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In recent years, archaeological research has relied on large datasets, both temporally and geographically, with some archaeologists discussing that there should be a shift towards a more scientific form of conducting archaeological research called “macroarchaeology.” Ironically, and contradictorily, this shift towards large-scale research has involved the use of inductive approaches, which means that archaeological material needs to be converted into universal quantitative values. The inductive approaches used by archaeologists today, as argued by Karl Popper, and other authors in recent years, cannot be considered scientific in the strict sense of the word, since there is always a degree of uncertainty in inductive reasoning. This study suggests that archaeological data can be considered as traces of the past, clues that allow us to reconstruct past phenomena. As Carlo Ginzburg’s evidential paradigm demonstrates, thinking of the past in terms of traces and clues is much more scientific than appears at first. In addition to traces and clues, a second interpretative procedure can be conducted on data. Based on Ginzburg’s conjectural paradigm and discussion on fiction, we can recognize the past as real, while at the same time, conjecture the several ways past agents could have acted otherwise.

For a graph G = (V , E) , the exponential second Zagreb index is defined as e M 2 (G) = ∑ u v ∈ E e d (u) d (v) , where d (v) is the degree of vertex v ∈ V. Recently, Eliasi (2022) posed a conjecture about (n , m) -graphs with maximum e M 2 when n ≤ m ≤ 2 n − 3. In this paper, we show that this conjecture is true. Furthermore, we determine the graphs with maximum e M 2 among all (n , m) -graphs when 2 n − 3 < m. [ABSTRACT FROM AUTHOR]

• We investigated experimentally the discovery of feedback-learning procedures. • In a dynamic business simulation, participants were incentivized to maximize profits. • Webackward-engineered procedures from recorded actions and information requests. • Anumber of participants discovered an effective heuristic learning procedure. • Implementation errors prevented many participants from realizing its full potential. Domain-general learning rules often enable decision makers to learn from outcome feedback which actions tend to achieve a desired goal. However, in novel and complex environments decision makers must explore how to learn, i.e., acquire procedural knowledge of how to elicit and evaluate outcome feedback that will enable them to navigate toward a desired goal despite the vastness of the set of possible policies. Using a dynamic business simulation, this study investigated: (1) whether and how frequently participants discovered an effective procedure to learn from outcome feedback that allowed them to navigate toward a policy that maximizes long-term business profit (and hence their monetary payoff from the experiment), and (2) whether high monetary incentives affected learning procedures and performance. We found that a number of participants discovered an effective learning procedure and succeeded in approximating the optimal policy. In line with the heuristic method, this learning procedure involved a simplification of the search space and the application of domain-general learning rules to this simplified space. Although the decision histories of about half of the participants feature the key aspect of the effective learning procedure—search among the different steady states of the dynamical system—implementation errors prevented many of the participants from realizing the full potential of the learning procedure. We found no evidence to suggest that high monetary incentives affect the effectiveness of learning. Overall, the study illustrates that a "prepared mind" can discover new, effective learning procedures, although their initial implementation may require substantial refinement. [ABSTRACT FROM AUTHOR]

We prove a conjecture of Udo Riese about the minimal ring of definition for principal series Weil characters of SL 2 (F p) , for p an odd prime. More precisely, we show that the (p + 1) / 2 -dimensional Weil characters can be realized over the ring of integers of Q (ε p) , where ε = (− 1) (p − 1) / 2 , and we provide explicit integral models over these quadratic rings. We do so by studying the Galois action on the integral models of Weil characters recently discovered by Yilong Wang. [ABSTRACT FROM AUTHOR]

The teaching-learning process is analyzed in a course for a group of professors who were taught subjects on Calculus, to study the episodes of problem-solving in them, focused on the identification of patterns and argumentation using counterexamples. The explanation and the argument in the classroom can be used together so that the argument (issued as a counterexample) supports the explanation (conjecture). Developing the mathematics class so that the above occurs is a form of interaction and how to encourage students to move from explanation to argumentation (placing a hybrid system). Furthermore, both forms of reasoning can influence dialogue protocols and strategies. In this work, the dialogue model is described as a tool to address the problem that arises when working with students.

