You omega know something when you know it, and know that you know it, and know that you know that you know it, and so on. This paper first argues that omega knowledge matters, in the sense that it is required for rational assertion, action, inquiry, and belief. The paper argues that existing accounts of omega knowledge face major challenges. One account is skeptical, claiming that we have no omega knowledge of any ordinary (...) claims about the world. Another account embraces the KK thesis, and identifies knowledge with omega knowledge. This position faces counterexamples, and struggles to make sense of inexact knowledge. The paper then develops a new account of knowledge, by proposing the principle of Reflective Luminosity: if you know that you know something, then you omega know it. I argue that Reflective Luminosity allows for omega knowledge while avoiding the problems for KK. (shrink)

You omega know p when you possess every iteration of knowledge of p. This book argues that omega knowledge plays a central role in philosophy. In particular, the book argues that omega knowledge is necessary for permissible assertion, action, inquiry, and belief. Although omega knowledge plays this important role, existing theories of omega knowledge are unsatisfying. One theory, KK, identifies knowledge with omega knowledge. This theory struggles to (...) accommodate cases of inexact knowledge. The other main theory is skeptical, claiming that we do not omega know any ordinary claims about the world. This book develops and critically compares three new theories of omega knowledge. (shrink)

This article focuses on the Omega Point, an essential concept in Teilhard de Chardin’s evolutionary metaphysics. In certain passages about the Omega Point, Teilhard mentions the primeval atom hypothesis, a theory about the beginning of the universe proposed by Georges Lemaître, another contemporary Jesuit priest who was also a scientist. Although Teilhard and Lemaître are essentially evolutionists, besides being Jesuit priests, their evolutionary metaphysics and their philosophies of science are radically divergent, and two important differences are presented here (...) – about the eventual cosmic determinism and about the relationship between scientific knowledge and religious beliefs. This article also shows how Teilhard’s original concept was projected into two cosmological theories in which it reveals an essential transfiguration by losing its initial anthropic and religious matrix – the cosmological anthropic principle, proposed by physicists John Barrow and Frank Tipler, and the Omega Point Theory proposed later by Frank Tipler. (shrink)

Let's say that _I fully know that p_ if I know that _p_, I know that I know that _p_, I know that I know that I know that _p_, and so on. Let's say that _I partially know that p_ if I know that _p_ but I don't fully know that _p_. What, if anything, do I fully know? What, if anything, do I partially know? One response in the literature is that I fully know everything that I know; (...) partial knowledge is impossible. This response is in tension with a plausible margin-for-error principle on knowledge. A different response in the literature is that I don't fully know anything; everything that I know, I partially know. Recently, Goldstein (2024, forthcoming) defended a third view, according to which I fully know some things and I partially know other things. While this seems plausible, Goldstein's account is based on denying the margin-for-error principle. In this paper, I show that the possibility of both full knowledge and partial knowledge is consistent with the margin-for-error principle. I also argue that the resulting picture of knowledge is well-motivated. (shrink)

Let's say that _I fully know that p_ if I know that _p_, I know that I know that _p_, I know that I know that I know that _p_, and so on. Let's say that _I partially know that p_ if I know that _p_ but I don't fully know that _p_. What, if anything, do I fully know? What, if anything, do I partially know? One response in the literature is that I fully know everything that I know; (...) partial knowledge is impossible. This response is in tension with a plausible margin-for-error principle on knowledge. A different response in the literature is that I don't fully know anything; everything that I know, I partially know. Recently, Simon Goldstein (2024, forthcoming) defended a third view, according to which I fully know some things and I partially know other things. While this seems plausible, Goldstein's account is based on denying the margin-for-error principle. In this paper, I show that the possibility of both full knowledge and partial knowledge is consistent with the margin-for-error principle. I also argue that the resulting picture of knowledge is well-motivated. (shrink)

The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgements of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point (...) of traditional philosophy of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Frege's concern about indiscernibility and circularity, while other are more recent, such as Baker's concern about the unreliability of small samplings in the setting of arithmetic. Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the~$\omega$-rule or to the non-computability and non-continuity of probability assignments. Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments, such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated. In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar. (shrink)

