Measuring Inconsistency

I provide a method of measuring the inconsistency of a set of sentences – from 1-consistency, corresponding to complete consistency, to 0-consistency, corresponding to the explicit presence of a contradiction. Using this notion to analyze the lottery paradox, one can see that the set of sentences capturing the paradox has a high degree of consistency (assuming, of course, a sufficiently large lottery). The measure of consistency, however, is not limited to paradoxes. I also provide results for general sets of sentences.     

Why wouldn't we cry? Love and loss along a river in decline

Along the upper reaches of the Ganga in the Indian Himalayas, devotees of the river and its Hindu Goddess decry the changes that are effecting the sanctity and continuity of its flow. Concerns include the impacts of development projects such as hydroelectric dams and the implications of climate shifts such as altered precipitation, warming temperatures, and melting glaciers. These forces of change are frequent subjects of commentary for those that fear the river's potential demise. This article draws from ethnographic research from 2008 to 2009 to highlight two of the main emotions cited by river devotees when they speak of its condition: love and loss. The feelings of intimacy are sometimes expressed through talk of identity (pehchaan) and in demands to ensure the river's uninterrupted flow. Expressions of loss are also shared verbally, through discourse, and they are evident in moments when people respond to significant changes in the river's appearance. After addressing discourses of concern for the Ganga, the article closes with the Government of India's decision to cancel the contested dams on the river's upper regions and to declare it an “eco-sensitive zone”. Such measures are important recognitions of emotive linkages with and dependencies on nature.     

Inconsistency and rank preservation

Conditions for rank preservation in a positive reciprocal matrix that is inconsistent are provided. Three methods of deriving ratio estimates are examined: the eigenvalue, the logarithmic least squares, and the least squares methods. It is shown that only the principal eigenvector directly deals with the question of inconsistency and captures the rank order inherent in the inconsistent data.     

Inconsistency in the A-Theory

This paper presents a new argument against A-theories of time. A-theorists hold that there is an objective now (present moment) and an objective flow of time, the latter constituted by the movement of the objective now through time. A-theorists therefore want to draw different pictures of reality—showing the objective now in different positions—depending upon the time at which the picture is drawn. In this paper it is argued that the times at which the different pictures are drawn may be taken to be normal times or hypertimes. If they are normal times then the A-theory is inconsistent, or else collapses to the B-theory—and appealing to primitive tense operators will not help A-theorists avoid this conclusion. If the times are hypertimes then the A-theory is consistent, but deeply problematic none the less.     

Inconsistency and scientific realism

I erect a framework within the semantic view of theories for explaining the empirical success of internally inconsistent models and theories, with scientific realism in mind. The framework is an instance of the ‘content-driven’ approach to inconsistency, advocated by both Norton (Philos Sci 54:327–350, 1987) and Smith (Stud Hist Philos Sci 19:429–445, 1988a, In: Fine A, Leplin J (eds) PSA1988, 1988b), whose ideas my analysis aims to clarify and substantiate.     

Inconsistency in natural languages

An argument for Trivialism, the view that natural languages are logically inconsistent, is provided that does not rely on contentious empirical assumptions about natural language terms such as “and” or “or.” Further, the view is defended against an important objection recently mounted against it by Thomas Hofweber.     

Pragmatic Inconsistency and Credibility

A critic may attack an arguer personally by pointing out that the arguer’s position is pragmatically inconsistent: the arguer does not practice what he preaches. A number of authors hold that such attacks can be part of a good argumentative discussion. However, there is a difficulty in accepting this kind of contribution as potentially legitimate, for the reason that there is nothing wrong for a protagonist to have an inconsistent position, in the sense of committing himself to mutually inconsistent propositions. If so, any such charge seems to be irrelevant. The questions to be answered in this essay are: what, if any, is the dialectical rationale for this type of criticism, and in what situations, if any, is this kind of charge dialectically legitimate? It will be shown that these attacks can be dialectically legitimate, in special circumstances, and that they can be seen as strategic?manoeuvres where a party attempts to reconcile his dialectical and his rhetorical objectives.     

Inconsistency in spatial knowledge

Two experiments examined whether spatial information judged from cognitive maps contains the functional euclidean properties of real maps. In Experiment 1, the six directions between sets of threetriad locations in a town were judged from memory. The angle formed by the two judged directions from a location to the other two locations in a triad was derived. The three derived angles of a triad were then summed. The derived angles were found to be biased toward 90 deg. The sum of the three derived angles of a triad also exceeded 180 deg, which violates the euclidean properties of real maps. In Experiment 2, subjects judged the direction between pairs of American cities in both directions. The judged directions were found to be consistently nonreversible, which is contrary to the properties of euclidean geometry. The study suggests that information judged from cognitive maps can contain internally inconsistent spatial properties, and the results are discussed in terms of current theories of spatial representation.     

Dynamic Inconsistency and Performable Plans

An agent may abandon an initiated action plan, although he doesnot acquire new information or encounter unforeseen obstacles.Such dynamic inconsistency can be to the agent';s guaranteeddisadvantage, and there is a debate on how it should rationallybe avoided. The main contenders are the sophisticated andthe resolute approaches. I argue that this debate is misconceived,since both approaches rely on false assumptions about theperformability of action plans. The debate can be reformulated,so as to avoid these mistaken assumptions. I try to show that sucha reformulation must rely on certain implausible claims.     

