This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology (...) does not use any of these notions and proposes a more physical treatment of mathematical objects separating the objects from tools used to study them. It both offers a possibility to create new numerical methods using infinities and infinitesimals in floating-point computations and allows one to study certain mathematical objects dealing with infinity more accurately than it is done traditionally. In these notes, we explain that even though both methodologies deal with infinities and infinitesimals, they are independent and represent two different philosophies of Mathematics that are not in a conflict. It is proved that texts :539–555, 2017; Gutman and Kutateladze in Sib Math J 49:835–841, 2008; Kutateladze in J Appl Ind Math 5:73–75, 2011) asserting that the ①-based methodology is a part of non-standard analysis unfortunately contain several logical fallacies. Their attempt to show that the ①-based methodology can be formalized within non-standard analysis is similar to trying to show that constructivism can be reduced to the traditional Mathematics. (shrink)

In this paper I am concerned with an analysis of negative existential sentences that contain proper names only by using negative or neutral free logic. I will compare different versions of neutral free logic with the standard system of negative free logic (Burge, Sainsbury) and aim to defend my version of neutral free logic that I have labeled non-standard neutral free logic.

In the fifth version of our reply article [26] to Imamura's critique, we recall that Neutrosophic Non-Standard Logic was never used by the neutrosophic community in any application, that the quarter-century old (1995-1998) neutrosophic operators criticized by Imamura were never used as they were improved soon after, but omits to talk about their development, and that in real-world applications we need to convert/approximate the hyperreals, monads and bi-nads of Non-Standard Analysis to tiny intervals with the desired precision; (...) otherwise they would be inapplicable. We pointed out several errors and false statements by Imamura [21] regarding the inf/sup of nonstandard subsets, also Imamura's "rigorous definition of neutrosophic logic" is incorrect, as is his definition of nonstandard unit interval, and we showed that there is no total order in Neutrosophic Computing and Machine Learning , Vol. 23, 2022 Florentin Smarandache, Definición mejorada de la lógica neutrosófica no estándar e introducción a los hiperreales neutrosóficos (Quinta versión) 2 the set of hyperreals (due to the recently introduced Neutrosophic Hyperreals which are indeterminate), so the Transfer Principle from R to R* is questionable. After his critique, several reply posts on non-standard theoretical neutrosophy followed in 2018-2022. As such, I extended the Nonstandard Analysis by adding the right-closed left monad, the left-closed right monad, the punctured binad (which we introduced in 1998), and the nonpunctured binad - all in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of the Nonstandard Unitary Interval and Nonstandard Neutrosophic Logic are presented, along with Nonstandard Neutrosophic Operators. (shrink)

In the light of the results obtained during the last two decades in analysis of signals by time series, it has become evident that the tools of non linear dynamics have their elective role of application in biological, and, in particular, in neuro-physiological and psycho-physiological studies. The basic concept in non linear analysis of experimental time series is that one of recurrence whose conceptual counterpart is represented from variedness and variability that are the foundations of complexity in dynamic (...) processes. Thus, the recurrence plots and the Recurrence Quantification Analysis (RQA) are discussed. It is shown that RQA represents the most general and correct methodology in investigation of experimental time series. By it we arrive to inspect the inner structure of the time series connected to the signals under investigation. Linked to RQA we prospect also the method CZF, recently introduced by us. It is able to account for a true estimation of variability of signals in time as well as in frequency domain. And, consequently, it may be used in conjunction with classical Fourier analysis, accounting however that it is inappropriate in analysis of non linear and non stationary experimental time series. The use of CZF method in fractal analysis is also considered in addition to standard index as Hurst exponent. A large field of possible applications in neurological as well as in psycho-physiological studies is given. Also, there are given examples of other and (possibly linked) applications as example the analysis of beat-to-beat fluctuations of human heartbeat intervals that is sovereign in psycho-physiological studies. We give applications on some different planes to evidence the particular sensitivity of such methods. We reach the objective to show that the previously exposed methods are also able to predict in advance the advent of ventricular tachycardia and/or of ventricular fibrillation. The RQA analysis gives good results. The CZF method gives the most excellent results showing that it is able to give very significant indexes of prediction. We also apply such methods in investigation of state anxiety, and proposing in detail a quantum like model of such phenomenological status of the mind. (shrink)

This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.

Does religious belief differ in any interesting way from other kinds of belief? For now, take ‘belief’ to mean how one takes the world to be, on the basis of which they act. Call beliefs like this ‘ordinary beliefs’. There are also more complicated, or abstract, beliefs. Call such beliefs ‘non-ordinary beliefs’. Are religious beliefs different in any significant or interesting way from what we call ‘standard belief’? Our analysis shows that they are not. Although the content of (...) religious belief is different, and sometimes so is the function, religious beliefs are still mental, dispositional attitudes that aim to provide a correct representation of the world. Therefore, religious beliefs are best understood as a sub-category of standard beliefs, alongside ordinary and non-ordinary beliefs. This account of religious belief provides further insight into the meaning of belief and supports a revision of a strict demarcation between standard and non-standard beliefs. (shrink)

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets (...) of reals are Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

Purpose: Due to the increase in energy demand and the effects of global warming, energy-efficient buildings have gained significant importance in the modern construction industry. To create a suitable framework with the aim of reducing energy consumption in the building sector, the external walls of a residential building were considered with two criteria of global warming potential and energy consumption. -/- Design/methodology/approach: In the first stage, to achieve a nearly zero-energy building, energy analysis was performed for 37 different states (...) of thermal insulation. Then, the insulation materials’ life cycle assessment was performed. These results were used to find a set of optimal modes in the Pareto front by using non-dominated sorting genetic algorithm II multi-objective genetic algorithm. Thus, based on the data obtained from this method, it was possible to compare and choose different thermal insulation materials based on the distance from the Pareto front, reducing the environmental effects. -/- Findings: The results showed that replacing the windows was possible to save 3.24% in energy consumption. Also, selecting the proper insulation reduced energy consumption value by 63.13%. Finally, this building can save 69.31% of energy consumption compared to the base building by following the zero-energy building standard. As a result, the Pareto curve was introduced as a guide for the optimal design of the building’s wall insulation. -/- Originality/value: The proposed method provides designers with a framework for latent carbon analysis to access quickly and select optimal scenarios. It can also be used without restrictions for other decisions with different goals and criteria. (shrink)

