We investigate the Tukey order in the class of Fσ ideals of subsets of ω. We show that no nontrivial Fσ ideal is Tukey below a Gδ ideal of compact sets. We introduce the notions of flat ideals and gradually flat ideals. We prove a dichotomy theorem for flat ideals isolating gradual flatness as the side of the dichotomy that is structurally good. We give diverse characterizations of gradual flatness among flat ideals using Tukey reductions and (...) games. For example, we show that gradually flat ideals are precisely those flat ideals that are Tukey below the ideal of density zero sets. (shrink)

We prove that there is a -ideal of compact sets which is strictly above in the Tukey order. Here is the collection of all compact nowhere dense subsets of the Cantor set. This answers a question of Louveau and Veličković asked in [Alain Louveau, Boban Veličković, Analytic ideals and cofinal types, Ann. Pure Appl. Logic 99 171–195].

In this paper, we study some new examples of ideals on $$\omega $$ with maximal Tukey type (that is, maximal among partial orders of size continuum). This discussion segues into an examination of a refinement of the Tukey order—known as the weak Rudin–Keisler order—and its structure when restricted to these ideals of maximal Tukey type. Mirroring a result of Fremlin (Note Mat 11:177–214, 1991) on the Tukey order, we also show that there is (...) an analytic P-ideal above all other analytic P-ideals in the weak Rudin–Keisler order. (shrink)

We formulate a restricted version of the Tukey-Teichmüller Theorem that we denote by (rTT). We then prove that (rTT) and (BPI) are equivalent in ZF and that (rTT) applies rather naturally to several equivalent forms of (BPI): Alexander Subbase Theorem, Stone Representation Theorem, Model Existence and Compactness Theorems for propositional and first-order logic. We also give two variations of (rTT) that we denote by (rTT)+ and (rTT)++; each is equivalent to (rTT) in ZF. The variation (rTT)++ applies rather (...) naturally to various Selection Lemmas due to Cowen, Engeler, and Rado. (shrink)

The generic ultrafilter${\cal G}_2 $forced by${\cal P}\left/\left$was recently proved to be neither maximum nor minimum in the Tukey order of ultrafilters, but it was left open where exactly in the Tukey order it lies. We prove${\cal G}_2 $that is in fact Tukey minimal over its projected Ramsey ultrafilter. Furthermore, we prove that for each${\cal G}_2 $, the collection of all nonprincipal ultrafilters Tukey reducible to the generic ultrafilter${\cal G}_k $forced by${\cal P}\left/{\rm{Fin}}^{ \otimes k} $forms (...) a chain of lengthk. Essential to the proof is the extraction of a dense subsetεkfrom +which we prove to be a topological Ramsey space. The spacesεk,k≥ 2, form a hierarchy of high dimensional Ellentuck spaces. New Ramsey-classification theorems for equivalence relations on fronts on εkare proved, extending the Pudlák–Rödl Theorem for fronts on the Ellentuck space, which are applied to find the Tukey and Rudin–Keisler structures below${\cal G}_k $. (shrink)

A general method for constructing a new class of topological Ramsey spaces is presented. Members of such spaces are infinite sequences of products of Fraïssé classes of finite relational structures satisfying the Ramsey property. The Product Ramsey Theorem of Sokič is extended to equivalence relations for finite products of structures from Fraïssé classes of finite relational structures satisfying the Ramsey property and the Order-Prescribed Free Amalgamation Property. This is essential to proving Ramsey-classification theorems for equivalence relations on fronts, generalizing (...) the Pudlák–Rödl Theorem to this class of topological Ramsey spaces. To each topological Ramsey space in this framework corresponds an associated ultrafilter satisfying some weak partition property. By using the correct Fraïssé classes, we construct topological Ramsey spaces which are dense in the partial orders of Baumgartner and Taylor generating p-points which are k-arrow but not \-arrow, and in a partial order of Blass producing a diamond shape in the Rudin-Keisler structure of p-points. Any space in our framework in which blocks are products of n many structures produces ultrafilters with initial Tukey structure exactly the Boolean algebra \\). If the number of Fraïssé classes on each block grows without bound, then the Tukey types of the p-points below the space’s associated ultrafilter have the structure exactly \. In contrast, the set of isomorphism types of any product of finitely many Fraïssé classes of finite relational structures satisfying the Ramsey property and the OPFAP, partially ordered by embedding, is realized as the initial Rudin-Keisler structure of some p-point generated by a space constructed from our template. (shrink)

