Logical Inconsistencies Research Articles

Abstract heterarchy: Time/state-scale re-entrant form

A heterarchy is a dynamical hierarchical system inheriting logical inconsistencies between levels. Because of these inconsistencies, it is very difficult to formalize a heterarchy as a dynamical system. Here, the essence of a heterarchy is proposed as a pair of the property of self-reference and the property of a frame problem interacting with each other. The coupling of them embodies a one-ity inheriting logical inconsistency. The property of self-reference and a frame problem are defined in terms of logical operations, and are replaced by two kinds of dynamical system, temporal dynamics and state-scale dynamics derived from the same “liar statement”. A modified tent map serving as the temporal dynamics is twisted and coupled with a tent map serving as the state-scale dynamics, and this results in a discontinuous self-similar map as a dynamical system. This reveals that the state-scale and temporal dynamics attribute to the system, and shows both robust and emergent behaviors.

Petersen et al. Respond to "Effect Modification by Time-varying Covariates"

We thank Robins et al. (1) for their thoughtful commentary on our article (2). Before responding, we wish to point out that they altered our notation slightly, using m rather than j to refer to the baseline time point. Robins et al. distinguish between two types of history-adjusted marginal structural models (HA-MSMs), those that consider an outcome at a fixed time point (“group 1,” or those with multiple baseline time points for a single time-point-specific outcome) and those that consider a moving outcome (“group 2,” or those that still use multiple baseline time points but use no more than a single baseline for each time-point-specific outcome). They raise the issue of model incompatibility and make the point that “only MSMs in group 1 can be incompatible and thus lead to logical inconsistencies” (1, p. 996). We concur with their discussion of the pitfalls that can be involved in modeling group 1 HA-MSMs and appreciate their emphasis on this issue. We make two major points in response. 1) As Robins et al. state explicitly (1), the pitfalls regarding model incompatibility do not apply to group 2 HA-MSMs. However, we discuss only group 2 HA-MSMs in our article (2). Therefore, we would like to clarify that the issue of model incompatibility raised in the commentary does not apply to the method outlined in our paper. 2) We feel that the method outlined in our paper for estimation of group 2 HA-MSMs constitutes a significant practical contribution, for the reasons stated below. First, as Robins et al. mention (1), group 2 HA-MSMs allow pooling of data across time and can thereby enhance the efficiency of the resulting estimators. Second, this approach provides insight into how effect estimates differ across strata defined by covariates measured at different time points. Our data example illustrates this application: Effect estimates at later time points following loss of viral suppression differed less between subjects with different CD4 T-cell counts than such estimates at earlier time points. We agree that this type of effect modification by time-dependent covariates is different from the effect modification in a group 1 HA-MSM, but we suggest that it is nonetheless both interesting and interpretable. Third, although the issue was beyond the scope of our article, group 2 HA-MSMs can be used to identify interesting dynamic treatment rules, in which treatment assignment is updated over time in response to changes in patient covariates (3). We appreciate Robins et al.’s focus on the confounding/ selection bias that can result from the way in which treatment prior to baseline was assigned. We agree that this is an important issue in the interpretation of HA-MSMs and their application to dynamic treatment rules, and we discuss it in more detail elsewhere (3, 4). Inclusion in V(j) (or V(m) in Robins et al.’s notation) of covariates sufficient to control confounding of past treatment guarantees that the parameter estimated is only a function of the distribution of the counterfactuals, whereas if this condition is not met, one estimates a causal effect for a selected subpopulation in which the selection was ruled by the treatment mechanism. For example, in our paper (2), we point out the potential role played by changes over time in the composition of the population remaining on nonsuppressive therapy. This issue can also arise in standard baseline-adjusted MSMs if the baseline history includes time-dependent covariates. Finally, Robins et al. raise an interesting philosophical question. They reason that the group 1 HA-MSM parameter, in spite of the fact that it is well-defined and identifiable, is not well-suited for modeling. One might argue in response that difficulty in modeling a specific parameter should be regarded as a welcome challenge by statisticians, rather than a motivation to avoid the parameter altogether. In the case of group 1 HA-MSMs, however, we wonder whether the issue is less that the parameter is difficult to model and more that in many instances it is not in fact the causal effect of interest. We look forward to future work exploring these issues.