Released mid-November 2022, Galactica is a set of six large language models (LLMs) of different sizes (from 125 M to 120B parameters) designed by Meta AI to achieve the ultimate ambition of “a single neural network for powering scientific tasks”, according to its accompanying whitepaper. It aims to carry out knowledge-intensive tasks, such as publication summarization, information ordering and protein annotation. However, just a few days after the release, Meta had to pull back the demo due to the strong (...) hallucinatory tendencies or underwhelming performances of the model. This article aims to study, through a critical threefold argument, the potential impacts of LLMs once deployed in the scientific value chain. Our first argument is a technical one. By examining the technicity of Galactica, it is possible to explain the descripancies between its promotional corporate discourse and abysmal outputs. Second, by going back to debates in both computer science and computational philosophy on the automation of abduction, we argue from the epistemological front that LLMs indeed cannot produce strong abductions and, therefore, claims about the automation of hypothesis generation remains chambering. Finally, our third argument is a sociological one. By conceptualizing the scientific field through Nancy Katherine Hayles’ cognitive assemblage theory, we aim to outline the potential steering of science by LLMs, mainly through information ordering. The core of our argument rests on the assertion that excessive control on information risks contravening a certain serendipitous aspect inherent to scientific discoveries. (shrink)

Accessing knowledge of a single knowledge source with different client applications often requires the help of mediator systems as middleware components. In the domain of theorem proving large efforts have been made to formalize knowledge for mathematics and verification issues, and to structure it in databases. But these databases are either specialized for a single client, or if the knowledge is stored in a general database, the services this database can provide are usually limited and hard (...) to adjust for a particular theorem prover. Only recently there have been initiatives to flexibly connect existing theorem proving systems into networked environments that contain large knowledge bases. An intermediate layer containing both, search and proving functionality can be used to mediate between the two. In this paper we motivate the need and discuss the requirements for mediators between mathematical knowledge bases and theorem proving systems. We also present an attempt at a concurrent mediator between a knowledge base and a proof planning system. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, (...) undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

The main title of Robert J. Russell's Cosmology from Alpha to Omega: The Creative Mutual Interaction of Theology and Science catches the substance of the essays; the subtitle his methodological vision. The mutualis modest as far as the influence from theology on science goes; in no way is Russell curtailing the pursuit of science. Driven by intellectual honesty, he holds that in the end religious convictions will have to stand the test of compatibility with scientific knowledge. And as (...) a Christian he believes core beliefs of Christianity, reformulated as needed, will be able to stand this test. The essays address the origin and contingency of our universe in relation to belief in creation, and his proposal for noninterventionist objective divine action. For him a stumbling block is natural evil; the evolutionary intelligibility of evil falls short of what would be desirable theologically. As steps toward an adequate eschatology Russell seeks to develop a more complex understanding of temporality, and proposes to understand the resurrection of Jesus as the First Instantiation of a New Law of the New Creation. This area is more in tension with current science, but that could be expected when one moves from creation to redemption. Within his self-imposed boundaries, these essays are well informed and well argued, and together they provide a sincere and sustained research program. (shrink)

This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality relates to the computational theory of mind; metaphysical modality; the types of mathematical modality; to the epistemic status of large cardinal axioms, undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal profile of rational intuition; (...) and to the types of intention, when the latter is interpreted as a modal mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. Chapter 3 provides an abstraction principle for epistemic intensions. Chapter 4 advances a two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states, by contrast to availing of modal axiom 4. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's "criterial" identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The epistemic two-dimensional truthmaker semantics developed in chapter 4 is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapter 8 examines the modal commitments of abstractionism, in particular necessitism, and epistemic modality and the epistemology of abstraction. Chapter 9 examines the modal profile of $\Omega$-logic in set theory. Chapter 10 examines the interaction between epistemic two-dimensional semantics and absolute decidability. Chapter 11 avails of modal coalgebraic automata to interpret the defining properties of indefinite extensibility, and avails of epistemic two-dimensional semantics in order to account for the interaction of the interpretational and objective modalities thereof. The hyperintensional, epistemic two-dimensional truthmaker semantics developed in chapter 4 is applied in chapters 8, 10, and 11. Chapter 12 provides a modal logic for rational intuition. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

