General Theory Research Articles

Exciton interacting with a moiré lattice: Polarons, strings, and optical probing of spin correlations

The ability to create and stack different atomically thin transition metal dichacogenide (TMD) layers on top of each other has opened up a rich playground for exploring new and interesting two-dimensional (2D) quantum phases. As a consequence of this remarkable development, there is presently a need for new sensors to probe these 2D layers, since conventional techniques for bulk materials such as x-ray and neutron scattering are inefficient. Here, we develop a general theory for how an exciton in a TMD monolayer couples to spin and charge correlations in an adjacent moiré lattice created by a TMD bilayer. Virtual tunneling of charge carriers, assumed for concreteness to be holes, between the moiré lattice and the monolayer combined with the presence of bound hole-exciton states, i.e., trions, give rise to an effective interaction between the moiré holes and the exciton. In addition to the Umklapp scattering, we show that this interaction is spin-dependent and therefore couples the exciton to the spin correlations of the moiré holes, which may be in- as well as out-of-plane. We then use our theory to examine two specific examples where the moiré holes form in-plane ferromagnetic or antiferromagnetic order. In both cases, the exciton creates spin waves in the moiré lattice, which we analyze by using a self-consistent Born approximation that includes such processes to infinite order. We show that the competition between magnetic order and exciton motion leads to the formation of a well-defined quasiparticle consisting of the exciton surrounded by a cloud of magnetic frustration in the moiré lattice sites below. For the antiferromagnet, we furthermore demonstrate the presence of the elusive geometric string excitations and discuss how they can be observed via their smoking gun energy dependence on the spin-spin coupling, which can be tuned by varying the twist angle of the moiré bilayer. All these phenomena have clear signatures in the exciton spectrum, and as such our results illustrate that excitons are promising quantum probes providing optical access to the spin correlations of new phases predicted to exist in TMD materials. Published by the American Physical Society 2024

Dynamical stability and phase space analysis of an emergent Universe with non-interacting and interacting fluids

Abstract We investigate the evolution of a flat Emergent Universe obtained with a non-linear equation of state (nEoS) in Einstein’s general theory of Relativity. The nEoS is equivalent to three different types of barotropic cosmic fluids, which are found from the nEoS parameter. The EU began expanding initially with no interactions among the cosmic fluids. However, one can assume an interaction that sets in at a time t ⩾ t i in the cosmic fluids, we study the evolution of the EU that accommodates the present observed Universe. We adopt dynamical system analysis to study the critical points of the autonomous system and the evolutionary behavior of an EU with or without interaction among the cosmic fluid components. We also study the stability of critical points and plot the phase portraits. The density parameters and the corresponding cosmological parameters are determined for both the non-interacting and interacting phases of the evolutionary dynamics of the Universe.

Strains and Maladaptive Behaviors among High School Students in Qatar: An Empirical Test of the General Strain Theory

Objectives: This study aims to test the core assumption of Agnew’s general strain theory(GST) in maladaptive behavior (substance use, suicidality, and school truancy). Testing the effects of strain variables (negative life events) on negative emotions that lead to maladaptive behaviors or criminal coping. The present study tests the validity and applicability of a widely known criminological (GST) theory in a non-Western culture. Moreover, one significant contribution of this study is its applicability and generalizability in an Arabian heterogeneous society and culture. Methods: A survey was used, and a questionnaire was developed to measure the GST major assumptions and maladaptive behavior (substance use, suicidality, and school truancy). The survey was distributed among students by trained teams in public schools. A sample of 4096 high school students was randomly selected from seven public schools in Qatar. Results:. Findings showed that some negative life events variables had the highest significant unique contribution (when holding other variables constant) on the maladaptive behaviors more than other variables. These variables are: Depression had the highest significant unique contribution to suicidality, followed by violent victimization and negative feelings. Assaults had the highest significant unique contribution to substance use, followed by delinquency and sexual harassment. Assaults had the most significant unique contribution to school truancy, followed by delinquency. Conclusions: Findings suggest limiting maladaptive behaviors and crimes by equipping students with crime-preventive traits, increasing social support, enhancing social control, and reducing exposure to crime-prone situations. Schools should educate students on managing negative emotions and stress, implement low-abiding coping methods, and conduct awareness campaigns on illegal coping methods to prevent criminal behavior.