Largely disparaged by readers since the eighteenth century but revered before then as a guide to living and dying well, the Tusculan Disputations has throughout its long reception been acknowledged as the most rhetorical of Cicero's dialogues. This essay takes as its point of departure not only this acknowledgment but the principal interlocutor's key comparison between finding the appropriate status or "issue" in a legal case and selecting a circumstantially sensitive strategy when offering consolation for the loss of a loved one. It argues, with the help of Cicero's rhetorical works, that he deploys rhetorical status , with its three questions (conjectural, definitive, and qualitative), to structure the conversation, thereby redressing the perceived failure of Plato's Phaedo to provide adequate guidance for navigating life's vexations, including pain, depression, anxiety, and death. [ABSTRACT FROM AUTHOR]

We report on an innovative design of algorithmic analysis that supports automatic online assessment of students' exploration of geometry propositions in a dynamic geometry environment. We hypothesized that difficulties with and misuse of terms or logic in conjectures are rooted in the early exploration stages of inquiry. We developed a generic activity format for if-then propositions and implemented the activity on a platform that collects and analyzes students' work. Finally, we searched for ways to use variation theory to analyze ninth-grade students' recorded work. We scored and classified data and found correlation between patterns in exploration stages and the conjectures students generated. We demonstrate how automatic identification of mistakes in the early stages is later reflected in the quality of conjectures. [ABSTRACT FROM AUTHOR]

The editions of Arnaut’s sestina and the history of its study reflect the general trend: both its editors and researchers endow trobadours’ lyrics with an elevated meaning. This is also noticeable when referring to their other poems; however, this tendency can be traced especially clearly in the case of sestina. In the early manuscripts A, B and S (13th century) its text is obscene: the key words-rhymes “cambra” (room) and “verja” (branch) have the meaning of obscene euphemisms, and the tornada itself frankly expresses the poet’s hope for a carnal union with his beloved. This variant of tornada seems to us a possible author’s ending of the poem, since it corresponds to its other verses. In addition, we believe that by singing the carnal and “close” love Arnaut argues with the famous song of love from afar by Jaufre Rudel. In the later manuscripts, the obscene sense of tornada became more obscure, and in the two of them — U (turn of the 13th–14th centuries) and C (15th century) — obvious is the intention of the scribes to put accent on the beauty of the poem rather than its content. In the editions of 19th–21st centuries the sense of the sestina and of its tornada has continued to be transformed in the same direction.

The exponential second Zagreb index of a graph G is defined as e M 2 (G) = ∑ x y ∈ E (G) e d x d y , where d x is the degree of vertex x. Recently, Eliasi (Discrete Appl Math 307:172–179, 2022) posed a conjecture about (n, m)-graphs with maximum exponential second Zagreb index, when n ≤ m ≤ 2 n - 3 . In this paper, we prove that this conjecture holds for all graphs whose diameter is not equal to three. [ABSTRACT FROM AUTHOR]

In this article we consider an even entire function of order one as the solution of the classical wave equation in one-dimensional space. We suggest a conjecture that this function has only purely real zeros in the entire complex plane. This is given as a new prospective on a nice connection with number theory and wave equation. [ABSTRACT FROM AUTHOR]

The purpose of this article is to present an interpretation of the novel One Hundred Years of Solitude, by Gabriel García Márquez, based on some of the varied readings generated about it by important Iberoamerican analysts. To achieve this goal, we first took the principles of Hermeneutic Pluralism as a guide which focuses on the abductive work with latent indicial elements in the texts as the key; after that, we abbreviated three readings of the garciamarquiana endeavor. Finally, let us interweave three more readings of the novel, showing the eternal return of violence, which unfolds from the beginning to continue shaping the collective future. [ABSTRACT FROM AUTHOR]

