A ring is said to be clean if every element of the ring can be written as a sum of an idempotent element and a unit element of the ring and a ring is said to be nil-clean if every element of the ring can be written as a sum of an idempotent element and a nilpotent element of the ring. In this paper, we generalize these arguments to symbolic 2-plithogenic structure. We introduce the structure of clean and nil-clean symbolic (...) 2-plithogenic rings and some of its elementary properties are presented. Also, we have found the equivalence between classical clean(nil-clean) ring R and the corresponding symbolic 2-plithogenic ring 2-SPR. (shrink)

The ethics of belief involves an inquiry into what beliefs are legitimate to hold, including religious beliefs. Whatever the criteria determined in such an investigation, adopting a belief that does not meet this criterion is seen as illegitimate and it is considered an ethical violation. English mathematician W. K. Clifford (d. 1879) defines “sufficient evidence” as a criterion in his famous essay, “The Ethics of Belief”. Clifford’s evidence-centered argument becomes one of the most frequent references in the evidentialist objection against (...) theism. It turns out that this argument is not functional in the face of the diversity of beliefs. In this context, different suggestions are presented about what the ethics of belief could be. American philosopher William James (d. 1810), one of the founding names of pragmatism, offers a new proposal. In his classic work, “The Will to Believe”, James claims that Clifford is wrong in seeking the requirement of evidence for all beliefs. Because it is not possible to prove beliefs from the passionate nature of human beings, especially religious beliefs. Following this distinction, James proposes a new criterion for religious beliefs: a religious belief can be vivid or dead, forced or avoidable; and momentous or trivial. If a religious belief is vivid, forced, and momentous, it is necessary to have the courage to believe in it instead of suspending it. James' proposal is often valued as a strong counter-challenge or defense of religious beliefs. However, this argument also has aspects that are open to criticism. One of them is that the will to believe argument concurrently accepts conflicting religious beliefs or, in other words, confronts the issue of religious diversity. According to J. Hick, for example, this argument inevitably results in religious pluralism, even though James does not want to. Contrary to Hick, S. F. Aikin claims that the will to believe does not result in religious pluralism. According to Aikin, who draws attention to the relationship of argument with pragmatism, James obscures religious beliefs and removes them from being claims about truth. Therefore, there is no contradiction in the classical sense. So, which of the objections is valid? Does the will-to-believe argument result in religious pluralism by legitimizing more than one religious belief at the same time, or does it make a purely pragmatic proposition by devaluing religious beliefs? Which religion do I have the right to believe in according to the will to believe? The aim of this article is to provide an answer to the mentioned question. In the article, unlike the current evaluations, it is argued that the argument is closely related to James's theory of knowledge, radical empiricism, not pragmatism as it is usually made. For this purpose, after showing the relationship between the arguments of Clifford and James, the argument will be re-examined in this context and it will be revealed that James has two steps regarding religious beliefs: to make religious beliefs independent from factual beliefs; leaving theism to accept a monistic vision of God and basing religion on mystical experience, which is an emotional experience. As details emerge, it will become clear that James defends a natural religion that excludes traditional religions in his philosophical system and that he defends the beliefs of a humanized religion. With an individual definition of religion based on emotion, James on the one hand ensures the commonality of religious feeling, on the other hand, he makes religion independent from the field of facts. Therefore, with this study, it will be seen that the argument of the will to believe does not aim to legitimize believing in traditional religions, and diversity is not a fundamental problem. (shrink)

R. S. Woolhouse; IV*—Leibniz's Reaction to Cartesian Interaction, Proceedings of the Aristotelian Society, Volume 86, Issue 1, 1 June 1986, Pages 69–82, https:/.

A comparative study of business related values among business students was conducted over the last 10 years in two neighbouring countries. Although Estonia and Finland are culturally related, according to an empirical study of managerial values, including the ethical values of business students, the two countries display significant differences. During the last decade, Estonia has changed from being a country characterised by an authoritarian, centralized, totalitarian state socialism, to a democratic country with a free market economy and different attitudes and (...) values. At the same time Finland has experienced almost a century of capitalism and democracy. It is argued that the differences in values exhibited by these two countries could be explained by using the institutional and historical context. The authors propose a model of value hierarchies in relation to institutionalism. (shrink)

When viewed the history of Islamic thought, it is seen that the scholars have made an effort to understand the nature of the speech of God and make sense of it. Essentially, understanding and grasping of the words of God are an effort to look from the physical realm to the metaphysical one. In spite of this fact, the scholars as the indomitable seekers of truth are in search of finding some clues to say about it. While some of them (...) consider the “divine speech” as an attribute of God, many others view it as a divine act. It is also admitted by all of them that whether being attributive or act of God, the reflection of the divine speech is the Qur’ân. In this sense, three views have been put forward on the question of the belonging of the Qur’ânic words. According to the dominant and preferred point of view among these views, Qur’ân belongs to God in terms of wording and meaning. Accordingly, the revelation of the Qur’ân, which was revealed to the Prophet Mohammed consists of both wording and meaning. Therefore, there is no intervention or contribution of Gabriel or Muhammad in constituting of Qur’ân. According to the second approach, the meaning of Qur’ânic text belongs to God, however, its words pertain to Mohammed. This view signals that Gabriel revealed nothing more than the meanings of Qur’ân. Mohammed understands the meanings conveyed to him and then said them in Arabic expression patterns and phrases. According to the third approach, the meanings of Qur’ânic text belongs to God, however, its words pertain to Gabriel. In other words, only meanings of text were given to Gabriel, and its words are formed by him. In the present study, the mentioned approaches which are put forward by scholars about the belonging of Qur’ânic words will be examined in terms of the integrity of the Qur’ân and Tafsir rumors (riwâyât) of the classical period. In a nutshell, it can be said that there is no disagreement among scholars in the field of the belonging of the meanings of Qur’ânic text to God. The main disagreement is whether the Qur’ânic words belong to God, Gabriel or Muhammad. Considering the integrity of Qur’ân and Tafsir rumors regarding to the circumstances of sending down of the Qur’ânic revelation, it has been determined that the prevailing view is more consistent than the other two views. (shrink)