We study ultrafilters onω2produced by forcing with the quotient of${\cal P}$(ω2) by the Fubini square of the Fréchet filter onω. We show that such an ultrafilter is a weak P-point but not a P-point and that the only nonprincipal ultrafilters strictly below it in the Rudin–Keisler order are a single isomorphism class of selective ultrafilters. We further show that it enjoys the strongest square-bracket partition relations that are possible for a non-P-point. We show that it is not basically generated (...) but that it shares with basically generated ultrafilters the property of not being at the top of the Tukey ordering. In fact, it is not Tukey-above [ω1]<ω, and it has only continuum many ultrafilters Tukey-below it. A tool in our proofs is the analysis of similar (but not the same) properties for ultrafilters obtained as the sum, over a selective ultrafilter, of nonisomorphic selective ultrafilters. (shrink)

The Ecclesiastical History of Orderic Vitalis has been called `the greatest of all medieval chronicles'. Written in Normandy between 1114 and 1141, it is a detailed history of the Norman people and their conquests, full of vivid, often penetrating portraits of the lives and characters of kings and queens, lords and bishops, simple knights, and humble villagers. The chronicle gives a unique, authentic picture of feudal society during a period of rapid change in church and state which saw the emergence (...) of the Anglo-Norman realm, the spread of new forms of monasticism, and the launching of the Crusades. Published in 1968, volume II of Marjorie Chibnall's six-volume edition of the Ecclesiastical History is now available for the first time in paperback. `a superbly edited Latin text and a unique English translation of the work of a major historian' American Historical Review `Mrs Chibnall is giving us... her edition of a classical medieval text which will itself become a classic of medieval scholarship.' Times Literary Supplement. (shrink)

Betrifft die Handschrift Cod. 555 der Burgerbibliothek Bern.

Edited with a facing-page English translation from the Latin text by: Chibnall, Marjorie.

After the three families divided up the state of Jin and the Tian family took over Qi, the political situation in the fourth century B.C.E. appeared even more chaotic. Wei conquered Chu's Luyang and Qin's Xihe, Qin defeated Wei at Shimen , and again at Shaoliang , and Wei moved its capital to Daliang. During the mid-Warring States period, Qin became dominant in the west, Qi in the east, Chu in the south, and Wei in the center. Rapid changes occurred (...) one after another; trickery and conflict were rampant. However, the shi , the intelligentsia, actually managed to expand their spheres of existence and activity accordingly in this state of tension between countries, states, and men. A few major states assembled quite a number of literati; and those men of the villages, who had in earlier times merely waited passively for opportunities to fall into their laps, crisscrossed the various feudal states; literati who previously had no cause to use military force became, one by one, the honored guests of the feudal lords. With the breakdown of the previously simple and obvious order, the gradually dismantling of the common body of the ancestral clan of the past, and the increasing complexities of social relationships after the dissolution of blood ties, social order became a matter of concern. Or, to reword this most practical issue: How could this universally chaotic society go from disorder to order? (shrink)

It is proved that for every positive integer n, the number of non-Tukey-equivalent directed sets of cardinality $\leq \aleph _n$ is at least $c_{n+2}$, the $(n+2)$ -Catalan number. Moreover, the class $\mathcal D_{\aleph _n}$ of directed sets of cardinality $\leq \aleph _n$ contains an isomorphic copy of the poset of Dyck $(n+2)$ -paths. Furthermore, we give a complete description whether two successive elements in the copy contain another directed set in between or not.