Fuzzy topological topographic mapping ( F T T M ) is a mathematical model that consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. The key to the model is its topological structure that can accommodate electrical or magnetic recorded brain signal. A sequence of FTTM, F T T M n , is an extension of FTTM whereby its form can be arranged in a symmetrical form, i.e., polygon. The special characteristic of F T T M , namely, the homeomorphisms between its components, allows the generation of new F T T M . The generated F T T M s can be represented as pseudo graphs. A pseudo-graph consists of vertices that signify the generated F T T M and edges that connect their incidence components. A graph of pseudo degree zero, G 0 (F T T M n k  ) , however, is a special type of graph where each of the F T T M components differs from its adjacent. A researcher posted a conjecture on G 0 3 (F T T M n 3) in 2014, and it was finally proven in 2021 by researchers who used their novel grid-based method. In this paper, the extended G 0 3 (F T T M n 3) , namely, the conjecture on G 0 4 (F T T M n 4) that was posed in 2018, is narrated and proven using simple mathematical induction. [ABSTRACT FROM AUTHOR]

Physical metrology inspections are crucial in semiconductor fabrication to ensure that wafers are fabricated within the production specification limits and to prevent faulty wafers from being shipped and installed in customer devices. However, it is not possible to examine every wafer, as such inspection would incur impractical costs on manpower, finances, and production cycle time (CT) of fabrication foundries (fabs). Virtual metrology (VM) presents an alternate approach to perform metrology inspection without incurring high costs using machine learning (ML) models. By leveraging historical equipment and process data, ML models can be calibrated to estimate the targeted metrology variables to estimate the quality of wafers, thereby performing virtual inspections on wafers. Recently, VM researchers have begun to introduce deep learning (DL) into VM research to examine its capability. Specifically, VM researchers experimented with a convolutional neural network (CNN). The targeted metrologies are those of plasma-based processes in both etching and chemical vapor deposition. The initial success has been reported by VM researchers. While various CNN-based VM models have been proposed for plasma-based fabrication processes, they have yet to be tested in the photolithography process. Motivated by the initial successes of CNN in plasma-based processes, this work is an initiative to experiment with CNN’s performance in predicting the overlay errors of the photolithography process. Using data from a real fab, this study first establishes a baseline using the methodology of a prior study. The prediction results of the proposed CNN model are then compared with the baseline. The results showed that the CNN could further reduce prediction errors.

Kelamcılar arasında zannî bilginin dinin temel itikadî ilkelerinin tespitinde belirleyici ve bağlayıcı olarak esas alınamayacağı görüşü hâkimdir. Bununla birlikte kesinlik ifade eden bilginin hangi kaynaklardan ve nasıl elde edileceği ve hangi bilgi türlerinin kat‘î olduğu hususu yoğun bir şekilde tartışılmıştır. Kat‘î ve zannî bilgi, delile dayanma açısından ortak bir noktada buluşmaktadır. Zannî bilgi, kesinlik ifade etmeyen aklî ve/veya naklî delille elde edilmektedir. Zan, mahiyet açısından vehim, şek, itikat ve ilim kavramlarıyla ilişkiliyken değer açısından ise daha çok ilim ve itikat kavramlarına yakın durmaktadır. Bir bilgi/hüküm zannîlik açısından derecelendirmeye tabi tutulduğunda, doğruluk tarafı ağır basıyorsa zan, zayıf kalıyorsa vehim vasfını almaktadır. Doğru olup-olmadığı eşit düzeyde ise bu hüküm şek ismiyle anılmaktadır. Aklî delilden elde edilen bilgi/hüküm sabit, değişmez ve uygunluk yönünden başka şekilde olmasına imkân vermeyecek bir kesinlikte olması halinde kat‘î bilgi adını alır. Kelâmcılar ulûhiyet bahislerinde (Allah’ın varlığı, birliği, kadim oluşu, sıfatların zat ile ilişkisi, Allah’ın âlemle ilişkisi, âlemin hadis oluşu gibi), nübüvvetin imkânı ve ispatında bu tür bilgi sağlayan kıyas, istikra, sebr ve taksim gibi aklî istidlal yöntemlerine başvurmuşlardır. Delil kesin bilgi sağlamıyorsa zan ifade eder, bu delil ayrıca zannî delil, emare olarak da nitelenir. Kelâmcılar aklî açıdan zan ifade eden meşhûrât, müsellemât, makbûlât ve temsilden oluşan bilgi türlerinin dinin temel itikadî konularını temellendirmekten ziyade muhataplarını ikna etmek ve muarızlarını ilzâm etmek için kullanmışlardır. Kelâmcılar temel itikadî konuların başında yer alan ulûhiyet bahislerinde daha çok aklî delilleri kullanmakla birlikte dinin temel konularını belirleyen nakle de önemli ölçüde yer vermişlerdir. Bu bağlamda kelâmcılar sübût ve delalet açısından kat’î olan naklî delili bağlayıcı ve belirleyici kabul etmişlerdir. Nitekim dinin temel itikadî ilkeleri sonuç itibariyle bu tür naklî delillere dayanmaktadır. Bununla birlikte kelâmcılar her ne kadar sübût ve delâlet açısından kat‘î olmayan haber-i vâhid gibi delilleri bağlayıcı kabul etmemişlerse de bazı sem‘î konularda bu türden delillerle istidlâlde bulunmuşlardır. Bu perspektiften hareket eden kelâmcılar ahiret ahvali kapsamında yer alan kabir azabı, mizan, şefaat, sırat gibi sem‘î konuları aklî istidlalden ziyade naklî delille temellendirmeye çalışmışlardır. Bu çalışma klasik kelâmî kaynaklarda tartışılagelen zannî bilginin istidlal değerini ve kullanım alanını konu edinmiş ve elde edilen veriler nitel bir yöntemle farklı açılardan değerlendirmeye tabi tutulmuştur. Bu cümleden olmak üzere zannî bilginin bazı tâli itikadî konularda geçerli olduğu ve kelâmda zannın istidlal değerinin olmadığı yönündeki söylemin mutlak olmadığı sonucuna varılmıştır.