The Rohingyas, the longest-standing stateless refugees in Malaysia, are continuously denied access to formal education. The UN Refugee Agency and local non-government organizations run learning centers that offer non-formal education to Rohingya children. Existing literature highlights that, in the absence of formal openings, alternative educational programmes remain the main provider of refugee education in Malaysia. This study, using the Inter-Agency Network for Education in Emergencies' five-domain framework, examines the educational standards provided to Rohingya refugees in Malaysia. The findings suggest that (...) most learning centers lack financial, human, and infrastructural resources. Lack of opportunity for secondary schooling makes primary education less worth it. Moreover, prevailing cultural and religious norms make it challenging for Rohingya children (especially girls) to access educational opportunities outside the community. National examinations and academic accreditation for learning are inaccessible to refugees, including Rohingyas. This paper deliberates on some immediate and long-term measures that can potentially address these issues. However, all actors, including UNHCR and the Malaysian government, must collaborate towards formulating a sustainable solution to this critical problem. (shrink)

A study was conducted regarding ways in which higher education institutions can improve ethics. Theoretical frameworks used included: Virtue ethics, deontological and environmental ethics theories. The total sampled written texts were 94. Non-probability sampling was used. The type that was used was online convenience sampling through web scraping. Philosophical assumption that guided this study was interpretivism and the approach was Qualitative. Case study was used as a design and content analysis as a method of data analysis. Some of (...) the findings of the study included but were not limited to the following: Higher education's ethical and professional standards are critical for retaining the trust of students, staff, and the larger society. Institutions that prioritise ethics and standards will be better positioned to carry out their goal and positively impact society. The study recommended the following to Higher education stakeholders: Create faculty-led ethics committees to evaluate and advise on ethical issues such as teaching, research, and academic freedom. Make certain that these committees are composed of a diverse spectrum of faculty members with ethics expertise; Create explicit rules and protocols for using AI, machine learning, and big data ethically in academic research and administrative processes. Address the issues of discrimination, privacy, and accountability in AI applications; and Involve alumni in ethics programs and projects to encourage them to support and contribute to ethical education and research. Create opportunities for alumni to advise students on how to develop ethical professions. (shrink)

Description In this paper, we propose an advanced mathematical framework centered around the Energy Number Field (E), which fundamentally avoids the conventional concept of zero by introducing a neutral ele- ment, νE. Through this approach, we redefine core mathematical constructs, including limits, continuity, differentiation, integration, and series summation, ensuring they operate seamlessly within a zero-less paradigm. We address and redefine matrix operations, topology, metric spaces, and complex analysis, aligning them with the principles of E. Additionally, we explore non-mappable properties (...) of energy numbers in the context of symmetry groups, non-standard fields, fractional calculus, and non-Euclidean geometries. By employing νE as the central element, our framework resolves conventional zero-related sin- gularities and computational anomalies, offering a novel perspective that bridges advanced mathematical theories with practical applications in physics, computational algorithms, and topological transforma- tions. This work paves the way for future research to experimentally validate these formulations and explore potential applications in advanced physics, quantum mechanics, and beyond. (shrink)

-/- A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. -/- Kalish-Montague proposed using vbtos to formalize definite descriptions, set abstracts {x: F}, minimalization in recursive function theory, etc. However, they gave no sematics for vbtos. Hatcher gave a semantics but one that has flaws. We give a correct (...) semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture was later proved independently by the authors and by Newton da Costa. -/- The expression (vy:F) is called a variable bound term (vbt). In case F has only y free, (vy:F) has the syntactic propreties of an individual constant; and under a suitable interpretation of the language vy:F) denotes an individual. By a semantic analysis of vbtos we mean a proposal for amending the standard notions of (1) "an interpretation o f a first -order language" and (2) " the denotation of a term under an interpretation and an assignment", such that (1') an interpretation o f a first -order language associates a set-theoretic structure with each vbto and (2') under any interpretation and assignment each vb t denotes an individual. (shrink)

In book 10 of the Republic we find a new argument for the division of the soul. The argument’s structure is similar to the arguments in book 4 but, unlike those arguments, it centres on a purely cognitive conflict: believing and disbelieving the same thing, at the same time. The argument presents two interpretive difficulties. First, it assumes that a conflict between a belief and an appearance—e.g. disbelieving that a stick partially immersed in water is, as it appears, bent—entails a (...) conflict between beliefs. Prima facie, there is only one belief, the belief that contradicts the appearance. Second, it is unclear what parts of the soul Plato intends to divide between: some argue that it is, as in book 4, a partition between a rational and a non-rational part; others argue that it is a new partition between a higher and a lower subdivision of the rational part. This paper offers solutions to both difficulties through an analysis of what Plato means by φαινόμενα, ‘appearances’, and δόξαι, ‘beliefs’. It is argued, first, that the relevant appearances are entirely sensory but nonetheless sufficiently belief-like to (a) warrant being called δόξαι and (b) oppose, by themselves, our beliefs; there is no need for a third mental state, a belief that assents to the appearance. A second claim concerns a central line in the argument, 602e4–6, that has served as the primary evidence that the partition is within the rational part of the soul. Those who wish to avoid this conclusion generally resort to alternative, and less natural, translations of 602e4–6. It is argued that this is unnecessary: once we have correctly understood sensory appearances, we see that the standard translation of 602e4–6 in fact entails a division between a rational and a non-rational part of the soul. (shrink)

