Fallibilists about looks deny that the relation of looking the same as is non-transitive. Regarding familiar examples of coloured patches suggesting that such a relation is non-transitive, they argue that, in fact, indiscriminable adjacent patches may well look different, despite their perceptual indiscriminability: it’s just that we cannot notice the relevant differences in the chromatic appearances of such patches. In this paper, I present an argument that fallibilism about looks requires commitment to an empirically false consequence. To succeed in deflecting (...) putative cases of non-transitivity, fallibilists would have to claim that there can’t be any perceptual limitations of any kind on human chromatic discrimination. But there are good reasons to think such limitations exist. (shrink)

This paper argues that decision problems and money-pump arguments should not be a deciding factor against accepting non-transitive better than relations. If the reasons to accept normative standpoints that entail a non-transitive better than relation are compelling enough, we ought to revise our decision method rather than the normative standpoints. The paper introduces the most common argument in favor of non-transitive better than relations. It then illustrates that there are different ways to reconceptualize rational choice so that rational choice is (...) possible also when the relevant better than relation is non-transitive. (shrink)

The aim of this article is to show that, just like in recent years Cobreros, Égré, Ripley and van Rooij provided a non-transitive counterpart of classical logic (meaning by this that all classically acceptable inferences are valid, but Cut and other metainferences are not) the same can be done for every Tarskian logic, with full generality. In order to establish this fact, we take a semantic approach, by showing that appropriate structures can be devised to characterize a non-transitive counterpart of (...) every Tarskian logic, starting from the logical matrices that are usually taken to render them. (shrink)

This paper establishes that the occasional identity relation and the contingent identity relation are both non-transitive and as such are not properly classified as identity relations. This is achieved by appealing to cases where multiple fissions and fusions occur simultaneously. These cases show that the contingent and occasional identity relations do not even satisfy the time-indexed and world-indexed versions of the transitivity requirement and hence are non-transitive relations.

The paper’s novelty is in combining two comparatively new fields of research: non-transitive logic and the proof method of correspondence analysis. To be more detailed, in this paper the latter is adapted to Weir’s non-transitive trivalent logic \({\mathbf{NC}}_{\mathbf{3}}\). As a result, for each binary extension of \({\mathbf{NC}}_{\mathbf{3}}\), we present a sound and complete Lemmon-style natural deduction system. Last, but not least, we stress the fact that Avron and his co-authors’ general method of obtaining _n_-sequent proof systems for any _n_-valent logic (...) with deterministic or non-deterministic matrices is not applicable to \({\mathbf{NC}}_{\mathbf{3}}\) and its binary extensions. (shrink)

Graham Priest takes the relation of identity to be non-transitive. In this paper, we are going to discuss several consequences of identity as a non-transitive relation. We will consider the Henkin-style completeness proof for classical first-order logic with a non-transitive “identity” predicate, Leibniz-identity in Priest’s second-order minimal logic of paradox, and the question whether or not identity of individuals should be defined as Leibniz-identity.

Logicians interested in naive theories of truth or set have proposed logical frameworks in which classical operational rules are retained but structural rules are restricted. One increasingly popular way to do this is by restricting transitivity of entailment. This paper discusses a series of logics in this tradition, in which the transitivity restrictions are effected by a determinacy constraint on assumptions occurring in both the major and minor premises of certain rules. Semantics and proof theory for 3-valued, continuum-valued (...) and surreal-valued semantics are given and the proof theory for the systems outlined. The framework is robust in the sense that no conditional, defined or primitive, which sustains the contraction principles underlying Curry paradoxes can be expressed. Classical recapture is smoothly achievable in the system which however is expressively limited and not semantically closed. The conclusion considers the issue of how to extend the system to capture full naive set theory. (shrink)

I defend, to a certain extent, the traditional view that perceptual indiscriminability is non-transitive. The argument proceeds by considering important recent work by Benj Hellie: Hellie argues that colour perception represents ‘inexactly’, and that this results in violations of the transitivity of colour indiscriminability. I show that Hellie’s argument remains inconclusive, since he does not demonstrate conclusively that colour perception really does represent inexactly. My own argument for the non-transitivity of perceptual indiscriminability uses inexactness instead as one horn (...) of a dilemma: the key idea is that there is a class of perceptual experiences which might plausibly be supposed either to represent inexactly or to represent exactly—but which demonstrate the non-transitivity of perceptual indiscriminability either way. (shrink)