The paper begins with a hypothetical story and asks: how should a Rawlsian political liberal state justify its coercion over Nozick, an unreasonable but intelligible citizen (UIC)? I use this thought experiment to illustrate a recent critique of political liberalism. It argues that political liberalism coerces UIC on a sectarian ground. Call it the sectarian critique. My paper addresses the sectarian critique from a political liberal perspective. I suggest a condition of state conjecture, which argues that the state officials should use conjecture to engage with UIC, like Nozick. This brings two benefits to the stability of a political liberal society. First, UIC may be convinced and become reasonable citizens. Secondly, the activity of offering conjectures can strengthen the public confidence of political liberalism as a valuable collective project. Although, eventually, some UIC may remain unpersuaded and be coerced on grounds that are unjustified to them, the force of the sectarian critique will be significantly weakened after the condition of state conjecture is fulfilled. [ABSTRACT FROM AUTHOR]

Где пролегает дистанция, разделившая прозу и поэзию, и в чем особенность ритма «Олинфских речей» Демосфена? Учитывая особенности применения т.н. «базисного тембра» (БТ) в заключительных пятисложниках всех сохранившихся периодов «Олинфских речей», можно говорить о новых путях выбора конъектуры к месту Dem. Olynth. 2.16, где встречается метрически неожиданная клаузула: согласно «Правилу Ф. Бласса», Демосфен избегает последовательности из 3 и более кратких слогов. Клаузула периода в Dem. Olynth. 2.16 могла располагаться раньше: «τῶν ἐν τῇ χώρᾳ» вместо «(δι-)ὰ τὸν πόλεμον». Предлагаемая клаузула содержит спондеи и имеет больший «просодический вес», чем «(δι-)ὰ τὸν πόλεμον». Это предпочтительно с т. зр. Ф. Бласса, однако встречает возражения А. Борнека, считавшего данный тип клаузул избегаемым, как минимум, у Цицерона и латинских ораторов. Разбор метро-звукового строя пятисложной клаузулы у Демосфена совершенно новый и способствует углублению исследований ритма и метра древнегреческой прозы, ее сходства и различия в отношении поэзии: лирики и драмы. Все клаузулы во всех трех «Олинфских речах» описаны в статье с применением «базисного тембра», нового исследовательского инструмента. Метрический разбор совмещен с уровнем звуковых средств выразительности. Автор согласен с Г. Хатчинсоном и Л. Пирсоном в методических предпочтениях, ведущих к признанию эстетического осмысления речей Демосфена важнейшей задачей исследователя.