Borrowing From Others: Appropriating Social Capital Theories for “Doing” HRD

The problem and the solution. In this conceptual study, social capital theories are used to illuminate the practice of borrowing theories for HRD research and practice. “Borrowing” from other disciplines is an implicit, taken-for-granted practice in HRD theory development that has avoided scrutiny. Since HRD is a multiparadigm discipline, borrowing theories from monoparadigm disciplines can cause theoretical and logical inconsistencies. This study offers a way to organize borrowed social capital theories by categorizing them by paradigm and, ultimately, by the goal of the research and the desired HRD outcome. The article then offers a six-step process for borrowing theories from other disciplines. Ultimately, the article seeks an answer to the question: How can/should HRD borrow social capital theories to help achieve various (and contested) HRD outcomes?

The problem of theodicy and the theology of the cross

Theodicy is the attempt to justify God’s righteousness and goodness amidst the experience of evil and suffering in the world. This article discusses Karl Barth’s Christological and Jürgen Moltmann’s eschatological approach to the problem of theodicy. The central theoretical argument is that the problem of theodicy poses a major hermeneutical challenge to Christianity that needs to be addressed, since it has implications for the way in which theology defines itself. Questions that arise are: What are the boundaries of theology? What are the grounds on which the question of theodicy must be asked? Is the Christian understanding of God’s omnipotence truly Scriptural? The modern formulation of theodicy finds its origin in the Enlighten- ment that approaches the problem from a theoretical framework based on human experience. This theoretical approach leads, however, to further logical inconsistencies. Theology must rather approach the problem in the same way as Scripture does, by taking the cross, resurrection and parousia of Christ as point of departure. The cross and resurrection are a sign that suffering is not part of God’s plan and at the same time an affirmation of God’s victory over suffering and evil.

Inconsistencies in self-reported drug use by adolescents in substance abuse treatment: Implications for outcome and performance measurements

This article presents an analysis of logical inconsistencies in adolescents' reporting of recent substance use to assess the potential effect of inaccurate reporting on measures of treatment outcomes and program performance. We used data on 1,463 clients from 10 adolescent treatment programs to assess the relationship between inconsistent reports and various factors that contribute to program assignment and treatment outcomes. Our results suggest that inconsistencies do not arise at random. Instead, inconsistencies are associated with program assignment and factors widely considered to influence treatment outcomes, including age at first use, living situation, race/ethnicity, and mental distress. We also found a positive relationship between level of inconsistent reporting of drug use and self-reports of improvement over time on several well-established treatment outcome measures. Our study highlights the need for greater awareness on the potential impact of inaccuracies in the reporting of substance use on outcome and performance measurements and that for the development of methodologies to improve accuracy.

Foundational Issues Concerning Taxa and Taxon Names

In a series of articles, Rieppel (2005, Biol. Philos. 20:465-487; 2006a, Cladistics 22:186-197; 2006b, Systematist 26:5-9), Keller et al. (2003, Bot. Rev. 69:93-110), and Nixon and Carpenter (2000, Cladistics 16:298-318) criticize the philosophical foundations of the PhyloCode. They argue that species and higher taxa are not individuals, and they reject the view that taxon names are rigid designators. Furthermore, they charge supporters of the individuality thesis and rigid designator theory with assuming essentialism, committing logical inconsistencies, and offering proposals that render taxonomy untestable. These charges are unsound. Such charges turn on confusions over rigid designator theory and the distinction between kinds and individuals. In addition, Rieppel's, Keller et al.'s, and Nixon and Carpenter's proposed alternatives are no better and have their own problems. The individuality thesis and rigid designator theory should not be quickly abandoned.