The BRAHMASUTRA of BADARAYANA represents the fundamental text of exegesis of Vedanta. The intent of Badarayana - the sage that for authority and realization of consciousness has been identified with Vyasa, the Rsi who ordered the texts of the Vedas - is that of providing the right perspective in the interpretation of the most profound and meaningful contents of the Upanisads. This had proven necessary in order to rectify some unilateral aspects propounded by several schools of thought, both orthodox (...) and non-orthodox. The Brahmasutra presents, in their simplicity and incisiveness, the assertions of the Sruti and of the Smrti, showing their concordance in the recognition of the Nirguna Brahman as the ultimate Realty. In his notes, RAPHAEL underlines the fact that Badarayana does not oppose the various philosophical schools, but the Rsi allows us to comprehend that their postulates cannot represent the ultimate Truth as expounded in the Vedas and in the Upanisads. Moreover, at times Raphael focuses on certain aspects of the Advaita Doctrine with references to the Western Tradition, and - making the relevant parallels to the philosophy of Parmenides, Plato, Plotinus, and so on - highlights the unity of the sole universal Tradition at the metaphysical level. (shrink)

Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for hyperfinite equivalence relations. In this paper, we introduce a family of properties of countable Borel equivalence relations which correspond to combinatorial cardinal characteristics of the continuum in the same way that Borel boundedness corresponds to the bounding number. We analyze some of the basic behavior of these properties, showing, e.g., that the property corresponding to (...) the splitting number coincides with smoothness. We then settle many of the implication relationships between the properties; these relationships turn out to be closely related to (but not the same as) the Borel Tukey ordering on cardinal characteristics. (shrink)

In this paper we start the analysis of the class, the class of cofinal types of directed sets of cofinality at most ℵ2. We compare elements of using the notion of Tukey reducibility. We isolate some simple cofinal types in, and then proceed to find some of these types which have an immediate successor in the Tukey ordering of.

I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what I will call the Cut-for-Formulas to Cut-for-Sets Theorem: for a set F and a binary relation |- on Power(F), if |- is finitary, monotonic, and satisfies cut for formulas, then it also satisfies cut for sets. I deduce the CF/CS Theorem from the Ultrafilter Theorem twice; each proof uses a different order-theoretic variant of the Tukey- Teichmüller Lemma. I then discuss relationships (...) between various cut-conditions in the absence of finitariness or of monotonicity. (shrink)

We extend the hierarchy of finite-dimensional Ellentuck spaces to infinite dimensions. Using uniform barriers [Formula: see text] on [Formula: see text] as the prototype structures, we construct a class of continuum many topological Ramsey spaces [Formula: see text] which are Ellentuck-like in nature, and form a linearly ordered hierarchy under projections. We prove new Ramsey-classification theorems for equivalence relations on fronts, and hence also on barriers, on the spaces [Formula: see text], extending the Pudlák–Rödl theorem for barriers on the Ellentuck (...) space. The inspiration for these spaces comes from continuing the iterative construction of the forcings [Formula: see text] to the countable transfinite. The [Formula: see text]-closed partial order [Formula: see text] is forcing equivalent to [Formula: see text], which forces a non-p-point ultrafilter [Formula: see text]. This work forms the basis for further work classifying the Rudin–Keisler and Tukey structures for the hierarchy of the generic ultrafilters [Formula: see text]. (shrink)