We study the projection of an element of fractional Gaussian noise onto its neighbouring elements. We prove some analytic results for the coefficients of this projection. In particular, we obtain recurrence relations for them. We also make several conjectures concerning the behaviour of these coefficients, provide numerical evidence supporting these conjectures, and study them theoretically in particular cases. As an auxiliary result of independent interest, we investigate the covariance function of fractional Gaussian noise, prove that it is completely monotone for H > 1 / 2 , and, in particular, monotone, convex, log-convex along with further useful properties. [ABSTRACT FROM AUTHOR]

This paper has two aims: (1) it develops and defends a fully-fledged account of the epistemic normativity of conjecture (2) it goes sharply against orthodoxy, in arguing that conjecture is epistemically more demanding than assertion. According to the view defended here, one's conjecture that p is permissible only if one knows that one has warrant, but not sufficient warrant to believe that p. I argue for my account on three independent grounds: (1) the Bach and Harnish account of the nature of communicative speech acts, (2) the plausible normative relation between assertion and other constatives, and (3) the normativity of belief in conjunction with constatives' epistemic function. [ABSTRACT FROM AUTHOR]

Abstract Performance/security trade-off is widely noticed in CFI research, however, we observe that not every CFI scheme is subject to the trade-off. Motivated by the key observation, we ask three questions: ➊ does trade-off really exist in different CFI schemes? ➋ if trade-off do exist, how do previous works comply with it? ➌ how can it inspire future research? Although the three questions probably cannot be directly answered, they are inspiring. We find that a deeper understanding of the nature of the trade-off will help answer the three questions. Accordingly, we proposed the GPT conjecture to pinpoint the trade-off in designing CFI schemes, which says that at most two out of three properties (fine granularity, acceptable performance, and preventive protection) could be achieved.

This article presents a new conjecture on Herodotus 1.51.3. [ABSTRACT FROM AUTHOR]

The paper seeks to present a semantico-functional analysis of the French verb falloir. The empirical data are obtained from a parallel corpus – the Corpus Parallèle de Textes Littéraires (CTLFR-LT), which is composed of French literary texts and their translations into Lithuanian. The paper uses quantitative, qualitative and comparative methods. It is based on the studies focusing on the polysemy of modal verbs (Chu 2010; Dendale 1994; Kronning 1988; Le Querler 2001; Rossari 2012) as well as on the development of discourse markers in language (Dostie 2004; Vold 2008). The findings show that the verb falloir, while maintaining its core meaning of necessity, can express conjecture. When it is used in patterns together with verbs of saying (verba cogitandi and dicendi) and verbs of visual perception, falloir no longer functions as a marker of necessity and becomes a pragmatic marker of connection and argumentation. The analysis of the translations of the French verb falloir into a typologically different language, Lithuanian, has also confirmed the entrenched use of the verb in question in the modal field of necessity and its rich functional potential in the French literary texts. The paper contributes to the existing contrastive studies between the French and Lithuanian languages, which are not numerous. The findings of the research could serve didactic purposes as well as add to the field of translation studies.

Let G be a simple graph with n vertices, m edges having Laplacian eigenvalues μ 1 , μ 2 , ... , μ n − 1 , μ n = 0. The Laplacian energy LE (G) is defined as LE (G) = ∑ i = 1 n | μ i − d ¯ | , where d ¯ = 2 m n is the average degree of G. Radenković and Gutman conjectured that among all trees of order n , the path graph P n has the smallest Laplacian energy. Let n (d) be the family of trees of order n having diameter d. In this paper, we show that Laplacian energy of any tree T ∈ n (4) is greater than the Laplacian energy of P n , thereby proving the conjecture for all trees of diameter 4. We also show the truth of conjecture for all trees with number of non-pendent vertices at most 9 n 2 5 − 2. Further, we give some sufficient conditions for the conjecture to hold for a tree of order n. [ABSTRACT FROM AUTHOR]