Critique of the foundations of time-dependent density-functional theory

The general expectation that, in principle, the time-dependent density-functional theory (TDDFT) is an exact formulation of the time evolution of an interacting $N$-electron system is critically reexamined. It is demonstrated that the previous TDDFT foundation, resting on four theorems by Runge and Gross (RG) [Phys. Rev. Lett. 52, 997 (1984)], is invalid because undefined phase factors corrupt the RG action integral functionals. Our finding confirms much of a previous analysis by van Leeuwen [Int. J. Mod. Phys. B 15, 1969 (2001)]. To analyze the RG theorems and other aspects of TDDFT, an utmost simplification of the Kohn-Sham (KS) concept has been introduced, in which the ground-state density is obtained from a single KS equation for one spatial (spinless) orbital. The time-dependent (TD) form of this radical Kohn-Sham (rKS) scheme, which has the same validity status as the ordinary KS version, has proved to be a valuable tool for analysis. The rKS concept is used to clarify also the alternative nonvariational formulation of TD KS theory. We argue that it is just a formal theory, allowing one to reproduce but not predict the time development of the exact density of the interacting $N$-electron system. Besides the issue of the formal exactness of TDDFT, it is shown that both the static and time-dependent KS linear response equations neglect the particle-particle ($p$-$p$) and hole-hole ($h$-$h$) matrix elements of the perturbing operator. For a local (multiplicative) operator this does not lead to a loss of information due to a remarkable general property of local operators. Accordingly, no logical inconsistency arises with respect to DFT, because DFT requires any external potential to be local. For a general nonlocal operator the error resulting from the neglected matrix elements is of second order in the electronic repulsion.

Paradox in Wave-Particle Duality

We report on the simultaneous determination of complementary wave and particle aspects of light in a double-slit type “welcher-weg” experiment beyond the limitations set by Bohr’s Principle of Complementarity. Applying classical logic, we verify the presence of sharp interference in the single photon regime, while reliably maintaining the information about the particular pinhole through which each individual photon had passed. This experiment poses interesting questions on the validity of Complementarity in cases where measurements techniques that avoid Heisenberg’s uncertainty principle and quantum entanglement are employed. We further argue that the application of classical concepts of waves and particles as embodied in Complementarity leads to a logical inconsistency in the interpretation of this experiment.

The fundamental equations of multi-species virtual population analysis and its variants

Two of the most significant developments in fisheries science are the single species virtual population analysis (SSVPA) and multi-species virtual population analysis (MSVPA). Since its development, MSVPA and its variants have been used in fish population studies, fish stock assessment, and the management of the fisheries in many parts of the world, including the North Sea, the Baltic Sea, the Barents Sea, the Bering Sea, Georges Bank, and the Benguela Current, and have been accepted as routine and essential tools for making efficient use of the world's major fisheries resources for food production, and for conserving and managing those resources. However, serious questions arise from the fact that some of their equations are “borrowed” straight from SSVPA, except for adding a species index. In this paper, I derive the fundamental equations of MSVPA and its variants as a system of ordinary differential equations (if the ages of fish are discrete) or as a system of first order partial differential–integral equations (if the ages of fish are continuous), both subject to appropriate constraints and boundary conditions (biological observations and data). Their formulation as well known mathematical problems has not only revealed their mathematical nature and hence laid the foundation for their speedy solution by use of a great variety of known and readily available mathematical techniques, but also revealed the logical inconsistency in the currently used MSVPA and its variants. This inconsistency highlights an urgent need to revise all past work on MSVPA and its variants, by replacing the existing equations of MSVPA and its variants with the fundamental equations derived above. Finally, I discuss (1) the conversion of data on the stomach contents of fish of different ages and of different species into their coefficients of suitability, (2) two possible extensions of the present work, (3) its general ecological and biological significance as a much needed practical method or routine for parameterizing a system of age- and time-dependent or more general Lotka–Volterra equations to understand the underlying mechanisms for the rapid changes of the ecosystems and for us to maintain a harmonious co-existence within a biological system, and (4) its significance to several areas of fisheries science, including food production, effective use and management of fisheries resources, marine and freshwater conservation, and the maintenance of a healthy aquatic environment.

