of God. Adhering to Aristotelian epistemology, which posits that all knowledge begins with the senses, Aquinas significantly deepens and expands the scope of its application, thereby forming the methodological apparatus of medieval rational theology. The questions of epistemology constitute a substantial part of Aquinas's philosophy, which has a distinctly scientific-theoretical character. Aquinas dedicates separate chapters not only in his most well-known works – "Summa Theologiae" and "Summa Philosophiae" – to the questions of the conditioning of thought and its nature and mechanisms of cognition. Epistemological issues are also adequately represented in works such as: "Commentary of Thomas Aquinas on Aristotle's Second Analytics," "Commentaries of Thomas Aquinas on Aristotle's Treatise 'On Interpretation,'" and "Commentary on Boethius's Treatise 'On the Trinity.'" The methodology of the research is presented as a combination of general scientific theoretical methods (analysis, synthesis, formal and dialectical approaches), as well as specialized philosophical methods: α) hermeneutic approach (for interpreting primary sources – the texts of Aristotle, Anselm of Canterbury, and Aquinas himself); β) causal analysis (the study pays considerable attention to the examination of the nature of cause-and-effect relationships). Results and scientific novelty. The implementation of this study has allowed for the following findings: α) the relevance of one of the "textbook" philosophical problems of the Middle Ages has been substantiated; β) an authorial systematization and philosophical interpretation of Aquinas's five proofs of God's existence has been presented; γ) the conditioning of the use of the inductive method in natural theology and its scientific advantage over the deductive method has been demonstrated; δ) the principle of applying induction in the pursuit of rational knowledge of God has been revealed; ε) the natural cognitive foundations for constructing Thomistic arguments in favor of God's existence have been identified. The results of the study can be applied as further scientific inquiries in the field of philosophical logic, theory of knowledge, and philosophy of science. The term "theologica," as stated in the title of the article, is borrowed from the eponymous trilogy of the Swiss theologian Hans Urs von Balthasar in the 20th century, dedicated to the problematics indicated in Thomism: how the infinite God can be comprehended in this world through phenomena (immanence), while remaining transcendent.

Abstract In view of the large number of complex operations generated in the application of integrated fuzzy systems, the efficiency of system processing is affected. Based on the basis of Zadeh fuzzy sets, the study introduces the concept of opposite negation, medium negation, and contradiction in philosophical negation and computer logic. After repeated research and demonstration of the internal relations, basic characteristics, and fusion conditions between the three kinds of logical negatives, it innovatively proposed IPLF.sets. Then, the evaluation set of various logical variables and their evolution forms can be directly involved in the calculation. And then, the full membership function f ( x ) with good approximation performance is constructed by fully verifying the operation rules and the feasibility of logical transformation under the premise of the known local membership function g ( x ). The IPLF.sets practical application of the results shows that (1) dealing with complex problems can be simplified and more efficient. (2) The output is valid, reasonable, and accurate. (3) The integration of philosophical logic enhances the ability to judge the fuzzy system and improves the evaluation accuracy.

In his recent paper, Priest proposes a formal model of dialectical logic (Priest [2023]. ‘The logical structure of dialectic’, History and Philosophy of Logic, 44 (2), 200–208.). This paper critically examines Priest’s formal model from two key perspectives: First, it assesses the model’s accuracy in describing the dialectical progression; second, it evaluates the model’s ability to explain this progression. The analysis reveals that Priest’s formal model falls short in both respects, as it neither accurately represents the dialectical progression nor provides a satisfactory explanation of it.

Transitional eras are the most significant, promising and contradictory moments of history giving rise to new political cosmos and nomos. Romanticism does not last long as a cultural and historical period, however, as a line of thought (political, state and legal thought in our case), it remains and manifests itself for long decades covering the entire 19th century and reviving in the revolutions of the 20th century. Political romantics embodied both individuality and collectivity, anarchism and conservatism, blending these elements within state and law processes so that binary thinking was rendered obsolete. The article describes the sources and ideas of political romanticism within the framework of the historical, legal, political and philosophical logic and offers the readers a legal analysis of the general postulates of this doctrine, in particular, the organic state concept. The author concludes that political romanticism as a style of government got along well with different statehood forms and political regimes producing a notable and sometimes a decisive impact on the latter.