Nicolaus Cusanus presents a subtle theory of alterity. We will show why Cusanus does not consistently assign humans a position superior to other living beings, even when strong anthropocentric arguments seem to be present. Kazuhiko Yamaki (2017: 280), e.g., has recently pointed out that the attribution of a privileged position to humans in the world already fails logically, because the complicatio-explicatio scheme applies to all creatures. I would like to follow up on Yamaki’s argument that Cusanus at this point is rather concerned with describing a specific relationship between God and the creatures or the world. If this argument is extended to the question of humans and animals in Cusanus as a whole, the way in which these relations are to be figured becomes the focus of consideration. Just as Cusanus, in cosmology and anthropology, examines the perspectivity of knowledge and the decentralization of the Earth (as a noble star among other stars) without falling into pure perspectivism or decentralism, so traits of this reflective and (figuratively) ‘living’ thinking must also apply to the description of the relationship of living beings to one another or in relation to their Creator.

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Fuzzy topological topographic mapping (FTTM) is a mathematical model that consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. The key to the model is its topological structure that can accommodate electrical or magnetic recorded brain signal. A sequence of FTTM, FTTMn, is an extension of FTTM whereby its form can be arranged in a symmetrical form, i.e., polygon. The special characteristic of FTTM, namely, the homeomorphisms between its components, allows the generation of new FTTM. The generated FTTMs can be represented as pseudo graphs. A pseudo-graph consists of vertices that signify the generated FTTM and edges that connect their incidence components. A graph of pseudo degree zero, G0(FTTMnk ), however, is a special type of graph where each of the FTTM components differs from its adjacent. A researcher posted a conjecture on G03(FTTMn3) in 2014, and it was finally proven in 2021 by researchers who used their novel grid-based method. In this paper, the extended G03(FTTMn3), namely, the conjecture on G04(FTTMn4) that was posed in 2018, is narrated and proven using simple mathematical induction.

Archaeology is currently bound to a series of metaphysical principles, one of which claims that reality is composed of a series of discrete objects. These discrete objects are fundamental metaphysical entities in archaeological science and posthumanist/New Materialist approaches and can be posited, assembled, counted, and consequently included in quantitative models (e.g. Big Data, Bayesian models) or network models (e.g. Actor-Network Theory). The work by Sørensen and Marila shows that archaeological reality is not that discrete, that some objects cannot be easily identified, and that perhaps reality is not always necessarily composed of discrete objects. The aim of this article is to take Sørensen and Marila’s arguments to their ultimate logical consequences: most archaeological theory today operates under the illusion of a general metaphysics. This illusion dictates not only that all of reality is composed of discrete objects, but that since reality manifests in a certain way, there has to be a methodology that accurately represents that reality. A brief discussion on the notion of “conjecture,” as conceived in certain historical theories, is also presented.

In the paper, the author presents bounds for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function. This result partially confirms one in a series of conjectures on completely monotonic degrees of remainders of asymptotic expansions for the logarithm of the gamma function and for polygamma functions.

Lambert's choice of genre for his Cosmological Letters – the scholarly correspondence – was conscious and well-founded, as it facilitated a certain form of reflection and presentation. Such letters enabled him to integrate more complex reasoning into the presentation of a specific problem than the scholarly dialogues that had been common since Fontenelle. Lambert needed to integrate sophisticated demonstrations from the theories of probability and teleology, as empirical knowledge was insufficient or unproven. With regard to his subject (the order of the comets, satellites, planets and galaxies of the universe), theonomistic and probabilistic cosmology could be convincingly communicated in the form of letters. [ABSTRACT FROM AUTHOR]

This paper concerns the internal structure of reasoning that, basically consisting in conjecturing and refuting, is too often identified with only deducing, abducing and refuting, that is, with just the deductive search of consequences, hypotheses and refutations. With such identification, it is forgotten that in addition to consequences and hypotheses, there is a third class of conjectures, speculations or proper guesses. Speculations are inferentially non-comparable, or orthogonal, with the premise, and generate creativity. It is presented a very simple formal view for the structure of Commonsense Reasoning, a mathematical model allowing to show the importance of speculations, and specially to start with its systematic computational search. [ABSTRACT FROM AUTHOR]