This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to the introduction (...) of infinitesimal probability values, which can be achieved using non-standard analysis. Our solution can be generalized to uncountable sample spaces, giving rise to a Non-Archimedean Probability (NAP) theory. Case 2: Large but finite lotteries. We propose application of the language of relative analysis (a type of non-standard analysis) to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’. -/- The second part presents a case study in social epistemology. We model a group of agents who update their opinions by averaging the opinions of other agents. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. The probability of ending up in an inconsistent belief state turns out to be always smaller than 2%. (shrink)

In this survey, a recent computational methodology paying a special attention to the separation of mathematical objects from numeral systems involved in their representation is described. It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework in all the situations requiring these notions. The methodology does not contradict Cantor’s and non-standard analysis views and is based on the Euclid’s Common Notion no. 5 “The whole is greater (...) than the part” applied to all quantities (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The methodology uses a computational device called the Infinity Computer (patented in USA and EU) working numerically (recall that traditional theories work with infinities and infinitesimals only symbolically) with infinite and infinitesimal numbers that can be written in a positional numeral system with an infinite radix. It is argued that numeral systems involved in computations limit our capabilities to compute and lead to ambiguities in theoretical assertions, as well. The introduced methodology gives the possibility to use the same numeral system for measuring infinite sets, working with divergent series, probability, fractals, optimization problems, numerical differentiation, ODEs, etc. (recall that traditionally different numerals lemniscate; Aleph zero, etc. are used in different situations related to infinity). Numerous numerical examples and theoretical illustrations are given. The accuracy of the achieved results is continuously compared with those obtained by traditional tools used to work with infinities and infinitesimals. In particular, it is shown that the new approach allows one to observe mathematical objects involved in the Hypotheses of Continuum and the Riemann zeta function with a higher accuracy than it is done by traditional tools. It is stressed that the hardness of both problems is not related to their nature but is a consequence of the weakness of traditional numeral systems used to study them. It is shown that the introduced methodology and numeral system change our perception of the mathematical objects studied in the two problems. (shrink)

This paper calls for a re-appraisal of McGee's analysis of the semantics, logic and probabilities of indicative conditionals presented in his 1989 paper Conditional probabilities and compounds of conditionals. The probabilistic measures introduced by McGee are given a new axiomatisation built on the principle that the antecedent of a conditional is probabilistically independent of the conditional and a more transparent method of constructing such measures is provided. McGee's Dutch book argument is restructured to more clearly reveal that it introduces (...) a novel contribution to the epistemology of semantic indeterminacy, and shows that its more controversial implications are unavoidable if we want to maintain the Ramsey Test along with the standard laws of probability. Importantly, it is shown that the counterexamples that have been levelled at McGee's analysis|generating a rather wide consensus that it yields `unintuitive' or `wrong' probabilities for compounds |fail to strike at their intended target; for to honour the intuitions of the counterexamples one must either give up the Ramsey Test or the standard laws of probability. It will be argued that we need to give up neither if we take the counterexamples as further evidence that the indicative conditional sometimes allows for a non-epistemic `causal' interpretation alongside its usual epistemic interpretation. (shrink)

The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with functions assuming infinite and infinitesimal values. It uses recently introduced infinite and infinitesimal numbers being in accordance with the principle ‘The part is less than the whole’ observed in the physical world around us. These numbers have a strong practical advantage with respect to traditional approaches: they are representable at (...) a new kind of a computer – the Infinity Computer – able to work numerically with all of them. An introduction to the theory of physical and mathematical continuity and differentiation (including subdifferentials) for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains is developed in the paper. This theory allows one to work with derivatives that can assume not only finite but infinite and infinitesimal values, as well. It is emphasized that the newly introduced notion of the physical continuity allows one to see the same mathematical object as a continuous or a discrete one, in dependence on the wish of the researcher, i.e., as it happens in the physical world where the same object can be viewed as a continuous or a discrete in dependence on the instrument of the observation used by the researcher. Connections between pure mathematical concepts and their computational realizations are continuously emphasized through the text. Numerous examples are given. (shrink)

A computational methodology called Grossone Infinity Computing introduced with the intention to allow one to work with infinities and infinitesimals numerically has been applied recently to a number of problems in numerical mathematics (optimization, numerical differentiation, numerical algorithms for solving ODEs, etc.). The possibility to use a specially developed computational device called the Infinity Computer (patented in USA and EU) for working with infinite and infinitesimal numbers numerically gives an additional advantage to this approach in comparison with traditional methodologies studying (...) infinities and infinitesimals only symbolically. The grossone methodology uses the Euclid’s Common Notion no. 5 ‘The whole is greater than the part’ and applies it to finite, infinite, and infinitesimal quantities and to finite and infinite sets and processes. It does not contradict Cantor’s and non-standard analysis views on infinity and can be considered as an applied development of their ideas. In this paper we consider infinite series and a particular attention is dedicated to divergent series with alternate signs. The Riemann series theorem states that conditionally convergent series can be rearranged in such a way that they either diverge or converge to an arbitrary real number. It is shown here that Riemann’s result is a consequence of the fact that symbol ∞ used traditionally does not allow us to express quantitatively the number of addends in the series, in other words, it just shows that the number of summands is infinite and does not allows us to count them. The usage of the grossone methodology allows us to see that (as it happens in the case where the number of addends is finite) rearrangements do not change the result for any sum with a fixed infinite number of summands. There are considered some traditional summation techniques such as Ramanujan summation producing results where to divergent series containing infinitely many positive integers negative results are assigned. It is shown that the careful counting of the number of addends in infinite series allows us to avoid this kind of results if grossone-based numerals are used. (shrink)

Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not related to the non-standard analysis) is used to work with finite, infinite, and infinitesimal numbers numerically. This can be done on a new kind of a computer – the Infinity Computer – able to work with all these types of numbers. The new computational tools both give (...) possibilities to execute computations of a new type and open new horizons for creating new mathematical models where a computational usage of infinite and/or infinitesimal numbers can be useful. A number of numerical examples showing the potential of the new approach and dealing with divergent series, limits, probability theory, linear algebra, and calculation of volumes of objects consisting of parts of different dimensions are given. (shrink)

This article argues that the standard model of political representation mischaracterises the structure of representation. After surveying the classical types of representation and their application to non-humans, the basic nature of representation is shown to have been unduly centred on interests, responsiveness and unidirectional protocols. It proposes a different structure by drawing inspiration from recent scholarship and developments in political philosophy, as well as the representation of non-human actors. It proposes an ontological grounding of representation in ‘irreducible multiplicity’, and (...) a structural analysis based on the concepts of claim and relation. This abstract form of representation can take into account both human and non-human cases, and works to ground different typologies. The relational structure of representation creates interests and preferences, subjects and actors, power dynamics and seemingly immutable identities. (shrink)

The paper argues that Toni Rønnow-Rasmussen’s fitting-attitude analysis of ‘good’ and ‘good for’ allows us to interpret and justify Kant’s Formula of Humanity (FH) in a constructive way. His classification of ‘good’ as a non-relational intrinsic final value and ‘good for’ as a relational extrinsic final value sheds light on two main features of FH, namely that it requires us to display a specific attitude to human beings, while also obligating us to recognize this value in the relational dimension. (...) Based on a reflection of what attitudes toward persons are fitting, we might well come to endorse that persons are “ends in themselves” and merit respect and recognition. I then argue (by way of an ethical reading of Kant’s demand to leave the state of nature and move to a rightful civil condition) that we have, in addition to a fitting attitude, deontic normative reasons (not mere pro tanto reasons) for making this very attitude toward persons the principal standard for our relations to others and to ourselves. (shrink)

Buddhist Illogic. The 2nd Century CE Indian philosopher Nagarjuna founded the Madhyamika (Middle Way) school of Mahayana Buddhism, which strongly influenced Chinese, Korean and Japanese (Ch’an or Zen) Buddhism, as well as Tibetan Buddhism. Nagarjuna is regarded by many Buddhist writers to this day as a very important philosopher, who they claim definitively proved the futility of ordinary human cognitive means. His writings include a series of arguments purporting to show the illogic of logic, the absurdity of reason. He considers (...) this the way to verbalize and justify the Buddhist doctrine of “emptiness” (Shunyata). These arguments attack some of the basic tenets and techniques of reasoning, such as the laws of thought (identity, non-contradiction and the excluded middle), conceptualization and predication, our common assumptions of self, entities and essences, as well as our beliefs in motion and causation. The present essay demonstrates the many sophistries involved in Nagarjuna’s arguments. He uses double standards, applying or ignoring the laws of thought and other norms as convenient to his goals; he manipulates his readers, by giving seemingly logical form (like the dilemma) to his discourse, while in fact engaged in non-sequiturs or appealing to doubtful premises; he plays with words, relying on unclear terminology, misleading equivocations and unfair fixations of meaning; and he ‘steals concepts’, using them to deny the very percepts on which they are based. Although a critique of the Madhyamika philosophical interpretation and defense of “emptiness”, Buddhist Illogic is not intended to dissuade readers from Buddhism. On the contrary, its aim to enhance personal awareness of actual cognitive processes, and so improve meditation. It is also an excellent primer on phenomenological epistemology. (shrink)

Davis called for “extreme caution” in the use of non-invasive brain stimulation to treat neurological disorders in children, due to gaps in scientific knowledge. We are sympathetic to his position. However, we must also address the ethical implications of applying this technology to minors. Compensatory trade-offs associated with NIBS present a challenge to its use in children, insofar as these trade-offs have the effect of limiting the child’s future options. The distinction between treatment and enhancement has some normative force here. (...) As the intervention moves away from being a treatment toward being an enhancement—and thus toward a more uncertain weighing of the benefits, risks, and costs—considerations of the child’s best interests diminish, and the need to protect the child’s autonomy looms larger. NIBS for enhancement involving trade-offs should therefore be delayed, if possible, until the child reaches a state of maturity and can make an informed, personal decision. NIBS for treatment, by contrast, is permissible insofar as it can be shown to be at least as safe and effective as currently approved treatments, which are themselves justified on a best interests standard. (shrink)

My goal in this paper is, to tentatively sketch and try defend some observations regarding the ontological dignity of object references, as they may be used from within in a formalized language. -/- Hence I try to explore, what properties objects are presupposed to have, in order to enter the universe of discourse of an interpreted formalized language. -/- First I review Frege′s analysis of the logical structure of truth value definite sentences of scientific colloquial language, to draw suggestions (...) from his saturated vs. unsaturated sentence components paradigm. -/- Next try investigate, in how far reference to non pure math objects might allow for a role as argument of a truth value function. Object kinds to be considered are: common sense objects, technical objects, humanities object kinds (social, psychical, ...), objects of art, ... , be they abstract, concrete, or in this respect mixed objects. -/- Then have a comment on the just referenced label abstract objects. -/- Next try to get an idea wrt the ontological significance of the fact, that pure math objects and functions in some important classical cases can be uniquely defined by means of categorical theories. Here, in the course of my argument, I have a little corollary wrt the standard model of first order Peano arithmetic, reducing the epistemological significance of the existence of the non standard models. -/- Next, wrt a special concept of a formalized empirical theory, I care for whether the impure math objects and mixed objects described here, and complying best with truth value function mapping, are also reliable candidates for the ontological commitment of such theories: and discuss an alternative, which reduces the ontological significance of the universe of discourse of the theories intended models. -/- In the end I sum up what is - from my point of view - the status quo, according to my respective findings. (shrink)

