We consider the modal logic of non-contingency in a general setting, without making special assumptions about the accessibility relation. The basic logic in this setting is axiomatized, and some of its extensions are discussed, with special attention to the expressive weakness of the language whose sole modal primitive is non-contingency , by comparison with the usual language based on necessity.

The view that species are individuals, as developed by Ghiselinand Hull, has been touted as explaining the role of type specimens intaxonomy. The kinship of this explanation with the Kripke-Putnam theoryof names has long been recognized. In light of this kinship, however,Hull's account of type specimens can be seen to entail two relatedinscrutability problems – unreasonable limits placed on the natureand extent of biological knowledge. An appreciation for these problemsinvites us to consider the proper relation between metaphysical andepistemological inquires in (...) the philosophy of science. (shrink)

Contingency and accident are two important notions in philosophy and philosophical logic. Their meanings are so close that they are mixed up sometimes, in both daily life and academic research. This indicates that it is necessary to study them in a unified framework. However, there has been no logical research on them together. In this paper, we propose a language of a bimodal logic with these two concepts, investigate its model-theoretical properties such as expressivity and frame definability. We axiomatize this (...) logic over various classes of frames, whose completeness proofs are shown with the help of a crucial schema. The interactions between contingency and accident can sharpen our understanding of both notions. Then we extend the logic to a dynamic case: public announcements. By finding the required reduction axioms, we obtain a complete axiomatization, which gives us a good application to Moore sentences. (shrink)

A proposition is noncontingent, if it is necessarily true or it is necessarily false. In an epistemic context, ‘a proposition is noncontingent’ means that you know whether the proposition is true. In this paper, we study contingency logic with the noncontingency operator? but without the necessity operator 2. This logic is not a normal modal logic, because?→ is not valid. Contingency logic cannot define many usual frame properties, and its expressive power is weaker than that of basic modal logic over (...) classes of models without reflexivity. These features make axiomatizing contingency logics nontrivial, especially for the axiomatization over symmetric frames. In this paper, we axiomatize contingency logics over various frame classes using a novel method other than the methods provided in the literature, based on the ‘almost-definability’ schema AD proposed in our previous work. We also present extensions of contingency logic with dynamic operators. Finally, we compare our work to the related work in the fields of contingency logic and ignorance logic, where the two research communities have similar results but are apparently unaware of each other’s work. One goal of our paper is to bridge this gap. (shrink)

The completeness of the axiomatization of contingency logic over symmetric frames has been thought of as a nontrivial job, the unimodal case of which cannot be generalized to the finitely multimodal case, which in turn cannot be generalized to the infinitely multimodal case. This paper deals with the completeness of symmetric contingency logic with unlimitedly many modalities, no matter whether the set of modalities is finite or infinite.

This work concerns the use of operators for past and future contingency in Priorean temporal logic. We will develop a system named C_t, whose language includes a propositional constant and prove that (I) C_t is complete with respect to a certain class of general frames and (II) the usual operators for past and future necessity are definable in such system. Furthermore, we will introduce the extension C_t(lin) that can be interpreted on linear and transitive general frames. The theoretical result of (...) the current work is that contingency can be treated as a primitive notion in reasoning about temporal modalities. (shrink)

Surveys and extens work that has been done in the past two years on 'tense logic' and is a sequel to the author's book, Time and Modality.

Biological taxonomists rely on the so-called ‘type method’ to regulate taxonomic nomenclature. For each newfound taxon, they lay down a ‘type specimen’ that carries with it the name of the taxon it belongs to. Even if a taxon’s circumscription is unknown and/or subject to change, it remains a necessary truth that the taxon’s type specimen falls within its boundaries. Philosophers have noted some time ago that this naming practice is in line with the causal theory of reference and its central (...) notion of rigid designation: a type specimen fixes the reference of a taxon name without defining it. Recently, however, this consensus has come under pressure in the pages of this journal. In a series of articles by Alex Levine, Joseph LaPorte, and Matthew Haber, it has been argued that type specimens belong only contingently to their species, and that this may bode problems for the relation between type method and causal theory. I will argue that this ‘contingency debate’ is a debate gone wrong, and that none of the arguments in defense of contingency withstand scrutiny. Taxonomic naming is not out of step with the causal theory, but conforms to it. However, I will also argue that this observation is itself in need of further explanation, since application of the type method in taxonomic practice is plagued by errors and ambiguities that threaten it with breaking down. Thus, the real question becomes why taxonomic naming conforms to the causal theory in the first place. I will show that the answer lies in the embedding of the type method into elaborate codes of nomenclature. (shrink)

Simple finite axiomatizations are given for versions of the modal logics K and K4 with non-contingency (or contingency) as the sole modal primitive. This answers two questions of I. L. Humberstone.

Monomodal logic has exactly two maximally normal logics, which are also the only quasi-normal logics that are Post complete, and they are complete for validity in Kripke frames. Here we show that addition of a propositional constant to monomodal logic allows the construction of continuum many maximally normal logics that are not valid in any Kripke frame, or even in any complete modal algebra. We also construct continuum many quasi-normal Post complete logics that are not normal. The set of extensions (...) of S4.3 is radically altered by the addition of a constant: we use it to construct continuum many such normal extensions of S4.3, and continuum many non-normal ones, none of which have the finite model property. But for logics with weakly transitive frames there are only eight maximally normal ones, of which five extend K4 and three extend S4. (shrink)

The paper introduces a contingential language extended with a propositional constant τ axiomatized in a system named KΔτ , which receives a semantical analysis via relational models. A definition of the necessity operator in terms of Δ and τ allows proving (i) that KΔτ is equivalent to a modal system named K□τ (ii) that both KΔτ and K□τ are tableau-decidable and complete with respect to the defined relational semantics (iii) that the modal τ -free fragment of KΔτ is exactly the (...) deontic system KD. In §4 it is proved that the modal τ -free fragment of a system KΔτw weaker than KΔτ is exactly the minimal normal system K. (shrink)

Monomodal logic has exactly two maximally normal logics, which are also the only quasi-normal logics that are Post complete, and they are complete for validity in Kripke frames. Here we show that addition of a propositional constant to monomodal logic allows the construction of continuum many maximally normal logics that are not valid in any Kripke frame, or even in any complete modal algebra. We also construct continuum many quasi-normal Post complete logics that are not normal. The set of extensions (...) of S4.3 is radically altered by the addition of a constant: we use it to construct continuum many such normal extensions of S4.3, and continuum many non-normal ones, none of which have the finite model property. But for logics with weakly transitive frames there are only eight maximally normal ones, of which five extend K4 and three extend S4. (shrink)