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In Antiquity, medical practice was conceptualized in the form of stochastic art. The conjectural approach (Stochastikê Technê) was at that time subjective: the physician aimed to cure his patient thanks to the gestures and remedies that were known to circumvent the hazards of the pathology. With the stochastic focus, the endpoint however remains uncertain. Failure is an ever-present threat. And, for that matter, some ethics that can get it right must be developed. Long before Bernoulli’s law of large numbers and Bayes’s theorem could mathematically model conjectures, it seems that the letter had developed intuitively in medical acts. Is the conjectural reasoning of ancient physicians reducible to calculation? Although its semeiotic form may make us think so, this hypothesis is problematized by the history of medicine. Is there any historical continuity or discontinuity in the medical act of conjecture?

Early Muslim philosophers, theologians, logicians and experts in jurisprudence understand knowledge as “firm true belief supported by evidence”. They consider conjectures as a kind of ignorance, the domain of certain knowledge confined in necessary truths; and the domain of uncertain knowledge limited to contingent facts. From their definitions and postulates, we can conclude that they took “having appropriate source” as the criterion of knowledge. For this reason, they included the qualifications “firm” and “immutable” in their definition of knowledge in lieu of distinction between the definition and the criterion of knowledge and separation of cognitive characteristic features of beliefs from the non- cognitive ones. Their approach in epistemology is externalistic but it accommodates foundationalism and fallibilism while evading epistemological relativism. In this approach, knowledge is defined as true belief with proper source. Having proper source is a criterion for knowledge which is not explicitly stated but is implied by different qualifications introduced by them. A source of belief is proper iff it bears a causal relation of some sort to the state of affairs the belief depicts.

I explain how Karl Popper resolved the problem of induction but not the pragmatic problem of induction. I show that Popper's proposed solution to the pragmatic problem of induction is inconsistent with his solution to the problem of induction. I explain how Popper’s falsificationist epistemology can solve the pragmatic problem of induction in the same negative way that it solves the problem of induction.

We study the projection of an element of fractional Gaussian noise onto its neighbouring elements. We prove some analytic results for the coefficients of this projection. In particular, we obtain recurrence relations for them. We also make several conjectures concerning the behaviour of these coefficients, provide numerical evidence supporting these conjectures, and study them theoretically in particular cases. As an auxiliary result of independent interest, we investigate the covariance function of fractional Gaussian noise, prove that it is completely monotone for H>1/2, and, in particular, monotone, convex, log-convex along with further useful properties.

There is a prevailing opinion that conjectural knowledge (zann) cannot be taken as a basis in determining the fundamental theological principles among the theologians. However, from which sources and how to obtain certainty (yaqīn) and which types of knowledge are definitive (qat'ī) have been discussed extensively. Certain and conjectural knowledge meet at a common point in terms of relying on evidence. Conjectural knowledge obtained via reasoning and/or religious scripture that do not express certainty. While conjectural knowledge has been essentially related to the concepts of estimation, doubt, belief and knowledge, by its in term of value, it is stands closer to the concepts of knowledge and belief. Conjectural knowledge contains different degrees of certainty. When it is chosen to be more certain, it is considered as a valid conjecture, when it is disregarded, it is considered as erroneous conjecture. If there is no choice for its certainty, then it is called doubt (shakk). If the information/judgment obtained through reasoning becomes fixed, unchangeable and in a coherence that does not allow it to be otherwise, then it is called definitive (qat'ī) knowledge. To achieve that, theologians generally used methods of argumentations like syllogism, induction, exhaustive investigation and disjunction (al-sabr wa'l-taqsīm) to provide such knowledge about divinity and prophethood. Theologians have used conjectural knowledge, which are based on endoxic (mashhūrāt), already granted (musallamāt) and acceptance of authority (maqbūlāt), in their dialectics to persuade their discussants, rather than to justify the fundamental theological issues of religion. While theologians mostly use rational proofs in theological issues, they also gave significant place to the scriptural narrative that determines the creed. In this context, theologians accepted the narrated evidence as binding and decisive, as long as it is certain in terms of both authenticity and implication. Ultimately, the fundamental theological principles of religion are based on these narrative evidences. Although the theologians do not accept single reports (khabar al-wahid) for their questionable authenticity, they also made inferences regarding subjects of traditions (sam'iyyāt). Acting from this perspective, theologians tried to justify with narrative evidence rather than rational arguments on these issues such as torment in grave, intercession (shafā'ah) and sirât, which are mostly matters of eschatology and the unseen (ghayb). Finally, it has been concluded that the conjectural knowledge is still valid in some secondary theological issues and the assumption that the conjectural knowledge has no deduction value in theology is not absolute. [ABSTRACT FROM AUTHOR]