Single-shot Quantum Signal Processing Interferometry

Quantum systems of infinite dimension, such as bosonic oscillators, provide vast resources for quantum sensing. Yet, a general theory on how to manipulate such bosonic modes for sensing beyond parameter estimation is unknown. We present a general algorithmic framework, quantum signal processing interferometry (QSPI), for quantum sensing at the fundamental limits of quantum mechanics by generalizing Ramsey-type interferometry. Our QSPI sensing protocol relies on performing nonlinear polynomial transformations on the oscillator's quadrature operators by generalizing quantum signal processing (QSP) from qubits to hybrid qubit-oscillator systems. We use our QSPI sensing framework to make efficient binary decisions on a displacement channel in the single-shot limit. Theoretical analysis suggests the sensing accuracy, given a single-shot qubit measurement, scales inversely with the sensing time or circuit depth of the algorithm. We further concatenate a series of such binary decisions to perform parameter estimation in a bit-by-bit fashion. Numerical simulations are performed to support these statements. Our QSPI protocol offers a unified framework for quantum sensing using continuous-variable bosonic systems beyond parameter estimation and establishes a promising avenue toward efficient and scalable quantum control and quantum sensing schemes beyond the NISQ era.

Leader safety storytelling: A qualitative analysis of the attributes of effective safety storytelling and its outcomes

Leadership, particularly leaders’ communication with workers, plays an important role in enhancing workplace safety. Yet despite this important role, the specific communication actions that a leader can utilise to communicate effectively remain unknown. Rooted in narrative persuasion and general leadership theory, the current study examines leaders’ safety storytelling as a specific leader communication action that can positively contribute to workplace safety. Based on a deductive qualitative content analysis of 41 interviews with leaders and subordinates, we examine the attributes of leader safety storytelling relevant to its effectiveness, as well as the outcomes perceived to be linked to effective leader safety storytelling. Findings show that nine storytelling attributes appear relevant to leader safety storytelling. Of these nine, six (i.e., relatability, realism, risk level, structure, descriptiveness and explicit appeals) were related to the story itself and three (i.e., delivery style, questions and visual aids) were related to the leader’s presentation of the story. Additionally, findings indicate that effective leader safety storytelling is perceived to be associated with eight outcomes: four represented perceived leader-related outcomes (i.e., workers’ perceptions of their leader’s approachability, trustworthiness, transformational leadership style, and safety commitment), and four represented perceived safety-related outcomes (i.e., workers’ safety behaviours, safety knowledge, safety motivation, and safety attitudes). We conclude by providing a conceptual framework for effective leader safety storytelling that can guide future research. Findings can also inform leader safety storytelling in practice by facilitating targeted guidance and interventions.

From individual to household decision‐making: A practical perspective on the base of the pyramid consumer

AbstractThis paper proposes a new household decision‐making model for base of pyramid (BoP) consumers. Many decision‐making models focus on general consumer behaviour theory, with few focusing on the resource constraints experienced at the BoP. By focusing on the dynamics of household decisions, the data collected bring a unique perspective to BoP consumer behaviour and extend recent work in the BoP domain. The study comprised qualitative interviews with 61 household representatives (representing 233 household members) to explore decision‐making, loyalty, budgeting, shopping and category trade‐offs. The study proposes a household‐focused decision‐making framework, which is far more characteristic of BoP consumer behaviour (as opposed to isolated individual decisions). The proposed framework reveals the impact of situations and financial constraints on BoP household decision‐making and how most households operate in both the formal and informal economy. Family obligation was observed to be a key factor, as well as how functional illiteracy drives brand loyalty but also creates embarrassment. Word of mouth trumps all other sources of information and, due to household complexities, there is significant decision‐maker ambiguity, making it hard to define a target audience with a communication strategy. Brands are important, but fundamental value is still key and there is inexorable monthly variation in finances, making category trade‐offs commonplace.