The main topics of this thesis are cardinal invariants, P -points and MAD families. Cardinal invariants of the continuum are cardinal numbers that are bigger than $\aleph _{0}$ and smaller or equal than $\mathfrak {c}.$ Of course, they are only interesting when they have some combinatorial or topological definition. An almost disjoint family is a family of infinite subsets of $\omega $ such that the intersection of any two of its elements is finite. A MAD family is a maximal (...) almost disjoint family. An ultrafilter $\mathcal {U}$ on $\omega $ is called a P-point if every countable $\mathcal {B\subseteq U}$ there is $X\in $ $\mathcal {U}$ such that $X\setminus B$ is finite for every $B\in \mathcal {B}.$ This kind of ultrafilters has been extensively studied, however there is still a large number of open questions about them.In the preliminaries we recall the principal properties of filters, ultrafilters, ideals, MAD families and cardinal invariants of the continuum. We present the construction of Shelah, Mildenberger, Raghavan, and Steprāns of a completely separable MAD family under $\mathfrak {s\leq a}.$ None of the results in this chapter are due to the author.The second chapter is dedicated to a principle of Sierpiński. The principle $\left $ of Sierpiński is the following statement: There is a family of functions $\left \{ \varphi _{n}:\omega _{1}\longrightarrow \omega _{1}\mid n\in \omega \right \} $ such that for every $I\in \left [ \omega _{1}\right ] ^{\omega _{1}}$ there is $n\in \omega $ for which $\varphi _{n}\left [ I\right ] =\omega _{1}.$ This principle was recently studied by Arnie Miller. He showed that this principle is equivalent to the following statement: There is a set $X=\left \{ f_{\alpha }\mid \alpha \alpha $ then $f_{\beta }\cap g$ is infinite. Miller showed that the principle of Sierpiński implies that non $\left =\omega _{1}.$ He asked if the converse was true, i.e., does non $\left =\omega _{1}$ imply the principle $\left $ of Sierpiński? We answer his question affirmatively. In other words, we show that non $\left =\omega _{1}$ is enough to construct an $\mathcal {IE}$ -Luzin set. It is not hard to see that the $\mathcal {IE}$ -Luzin set we constructed is meager. This is no coincidence, because with the aid of an inaccessible cardinal, we construct a model where non $\left =\omega _{1}$ and every $\mathcal {IE}$ -Luzin set is meager.The third chapter is dedicated to a conjecture of Hrušák. Michael Hrušák conjectured the following: Every Borel cardinal invariant is either at most non $\left $ or at least cov $\left $. Although the veracity of this conjecture is still an open problem, we were able to obtain some partial results: The conjecture is false for “Borel invariants of $\omega _{1}^{\omega }$ ” nevertheless, it is true for a large class of definable invariants. This is part of a joint work with Michael Hrušák and Jindřich Zapletal.In the fourth chapter we present a survey on destructibility of ideals and MAD families. We prove several classic theorems, but we also prove some new results. For example, we show that every almost disjoint family of size less than $\mathfrak {c}$ can be extended to a Cohen indestructible MAD family is equivalent to $\mathfrak {b=c}$. A MAD family $\mathcal {A}$ is Shelah–Steprāns if for every $X\subseteq \left [ \omega \right ] ^{<\omega }\setminus \left \{ \emptyset \right \} $ either there is $A\in \mathcal {I}\left $ such that $s\cap A\neq \emptyset $ for every $s\in X$ or there is $B\in \mathcal {I}\left $ that contains infinitely many elements of X $ denotes the ideal generated by $\mathcal {A}$ ). This concept was introduced by Raghavan which is connected to the notion of “strongly separable” introduced by Shelah and Steprāns. We prove that Shelah–Steprāns MAD families have very strong indestructibility properties: Shelah–Steprāns MAD families are indestructible for “many” definable forcings that does not add dominating reals. According to the author’s best knowledge, this is the strongest notion that has been considered in the literature so far. In spite of their strong indestructibility, Shelah–Steprāns MAD families can be destroyed by a ccc forcing that does not add unsplit or dominating reals. We also consider some strong combinatorial properties of MAD families and show the relationships between them.The fifth chapter is one of the most important chapters in the thesis. A MAD family $\mathcal {A}$ is called $+$ -Ramsey if every tree that branches into $\mathcal {I}\left $ -positive sets has an $\mathcal {I}\left $ -positive branch. Michael Hrušák’s first published question is the following: Is there a $+$ -Ramsey MAD family? It was previously known that such families can consistently exist. However, there was no construction of such families using only the axioms of ZFC. We solve this problem by constructing such a family without any extra assumptions.In the fourth and fifth chapters, we introduce several notions of MAD families, in the sixth chapter we prove several implications and non implications between them. We construct several MAD families with different properties.In the seventh chapter we build models without P -points. We show that there are no P -points after adding Silver reals either iteratively or by the side by side product. These results have some important consequences: The first one is that is its possible to get rid of P -points using only definable forcings. This answers a question of Michael Hrušák. We can also use our results to build models with no P -points and with arbitrarily large continuum, which was also an open question. These results were obtained with David Chodounský.prepared by Osvaldo Guzmán GonzálezE-mail : oguzman@matmor.unam.mxURL : https://arxiv.org/abs/1810.09680. (shrink)