According to strong composition as identity, the logical principles of one–one and plural identity can and should be extended to the relation between a whole and its parts. Otherwise, composition would not be legitimately regarded as an identity relation. In particular, several defenders of strong CAI have attempted to extend Leibniz’s Law to composition. However, much less attention has been paid to another, not less important feature of standard identity: a standard identity statement is true iff its terms (...) are coreferential. We contend that, if coreferentiality is dropped, indiscernibility is no help in making composition a genuine identity relation. To this aim, we analyse as a case study Cotnoir’s theory of general identity, in which indiscernibility is obtained thanks to a revisionary semantics and true identity statements are allowed to connect non-coreferential terms. We extend Cotnoir’s strategy for indiscernibility to the relation of comaternity, and we show that, neither in the case of composition nor in that of comaternity, indiscernibility contibutes to show that they are genuine identity relations. Finally, we compare Cotnoir’s approach with other versions of strong CAI endorsed by Wallace, Bøhn, and Hovda, and canvass the extent to which they violate coreferentiality. The comparative analysis shows that, in order to preserve coreferentiality, strong CAI is forced to adopt a non-standard semantic treatment of the singular/plural distinction. (shrink)

In this paper, I aim to present the main components of my non-standard interpretation of Frege’s views on existence to the English-speaking public. First, I will outline the standard interpretation and show how to a great but not full extent the standard interpretation can be justified on the basis of Frege’s writings. Second, I show that the main error of the standard interpretation consists in the assimilation of the contents of the ordinary language expressions “exist” and (...) “there is” according to Frege. Third, I evaluate possible sources for this unfounded assimilation. After that, I outline my alternative interpretation that distinguishes in opposition to other non-standard interpretations between a substantive and a deflationary part of Frege’s complete conception of existence in analogy to Frege’s analysis of truth and negation. Fifthly, I justify my interpretation by the reconstruction of a so far overlooked master argument of Frege against the above-mentioned assimilation. In the last section, I introduce and discuss five objections against my interpretation that came to my attention. (shrink)

Epistemic injustices are wrongs that agents can suffer in their capacity as knowers. In this article, I offer a conceptualisation of a phenomenon I call anticipatory epistemic injustice, which I claim is a distinct and particularly pernicious type of epistemic injustice worthy of independent analysis. I take anticipatory epistemic injustice to consist in the wrongs that agents can suffer as a result of anticipated challenges in their process of taking up testimony-sharing opportunities. I distinguish my account from paradigmatic cases (...) of epistemic injustice, such as Miranda Fricker’s concepts of testimonial injustice and hermeneutical injustice; additionally, I differentiate my view from Kristie Dotson’s account of testimonial smothering. I argue, ultimately, that anticipatory epistemic injustice is a useful addition to our current taxonomy of epistemic injustices, as it has promising explanatory potential for a range of non-standard cases of epistemic injustice. (shrink)

In recent years, genetically engineered (GE) mosquitoes have been proposed as a public health measure against the high incidence of mosquito-borne diseases among the poor in regions of the global South. While uncertainties as well as risks for humans and ecosystems are entailed by the open-release of GE mosquitoes, a powerful global health governance non-state organization is funding the development of and advocating the use of those bio-technologies as public health tools. In August 2016, the US Food and Drug Agency (...) (FDA) approved the uncaged field trial of a GE Aedes aegypti mosquito in Key Haven, Florida. The FDA’s decision was based on its assessment of the risks of the proposed experimental public health research project. The FDA is considered a global regulatory standard setter. So, its approval of the uncaged field trial could be used by proponents of GE mosquitoes to urge countries in the global South to permit the use of those bio-technologies. -/- From a public health ethics perspective, this paper evaluates the FDA’s 2016 risk assessment of the proposed uncaged field trial of the GE mosquito to determine whether it qualified as a realistic risk evaluation. -/- The FDA’s risk assessment of the proposed uncaged field trial did not proximate the conditions under which the GE mosquitoes would be used in regions of the global South where there is a high prevalence of mosquito-borne diseases. -/- Given that health and disease have political-economic determinants, whether a risk assessment of a product is realistic or not particularly matters with respect to interventions meant for public health problems that disproportionately impact socio-economically marginalized populations. If ineffective public health interventions are adopted based on risk evaluations that do not closely mirror the conditions under which those products would actually be used, there could be public health and ethical costs for those populations. (shrink)

We use imperatives to refute a naïve analysis of update potentials (force-operators attaching to sentences), arguing for a dynamic analysis of imperative force as restrictable, directed, and embeddable. We propose a dynamic, non-modal analysis of conditional imperatives, as a counterpoint to static, modal analyses. Our analysis retains Kratzer's analysis of if-clauses as restrictors of some operator, but avoids typing it as a generalized quantifier over worlds (against her), instead as a dynamic force operator. Arguments for (...) a restrictor treatment (but against a quantificational treatment) are mustered, and we propose a novel analysis of update on conditional imperatives (and an independently motivated revision of the standard ordering-semantics for root modals that makes use of it). Finally, we argue that imperative force is embeddable under an operation much like dynamic conjunction. (shrink)

Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, (...) and so forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

A pressing problem for many non-realist1 theories concerning various specific subject matters is the challenge of making sense of our ordinary propositional attitude claims related to the subject in question. Famously in the case of ethics, to take one example, we have in ordinary language prima facie ascriptions of beliefs and desires involving moral properties and relationships. In the case, for instance, of “Jason believes that Kylie is virtuous”, we appear to have a belief which takes Kylie to be a (...) certain way. If Jason desires that Kylie acts as she ought, he appears to have a desire which has as its content that Kylie perform actions of a certain sort (i.e. the actions that she ought to perform). However, for non-cognitivists in ethics who reject the idea that sentences such as “Kylie is virtuous” or “Kylie acts as she ought” are in the business of making truth-apt claims, or representing that certain moral features are possessed by objects or events, or even, in extreme cases, that such claims express propositions at all, the semantic analysis of the example propositional attitude claims made about Jason will have to be non-standard. (This is merely an application of the well-known “Frege-Geach problem” (see Geach 1965) to the case of embedding moral vocabulary in propositional-attitude ascriptions.). (shrink)