ЭКИНЧИ ТАРТИПТЕГИ ТУУНДУСУНА КАРАТА ЧЕЧИЛБЕГЕН ДИФФЕРЕНЦИАЛДЫК ТЕҢДЕМЕ ҮЧҮН ЧЕКТИК МАСЕЛЕНИН ЧЫГАРЫЛЫШЫН КОЛЛОКАЦИЯ-АСИМПТОТИКАЛЫК МЕТОД МЕНЕН ТАБУУ

Boundary value problems for ordinary differential equations is one of the sections of the general theory of differential equations. The difference between the boundary value problem and the Cauchy problem is that the solution of the differential equation must satisfy boundary conditions connecting the values of the desired function at more than one point. The most common boundary value problem refers to two-point boundary value problems for which boundary conditions are set at two points at the ends of the interval on which solutions are being sought. In addition, the special case of two-point boundary value problems also covers such an important section of the theory of differential equations as the theory of oscillations. In this article, the problem of constructing an asymptotic expansion in a small parameter for solving a boundary value problem for a second-order differential equation of an unresolved relative to the highest derivative of the desired solution is considered. The solution of the boundary value problem is found according to the algorithm of the collocation-asymptotic method. A numerical example of a boundary value problem is considered and an asymptotic decomposition is constructed for solving problems with a relatively small parameter, including the first two terms of the expansions.

Recall tempo of Hebbian sequences depends on the interplay of Hebbian kernel with tutor signal timing

Understanding how neural circuits generate sequential activity is a longstanding challenge. While foundational theoretical models have shown how sequences can be stored as memories in neural networks with Hebbian plasticity rules, these models considered only a narrow range of Hebbian rules. Here, we introduce a model for arbitrary Hebbian plasticity rules, capturing the diversity of spike-timing-dependent synaptic plasticity seen in experiments, and show how the choice of these rules and of neural activity patterns influences sequence memory formation and retrieval. In particular, we derive a general theory that predicts the tempo of sequence replay. This theory lays a foundation for explaining how cortical tutor signals might give rise to motor actions that eventually become "automatic." Our theory also captures the impact of changing the tempo of the tutor signal. Beyond shedding light on biological circuits, this theory has relevance in artificial intelligence by laying a foundation for frameworks whereby slow and computationally expensive deliberation can be stored as memories and eventually replaced by inexpensive recall.

Arctic curves of the T-system with slanted initial data

We study the T-system of type A∞ , also known as the octahedron recurrence/equation, viewed as a 2+1 -dimensional discrete evolution equation. Generalizing earlier work on arctic curves for the Aztec Diamond obtained from solutions of the octahedron recurrence with ‘flat’ initial data, we consider initial data along parallel ‘slanted’ planes perpendicular to an arbitrary admissible direction (r,s,t)∈Z+3 . The corresponding solutions of the T-system are interpreted as partition functions of dimer models on some suitable ‘pinecone’ graphs introduced by Bousquet–Mélou, Propp, and West in 2009. The T-system formulation and some exact solutions in uniform or periodic cases allow us to explore the thermodynamic limit of the corresponding dimer models and to derive exact arctic curves separating the various phases of the system. This direct approach bypasses the standard general theory of dimers using the Kasteleyn matrix approach and uses instead the theory of Analytic Combinatorics in Several Variables, by focusing on a linear system obeyed by the dimer density generating function.