The purpose of this study is to understand the characteristics of mathematical reasoning of elementary preservice teachers (EPTs). For this purpose, 68 EPTs were presented with two tasks related to mathematical reasoning, and their written responses were analyzed. The EPTs' mathematical reasonings were investigated on the one hand as a whole and on the other hand between the three groups -the full successful, partial successful, and unsuccessful provers-, with focusing on the affordances from and strategies for using examples proposed in the CAPS framework. As the results of this study, it was revealed that the EPTs had insufficient competencies in terms of exploring with examples, finding structural features, building generalizations, developing conjectures, and producing proofs. In contrast, the EPTs had great strength with regard to representing their chosen examples in formal expression, which was a decisive contributor on the one hand but an impediment on the other in producing valid justifications to the given conjectures. Based on the results, the implications for elementary preservice teacher education were suggested.

Over years of collaborating with elementary-school teachers to research students' thinking about the "big ideas" of K-6 mathematics, particular attention was given to generalizations about the operations-addition, subtraction, multiplication, and division-and arguments that explain why these generalizations are true. Through this work, we created a model of five phases that separate different points of focus in the complex process of formulating and proving such generalizations: 1) noticing patterns, 2) articulating conjectures, 3) representing with specific examples, 4) creating representation-based arguments, and 5) comparing and contrasting operations. In this paper, we illustrate the phases with classroom examples as students investigate a set of generalizations. We then present assessment results from classrooms of project teachers who engaged their students in this content.

The article discusses the changes introduced by the successive editors of Adam Mickiewicz's narrative poem to the text version published by the poet himself. The most important one is undoubtedly the addition of the poem considered the "epilogue" to Pan Tadeusz, allegedly lost by Mickiewicz. No less radical are the interventions consisting in supplementing the text with fragments from the autograph or with the poet's later additions made to the already printed text, as well as in corrective conjectures in instances regarded by the publisher as slips of the pen. The article compares the surviving authorial versions of the text, demonstrating that Mickiewicz himself treated his work as a continual process and tested new solutions on various occasions; however, there is no evidence that he intended to introduce them into the printed text. [ABSTRACT FROM AUTHOR]

The "Sacred Soul" is a term used by philosophers to often name a person who is severely alike. Mulla Sadra and Qazi Saeed both believe in the connection between this soul and the soul of the Prophet, which necessitates the recognition of its characteristics. In this paper, by direct reference to their works, in the first step, the features of the sacred soul are explained and then, by examining the relation of the holy soul and Prophetic soul, the question of the possibility of access of other human beings to the standard of the soul is evaluated. It must be said that the difference between the ontological and anthropological grounds of Mulla Sadra and Qazi Saeed has led to a difference of opinion between the two thinkers. According to the omnipotence of the existence and the formation of existence, the essential movement and the union of the intelligent and the intelligible ranks the arrogance for a sacred soul from the man that can Conjecture to the soul of the Prophet, but Qazi Saeed who did not accept these bases, reveals the instances of a sacred soul in the universal soul and the soul. Despite this difference in appearance, the relationship of the soul with the soul of the Prophet and other human populations in the thoughts of these two great philosophers is very close, to the extent that their difference of opinion cannot be regarded as a literal contribution of a sacred soul in their philosophical system.