One of the important areas of study of religious psychology is to examine the reflection of worship in the spiritual life of individuals in the context of worship psychology. In this field survey, the relations between the level of meaning in life and hopelessness of individuals who performed the ʿUmra worship are examined. The study is conducted with 214 Turkish participants who performed ʿumra in Saudi Arabia. The collected data is analyzed by questionnaire technique. "Personal Information Form", " Meaning in (...) Life Questionnaire (MLQ)" and "Beck Hopelessness Scale" are used as data collection tools. The obtained data is analyzed in the SPSS 23.0 statistical program. One Sample t-Test, Pearson Moments Multiplication Correlation Analysis, Independent Sampling t-Test, One Way ANOVA and Tukey HSD tests are used to analyse the data. It is found that the research group's level of meaning in life above average; the level of hopelessness is below average significantly. There is a significant negative correlation between meaning in life and hopelessness, feelings about the future, loss of motivation, expectation about the future. There is a significant positive correlation between searched meaning and hopelessness and loss of motivation.Summary: Many religions have some types of worship involving visiting places considered as sacred and performing some rituals there. In Islam it is called ʿUmra, which is visiting the Kaʿba without being dependent on a certain time frame except for the pilgrimage month. There are certain rites to perform ʿumra, such as entering a state of iḥrām (ritual purity in which certain actions are not permissible), completing circumambulation, and saʿy (striving to do a certain act; walking) between the hills of al-Ṣafā and al-Marwa. ʿUmra worship is a comprehensive and versatile worship, which contains psychological, sociological, physical and financial characteristics.Studying the relationship between religious beliefs and practices, the religious rituals and their psychological effects and functions of ceremonies are the some essential research topics of Psychology of Religion. Existing research in this area usually reveals the existence of a positive relationship between the religious beliefs and practices and between meaning in life and hope. Individuals who believe in a religion can find a meaning and purpose in life through prayer and worship, and at the same time have more positive future expectation to endure the difficulties of life. Meaning and hope are intertwined, which complete each other. Hopelessness is closely related to depression and suicidal desire. There is a need to find meaning and purpose in life in order to hold on to life, and for looking to the future with confidence, and overcoming difficulties.It is known that people tend to be more religious and concentrating worship during periods of loss of meaning for various reasons. ʿUmra, which includes almost all type of worship, is a special worship, which has the potential to contribute to the individual's intense emotional life for gaining new awareness and developing different behaviours to cope with such difficulties. It is because the individual would have many experiences to see the cause of existence, the meaning of his/her life, and his/her future expectation during the ʿumra worship. Thus, he/she can overcome his/her hopelessness and loss of meaning and look to the situation from different perspectives. Therefore, in this study, the following questions are explored: Does ʿumra make a positive contribution to the psychological experience of the individuals, as expected? Does ʿumra has any effect on the level of loss of meaning and