College Students are Helping Each Other Cheat in the Group Chat and Here’s Why

ABSTRACT When students have a space of their own, unobserved by professors and administrators, where they can freely talk about their classes and share their coursework, many engage in academic dishonesty. But, as observed in the present study, cheating is not a foregone conclusion for students who decide to join an online group chat. The present study examined N = 30 GroupMe chatrooms associated with undergraduate classes at a mid-sized “Southern State University” – observing academic dishonesty how it happens, when it happens. Significant associations rooted in techniques of neutralization and general strain theory were observed for both the solicitation of academic dishonesty and responses to those solicitations. As hypothesized, greater academic dishonesty was observed for appeals to higher loyalties and denial of responsibility. While the denial of injury and condemnation of the condemners each corresponded with greater solicitation of academic dishonesty, no effects were observed for responses to solicitation. The removal of positively valued stimuli also corresponded with more academic dishonesty. However, the presentation of negatively valued stimuli and failure to achieve positively valued goals were, unexpectedly, associated with less of this kind of behavior. Implications for designing out academic dishonesty are proposed within the context of these findings.

Philosophy without natural kinds: a reply to Reydon & Ereshefsky

The tradition of natural kinds has shaped philosophical debates about scientific classification but has come under growing criticism. Responding to this criticism, Reydon and Ereshefsky present their grounded functionality account as a strategy for updating and defending the tradition of natural kinds. This article argues that grounded functionality does indeed provide a fruitful philosophical approach to scientific classification but does not convince as a general theory of natural kinds. Instead, the strengths and limitations of Reydon and Ereshefsky’s account illustrate why it is time to move beyond general definitions of “natural kind” and experiment with new philosophical frameworks.

On Verbal Humour Translation from English to Chinese in Subtitles of Stand-up Comedies under the General Theory of Verbal Humour

Apart from the increase in local TV or network programs of stand-up comedies, many Chinese translators have translated English stand-up comedies online. In the light of Attardo’s General Theory of Verbal Humour, this research aims to discuss the translation effect of verbal humour in accordance with the six Knowledge Resources from the GTVH. After a qualitative analysis of research data, this research demonstrates the translatability of verbal humour in stand-up comedies.

Developing an MLA-test for young learners – insights from measurement theory and language testing

This article presents the process of constructing and validating a test of metalinguistic awareness (MLA) for young school children (age 8–10). The test was developed between 2021 and 2023 as part of the MetaLearn research project, financed by The Research Council of Norway. The research team defines MLA as using metalinguistic knowledge at a point in real time. To develop the test, the research team relied heavily on general measurement theory (psychometrics) and insights from the field of language testing and assessment. This aids in the process of developing a practical and user-friendly MLA-test which yields valid scores and reliably measures the state and the development of MLA. This innovative approach to MLA testing offers explicitness about the theoretical construct of the test and at the same time contributes to controlling the difficulty and discriminatory power of each test item. We argue that the test development process presented here is useful when developing tests of MLA and similar concepts, as it facilitates comparison of results as well as replicability. This development process and its detailed description also make it possible to adapt the MetaLearn MLA-test to other contexts.

Semiotics After Geontopower Some Preliminary Thoughts

This essay is part of a book project, tentatively titled, Do We Need a Semiotics After Geontopower? The essay begins with an overview of the atmospheric conditions of an old debate about how to liberate theories of mind, communication and language from their humanist enclosure. It does so by highlighting a few scientific and public debates about what constitutes evidence of prehuman, and nonhuman animal and plant forms of mind and communication. The purpose of this brief foray into complicated debates is to conjure the sense-intuitions circulating around these arguments about the political and ethical stakes of describing a kind of existence as having this or that quality of language and mind. The essay then puts pressure on how these sense-intuitions about communication and mind are scaled—how a sense of the stakes of mind to the treatment of existence becomes a quest to model a general theory of a post-humanist mind. This takes me to the commonalities between a certain way of producing a posthumanist mind and the strategies of environmental protect within the movement for the rights of nature. Why do these approaches feel to some like they are the best way of verifying that prehuman, nonhuman animal and plant forms, and nonlife have semiotic capacities as one supports First Nation and Indigenous earthkin?The essay ends by summarizing the broader content and stakes of Do We Need a Semiotics After Geontopower?