The paper discusses the answering machine puzzle and cases of non-standard uses of ‘I’. It offers an analysis of the phenomena that is conservative with respect to the Kaplanian account of indexicality. The point of departure of the paper is the observation that some proper indexicals have demonstrative uses. It is argued that treating some occurrences of ‘now’ as cases of such uses results in an intuitive and simple solution to the answering machine puzzle. At the same time, (...) treating some occurrences of ‘I’ in an analogous manner explains away the impression that some non-standard uses of ‘I’ enforce a modification of the standard semantics of the first-person pronoun. (shrink)

Abstract: This paper presents a non-standard approach to emergence that describes the foundational stages of the development of emergence, including the factors that initiate the progressive stages of its development. Observing that emergence is a naturally occurring creative process in the universe, the focus of the paper is a strictly realist analysis of the intrinsic qualities of emergence. Emergence brings things into existence, things such as objects, qualities, relations, and systems. The process of emergence develops, becoming increasingly complex (...) as additional factors come to play roles in the process. The paper describes a diagram of the foundational stages of the development of emergence that shows what additional factors initiate the progressive stages of its development. The diagram displays the origins of factors such as the contact relation and the cause relation, among others. Factors that originate in the stages of the foundational development of emergence play roles in the forms of emergence that occur in highly complex situations like geology, biology, sociology, ecology, and cosmology. Understanding the foundational stages of emergence can enhance understanding in all the disciplines. The paper explains how emergence is a component of science based transdisciplinarity. It presents a new paradigm for understanding the intrinsic nature of emergence. The intention is to make the understanding of emergence useful by way of a strictly realist approach based on observation. The goal is to provide scientists with a practical method for the identification and mapping of emergence in systems of interest. (shrink)

Much of contemporary philosophy of mind is marked by a dissatisfaction with the two main positions in the field, standard materialism and standard dualism, and hence with the search for alternatives. My concern in this paper is with two such alternatives. The first, which I will call non-standard materialism, is a position I have defended in a number of places, and which may take various forms. The second, panpsychism, has been defended and explored by a number of (...) recent writers. My main goals are: (a) to explain the differences between these positions; and (b) to suggest that non-standard materialism is more plausible than panpsychism. (shrink)

The primary purpose of depictive works of pornography, we take it, is sexual arousal through sexually explicit representations; what we callprototypical pornography satisfies those aims through the adoption of a ceteris paribus maximally realistic depictive style. Given that the purpose of sexual arousal seems best fulfilled by establishing the most robust connections between the viewer and the depictive subject, we find it curious that not all works of pornography aspire to prototypical status. Accordingly, we target for philosophical scrutiny several non- (...) class='Hi'>standard but putatively pornographic forms: Tijuana Bibles, hentai manga, and slash-fiction. We find that works of these genres possess certain depictively or fictively oriented properties that appear at least prima facie incompatible with prototypical pornography, and thereby to pose two pressing questions that anyprima facie viable analysis of pornography must answer: the depiction question and the fiction question. By answering these questions, we can not only arrive at a deeper understanding of the aims of pornography and the reasons for which significant sub-genres of pornography might diverge from the prototypical ideal, but also perhaps better understand what lies at pornography’s edge, and so better understand the ways in which pornography might relate to what lies beyond. (shrink)

This thesis examines the key moral principles that should govern decision-making by police and military when using lethal force. To this end, it provides an ethical analysis of the following question: Under what circumstances, if any, is it morally justified for the agents of state-sanctioned security institutions to use lethal force, in particular the police and the military? Recent literature in this area suggests that modern conflicts involve new and unique features that render conventional ways of thinking about the (...) ethics of armed conflict, and the use of lethal force, as inadequate or redundant. In particular, there is an increased concern with the moral difficulties created by “non-standard” cases. This is where the police or military are obliged to operate outside their conventional contexts. In such non-standard cases, on what moral basis can (or should) state actors – especially the police and military – use lethal force? One approach argues that there is nothing morally exceptional about the use of lethal force by police or military. This says the only available moral justification for using lethal force is killing in self-defence or defence of others. In contrast, I use an institutional approach to develop a moral framework for the state’s morally exceptional use of lethal force. The institutional approach is concerned with the ends (telos) or purpose of a social institution. It says that the moral purpose of a social institution alters the moral responsibilities of its agents; what is referred to as role morality. My analysis demonstrates that there is an important moral distinction between justified killing in self-defence and state-sanctioned uses of lethal force. My claim is that police and military uses of lethal force are not morally justified in the same way as the average person’s use of lethal force (i.e. self-defence or defence of others). Instead, I argue that the state-sanctioned institutional role of police and military give these state actors special moral duties, and therefore exceptional moral justification, for using lethal force. I argue that the institutional end of the police is the preservation of public safety. This includes using lethal force where it is necessary to protect life and prevent serious injury to jurisdictional inhabitants. In contrast, a morally responsible state uses military force to defend the “common good.” That is, when it is necessary to defend the peaceful functioning of a state from armed threats or other forms of political violence. I then conclude that non-standard cases require the addition of jus ad vim (or the just use of military force short-of-war) as a hybrid element to the moral framework for the state-sanctioned use of lethal force. This provides a better way of applying ethics to the use of military force when defending the common good against serious threats in non-standard cases. This is because jus ad vim complements the conventional military paradigm by permitting the use of military capabilities to defend the common good. But, at the same time, it inhibits the move towards the more destructive levels of violence characteristic of conventional warfighting. (shrink)