National Missile Defense and Deterrence

The current stance of the Bush administration has renewed debate on the implications of national missile defense. While a large part of that debate concerns its technical and economic feasibility, there is also considerable debate concerning the ramifications of national missile defense for international peace and stability. Unfortunately, few studies have analyzed the implications of missile defense through the lens of deterrence theory. Those that have were based on classical deterrence theory, which is plagued by a variety of logical inconsistencies and empirical anomalies. Accordingly, I examine the implications of national missile defense for deterrence from the vantage point of an alternative theory of deterrence, perfect deterrence theory. The results indicate that national missile defense generally enhances the stability of deterrence; the greatest threat missile defense poses is causing dissatisfaction in potential challengers.

Expressivism, Logic, Consistency, and Moral Dilemmas

On an expressivist view, ethical claims are understood as expressions of our attitudes, desires, and feelings. A famous puzzle for this view concerns the use of logic in ethical reasoning, and two standard treatments try to solve the puzzle by explaining logical inconsistency in terms of conflicting attitudes. I argue, however, that this general strategy fails: because we can reason effectively even in the presence of conflicting moral attitudes – in cases of moral dilemmas – avoiding these conflicts cannot be a ground for correct moral reasoning. The result is a dilemma for expressivists: if they take all kinds of attitudes to be under consideration, then conflict cannot play the required role, since attitudes can fail to be compatible in cases of moral conflict. If they restrict attention to ‘all-in attitudes’ or to intentions or plans, then there is an important notion of obligation, used in standard arguments – one for which conflicts are allowed – that they fail to capture. I explain why expressivists should be especially tolerant of conflicting attitudes, and I conclude that they should pursue a different strategy for grounding logical normativity.

Application of molecular clocks in ornithology revisited

Molecular clocks have seen many applications in ornithology, but many applications are uncritical. In this commentary, I point out logical inconsistencies in many uses of clocks in avian molecular systematics. I call for greater rigor in application of molecular clocks – clocks should only be used when clocklike behavior has been tested and confirmed, and when appropriate calibrations are available. Authors and reviewers should insist on such rigor to assure that systematics is indeed scientific, and not just storytelling.

Mineral activity–composition relations and petrological calculations involving cation equipartition in multisite minerals: a logical inconsistency

AbstractEquipartition is an assumption that preserves the same relative fraction of the cations on each site, originally used just to distribute cations such as Fe and Mg over two or more sites during mineral recalculation. This approximation has been used in almost all thermometry and barometry applications in petrology involving pyroxene, amphibole, chlorite and biotite mica. It has also become the default approach used in deriving activity–composition relations in multisite minerals where details of element partitioning among the sites is unknown and therefore assumed to be random. It is shown that, where a third element, such as Al, resides on just one of the sites, equipartition introduces a serious logical and numerical inconsistency between the enthalpy and entropy of mixing. In particular, application of equipartition is demonstrated to be equivalent to treating the solution as one in which all cations reside on one type of site. For example, in the case of aluminous orthopyroxene the equipartition assumption implies that Fe, Mg and Al are distributed across two identical sites, and that end‐members such as Mg‐tschermak's pyroxene have enthalpies characterized by a totally disordered distribution of Mg and Al over the M2 and M1 sites. Clearly this is unsupportable, and solid solutions should be treated with appropriate thermodynamics for order–disorder. For phases where element partitioning data are unavailable, we offer a simple alternative strategy, using the ordering of Fe and Mg on M1 and M2 sites in biotite as an example.