hopelessness that accompanies the psychological troubles? How does the demographic variables make difference in the level of meaning in life and hopelessness of individuals who perform ʿumra? In order to find answers to these questions, the relationship between the meaning of life - the hopelessness and the ʿumra was investigated. For this purpose, the meaning and hopelessness levels of the individuals who are performing ʿumra worship were measured by psychometric methods and the relations between them were analyzed. In addition, it has been tested whether there is a difference in the meaning in life and hopelessness according to demographic variables such as gender, marital status and educational status. 214 people aged between 18-82 years participated in the research. The survey data was collected from Turkish participants who perform ʿumra in the cities of Mecca and Medina in Saudi Arabia in May 2015. "Personal Information Form", " Meaning in Life Questionnaire (MLQ)" and "Beck Hopelessness Scale" were used as data collection tools. The obtained data were analyzed in the SPSS 23.0 statistical program. One Sample t-Test, Pearson Moments Multiplication Correlation Analysis, Independent Sampling t-Test, One Way ANOVA and Tukey HSD tests were used for the purpose of analysis of the data.The most important finding of the survey is meaning in life scores of individuals who are performing the ʿumra are above average (t = 20,50; p ˂ 0,01); and scores of hopelessness are below average significantly (t = -29,80; p ˂0,01). There is a significant negative correlation between presence of meaning subscale and hopelessness (r = -,288; p ˂ 0,01); and positive correlation between search for meaning subscale and hopelessness (r =,169; p ˂ 0,05) and loss of motivation (r =,285; p ˂ 0,01). The findings show that ʿumra can affect the meaning in life positively and the hopelessness negatively. There was no significant difference between the meaning in life scores and education level and gender variable (p ˃ 0,05). As the level of education increases, hopelessness scores decrease significantly (F = 2, 627; p ˂ 0,05). Hopelessness scores show a significant difference according to gender (t = -2,708; p ˂ 0,01). Men's hopelessness levels are significantly higher than women’s. Moreover, the meaning in life of married individuals is significantly higher than single individuals (F = 3,859; p ˂ 0,05). As the age and developmental stages progressed, meaning in life (F = 7,274; p ˂ 0,01) and hopelessness scores (F = 8,119; p ˂ 0,01) significantly increased.ʿUmra may have a rapid and intensive effect on the psychology of the individual and his/her sense of world. Relevant studies in the literature also imply such results. Since ʿumra is both a journey and a collective worship, it involves many types of worship, such as praying, reading scripture, repentance and so on. The findings of this study were discussed with reference to the findings about pilgrimage and the findings of study of meaning in life and hopelessness in different samples. On the other hand, the conditions in which the data collected, the study group chosen, the instruments and techniques used for this research constitute the limitations of the present study. However, the time period in which the worship was practiced and reaching the participants in these places of worship, and the measurement of the level meaning in life and hopelessness associated with their worship of ʿumra indicates the importance and originality of this research. The results can be used in other research projects. Studies on the different psychological effects of ʿumra worship can be enriched by longitudinal investigations. (shrink)