A theory of phonon-induced friction on molecular adsorbates

In this manuscript, we provide a general theory for how surface phonons couple to molecular adsorbates. Our theory maps the extended dynamics of a surface's atomic vibrational motions to a generalized Langevin equation, and by doing so captures these dynamics in a single quantity: the non-Markovian friction. The different frequency components of this friction are the phonon modes of the surface slab weighted by their coupling to the adsorbate degrees of freedom. Using this formalism, we demonstrate that physisorbed species couple primarily to acoustic phonons while chemisorbed species couple to dispersionless local vibrations. We subsequently derive equations for phonon-adjusted reaction rates using transition state theory and demonstrate that these corrections improve agreement with experimental results for CO desorption rates from Pt(111).

Crustal stress buildup/relaxation and pore pressure in preparation and sequential brittle-shear fault rupture — Implications for a general theory of earthquake nucleation

Compelling geoscience evidence has heightened the appreciation of abnormal (suprahydrostatic, sub/quasi/supralithostatic) pore pressure and multimode (brittle-shear) fault rupture leading to seismicity. However, preparation and rupture nucleation are yet to be adequately constrained and quantitatively modeled. This challenges crucial schemes, notably physics-based earthquake forecasting/prediction. In this multidisciplinary study, the transitions and associated critical points linking the preexisting fluid overpressure in the fault patches, temporal crustal stress, and sequential brittle-shear fault failure were considered. In preparation, tectonic loading was accompanied by processes such as off-fault yielding, permeability enhancement, and foreshocks that facilitate local/regional stress relaxation. Subsequent equalization of stress and the preexisting local overpressure triggers hydraulic fracturing that destabilizes major asperities. Almost instant shear failure follows with the spatially varying rupture velocity/intensity of the frictional slip because of localized asperity stress and syn-slip fluid-/melt-driven fracturing/dilation and lubrication. Based on the aforementioned critical points, quantitative modeling associated stress drop with the evolution of the stress and pore pressure. Equations for the time to onset of stress relaxation and time to rupture were derived using fluid flow and viscoelastic models. The seismic moment was estimated with classical seismological relations after modifications accounting for the smaller surface area during frictional slip. For retrospective testing, two cases of induced seismicity (2016 Fairview, Oklahoma, USA, and 2017 Pohang, South Korea) and multiple cases of natural seismicity (including the 2024 Noto Peninsula earthquake, Japan) were considered. The replication of triggering mechanisms, source properties, and time to rupture suggested that stress temporal relaxation and triggered anomalies (STRATA) encompass fundamental hydromechanical processes in seismogenesis. The setting and scale invariance of STRATA suggest it might be a general theory of earthquake nucleation. Based on the identified preparatory processes/retrospective validations, a physics-based earthquake forecasting/prediction scheme was developed. The nurseries/hypocenters of impending earthquakes are identified through the simultaneous consideration of locally preexisting fluid overpressure and spatiotemporal analysis of stress relaxation. Event size and rupture timing are estimated with the derived relations herein.