Viète's Controversy with Clavius Over the Truly Gregorian Calendar

Some twenty years after the Gregorian calendar reform, towards the end of his life, Francois Viete published his own calendar proposal. This treatise contains a sharp attack against the Jesuit scholar Clavius, the mathematical mind behind the reform. Understandably enough, Clavius prepared a negative reply. Viete heard of it and exploded in a fit of rage, ``I demonstrated that you are a false mathematician [ . . . ], and a false theologian.'' Sadly, Clavius' rejection, added as a chapter to his monumental apology of the Gregorian reform, appeared when Viete had already passed away. Viete seriously believed that the true aim of the Gregorian reform has been betrayed and he was furious about some logical inconsistencies which he claimed to have found in Clavius' calendar. Clavius apparently confused solar day and epactal day (or ``tithi''), the thirtieth part of a lunar month. This is the very core of Viete's attack against Clavius whom he accused of having introduced a false lunar period (``falsa periodus lunaris''). But his own work has some logical inconsistencies too. For instance, he reproaches Clavius for having introduced lunar months of 31 days which, indeed, are unrealistic. Grievously, his own rules can likewise give rise to lunations of unnatural lengths. In order to understand these subtle twists reader and author must work largely through both Clavius and Viete's methods of Easter reckoning. The fruit of all those efforts might be an insight into Viete's clear mathematical thinking. His calendar, however, was never considered.

Controversial Therapies for Developmental Disabilities: Fad, Fashion, and Science in Professional Practice

Back to table of contents Previous article Next article Book ReviewFull AccessControversial Therapies for Developmental Disabilities: Fad, Fashion, and Science in Professional PracticeAudrey R. Newell M.D., M.S.Audrey R. Newell M.D., M.S.Search for more papers by this authorPublished Online:1 Oct 2006https://doi.org/10.1176/ps.2006.57.10.1536aAboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail Scholars know that they must present information in carefully measured, objective, academic prose. But sometimes, an academic has to let loose, chuck all the pretense of objectivity, and tell people what he or she really thinks. The contributors in this volume have done just that.Thirty-two authors from the fields of psychology, law, and education have written 28 chapters on a variety of approaches to the treatment of children and adults with developmental disabilities. They point out logical inconsistencies in the use of mainstreaming as a panacea for all disabilities. Why, for example, would we expect a general education teacher or a second grade classmate to do a better job of teaching reading to a child who is cognitively impaired than a special education teacher who offers "the intensive, focused, relentless instruction that many children with disabilities require if they are able to make reasonable progress?" And how can they do that while still doing justice to the regular education curriculum?Separate articles attack sensory integration therapy, facilitated communication, and the whole-language approach to teaching reading. Authors assert that there is no evidence that these therapies work. A chapter on person-centered planning describes the committee as a "Ouija Board" and the procedure as a mushy way of making both the patient and the planners on the team feel good about the process, despite the lack of measurable goals and evidence-based procedures to reach those goals.One of the most informative chapters was written by an attorney. Parents who want their children to receive the services of a professional skilled in applied behavior analysis can make two arguments in court: failure to use a scientifically proven treatment constitutes negligence, and it is malpractice for an organization to choose ideology over science in order to utilize methods that are still considered experimental without obtaining informed consent and advising parents about proven treatment methods.Another interesting chapter describes the origin and appeal of some of the current fads. "The processes by which behavior analysis works are slow and methodical, difficult and expensive, empirical rather than values based, not at all as dramatic and fun as exotic machines and cheerful dolphins, and rarely result in claims of instant breakthroughs, miracles, or cures."The underlying assumption, repeated endlessly throughout the book, is that the methods of applied behavior analysis and similar carefully structured approaches with well-defined steps and measurable goals are far superior to any other treatment approaches. However, the authors are guilty of the same sins for which they criticize others. They do not provide a description of applied behavior analysis and the evidence for its efficacy, let alone its superiority to other methods. The authors criticize the whole-language approach to teaching beginners to read but do not describe the evidence that phonics-based approaches are superior—even though there is an abundance of such evidence.I enjoyed this book because I share many of the same biases and can imagine how cathartic it was for the authors to ventilate their frustrations. I now have new ways to articulate some of my views the next time I go to an Individual Education Program committee at a school. However, parents and professionals who are seeking to explain and justify the need for their child to receive the services of a skilled behavior analyst; structured, phonics-based reading instruction; or speech therapy with targeted practice of specific words, grammatical forms, and pragmatic rules need to come to the meeting with a detailed and specific description of the services their child needs and solid evidence to support their requests. This book does not give them that.Dr. Newell is affiliated with the Department of Medical Education, Oakwood Hospital, Dearborn, Michigan, and University of Michigan, Ann Arbor. FiguresReferencesCited byDetailsCited ByNone Volume 57Issue 10 October, 2006Pages 1536-1537PSYCHIATRIC SERVICES October 2006 Volume 57 Number 10 Metrics PDF download History Published online 1 October 2006 Published in print 1 October 2006