Governments standardly deploy a distinction between goods and services in assessing economic health and tracking national income statistics, of which medical goods and services carry significant importance. In what follows we draw on Basic Formal Ontology (BFO) to introduce a third kind of entity called patterns, which help capture the various ways in which goods and services are intertwined and help also to show how many services generate a new kind of non-goods-related products. Patterns are an overlooked yet essential features (...) of many economic sectors including medicine. Studying patterns offers new insights into various components of economic analysis, including outcomes-oriented evaluations of medical services and the value of human capital in the medical sphere. (shrink)

Few views are as widely held as the Standard View of Identity. Here I am concerned with minority views that depart from the standard account. First, I attempt to illuminate such views and the debates concerning them by identifying the principles of identity at issue, articulating some of the assumptions underlying the debates, and presenting some of the evidence used against the Standard View of Identity. Second, I enter two of these debates myself. I first defend two (...) Non-Standard Views of Identity from the charge that they violate a principle of identity, namely the Transitivity of Identity. I then present an overlooked consequence of another Non-Standard View of Identity that challenges the view on one of its own methodological principles. Third, I draw on recent work in ontological and parthood pluralism to show how one might be led to think that there is more than one way of being identical. That is, I show how one might be an identity pluralist. (shrink)

In 1980 F. Wattenberg constructed the Dedekind completion

d of the Robinson non-archimedean field

and established basic algebraic properties of

d [6]. In 1985 H. Gonshor established further fundamental properties of

d [7].In [4] important construction of summation of countable sequence of Wattenberg numbers was proposed and corresponding basic properties of such summation were considered. In this paper the important applications of the Dedekind completion

d in transcendental number theory were considered. We dealing using set theory ZFC
(
-model of ZFC).Given (...) an class of analytic functions of one complex variable f  

z, we investigate the arithmetic nature of the values of fz at transcendental points en, n  .Main results are: (i) the both numbers e
 and e   are irrational, (ii) number ee is transcendental. Nontrivial generalization of the Lindemann- Weierstrass theorem is obtained. (shrink)

We present a technique for the analysis of pattern formation by a class of models for the formation of ocular dominance stripes in the striate cortex of some mammals. The method, which employs the adiabatic approximation to derive a set of ordinary differential equations for patterning modes, has been successfully applied to reaction-diffusion models for striped patterns [1]. Models of ocular dominance stripes have been studied [2,3] by computation, or by linearization of the model equations. These techniques do not (...) provide a rationale for the origin of the stripes. We show here that stripe formation is a non-linear property of the models. Our analysis indicates that stripe selection is closely linked to a property in the dynamics of the models which arises from a symmetry between ipsilateral and contralateral synapses to the visual cortex of a given hemisphere. (shrink)

Sentencing outcomes turn on moral and evaluative determinations. For example, a finding of “irreparable corruption” is generally a precondition for juvenile life without parole. A finding that the “aggravating factors outweigh the mitigating factors” determines whether a defendant receives the death penalty. Should such moral determinations that expose defendants to extraordinary penalties be subject to a standard of proof? A broad range of federal and state courts have purported to decide this issue “in the abstract and without reference to (...) our sentencing case law,” as the Supreme Court recently put it. Kansas v. Carr, 577 U.S. 108, 119 (2016). According to these courts, “it would mean nothing” to ask whether the defendant “deserves mercy beyond a reasonable doubt” or “more-likely-than-not deserves it” because moral questions are not “factual.” Instead, moral determinations are highly subjective “value calls” to which concepts of doubt and certainty do not intelligibly apply. -/- Implicit in these rulings is a controversial view of the nature of moral judgment. This Article traces the contours of the view and argues that it is out of step with the way the broader public thinks about morality and fails to address the issues defendants have raised. Courts should avoid wading into such controversial waters for two reasons. First, the judiciary has historically maintained neutrality on issues of significant public concern. Second, even if moral determinations are not factual, applying a standard of proof to at least some moral decisions at sentencing would change the outcome of the sentencer’s deliberations, and improve the legitimacy of the legal system. For the reasonableness of doubt depends on context; and moral questions—"are you certain the defendant deserves death?”—make salient the stakes relative to which a person should decide what to believe about ordinary empirical matters. On the resulting view, reasonable doubt in the final moral analysis is not just intelligible, but essential for correcting a bias in the structure of the bifurcated criminal trial that systematically disadvantages defendants: the tendency for de-contextualized "factual findings” in the guilt phase to control outcomes at sentencing. (shrink)

The paper proposes (1.) a non-standard interpretation of the proverbial expression “deuteros plous” by giving a fresh look to Phaedo, 99c9-d1. Then (2.) it proceeds to the philosophical problem raised in this passage according to this interpretation, that is, the problem of the “hypothesis” or the “unproved principle”. It indicates finally (3.) the kernel of truth contained in the standard Interpretation and it concludes with some remarks on the “weakness of the logoi”.

I propose an analysis of lying with uninformative speech acts. The orthodox view states that lying is restricted to assertions. However, the growing case for non-assertoric lies made by presuppositions or conventional implicatures challenges this orthodoxy. So far, the only presuppositions to have been considered as lies were informative presuppositions. In fact, uninformative lies were not discussed in the philosophical literature. However, limiting the possibility of lying to informative speech acts is too restrictive. Firstly, I show that standard, (...) uninformative presuppositions can also be lies. Secondly, I extend this picture into uninformative lies made by declarative statements. To implement my proposal, I do not need a new definition of lying. Recently popular commitment-based definitions of lying are able to properly handle uninformative lies. (shrink)