In this paper we first develop a logic independent account of relevant implication. We propose a stipulative denition of what it means for a multiset of premises to relevantly L-imply a multiset of conclusions, where L is a Tarskian consequence relation: the premises relevantly imply the conclusions iff there is an abstraction of the pair such that the abstracted premises L-imply the abstracted conclusions and none of the abstracted premises or the abstracted conclusions can be omitted while still maintaining valid (...) L-consequence. Subsequently we apply this denition to the classical logic consequence relation to obtain NTR-consequence, i.e. the relevant CL-consequence relation in our sense, and develop a sequent calculus that is sound and complete with regard to relevant CL-consequence. We present a sound and complete sequent calculus for NTR. In a next step we add rules for an object language relevant implication to the sequent calculus. The object language implication reflects exactly the NTR-consequence relation. One can see the resulting logic NTR-> as a relevant logic in the traditional sense of the word. By means of a translation to the relevant logic R, we show that the presented logic NTR is very close to relevance logics in the Anderson-Belnap-Dunn-Routley-Meyer tradition. However, unlike usual relevant logics, NTR is decidable for the full language, Disjunctive Syllogism and Adjunction are valid, and neither Modus Ponens nor the Cut rule are admissible. (shrink)

Suppose you are presented with three red objects. You are then asked to take a careful look at each possible pair of objects, and to decide whether or not their members look chromatically the same. You carry out the instructions thoroughly, and the following propositions sum up the results of your empirical investigation: <blockquote> i. red object #1 looks the same in colour as red object #2. </blockquote> ii. red object #2 looks the same in colour as red object #3.

Recent work has brought to prominence the idea that some utterances contain occurrences of noun phrases that not only corefer, but do so in a particularly guaranteed or explicit way—call such occurrences ‘de jure coreferential’. Studies of de jure coreference have considered both the characteristics of the relation, and its explanation. Pinillos (154(2):301–324, 2011) argues that de jure coreference is non-transitive, and uses this as part of his argument for a new semantic primitive explaining de jure coreference. In this paper, (...) I draw attention to a neglected distinction between de jure coreference and another kind of coreference with which it might easily be confused. I then consider Pinillos’s claim that de jure coreference is non-transitive, and conclude that even using Pinillos’s definition of de jure coreference, it is far from straightforward that he has demonstrated the non-transitivity of de jure coreference. I question whether Pinillos’s characterisation of de jure coreference is adequate, and offer a plausible alternative characterisation. I show that on this new characterisation, there is no evidence that the relation is non-transitive. (shrink)

In this paper, I argue that those who accept the conceptualist view in the philosophy of perception should reject the traditional view that colour indiscriminability is non-transitive. I start by outlining the general strategy that conceptualists have adopted in response to the familiar ‘fineness of grain’ objection, and I show why a commitment to what I call the indiscriminability claim seems to form a natural part of this strategy. I then show how together, the indiscriminability claim and the non-transitivity (...) claim –the claim that colour indiscriminability is non-transitive –entail a further, suspicious-looking claim that I call the problematic claim. My argument then splits into two parts. In the first part, I show why the conceptualist does indeed need to reject the problematic claim. Given that this claim is jointly entailed by the indiscriminability claim and the non-transitivity claim, the conceptualist is then left with a straight choice: reject the indiscriminability claim, or reject the non-transitivity claim. In the second part, I then explain why the conceptualist should choose the latter option. (shrink)

Among other virtues, Mental Files Theory provides a straightforward explanation of de jure coreference, i.e. identity of referent guaranteed by meaning alone: de jure coreference holds between terms when these are associated with the same mental file from which they inherit their reference. In this paper, I discuss an objection that Angel Pinillos raises against Mental Files Theory and other similar theories: the theory predicts that de jure coreference should be transitive, just like identity. Yet there are cases, involving ‘slash-terms’, (...) in which transitivity fails, or so it seems. In his book Mental Files, Recanati replies that the mental files theorist can accommodate Pinillos’ exceptions by offering a refined model of merging files, the ‘partial merging’ model. While agreeing with Recanati on the need for such a model, I contend that, pace Recanati and Pinillos, de jure coreference is transitive even in the presence of slash-terms. I will first show that paradoxical consequences ensue if slash-terms are said to de jure corefer with several basic terms at once. Then, building on two different accounts Recanati gives of referential confusion, I will show that on both views, de jure coreference cannot hold because of the behaviour of confused slash-terms. I will conclude that, in Mental Files Theory, a slash-term can, at most, de jure corefer with only one basic term per context. (shrink)

There is a mistake in the definition of the covering criterion on page 6.