The Logic of Exception: A structural reading of the foundational texts of psychoanalysis

This paper is premised on Lacan's demonstration that the unconscious is structured like a language. Reading psychoanalytic texts structurally shows that the unconscious and civilisation share the same structure, named “Oedipus complex” by Freud and “law of symbolisation” by Lacan. Freud uncovered this structure when a logical inconsistency in his Oedipal theory–the absence of an external prohibitive instance – led him to hypothesise an anthropological account of the origin of law and so civilisation. If Lacan convincingly subsumes this logical inconsistency under his concept of jouissance, Freud's Oedipal fictions remain useful as they formalise the minimal conditions for modern civilisation: an empty place of power, formal equality before the law and an operational ethical system. These requirements are structural and imply nothing as to the value of a given social organisation.

Exploitation: A Modern Approach

Political economists who have abandoned the Marxian labor theory of value during the past few decades due to logical inconsistencies have failed to replace it with a logically sound theory that explains how and why the employment relationship is almost always exploitative even when labor markets are competitive. This article argues for a sacrifice-based theory of economic justice rather than the contribution-based theory implicit in the Marxian labor theory of value and uses a simple theoretical framework to explain not only why the employment relationship is exploitative but also why credit relations and goods trading can be exploitative as well.

Narrative Indeterminacy and Logical Inconsistency in The Step Not Beyond

Narrative Indeterminacy and Logical Inconsistency in The Step Not Beyond

Relative risk of a shuffled deck: a generalizable logical consistency criterion for sample selection in health state valuation studies

In a health state valuation study, respondents may be asked to rank a deck of cards, with each card representing a particular health state. A logical inconsistency occurs when a more severe health state card is ranked higher than a less severe card. Occasional inconsistencies may be justified by errors in judgment or measurement. However, when respondents return shuffled decks, their responses must be removed from the sample; otherwise, valuation estimates will be biased toward the median. In this paper, we present a logical consistency criterion for sample selection in health state valuation studies. This statistical criterion is based on the relative risk of a shuffled deck and generalizable to all health state classification systems, subsets (or decks) of health states, and valuation techniques. We applied the criterion to secondary data collected from 4048 United States and 3395 United Kingdom respondents. In both studies, respondents evaluated 12-card decks of EQ-5D health states using time trade-off and visual analog scale techniques. Among the UK respondents, a small portion (approximately 5%) did not satisfy the criterion; their exclusion significantly changed the sample characteristics and the mean value estimates of the EQ-5D health states. Similar results were found among the US respondents.

Electoral College Reform is Heating Up, and Posing Some Tough Choices

Electoral College reform is beginning to get some attention, with two different emphases: a move to institute a nationwide popular vote without a constitutional amendment, and a move to forbid faithless electoral votes. There is no logical incompatibility between the two, but in political and public policy terms, there are tensions between them. This paper evaluates the relative merits and importance of the two efforts and explores the tensions in simultaneous pursuit of the two.