BackgroundOne of the preferences working in the Generation Z is based on their motivational work values. The relevance of job choices with the work values will contribute to student career planning. The work value instrument among generations is one of the popular instruments used to measure final year students' work value, yet few studies of the psychometric properties of non-English language versions of this instrument. This study's objectives were to adapt a questionnaire of work value in Indonesian final year university (...) students.MethodsThe number of participants in this study was 316 students in Indonesia, comprised of final year students from various majors who were selected by quota sampling. The instrument consisted of 5 dimensions of value, including leisure, extrinsic rewards, intrinsic rewards, altruistic rewards, and social rewards. The reliability analysis was performed using McDonald's Omega, the evidence of validity was obtained from test content, internal structure through confirmatory factor analysis, and evidence-based in relation to other variable has conducted the correlation between work value and career development learning using the Pearson's correlation coefficient.ResultsThe results showed that the work values instrument had good psychometric properties, including good reliability, good content validity, and internal structure. In CFA, the two-factor structure showed satisfactory model fit. Moreover, the correlation of work value with career development learning builds stronger validity evidence on this instrument.ConclusionThe adapted instrument can be used practically to identify work value preferences of final year students to help them choose a work preference and setup the career planning before graduating. The result could be of interest for the researcher in work value, motivational work, and career areas in higher education. To the best of our knowledge, there have been no reports about the adaptation of work value instruments in Indonesian final year university students. (shrink)

Introduction: After the outbreak of COVID-19, psychological hotlines functioned as a main channel of psychological assistance and required a large number of professionals to provide services. These hotlines mostly offered a single-use service with short session times and allowed callers to retain anonymity. They functioned as a psychological counseling service for stress experienced in the COVID-19 public health emergency. Hotline psychological counselors must meet special competency requirements. The selection and evaluation tools for recruiting hotline counselors need to be developed.Materials and (...) Methods: The initial scale of competence for psychological hotline counselors was formed by expert evaluation based on theoretical constructs and by using the Delphi method. A link to the questionnaire was sent to a WeChat group of counselors from 36 major psychological hotlines in China in two stages. The questionnaire consisted of questions to elicit basic demographic information and the initial competence scale. In the first phase, 343 valid samples were used to perform exploratory factor analysis. In the second phase, 334 valid samples were used to perform confirmatory factor analysis. The status of the competence of psychological hotline counselors was also analyzed.Results: The factor structure of the Psychological Hotline Counselor Competence Scale was verified and defined in terms of skills, attitude, and knowledge. The results of exploratory factor analysis and confirmatory factor analysis showed that the scale has good reliability and validity. The McDonald’s omega for each factor was calculated. Meanwhile, it was found that the psychological hotline counselors’ self-assessed competence had a high average score.Conclusion: The Competence Scale for Psychological Hotline Counselors for Major Public Emergencies developed in this study has good reliability and validity, and can be a reliable tool for organizing psychological assistance and screening hotline psychological counselors during public emergencies in the future. (shrink)

This paper aims to contribute to the analysis of the nature of mathematical modality and hyperintensionality, and to the applications of the latter to absolute decidability. Rather than countenancing the interpretational type of mathematical modality as a primitive, I argue that the interpretational type of mathematical modality is a species of epistemic modality. I argue, then, that the framework of two-dimensional semantics ought to be applied to the mathematical setting. The framework permits of a formally precise account of the priority (...) and relation between epistemic mathematical modality and metaphysical mathematical modality. The discrepancy between the modal systems governing the parameters in the two-dimensional intensional setting provides an explanation of the difference between the metaphysical possibility of absolute decidability and our knowledge thereof. I also advance a topic-sensitive epistemic two-dimensional truthmaker semantics, if hyperintensional approaches are to be preferred to possible worlds semantics. I examine the relation between two-dimensional hyperintensional states and epistemic set theory, providing two-dimensional hyperintensional formalizations of the modal logic of ZFC, large cardinal axioms, $\Omega$-logic, and the Epistemic Church-Turing Thesis. (shrink)

