Marian Călborean

While the Sorites paradox is often presented in a propositional conditional form, it can be recast using disjunctive, conjunctive, or modus tollens syllogism. This paper challenges Kit Fine’s claim that only the conjunctive form is motivated. All four propositional forms are effective because they express three deeper, first-order principles: (1) the familiar principle of Tolerance, (2) the often-implicit assumption of Monotonicity, and (3) a novel claim I call Local Interdefinability (LI). LI is the thesis – motivated by contextualist empirical observations and by the salience of vague contraries – that for adjacent members of a soritical series, vague contraries (such as “tall” and “short”) function as contradictories. LI lets the conjunctive form proceed without any explicit elimination of double negation. Moreover, Kit Fine’s case against the conditional form loses its force since LI covers the gap between the conjunctive and conditional forms, and his case against the disjunctive form is undermined by the rejection of Monotonicity. The paper concludes that the unity of the Sorites paradox lies above the propositional level.

This note introduces the core intuition and basic construction of split epistemic languages, a novel framework for modeling incomplete descriptions in epistemic logic. Standard Kripke models often overstate what agents can plausibly formulate by presupposing a shared maximal language. The proposed remedy is to assign each agent a sub-language called "split language", generated from only those concepts which they can grasp. By blocking inexpressible formulas at the syntactic level, this approach distinguishes lack of information (uncertainty) and lack of conception (unawareness), solving some standard puzzles of epistemic logic. This note presents the initial problem statement, the core intuition and basic formal machinery, together with several applications which demonstrate the framework's applicability. [uploaded the published version correcting some a typos on 15.04.2026]

(penultimate version) Ca omagiu adus cercetărilor logico-filosofice ale lui Mircea Dumitru, articolul urmărește tema justificării filosofice a logicii clasice de ordinul doi în special și a logicilor clasice de ordin superior în general, din două perspective. Perspectiva matematicii aplicate, studiată de Timothy Williamson, care evidențiază sprijinul abductiv adus de aplicarea la lume a unei logici. Și perspectiva, inspirată de Mircea Dumitru, a identificării logicilor modale propoziționale cu un fragment al logicii de ordinul doi, care evidențiază legătura între logică și metafizică.

Vagueness challenges the boundaries of classical logic by exposing how incremental changes—like adding a single hair to a bald man—lead one to paradoxical conclusions. Without claiming exhaustivity, this study compares ten philosophical logics for vagueness —nine non-classical: trivaluationism, fuzzy logic, supervaluationism, non-numerical degree-based, probabilism, fuzzy plurivaluationism, “truer”-based, non-transitivism, compatibilism, and one classical: epistemicism—each offering a distinct way to replace or refine classical logic. The guiding question is: What minimal modifications allow us to preserve most workings of classical logic while embracing the graduality and inexactitude characteristic of vagueness? Through a comparative method, the study explores four axes: (1) truth values, (2) operators and truth-functionality, (3) semantics, (4) truth, validity and the Sorites paradox, and concludes with comparative tables and brief evaluative remarks.

Wisdom and Judgement. The Types and Limits of Legal Indeterminacy. The problem of vagueness in the philosophy of language concerns the indeterminacy of notions in ordinary language and whether vagueness can be eliminated or not. The article applies the analysis of vagueness to the legal field, employing some examples from Romanian and foreign law. The analysis starts from the central notions of norm, law, and statute, then discusses the issues raised by indeterminacy and their relevance for the debate between positivism and interpretivism in the philosophy of law, finally raising the challenge of the Sorites paradox. Against this backdrop, a distinction between positive and negative legal indeterminacy is introduced, which leads to an argument that judicial bivalence is the only remedy for the problems inherent in the aggregation of norms. The final conclusion is that, in democratic societies, indeterminacy does not undermine the ideal of the rule of law.

I this paper I give minimal axioms for the ontology of time, especially A-theories and B-theories and I derive philosophically interesting lemmas. The exercise is set-theoretical, defining all notions and indicating assumptions and philosophical points of disagreement, while being easy to translate to other formal expressions. The issue of a logic for A-theories of time is treated towards the end, where I sketch ‘copresent’ operators for capturing the idea of temporal passage. The main conclusion will be that, while circularity threatens both families of theories, the growing block theory (belonging to the A-theory) is the least objectionable philosophically.

A constant of Frege’s writing is his rejection of indeterminate predicates as found in natural language. This paper follows Frege’s remarks on vagueness from the early "Begriffsschrift” to his mature works, drawing brief parallels with the main contemporary theories of vagueness. I critically examine Frege’s arguments for the inconsistency of natural language and argue that the inability to accommodate vagueness in his mature ontology is mainly due to heuristic rules of thumb which Frege took as essential, not to a deep problem in his fundamental apparatus.