Entropy of dynamical black holes

We propose a new formula for the entropy of a dynamical black hole—valid to leading order for perturbations off of a stationary black hole background—in an arbitrary classical diffeomorphism covariant Lagrangian theory of gravity in n dimensions. In stationary eras, this formula agrees with the usual Noether charge formula, but in nonstationary eras, we obtain a nontrivial correction term. In particular, in general relativity, our formula for the entropy of a dynamical black hole differs from the standard Bekenstein-Hawking formula A/4 by a term involving the integral of the expansion of the null generators of the horizon. We show that, to leading perturbative order, our dynamical entropy in general relativity is equal to 1/4 of the area of the apparent horizon. Our formula for entropy in a general theory of gravity is obtained from the requirement that a “local physical process version” of the first law of black hole thermodynamics hold for perturbations of a stationary black hole. It follows immediately that for first order perturbations sourced by external matter that satisfies the null energy condition, our entropy obeys the second law of black hole thermodynamics. For vacuum perturbations, the leading-order change in entropy occurs at second order in perturbation theory, and the second law is obeyed at leading order if and only if the modified canonical energy flux is positive (as is the case in general relativity but presumably would not hold in more general theories of gravity). Our formula for the entropy of a dynamical black hole differs from a formula proposed independently by Dong and by Wall. We obtain the general relationship between their formula and ours. We then consider the generalized second law in semiclassical gravity for first order perturbations of a stationary black hole. We show that the validity of the quantum null energy condition (QNEC) on a Killing horizon is equivalent to the generalized second law using our notion of black hole entropy but using a modified notion of von Neumann entropy for matter. On the other hand, the generalized second law for the Dong-Wall entropy is equivalent to an integrated version of QNEC, using the unmodified von Neumann entropy for the entropy of matter. Published by the American Physical Society 2024

A method for characterizing disease emergence curves from paired pathogen detection and serology data

Abstract Wildlife disease surveillance programs and research studies track infection and identify risk factors for wild populations, humans and agriculture. Often, several types of samples are collected from individuals to provide more complete information about an animal's infection history. Methods that jointly analyse multiple data streams to study disease emergence and drivers of infection via epidemiological process models remain underdeveloped. Joint‐analysis methods can more thoroughly analyse all available data, more precisely quantifying epidemic processes, outbreak status, and risks. We contribute a paired data modelling approach that analyses multiple samples from individuals. We use ‘characterization maps’ to link paired data to epidemiological processes through a hierarchical statistical observation model. Our approach can provide both Bayesian and frequentist estimates of epidemiological parameters and state. Our approach can also incorporate test sensitivity and specificity, and we propose model fit diagnostics. We motivate our approach through the need to use paired pathogen and antibody detection tests to estimate parameters and infection trajectories for the widely applicable susceptible, infectious, recovered (SIR) model. We contribute general formulas to link characterization maps to arbitrary process models and datasets and an extended SIR model that better accommodates paired data. We find via simulation that paired data can more efficiently estimate SIR parameters than unpaired data, requiring samples from 5 to 10 times fewer individuals. We use our method to study SARS‐CoV‐2 in wild white‐tailed deer (Odocoileus virginianus) from three counties in the United States. Estimates for average infectious times corroborate captive animal studies. The estimated average cumulative proportion of infected deer across the three counties is 73%, and the basic reproductive number (R0) is 1.88. Wildlife disease surveillance programs and research studies can use our methods to jointly analyse paired data to estimate epidemiological process parameters and track outbreaks. Paired data analyses can improve precision and accuracy when sampling is limited. Our methods use general statistical theory to let applications extend beyond the SIR model we consider and to more complicated examples of paired data. The methods can also be embedded in larger hierarchical models to provide landscape‐scale risk assessment and identify drivers of infection.

Estudio del formante <i>-ina </i>y<i> -oide</i> como sufijo de creación léxica con efectos cómicos en la red social <i>Twitter</i>

This research aims to examine humor as a pragmatic-social phenomenon applied to the use of two Greco-Latin formants with comic intention. This objective seeks to demonstrate the use of two elements with Greco-Latin roots in the formation of a humorous pattern that manifests itself in the virtual environment. To achieve this, both suffixes have been applied to lexical bases that are in principle unrelated to these elements. This research will provide a brief explanation of the suffixes -ina and -oide, commonly used in the scientific-technical field, but in this case they are adopted by speakers as a strategy to generate comedy in the virtual environment of the social network Twitter. Finally, the General Theory of Verbal Humor will be applied to the 756 tweets that make up the compiled corpus. A pragmatic analysis of the most representative texts in which both suffixes published on said platform are used will be presented and will serve as an example of such uses.