The constantly accelerating progress of contemporary natural science is indissolubly associated with the development and use of mathematics and with the processes of mathematical modeling of the phenomena of nature. The essence of this diverse and highly fertile interaction of mathematics and natural science and the dialectics of this interaction can only be disclosed through analysis of the nature of theoretical notions in general. Today, above all in the ranks of materialistically minded researchers, it is generally accepted that theory possesses (...) a value of its own. Contrary to positivist concepts of the nature of our knowledge, the meaning and significance of theory do not consist merely of the recording of experimental data, their classification and notation in abbreviated form. The meaning of theory is considerably more significant and is revealed, above all, in its explanatory and predictive functions. Contemporary theoretical knowledge is quite advanced and comprises a highly complex system, relatively self-contained and capable of internal development. Mathematics is the most interesting and distinctive phenomenon in the system of theoretical knowledge, in the system of science in general. It is in its dialectical development that the internal force and dynamics of the development of theory, in the very broadest sense of that word, find expression. Paul Lafargue tells us that Karl Marx held that "science only attains perfection when it succeeds in making use of mathematics" . In many fields of research the formulation of new ideas and concepts rests upon mathematics, its concepts and notions, and "is suggested" by the latter. "Mathematics," writes F. Dyson, "is the main source of the notions and principles out of which new theories are created" . The basic significance of mathematics to theory has been noted by outstanding thinkers over the course of the entire history of development of science. Today the expressive phrase, "the mathematization of knowledge," has come into general currency as a description of the principal direction of growth of theoretical notions in natural science. However, with respect to the growth of modern theoretical physics in general, the statement that it develops primarily by the method of the mathematical hypothesis has general validity. For example, the principal findings and discoveries of quantum theory and particle physics, starting from the corpuscularwave dualism and terminating with the omega minus hyperon and hypothetical quarks, were obtained or made "at the tip of a mathematician's pen.". (shrink)

The primary objective of the research was to validate the Emotional Leadership Questionnaire for Training, as proposed by McKee et al. (2008). The study included a sample of 97 school principals. An analysis of the original questionnaire was conducted, which comprises four factors and 25 items. Of these, three items and 13 factors were retained. The results demonstrated an optimal fit of the model and high-reliability indices. This instrument provides a practical self-perception tool to assess emotional leadership, underscoring the importance (...) of empathy, adaptability, and self-knowledge in the training of school principals. The content validity was established through the assessment of 15 experts using Lawshe's formula, which demonstrated the validity of all items and dimensions. The reliability was evaluated through Cronbach's alpha and Omega indices, which yielded values between 0.77 and 0.86 and between 0.79 and 0.87, respectively. These results indicate high reliability for all factors. Construct validity was confirmed through confirmatory factor analysis. (shrink)

The essays in this volume represent an approach to human knowledge that has had a profound influence on many recent thinkers. Popper breaks with a traditional commonsense theory of knowledge that can be traced back to Aristotle. A realist and fallibilist, he argues closely and in simple language that scientific knowledge, once stated in human language, is no longer part of ourselves but a separate entity that grows through critical selection.

The Metaphysics of Knowledge presents the thesis that knowledge is an absolutely fundamental relation, with an indispensable role to play in metaphysics, philosophical logic, and philosophy of mind and language. Knowledge has been generally assumed to be a propositional attitude like belief. But Keith Hossack argues that knowledge is not a relation to a content; rather, it a relation to a fact. This point of view allows us to explain many of the concepts of philosophical logic (...) in terms of knowledge. Hossack provides a theory of facts as structured combinations of particulars and universals, and presents a theory of content as the property of a mental act that determines its value for getting knowledge. He also defends a theory of representation in which the conceptual structure of a content is taken to picture the fact it represents. This permits definitions to be given of reference, truth, and necessity in terms of knowledge. Turning to the metaphysics of mind and language, Hossack argues that a conscious state is one that is identical with knowledge of its own occurrence. This allows us to characterize subjectivity, and, by illuminating the "I"-concept, allows us to gain a better understanding of the concept of a person. Language is then explained in terms of knowledge, as a device used by a community of persons for exchanging knowledge by testimony. The Metaphysics of Knowledge concludes that knowledge is too fundamental to be constituted by something else, such as one's functional or physical state; other things may cause knowledge, but do not constitute it. (shrink)

The doctrine of abstraction is fundamental to the Aristotelian-Thomistic theory of knowledge. The article seeks to present the foundation for this doctrine, from both the epistemological and the ontological points of view, examining the conditions in which abstraction is legitimate, according to its various modes, giving rise to different types of knowledge and grounding the division of the speculative sciences. The analysis is based above all upon the profound analysis of the Angelic Doctor in his commentary on the (...) De Trinitate of Boethius, but also comparing this with other parallel texts in his Opera Omnia. (shrink)

Plato’s Statesman offers us interesting elements of his educational theory; it can be seen as a help towards attaining a greater knowledge of truth. This article begins with a brief introduction to this work, and then presents an analysis of several ideas that appear throughout the text, with a special emphasis on those dealing directly or indirectly with the theme of education and human communication. The article concludes with a summary of the main issues examined in the work.