Artificial Intelligence (AI) is already having a major impact on society. As a result, many organizations have launched a wide range of initiatives to establish ethical principles for the adoption of socially beneficial AI. Unfortunately, the sheer volume of proposed principles threatens to overwhelm and confuse. How might this problem of ‘principle proliferation’ be solved? In this paper, we report the results of a fine-grained analysis of several of the highest-profile sets of ethical principles for AI. We assess whether (...) these principles converge upon a set of agreed-upon principles, or diverge, with significant disagreement over what constitutes ‘ethical AI.’ Our analysis finds a high degree of overlap among the sets of principles we analyze. We then identify an overarching framework consisting of five core principles for ethical AI. Four of them are core principles commonly used in bioethics: beneficence, non-maleficence, autonomy, and justice. On the basis of our comparative analysis, we argue that a new principle is needed in addition: explicability, understood as incorporating both the epistemological sense of intelligibility (as an answer to the question ‘how does it work?’) and in the ethical sense of accountability (as an answer to the question: ‘who is responsible for the way it works?’). In the ensuing discussion, we note the limitations and assess the implications of this ethical framework for future efforts to create laws, rules, technical standards, and best practices for ethical AI in a wide range of contexts. (shrink)

Gideon Rosen has recently sketched an argument which aims to establish that the notion of metaphysical modality is systematically ambiguous. His argument contains a crucial sub-argument which has been used to argue for Metaphysical Contingentism, the view that some claims of fundamental metaphysics are metaphysically contingent rather than necessary. In this paper, Rosen’s argument is explicated in detail and it is argued that the most straight-forward reconstruction fails to support its intended conclusion. Two possible ways to save the argument are (...) rebutted and it is furthermore argued that the crucial sub-argument only supports a rather particular variant of Metaphysical Contingentism. (shrink)

There is no uniquely standard concept of an effectively decidable set of real numbers or real n-tuples. Here we consider three notions: decidability up to measure zero [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382], which we abbreviate d.m.z.; recursive approximability [or r.a.; K.-I. Ko, Complexity Theory of Real Functions, Birkhäuser, Boston, 1991]; and decidability ignoring boundaries [d.i.b.; W.C. Myrvold, The decision problem for entanglement, in: (...) R.S. Cohen et al. (Eds.), Potentiality, Entanglement, and Passion-at-a-Distance: Quantum Mechanical Studies fo Abner Shimony, Vol. 2, Kluwer Academic Publishers, Great Britain, 1997, pp. 177–190]. Unlike some others in the literature, these notions apply not only to certain nice sets, but to general sets in Rn and other appropriate spaces. We consider some motivations for these concepts and the logical relations between them. It has been argued that d.m.z. is especially appropriate for physical applications, and on Rn with the standard measure, it is strictly stronger than r.a. [M.W. Parker, Undecidability in Rn: Riddled basins, the KAM tori, and the stability of the solar system, Phil. Sci. 70(2) (2003) 359–382]. Here we show that this is the only implication that holds among our three decidabilities in that setting. Under arbitrary measures, even this implication fails. Yet for intervals of non-zero length, and more generally, convex sets of non-zero measure, the three concepts are equivalent. (shrink)

The aim of this paper is to lay the groundwork for extending the idea of transparent introspection to wishes. First, I elucidate the notion of transparent introspection and highlight its advantages over rival accounts of self-knowledge. Then I pose several problems that seem to obstruct the extension of transparent introspection to wishes. In order to overcome these problems, I call into question the standard propositional attitude analysis of non-doxastic attitudes. My considerations lead to a non-orthodox account of attitudes (...) in general and wishes in particular in light of which the problems presented in Sect. 2 disappear. (shrink)

The relative merits of standard mereology have received quite a bit of attention in recent years from metaphysicians concerned with the part/whole properties of material objects. A question that has not been pursued to the same degree, however, is what sort of semantic repercussions a commitment to mereological sums in the standard sense might have in particular on the predicted behavior of singular terms and our practices of using such terms to refer to objects. The apparent mismatch between (...) our actual referential practices and the persistence conditions attributed to material objects by the supporters of standard mereology puts these philosophers, other things being equal, at a disadvantage compared to those whose ontology matches more closely the observed behavior of singular terms, as they are commonly used in ordinary discourse. To alleviate this problem, David Lewis leans heavily on his distinction between natural and non-natural properties. I argue in this paper that Lewis’ already heavily burdened natural/non-natural distinction among properties is not enough to avoid Quinean indeterminacy for singular terms. Those who are in the business of giving an analysis of constructions involving full-fledged predication, as opposed to the mere spatial overlap of denotations, will thus want to go in for an ontology that places more stringent structural constraints on the referents of singular terms than would be supplied by standard mereology. (shrink)

A study was conducted on ethical leadership in institutions of higher education. Objectives of the study were: (i). Illustrate theories of ethical leadership in higher education institutions; (ii) Determine importance of ethical leadership in higher education institutions; and (iii) Determine challenges facing ethical leadership in institutions of higher learning. The total number of written texts sampled was 32. The researcher employed non-probability sampling. The type employed was online convenience sampling using web scraping. The interpretivism philosophical assumption led this investigation, and (...) the qualitative approach was used. Case study was employed as a design and content analysis as a data analysis tool. The study found out that ethical leadership is essential in higher education institutions because it establishes a solid ethical foundation, fosters an environment of integrity, and contributes to the institutions' long-term success and viability. It acts as a model for all stakeholders, motivating them to follow ethical concepts and values in their academic pursuits and institutional responsibilities. The challenges of ethical leadership in higher education institutions range from fiscal limits to issues about diversity, governance, and technology. It is vital for higher education institutions to address these concerns in order to maintain their integrity and efficiency. Recommendations included but were not limited to the following: (i)Ethical leaders should model the behaviour they expect from their staff and students. Show integrity, honesty, and justice in your acts and decisions; (ii) Establish Clear Ethical Standards: Develop an ethical code or set of fundamental ideas for your educational community. Ensure that these expectations are communicated to all stakeholders, including staff, students, parents, and the general public;(iii). Encourage Open Communication: Create an environment in which faculty and students can express concerns and report unethical behaviour. Encourage transparency and active listening while responding to remarks; and (iv). Ethical Decision-Making Training: Provide leaders and personnel with ethical decision-making training and professional development opportunities. Use case studies and real-life occurrences to help in discussions about ethical quandaries. (shrink)