The current study aims to examine the hope levels of theology students in the context of their education level. The correlational (relational) screening method was used in this study. The sample of the study consists of a total of 429 students (328 girls, 101 boys) studying at the Faculty of Theology at Erzincan Binali Yildirim University. Hope levels of the students were determined by Karaca-Kandemir Hope Scale developed by Karaca and Kandemir. The scale consists of three sub-dimensions: goal-oriented, hope and (...) significance, and stability. One-way analysis of variance (ANO-VA) was used for data analysis. According to the findings obtained as a result of the analysis, it is seen that the education levels of the Theology Faculty students cause differentiation in terms of goal-oriented and stability which are sub-dimensions of hope; however, it was found that the scale did not cause any difference in terms of hope and meaningfulness subscale and total hope levels. This finding did not corroborate the research hypothesis that the higher the education level of theology faculty students, the higher their hope level. The results, however, give an idea that theology education can have a positive effect on students' hope levels.Summary: Hope, which is a fundamental feature of human existence, has many functions, both individually and socially. Hope, which is one of the main characteristics that distinguish human beings from other beings, is one of the most powerful tools that help create and implement future designs of individuals and societies. It is possible to see this powerful effect of hope in the object of all human works and actions such as art, literature, and architecture. However, despite the expressed impact of hope, religion, which accompanies it in the existential journey of humanity and is one of its most influential sources of motivation, has the potential to produce a highly useful function on hope. Because religion demands the individual to be future-oriented rather than the past. This demand of religion does not mean that the past actions of the individual and society have no importance. While building the future of the individual and society on lessons learned from the past, religion orders that he should not be a prisoner of his past and that he hopes for the energy he has produced by taking shelter in the attributes of Allah, Most Gracious and Merciful. For this reason, the Qur'an equates despair of Allah's mercy with coming out of religion (Yusuf 12 / / 87).Despite the strong relations between religion and hope, empirical studies on the issue are not yet adequate. However, in recent times, especially with the effect of Positive Psychology, it is a fact that empirical studies have been carried out to determine the relationship of these emotions with religiosity about positive emotions such as patience, optimism, empathy, and self-regulation. One of the positive emotions expressed is hope. However, it is seen that some empirical studies have been conducted on the relationship between hope and religiosity. However, apart from these studies, empirical studies on higher education levels are needed in order to reveal the relationship between hope and religiosity in a healthier way. Because of the strong relationship between religion and hope, it is expected that there will be an increase in parallel with the religious education taken in higher education. From this point of view, this study primarily aims to reveal the strong connection between religion and hope. The main problem of this study, which is based on the primary hypothesis that learning religion at a higher education level, will increase the level of hope of students, is the relationship between theology education and hope. In this study, which was conducted to determine the hope levels of the students of the Faculty of Theology, the method of collecting information related to the questionnaire technique used in the screening model was used.The population of the study consists of 744 students enrolled in Erzincan Binali Yıldırım University Theology Faculty in the fall semester of 2018-2019 academic year. The sample group of the research is 429 students in the faculty during the application period. Accordingly, 144 (33.6%) of the total students in the sample group were in the “preparatory class,” 79 (18.4%) were in the “first grade”, and 78 (18.2%) were in the “second grade,” while 60 (14.0%) were in the “third grade,” 68 (15.9%) were in the “fourth grade.”“Personal Data Questionnaire” and “Karaca-Kandemir’s Hope Scale” were used as data collection instruments. In the “Personal Data Questionnaire,” there are questions about the learning levels of the working group.Karaca-Kandemir’s Hope Scale, which is used in the study, is a scale developed by Karaca and Kandemir based on their cultural codes to determine the hope levels of individuals.The scale is a 5-point Likert type and consists of three sub-dimensions: “goal-oriented,” “hope and meaningfulness,” and “stability.” Of the 13 items in the scale, 8 (1, 2, 4, 5, 7, 9, 10 and 12) had a positive sentence structure such as “Dreaming about the future excites me,” 5 of them (3, 6, 8, 11 and 13) it has a negative sentence structure such as “I cannot bring the end of a job easily after starting a job.” In the scoring phase of the hope scale, negative sentences were reversed. While the lowest score that can be obtained from the “goal-oriented” dimension of the scale is 5, the highest score is 25; the lowest score that can be obtained from the dimension of “hope and meaningfulness” is 4, the highest score is 20; the lowest score that can be obtained from the “stability” sub-dimension is 4, while the highest score is 20. As a result, the lowest score that can be obtained from the total of the scale is 13, and the highest score is 65. Low scores from the scale indicate that the individual's level of hope is low, and high scores indicate high levels of hope.In order to determine the differentiation between class levels, Single Factor Analysis of Variance-ANOVA was applied to the data set. As a result of the analysis, multiple comparisons were made between the means with statistically significant differences. For this purpose, Post Hoc LSD and Tukey HSD tests were used to determine the source of the difference. The significance level of “.05 “ was taken as a criterion for all these operations. In the research, it was seen that the education they received from the Faculty of Theology students caused a differentiation in the “goal-oriented and stability” sub-dimension of hope; however, “hope and meaningfulness” subscale and “total hope” did not cause any differentiation. This result did not confirm the research hypothesis that “the level of hope differs according to class (education) level and the level of hope increases as the level of education (education) increases hope. However, in the “goal-oriented” dimension of hope, the second and third-grade students of fourth-grade students; In terms of “stability” dimension, the fact that the first-grade students scored significantly higher than the preparatory class students gives an important idea that the education received in the Faculty of Theology can have an effect on hope. However, it is thought that similar studies that will be conducted with a large sample group and centering on all dimensions and hopes of religiosity will produce remarkable results. (shrink)