The concept of transitional justice has been widely discussed inThailand following the massacre of the Red Shirt protesters in 2010, whichresulted in the highest death toll resulting from a military action againstpolitical protestors in Thai history. The eighth anniversary of that tragedyoffers an opportunity to analyse Thailand’s response to the use of militaryviolence against these political activists. This analysis is performed throughthe application of the seven conceptual components of transitional justice:regime change, finding truth, prosecution, security sector reform, victimscenteredness,reparation, and memorialization. (...) The current study is based onan analysis of various textual sources, such as books, journal articles, newsarticles, online sources, and other documents. The evidence shows that in thecase of Thailand, as in other countries, if the first component, regime change, isnot realised such that the authoritarian regime is replaced by one that is civilianand democratic, then justice for past violence can never be established. As aresult, the remaining six components of transitional justice in Thailand havebeen applied in a distorted and incorrect manner in the past eight years. (shrink)

This paper aims to argue for, else illustrate the epistemological significance of the use of non transitive similarity relations, mapping only to "types", as methodologically being on a par with the use of transitive similarity relations (equivalence relations), mapping as well to "predicates". -/- In this paper the sketch of an exact but simple geometrical model of the above construct is followed by mentioning respective use cases for non transitive similarity relations from science and humanities. A well known metaphysics example (...) is elaborated along these lines to some extent. (shrink)

The problem of unification in a normal modal logic $L$ can be defined as follows: given a formula $\varphi$, determine whether there exists a substitution $\sigma$ such that $\sigma $ is in $L$. In this paper, we prove that for several non-symmetric non-transitive modal logics, there exists unifiable formulas that possess no minimal complete set of unifiers.

Unconscious logical inference seems to rely on the syntactic structures of mental representations (Quilty-Dunn & Mandelbaum 2018). Other transitions, such as transitions using iconic representations and associative transitions, are harder to assimilate to syntax-based theories. Here we tackle these difficulties head on in the interest of a fuller taxonomy of mental transitions. Along the way we discuss how icons can be compositional without having constituent structure, and expand and defend the “symmetry condition” on Associationism (the idea that associative links and (...) transitions are perfectly symmetric). In the end, we show how a BIT (“bare inferential transition”) theory can cohabitate with these other non-inferential mental transitions. (shrink)

Truth and Reconciliation Commissions (TRCs) have become a widely used tool to reconcile societies in the aftermath of widespread injustice or social and political conflict in a state. This article focuses on TRCs that take place in non-transitional societies in which the political and social structures, institutions, and power relations have largely remained in place since the time of injustice. Furthermore, it will focus on one particular injustice that TRCs try to address through the practice of truth-telling, namely the eradication (...) of epistemic injustice. The article takes the Canadian and Norwegian TRCs as two examples to show that under conditions of enduring injustice, willful ignorance of the majority, and power inequality, TRCs might create a double bind for victims which makes them choose between epistemic exploitation and continued injustices based on the majority's ignorance. The article argues that the set-up and accompanying measures of TRCs are of the utmost importance if TRCs in non-transitional societies are to overcome epistemic injustice, instead of creating new relations of exploitation. (shrink)

This paper tests a novel implication of the original version of prospect theory (Kahneman and Tversky, 1979): that choices may systematically violate transitivity. Some have interpreted this implication as a weakness, viewing it as an anomaly generated by the ‘editing phase’ of prospect theory which can be rendered redundant by an appropriate re-specification of the preference function. Although there is some existing evidence that transitivity fails descriptively, the particular form of non-transitivity implied by prospect theory is quite (...) distinctive and hence presents an ideal opportunity to expose that theory to test. An experiment is reported which reveals strong evidence of the predicted intransitivity. It is argued that the existence of this new form of non-transitive behaviour presents a fresh theoretical challenge to those seeking descriptively adequate theories of choice behaviour, and a particular challenge to those who seek explanations within the conventional economic paradigm of utility maximisation. (shrink)

This paper discusses a relational modeling of measurement which is complementary to the standard representational point of view: by focusing on the experimental character of the measurand-related comparison between objects, this modeling emphasizes the role of the measuring systems as the devices which operatively perform such a comparison. The non-idealities of the operation are formalized in terms of non-transitivity of the substitutability relation between measured objects, due to the uncertainty on the measurand value remaining after the measurement. The metrological (...) structure of traceability is shown to be an effective solution to cope with the problem of the general non-transitivity of measurement results. A preliminary theory is introduced as a possible formalization for the presented model. (shrink)

ABSTRACT This paper deals with the linguistic phenomenon of vagueness. Based on certain observations regarding the intuitions and linguistic practices of the philosophically informed speaker, we make a series of assumptions concerning the nature and characteristics of the phenomenon. Vagueness is treated as an emerging phenomenon, caused, in essence, by the messy way in which linguistic communities reach classificatory equilibria. Any talk of ‘meaning’, ‘truth’, and such is treated as an indirect way of attempting to describe such equilibria, and it (...) is in regard to these that ascriptions of truth are here relativised. Given such assumptions, we then proceed to formulate and study a semantic theory for languages that contain vague predicates. Finally, we describe two proof systems, one based on trees, and a natural deduction system in the style of Fitch, and outline the appropriate proofs of soundness and completeness. (shrink)

Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.