Abstract What is the proper way to transfinitely extend the usual hierarchy of finite metainferential levels? McAllister ( Journal of Philosophical Logic, 51 , 1345–1365, 2022; Belief Revision About Logic , PhD Thesis, University of Auckland, 2024) has proven that classical logic and numerous other logics are non-unique in classical set theory. On the basis of these results, she argues for a range of philosophical consequences, including problems for logical monism, classical set theory, and the identification of logics. This paper demonstrates that McAllister’s key results are merely artifacts of the level labels which she adds to the transfinite hierarchy. It is proven that, in the absence of labels, every logic is unique in classical set theory. Moreover, I argue that if labels are not innocent additions, but instead influence the results in substantial ways, then they must be left out of the hierarchy. Therefore, in the final analysis, every logic is unique. The various problems which McAllister extracts from non-uniqueness accordingly dissolve.

Abstract A new theory of paradox is presented and defended. According to this theory, something is a paradox if and only if a subject cannot believe it, or something about it, despite having tried. Three rival theories are criticised and rejected. Section 1 rejects the theory according to which a paradox is an inconsistent set of individually plausible propositions. Section 2 rejects the Quinean account according to which a paradox is an apparently absurd conclusion that is apparently sustained by an argument. Section 3 rejects the theory according to which a paradox is a question or pseudo-question that suspends us between too many good answers. Section 4 introduces the proposed alternative theory and shows how it improves on previous accounts. Section 5 elaborates the account in the direction of philosophical logic. Section 6 addresses the identity and proper individuation of paradoxes. Section 7 gives a concluding reflection on the epistemic value of finding things paradoxical.

The sorites paradox reveals the tension between the vagueness of natural language and the principles of classical logic. It has sparked significant contemporary debates in logical philosophy. Traditional binary logic struggles to face the challenges posed by ambiguous predicates. Researchers have proposed various solutions, such as degree theory, supervaluationism, and many-valued logic, but all face interpretive limitations. This paper systematically examines the logical structure of the sorites paradox and focuses on Williamsons epistemicist theory. Epistemicism maintains that ambiguous predicates possess objective and precise boundaries, though these lie beyond human cognitive reach and remain unknowable. By introducing the notion of unknowability, this theory preserves the validity of classical logic while offering a unique framework for addressing vagueness. This paper analyzes the mathematical logic foundations of epistemicism and its applied value in natural language analysis, legal reasoning, and ethical judgment, highlighting its advantages in theoretical simplicity, interpretive consistency, and intuitive rationality. Although epistemicism still faces challenges such as boundary arbitrariness and higher-order fuzziness, it has significant importance in resolving the sorites paradox and promoting interdiscipcolinary exchange. Finally, this paper proposes that future studies on epistemicism should focus on these three aspects: formal expansion, comparative studies, and interdisciplinary integration.

Abstract Work in the field of feminist logic is still rather scarce and the field itself remains a contested area of study, but still, it is developing. One approach concentrates on analyzing logical systems with respect to structural features that may perpetuate sexism and oppression or, on the other hand, features that may be helpful for resisting and opposing these social phenomena. Upon this assumption, I want to investigate possible applications of queer feminist views on (philosophy of) logic with respect to a very specific group, namely contradictory logics, i.e., logical systems containing contradictions in their set of theorems. I want to show that, on the one hand, the formal set-up of contradictory logics makes them well-suited from the perspectives of feminist logic and, on the other hand, that queer feminist theories provide a relevant, and so far undeveloped, conceptual motivation for contradictory logics. Thus, bringing together contradictory logics and queer feminist theories may prove fruitful both as a ‘real-life’ motivation for these peripheral logical systems and as a formal basis for a philosophical field that is still characterized by a distrust of formalism.

In this paper I discuss the intricate relationship between logic and tradition and its crucial role in al-Farabi's political philosophy. An illustrative historical example of this relationship is Mattā–al-Sirāfi debate, particularly its focus on the conflict between logic and grammar and the problem of intelligibles. These issues are pivotal in my exposition of al-Farabi's philosophy of logic. The relation of logic to grammar possesses characteristics independent of specific traditions. To explain this, I introduce the concept of ‘meta-tradition’ where intelligibles and the path to attaining them, are situated. This path is depicted in the philosophies of Plato and Aristotle and, according to al-Farabi's view, both philosophers shared the same understanding of happiness, which is only attainable through the widespread adoption of philosophy. This requires an education system that al-Farabi's approach to logic and his articulation of it, provide the framework for such a system, enabling the propagation of philosophical thought throughout the virtuous city.