We study cardinal invariants of systems of meager hereditary families of subsets of ω connected with the collapse of the continuum by Sacks forcing S and we obtain a cardinal invariant yω such that S collapses the continuum to yω and y ≤ yω ≤ b. Applying the Baumgartner-Dordal theorem on preservation of eventually narrow sequences we obtain the consistency of y = yω < b. We define two relations $\leq _{0}^{\ast}$ and $\leq _{1}^{\ast}$ on the set $(^{\omega}\omega)_{{\rm Fin}}$ of (...) finite-to-one functions which are Tukey equivalent to the eventual dominance relation of functions such that if $\germ{F}\subseteq (^{\omega}\omega)_{Fin}$ is $\leq _{1}^{\ast}$ -unbounded, well-ordered by $\leq _{1}^{\ast}$ , and not $\leq _{0}^{\ast}$ -dominating, then there is a nonmeager p-ideal. The existence of such a system F follows from Martin's axiom. This is an analogue of the results of [3], [9, 10] for increasing functions. (shrink)

We study the following natural strong variant of destroying Borel ideals: $\mathbb {P}$ $+$ -destroys $\mathcal {I}$ if $\mathbb {P}$ adds an $\mathcal {I}$ -positive set which has finite intersection with every $A\in \mathcal {I}\cap V$. Also, we discuss the associated variants $$ \begin{align*} \mathrm{non}^*(\mathcal{I},+)=&\min\big\{|\mathcal{Y}|:\mathcal{Y}\subseteq\mathcal{I}^+,\; \forall\;A\in\mathcal{I}\;\exists\;Y\in\mathcal{Y}\;|A\cap Y| \omega $ ; (4) we characterise when the Laver–Prikry, $\mathbb {L}(\mathcal {I}^*)$ -generic real $+$ -destroys $\mathcal {I}$, and in the case of P-ideals, when exactly $\mathbb {L}(\mathcal {I}^*)$ $+$ -destroys $\mathcal {I}$ ; (...) and (5) we briefly discuss an even stronger form of destroying ideals closely related to the additivity of the null ideal. (shrink)

We prove that consistently the Lebesgue null ideal is not Tukey reducible to the Silver null ideal. This contrasts with the situation for the meager ideal which, by a recent result of the author, Spinas [Silver trees and Cohen reals, Israel J. Math. 211 473–480] is Tukey reducible to the Silver ideal.

A theory of higher-order vagueness for partially-defined, context-sensitive predicates like is blue is offered. According to the theory, the predicate is determinately blue means roughly is an object o such that the claim that o is blue is a necessary consequence of the rules of the language plus the underlying non-linguistic facts in the world. Because the question of which rules count as rules of the language is itself vague, the predicate is determinately blue is both vague and partial (...) in a sense analogous (though not completely identical) to the sense in which is blue is vague and partial. However, higher-order vagueness stops there. Although the anti-extension of is determinately blue differs from that of is blue, further iterations of determinately have no semantic effect. The paper closes with a discussion of the need to posit sharp and precise lines dividing the range of potential application of a vague predicate into semantically distinct categories. It is argued that this is less of a problem for the present theory than for many others, because the categories into which the range is divided by the present theory -- like the category of counting as blue because the rules of the language offer speakers no discretion, as opposed to the category of counting as blue because speakers have invoked an absolute minimum of discretion in adjusting the contextually sensitive boundaries of the predicate -- are not those that the linguistic competence of ordinary speakers equips them to make highly accurate and reliable judgments about. (shrink)

There are inequalities between cardinal characteristics of the continuum that are true in any model of ZFC, but without a Borel morphism proving the inequality. We answer some questions from Blass [1].

You have higher-order uncertainty iff you are uncertain of what opinions you should have. I defend three claims about it. First, the higher-order evidence debate can be helpfully reframed in terms of higher-order uncertainty. The central question becomes how your first- and higher-order opinions should relate—a precise question that can be embedded within a general, tractable framework. Second, this question is nontrivial. Rational higher-order uncertainty is pervasive, and lies at the foundations of the epistemology of (...) disagreement. Third, the answer is not obvious. The Enkratic Intuition---that your first-order opinions must “line up” with your higher-order opinions---is incorrect; epistemic akrasia can be rational. If all this is right, then it leaves us without answers---but with a clear picture of the question, and a fruitful strategy for pursuing it. (shrink)

This work describes the concept of bond order. It shows that covalent bond energy is correlated to bond order. Simple expressions which included bond order are introduced to calculate bond energies of homo-nuclear and hetero-nuclear bonds. Calculated values of bond energies are compared with literature values and show there is very good agreement between and calculated and experimental values in the vast majority of cases. Bond order reveals the strength of a bond and shows the number (...) of bonds in both homo-nuclear and hetero-nuclear covalent bonds. (shrink)

The gap between the limited human sense of how living entities change over time and the ways in which living systems change is one of the most potent uncertainties in ecological knowledge. This gap remains a significant source of problems and errors for those working with the transformations of living systems. This article foregrounds Mary Catherine Bateson’s cybernetic practice of working with narratives in order to cultivate better understanding and responses to change, at the level of both societies and (...) individuals. To do so, I investigate some significant moments, encounters and projects that connect her practice to the ecological ideas of her father, Gregory Bateson and situate their ideas on abduction, metaphor, recursion and narrative within broader discussions of ecological change. The Batesons did not seek a particular attitudinal change towards the transformation of selves, cities and worlds but rather sought to change the very understanding of what an attitude towards change should be, a distinction that is worth pondering given the challenges of attending to change within the present ecological crisis. (shrink)