Heated debates stemming from the confrontation of scientific knowledge with the biblical picture of the creation of man, which had followed the publication of Darwin's theory of evolution, became far less prominent in the second half of the 20th century. This was due to two factors: first, the theory of evolution was partly accepted in theological circles and at the same time biologists showed a growing awareness of the limited epistemological scope of the competence of the natural sciences. This (...) lesson from the history, however, seems to have been forgotten by many who now and again return to controversies which more often than not are caused by ideological quarrels over religion, with true scholarship being too easily lost from sight. The paper reminds some of the history of the controversy in question and suggests that at least some of the current problems regarding evolution˗and˗ creation controversy may have already found their solutions. In part 1, “The Theory of Evolution and the Creation of the Human” it deals with the general issue of human origins. In part 2, “Monogenism and Original Sin” it explores the notion of the ‘first human’ as it is employed in biology and in theology, and shows its completely different meaning in these two realms of knowledge which helps to resolve the recurrent controversy over monogenism. (shrink)

Philosophy and curriculum planning.--The nature and structure of curriculum objectives.--Liberal education and the nature of knowledge.--Realms of meaning and forms of knowledge.--Language and thought.--The forms of knowledge re-visited.--What is teaching?--The logical and psychological aspects of teaching a subject.--Curriculum integration.--Literature and the fine arts as a unique form of knowledge.--The two-cultures, science and moral education.--Morals, religion and the maintained school.

There has been a distinct trend in modern thought to be deeply suspicious and critical of the human mind's ability to gain genuine access to any reality that transcends the world or the mind. As such, much modern reflection on the mind's relationship to a transcendent God has either banished God from the realm of the cognitively accessible or found ways to evacuate God of his transcendence, and reduce God to a concept or idea in the mind. In this book, (...) I directly challenge negative modern understandings of the mind's relationship to God, and advance the provocative claim that the human mind is not "bounded" on the outside but actually remains "open" to the world and to God. As such, the mind is able to know the world and God with varying degrees of objectivity. I turn to Thomas Aquinas in order to explicate as well as defend important claims that Aquinas makes about human cognition as well as our knowledge of God. (shrink)

The article examines some lesser known contributions of Maritain’s thought to Vatican II and to the post-conciliar debate: namely, a focus on philosophical wisdom, the question of truth, the relation between faith and reason, and the realism of human knowledge. Particularly relevant in these themes are Maritain’s reflections contained in a memorandum written to Paul VI, in The Peasant of the Garonne, and in Paul VI’s “Credo of the People of God”, of which one can discern the development and (...) structure proposed by the French philosopher. (shrink)

The Standard View in epistemology is that knowledge is justified, true belief plus something else. This chapter argues that Standard View should be rejected: knowledge does not require justification. The nature of knowledge and the nature of justification can be better understood if we stop viewing justification as one of the necessary conditions for knowledge.

In this note, the problem of tracking random references and rejecting random perturbations in a quadrotor, both generated by an auxiliary system named exosystem, is solved by extending the deterministic tracking problem to the area of stochastic processes. Besides, it is considered that only a part of the state vector of the quadrotor is available through measurements. As a consequence, the state vector of the plant must be estimated in order to close the control loop. On this basis, a controller (...) to track random references and to reject random perturbations is developed by combining a Kalman filter to estimate the references and perturbations of an exosystem and an observer to estimate the states of a quadrotor. Besides, to obtain a more practical controller, the analysis is carried out in discrete time. Numerical simulations are used in a quadrotor to confirm the validity and effectiveness of the proposed control. (shrink)

The anthropological approach is the central focus of this study. Laboratories are looked upon with the innocent eye of the traveller in exotic lands, and the societies found in these places are observed with the objective yet compassionate eye of the visitor from a quite other cultural milieu. There are many surprises that await us if we enter a laboratory in this frame of mind... This study is a realistic enterprise, an attempt to truly represent the social order of life (...) in laboratories and institutes of research, just as they are. By bringing the philosophical issues to the surface as matters not of prejudgement but as matters of concern, Karin Knorr-Cetina has developed the first really positive challenge to the philosophy of science since the days of paradigms and internal definitions of meanings. (shrink)