„My sole purpose in this paper is to try and correct what I take to be a common misinterpretation of Hume’s opinions on mathematics. I shall not enquire whether he was right or wrong in holding these opinions. Nor shall I offer opinions of my own.“.

If educators are to educate they must be accorded some level of trust. Anthony Giddens claims that because trust is not easily created, it is now being replaced with ‘confidence’ because this latter disposition is much easier to give and is more convenient. It is argued in this paper that this shift from trust to confidence stifles education because emphasis is placed solely upon qualifications and competence, and is neglectful of disclosing one’s motives and desires—which are considered to be essential (...) elements for relationships and communities which depend upon trust. Therefore, educators ought to seek to become more trustworthy by going beyond evidence-based practices and codes of ethics, towards articulating a developed personal philosophy of education outlining the ultimate end-purposes to which they aspire. Through such a philosophy, educators identify their ultimate desires and commitments and this self-disclosure can make trust-giving more likely. Demonstrated evidence of achievements and qualifications encourage confidence and this has some value. In addition to these artefacts of evidence, it is argued here that educators must also articulate what they actually desire. This can be understood as John Dewey’s virtue of ‘genuine interest’ which he characterises as being wholehearted, persistent and impartial. For educators, this is often represented in our personal philosophy of education and because it is personal, it is also existential in the sense that it pertains to giving sense, meaning and purpose to all of our activities and way of life for which we are individually responsible and passionately committed to as professionals. As a consequence of being existential, our philosophy and our commitment to it has an intellectual and moral aspect and because it reaches to the very depths of our raison d’être, it pertains to our passion as described by Søren Kierkegaard. This paper shall draw upon Dewey’s notion of wholeheartedness and Kierkegaard’s notion of purity of heart, to make the case that if educators embrace these in their practices, we may become more trustworthy. (shrink)

The article studies two related issues. First, it introduces the notion of the contraposition of quantifiers which is a “dual” notion of symmetry and has similar relations to co-intersectivity as symmetry has to intersectivity. Second, it shows how symmetry and contraposition can be generalised to higher order type quantifiers, while preserving their relations with other notions from generalized quantifiers theory.

Invited talk at the so-called Thursday Lecture, Oct 25, at the Hoger Instituut voor Wijsbegeerte the International Programme at the Institute of Philosophy at the University of Leuven, Belgium. Focus was on the distinction between good and good-for.

R. A. Duff; III*—Socratic Suicide?, Proceedings of the Aristotelian Society, Volume 83, Issue 1, 1 June 1983, Pages 35–48, https://doi.org/10.1093/aristotelian/.

Gottfried Wilhelm Leibniz (1646-1716) was one of the seventeenth century's most important thinkers. A philosopher, mathematician and scientist, his work is comparable in scope and importance only to that of Newton and Descartes. His work dominated German philosophy until Kant, and was revived in the early part of this century when his important work on logic was re-discovered. This four volume set contains 97 of the most important essays ever written about Leibniz's work. The selection has been made to bring (...) out the scope of Leibniz's work in all the areas he wrote upon, as well as its importance to contemporary philosophy and the history of philosophy. It will be an essential reference work for anyone concerned with seventeenth century philosophy and science, as well as to all Leibniz specialists. (shrink)

In this article the contemporary debate between realism and anti-realism in analytical philosophy is analysed and discussed. It is claimed that the nature of the reference relation which holds between language and the world is central in this discussion which has both logical, semantical, and epistemological aspects. In a first part A. Tarski's (semantic) theory of thru th is explained and it is shown how, amongst several theories of truth, Tarski's may be called a realist one. However, a Tarski-style semantics (...) need not lead to a realist theory of Truth and Reference, as is shown in a subsequent part. Here H. Putnam's views on these matters are discussed. It is shown how Putnam in the course of his intellectual history has changed his view from a realist to an anti-realist position. Putnam's arguments show the importance of logical and metalogical issues in the debate. In a final part Putnam's views are criticized and it is shown how a line of argument, analogous to Putnam's, may lead to a realist theory of meaning and reference. (shrink)

The potential benefits of embryonic stem cell research have been clarified by the last ten years of research so that it is necessary to re-examine the foundations for the restrictions imposed on this research. Those who believe that life begins at the moment of fertilization and is imbued with a full complement of human rights have opposed all embryonic research. As one who accepts this premise, I will demonstrate that there are certain limited circumstances in which parents may donate embryos (...) to establish stem cell lines that fully respect the rights of the embryonic person. In these circumstances, their action is morally equivalent to organ donation from a dying child to save the lives of others. (shrink)