Arguments based on Leibniz's Law seem to show that there is no room for either indefinite or contingent identity. The arguments seem to prove too much, but their conclusion is hard to resist if we want to keep Leibniz's Law. We present a novel approach to this issue, based on an appropriate modification of the notion of logical consequence.

Derek Parfit presents his Mere Addition Paradox in order to demonstrate that it is extremely difficult to avoid the Repugnant Conclusion. And in order to avoid it, Parfit has embraced perfectionism. However, Stuart Rachels and Larry Temkin, taking their lead from Parfit, have concluded, instead, that the Repugnant Conclusion can be avoided by denying the axiom of transitivity with respect to the all-things-considered-better-than relation. But this seems to present a major challenge to how we evaluate normatively. In this article (...) I show how the Mere Addition Paradox and the Repugnant Conclusion can both be avoided without subscribing to perfectionism, and without sacrificing the axiom of transitivity. (shrink)

Many of our categorization experiences are non-transitive. For some objects a, b and c, a and b can appear indistinguishable, and likewise b and c, but a and c can appear distinguishable. Many categories also appear to be smooth; transitions between cases are not experienced as sharp, but rather as continuous. These two features of our categorization experiences tend to be addressed separately. Moreover, many views model smoothness by making use of infinite degrees. This paper presents a methodological strategy that (...) shows how solving the transitivity problem first can thereby introduce explanatory resources that feed into an account of smoothness without having to make use of infinite degrees. (shrink)

ABSTRACTWhile extant replies to Jonathan Schaffer’s putative counterexamples to the transitivity of grounding have made significant strides against the charge of transitivity failure, the replies pay insufficient attention to the common structure of the counterexamples, overlooking a deeper structural feature that contributes to their prima facie plausibility. Putative counterexamples to the transitivity of grounding, I argue, trade on the distinction between what I call ‘rigid’ and ‘non-rigid’ grounding, and confusion over how rigid and non-rigid grounding react when (...) combined pumps the intuition that the counterexamples’ chained conclusions are false. The rigid/non-rigid grounding distinction also reveals plausible weakening inference rules that have been overlooked in treatments of the logic of grounding. (shrink)

Although the theory of greatest-element rationalizability and maximalelement rationalizability on general domains and without full transitivity of rationalizing relations is well-developed in the literature, these standard notions of rational choice are often considered to be too demanding. An alternative definition of rationality of choice is that of non-deteriorating choice, which requires that the chosen alternatives must be judged at least as good as a reference alternative. In game theory, this definition is well-known under the name of individual rationality when (...) the reference alternative is construed to be the status quo. This alternative form of rationality of individual and social choice is characterized in this paper on general domains and without full transitivity of rationalizing relations. (shrink)

The author argues for the importance of non-Markovian causality in the social sciences because Markovian conditions often cannot be satisfied. Two theorems giving conditions for non-Markovian causes to be transitive are proved. Applications of non-Markovian causality in psychology and economics are outlined.

The term “origin” is associated with a beginning, a debut, a birth. Expressions such as “the origin of life” or “the origin of man” suggest unique moments linked to remarkable phenomena. In the following pages, we will attempt to show that, since its birth, the universe has been undergoing a process of self-organization. The appearance of life on Earth represents one of the stages in this process.

The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but in all the examples considered there it remains symmetric. Here we present a class of binary models where the transition probability is not symmetric, using the extreme points of the unit interval in an order unit space as quantum logic. We show that their state spaces are strictly convex smooth (...) compact convex sets and that each such set _K_ gives rise to a quantum logic of this class with the state space _K_. The transition probabilities are symmetric iff _K_ is the unit ball in a Hilbert space. In this case, the quantum logic becomes identical with the projection lattice in a spin factor which is a special type of formally real Jordan algebra. (shrink)

If the cultural variations concerning knowledge and research on ordinary reasoning are part of cultural history, what kind of historiographical method is needed in order to present the history of its evolution? This paper proposes to introduce the study of theories of reasoning into a historiographic perspective because we assume that the answer to the previous question does not only depend of internal controversies about how reasoning performance is explained by current theories of reasoning. [...].