On Ramsey’s Rejection of Keynes’s Mathematical Lattice Structure and Interval Valued Probabilities in the A Treatise on Probability

Henry E. Kyburg was able to demonstrate that Keynes had a qualitative, graphical understanding of interval probability based on his careful analysis of Keynes’s diagram on page 39 of the A Treatise on Probability. Kyburg showed in four different papers, published in 1995,1999,2003 and 2010, that Keynes’s diagram on page 39 is a mathematical lattice structure encompassing interval valued probability. However, Kyburg rejected any conclusion that Keynes had provided a mathematical, quantitative theory of interval valued probability. Kyburg did recognize that Keynes had an intuitive understanding about the nature of interval valued probability, but that the best that Keynes had been able to accomplish in this regard in his A Treatise on Probability was to offer some hints, ideas, or suggestions. This is the same conclusion put forth by all members of ISIPTA since 1999. Of course, Keynes had provided a complete mathematical, quantitative theory, in Parts II and III of the A Treatise on Probability, of interval valued probability in chapters XV, XVI, XVII, XX, and XXII. Keynes’s interval valued theory was based on Boole’s original theory of interval valued probability that Kyburg and all members of ISIPTA have overlooked. Kyburg makes a very interesting point about the deficiencies of Ramsey, as regards Keynes’s graphical presentation (see Keynes, 1921, p.161, ft.2) that were based on Boole’s approach. Boole’s mathematical, lattice structure of upper and lower probabilities, that Boole demonstrated had least and greatest limits, narrowest limit, maximum limit, highest, inferior numerical limit, highest minor limit, greatest minor numerical limit, etc. (Boole,1854,pp.288,293,305- 313,317-324)all involve a mathematical lattice structure .All of these terms mean that Boole is solving for a greatest lower bound and/or a least upper bound with his solutions methods, which involved using second order, quadratic equations and third order ,cubic equations. Such greatest lower bounds and least upper bounds automatically specify a mathematical lattice structure to Boole’s partial orderings of probabilities: “What is curious is that the mathematician -philosopher, Frank Ramsey, paid no attention to this structure in his review of the Treatise (Ramsey, 1922) …” (Kyburg,2010, p.26). Actually, Kyburg must have known that Ramsey had never made any comment on Keynes’s graphical demonstration on page 39 of Keynes’s A Treatise on Probability in any publication in his life. The reason is very simple. Ramsey knew that the mathematical lattice demonstration on p.39 showed that his theory of exact and precise, additive probability, illustrated by Keynes with the linear line OAI, is a very, very special case of Keynes’s general theory. Therefore, Ramsey had to reject the foundation for the construction of any type of mathematical lattice structure, which was Keynes’s Boolean relational, propositional logic. Kyburg recognized that Ramsey’s criticism was directed at this foundation: “That there is an out-and-out conflict between Keynes and Ramsey ….becomes clear in the fourth part of Ramsey’s essay…Now it is all very well for Ramsey modestly to admit that he sees no logical relation of probability such as the one that Keynes seeks to draw our attention to[author’s note-Kyburg has completely overlooked that such an objective , logical probability relation was first specified by Boole, not Keynes],but wants to go further than that. It is clear that Ramsey wants to claim that there is no such relation.” (Kyburg, 2010, p.29; italics is Kyburg’s). Ramsey, in fact, did claim this. I have noted many, many times in the papers that I have written on this topic over the last 15 years that are available at SSRN, Researchgate and Academia, that Keynes, if he had actually ever thought himself threatened by Ramsey’s claims, could have, either with or without Bertrand Russell’s assistance ,completely and totally crushed Ramsey intellectually by simply making the following hypothetical one sentence statement at any Apostles meeting from 1922 to 1929: “My objective, logical probability relations are identical to Boole’s logical, probability relations as discussed in chapter I and XVI of his The Laws of Thought (1854).” That, of course, would have been the beginning of the end of Ramsey’s academic career