Inconsistency Theories of Semantic Paradox

It is argued that a certain form of the view that the semantic paradoxes show that natural languages are "inconsistent" provides the best response to the semantic paradoxes. After extended discussions of the views of Kirk Ludwig and Matti Eklund, it is argued that in its strongest formulation the view maintains that understanding a natural language is sharing cognition of an inconsistent semantic theory for that language with other speakers. A number of aspects of this approach are discussed and a few objections are entertained.     

An Inconsistency in the Knowledge Argument

I argue that Frank Jackson's knowledge argument cannot succeedin showing that qualia are epiphenomenal. The reason for this is that there is, given thestructure of the argument, an irreconcilable tension between his support for the claim thatqualia are non-physical and his conclusion that they are epiphenomenal. The source of the tensionis that his argument for the non-physical character of qualia is plausible only on theassumption that they have causal efficacy, while his argument for the epiphenomenal characterof qualia is plausible only on the assumption that they are non-physical. Since these two argumentscannot be combined coherently, the most Jackson's argument can establish is thatqualia are non-physical.     

Self-Reported Cognitive Inconsistency in Older Adults

ABSTRACT

Insight into one's own cognitive abilities, or metacognition, has been widely studied in developmental psychology. Relevance to the clinician is high, as memory complaints in older adults show an association with impending dementia, even after controlling for likely confounds. Another candidate marker of impending dementia under study is inconsistency in cognitive performance over short time intervals. Although there has been a recent proliferation of studies of cognitive inconsistency in older adults, to date, no one has examined adults' self-perceptions of cognitive inconsistency. Ninety-four community-dwelling older adults (aged 70–91) were randomly selected from a parent longitudinal study of short-term inconsistency and long-term cognitive change in aging. Participants completed a novel 40-item self-report measure of everyday cognitive inconsistency, including parallel scales indexing perceived inconsistency 5 years ago and at present, yielding measures of past, present, and 5-year change in inconsistency. The questionnaire showed acceptable psychometric characteristics. The sample reported an increase in perceived inconsistency over time. Higher reported present inconsistency and greater 5-year increase in inconsistency were associated with noncognitive (e.g., older age, poorer ADLs, poorer health, higher depression), metacognitive (e.g., poorer self-rated memory) and neuropsychological (e.g., poorer performance and greater 5-year decline in global cognitive status, vocabulary, and memory) measures. Correlations between self-reported inconsistency and neuropsychological performance were attenuated, but largely persisted when self-rated memory and age were controlled. Observed relationships between self-reported inconsistency and measures of neuropsychological (including memory) status and decline suggest that self-perceived inconsistency may be an area of relevance in evaluating older adults for memory disorders.     

Getting the Most Out of Inconsistency

In this paper we look at two classic methods of deriving consequences from inconsistent premises: Rescher-Manor and Schotch-Jennings. The overall goal of the project is to confine the method of drawing consequences from inconsistent sets to those that do not require reference to any information outside of very general facts about the set of premises. Methods in belief revision often require imposing assumptions on premises, e.g., which are the important premises, how the premises relate in non-logical ways. Such assumptions enable one to select a reasonable collection of formulas from all the formulas of the language (the set of consequences of an inconsistent set). Basic versions of the classic methods only use logical relations between the premises. We compare and criticize each of the classic views with an eye to combining the views to get the most out of inconsistent premises. We do this in a way that will respect the theoretical grounding of each view while meeting our other restrictions.     

A Variable Response Inconsistency scale and a True Response Inconsistency scale for the Millon Adolescent Clinical Inventory

Variable Response Inconsistency (M-VRIN) and True Response Inconsistency (M-TRIN) scales were developed for the Millon Adolescent Clinical Inventory using 104 male and 78 female delinquents, ages 13-17 years. M-VRIN efficacy was assessed by comparing nonrandom protocols of 76 male and 34 female delinquents, ages 13-17 years, with 100 computer-generated random protocols. Nonrandom protocols were screened using a matched-pair Minnesota Multiphasic Personality Inventory-Adolescent or Jesness Inventory. M-TRIN efficacy was assessed by comparing protocols with 160 simulated acquiescent and nonacquiescent protocols. Specificities of .95 or higher showed sensitivities up to .89 for M-VRIN, and .90 and .79 for M-TRIN. Predictive power and overall effectiveness are reported for several base rates. Small relationships may exist between M-VRIN and race, and between M-TRIN and gender.     

Internal Inconsistency in the Eysenck Psychoticism Scale

We explored emotional accompaniments to stages of a musician's cycle of creativity through interviews with musicians. Creativity was defined in terms of performance or composition. These musicians described strong emotional vacillations that occur across the creative cycle and discussed ways of dealing with emotional issues involved in moving from one work to the next. Parallels were drawn between emotional aspects of completing a performance or composition to emotional aspects of termination in psychotherapy. Suggestions were offered to musicians for means of dealing with naturally occurring but powerful emotional components of creativity. In addition, some of the musicians suggested that music educators consider teaching students about potential emotional issues that may accompany creative effort. An integration of these issues into music education programs might better prepare students for careers as professional musicians.