The author describes the conceptual, terminological, and stylistic principles of their translation of the corpus of works of the Pythagorean tradition into Ukrainian. The main translation strategy is based on the principle of balancing semantic fidelity to historical meanings with adaptation to modern Ukrainian academic usage. The translation was carried out considering the interdisciplinary context: medical, psychological, aesthetic, ethical, political. A defining feature is the combination of philological accuracy with hermeneutic interpretation, which allows conveying not only the content but also the philosophical logic, stylistics, and symbolism of Pythagorean cosmology, ontology, epistemology, and moral anthropology.

Abstract I argue that the continued focus on the possibility question - whether feminist logic can exist as a respectable practice - has several harmful consequences. First, it invites the association of feminist logic with substantial positions in the philosophy of logic, which unnecessarily leaves room for dismissing the field a priori. Second, it invites a systematic reading of feminist logicians as arguing in isolation from their logical practice, which can hide some genuine possibilities for the field. To avoid these issues, I propose a very broad characterization of feminist logic as a kind of practice which addresses some harmful aspect of dominant practices by focusing on their interaction with logical practices. This characterization trivializes the possibility question, enforces no particular conception of logic to the exclusion of others, yet leaves room for both conservative and radical approaches.

An essential feature of Wittgenstein's early philosophy of logic is the conjecture of a positive solution to the question of whether logical truth in first-order logic is decidable (Entscheidungsproblem). It is often argued that the proofs of a negative solution to the Entscheidungsproblem presented in the 1930s refuted Wittgenstein's early conception of logic. However, we argue Wittgenstein's philosophy of logic does not share the principles assumed by the proof strategies of those undecidability proofs. Thus, the undecidability proofs do not refute Wittgenstein's philosophy of logic based on its own convictions. Therefore, we provide a purely logical refutation of Wittgenstein's early philosophy of logic that does not depend on assumptions that he does not accept. Wittgenstein claimed that the logical properties of first-order logic are decidable based on patterns in a suitable notation for first-order logic. We explain why this conviction is mistaken.

This article is an unaltered reproduction of my 1992 MSc. dissertation at the London School of Economics and Political Science (LSE), with very minor editorial amendments, and a new introduction explaining why its publication is timely in the wake of the current debate around 'the adoption problem' in the philosophy of logic.

In this paper my aim is to recover and use an argument outlined by Suárez concerning the philosophy of quantum logics, which I have termed “Suárez's Paradox”. Although originally written in 1992, this argument has only recently come to light through its publication. After briefly introducing the essentials of standard quantum logics formalism and the classical philosophical discussions associated in a nutshell, I will present an actualised version of the Suárez's Paradox inserting it in the philosophy of quantum logics discussion highlighting several non-trivial philosophical implications.

Self-evidence and demonstrable truths are recurring themes in philosophy, logic and ethics. This article addresses these notions in the work of Peter Geach and Willard Quine, namely, Reason and Argument and The Web of Belief, respectively. It concludes by referring to the case of a planning permission for a tourist mega-complex development project at Ramla l-Ħamra Valley, Gozo, the mythical island of Ogygia, the abode of Atlas’ daughter Calypso, in Homer’s epic, The Odyssey.The arguments for the revocation of this permit were grounded on the philosophy of logic of Geach and Quine, namely that truth may not be self-evident, but it is demonstrable.

Abstract This paper is a study of Objectual Quantifier Theory, the view that quantificational noun phrases, such as every woman and some pig, denote generic individuals, such as the arbitrary woman and the indefinite pig. We explore the motivations for this view and various ways of developing it, taking inspiration from and expanding upon Kit Fine’s work on arbitrary objects (Fine, Proceedings of the Aristotelian Society, Supplementary Volumes, 57, 55–77 1983; Journal of Philosophical Logic, 14(1), 57–107 1985; Reasoning with Arbitrary Objects 1985). Our discussion centres around the task of delivering a compositional treatment of quantifier phrases in natural language. In the first part of the paper, we explore the potential for applying and extending Fine’s framework in the interpretation of quantifier expressions, developing desiderata for a successful theory. In the second part of the paper, we develop our positive theory, which we call Objectual Quantifier Theory, as a theory of quantification in natural language. We argue that Objectual Quantifier Theory is at least as empirically powerful as Generalized Quantifier Theory.