In this seminal work, acclaimed philosopher Bernhard Waldenfels deals with the problem of the nature of order after the “shattering of the world,” and the loss of the idea of a universal or fundamental order._ _ Order in the Twilight__ unites phenomenological methodology with recent work on the theory of order, normativity, and dialogue, as well as structuralism and Gestalt theory. Philosophically stringent, it expresses a more optimistic attitude than much modern philosophy, especially deconstruction._ Waldenfels passes (...) the question of order through numerous defining aspects, and concludes that there is not one global order, but rather various conflicting domains of order. Whenever the boundary of a vital or experiential domain is crossed, a discourse speaks at the boundary, not about it, and across a threshold without abolishing it. The rest is rationalization, i.e., an attempt to find a place in the respective order for what is to-be-ordered. But why, the author concludes, should a theory be more unambiguous than reality? _ Order in the Twilight__ is an important book at this time, because it may help lift the humanities out of the skeptical, relativistic disarray in which they have been embroiled in recent decades. Waldenfels does not attempt to dictate what reality should be; rather, he is open to any valid evidences. His book offers a solid footing to the human and social sciences as they seek to escape from deconstructive irrationalism. (shrink)

On at least one of its uses, ‘higher-order evidence’ refers to evidence about what opinions are rationalized by your evidence. This chapter surveys the foundational epistemological questions raised by such evidence, the methods that have proven useful for answering them, and the potential consequences and applications of such answers.

This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics used in metaphysics, (...) and indicate a number of questions which can be raised in such systems using logical vocabulary alone. Using a further example, we return to applications of higher-order logics in metaphysics. We also mention key developments in the history of higher-order logic as it pertains to metaphysics. Finally, we mention certain arguments which have been raised against the use of higher-order logic, and some ways of responding to them. (shrink)

Due to their reliance on constitutive higher-order representing to generate the qualities of which the subject is consciously aware, I argue that the major existing higher-order representational theories of consciousness insulate us from our first-order sensory states. In fact on these views we are never properly conscious of our sensory states at all. In their place I offer a new higher-order theory of consciousness, with a view to making us suitably intimate with our sensory states in (...) experience. This theory relies on the idea of ‘quoting’ sensory qualities, so is dubbed the ‘quotational higher-order thought theory’. I argue that it can capture something of the idea that we are ‘acquainted’ with our conscious states without slipping beyond the pale for naturalists, whilst also providing satisfying treatments of traditional problems for higher-order theories concerning representational mismatch. The theory achieves this by abandoning a representational mechanism for mental intentionality, in favour of one based on ‘embedding’. (shrink)

An overview of higher-order representational theories of consciousness. Representational theories of consciousness attempt to reduce consciousness to “mental representations” rather than directly to neural or other physical states. This approach has been fairly popular over the past few decades. Examples include first-order representationalism (FOR) which attempts to explain conscious experience primarily in terms of world-directed (or first-order) intentional states (Tye 2005) as well as several versions of higher-order representationalism (HOR) which holds that what makes a mental (...) state M conscious is that it is the object of some kind of higher-order mental state directed at M. The primary focus of this entry is on HOR and especially higher-order thought (HOT) theory. The key question that should be answered by any theory of consciousness is: What makes a mental state a conscious mental state? Section 1 introduces the overall representationalist approach to consciousness and briefly discuss Tye’s FOR. Section 2 presents three major versions of HOR: higher-order thought theory, dispositional higher-order thought theory, and higher-order perception theory. In section 3, a number of common and important objections and replies are presented. Section 4 briefly outlines a close connection between HOT theory and conceptualism, that is, the claim that the representational content of a perceptual experience is entirely determined by the conceptual capacities the perceiver brings to bear in her experience. Section 5 examines several hybrid higher-order and “self-representational” theories of consciousness which all hold that conscious states are self-directed in some way. Section 6 addresses the potentially damaging claim that HOT theory requires neural activity in the prefrontal cortex (PFC) in order for one to have conscious states. (shrink)