Science, Logic, and Mathematics

Trail-And-Error machines have been proposed by Hintikka and Mutanen as an alternative formulation of the notion of computation. These machines extend the capabilities of the Turing machine and widen the theory of computation.

We review some ideas about the quantum physics of black hole information storage and processing in terms of a general phenomenon of quantum criticality.

In the paper I analyze two features of the genre of the pedagogical. First is a particular usage of “should” statements where one can identify an effect of erasing present normative behavior, while that which is postulated is turned into an unattainable ideal, or a value. Second, I analyze “presumptive tautologies” in the discourse of aims of education. I focus on negative dimensions of these two features and, using theoretical insights from Laclau and Rancière, I connect them to the work (...) of negativity in political ontology so that the relation between the pedagogical and the political can thus be re-articulated. (shrink)

An Introduction to data ethics, focusing on questions of privacy and personal identity in the economic world as it is defined by big data technologies, artificial intelligence, and algorithmic capitalism. -/- Originally published in The Business Ethics Workshop, 3rd Edition, by Boston Acacdemic Publishing / FlatWorld Knowledge.

Regier, Kay, and Khetarpal report the results of computer simulations that cluster color stimuli on the basis of their coordinates in CIELAB space, one of two commonly used perceptual color spaces. Regier and coauthors find partitions of those stimuli that are strikingly similar to the way actual color lexicons partition color space. They do not argue for the custom-made clustering method used in their simulations, nor for the assumption of CIELAB space. The present paper aims to answer the question to (...) what extent their computational results depend on these assumptions. It does this by applying a great variety of known clustering methods to Regier et al.’s stimuli, and by assuming not only CIELAB space but also CIELUV space, the other main color space. (shrink)

Comparativism is the view that comparative beliefs (e.g., believing p to be more likely than q) are more fundamental than partial beliefs (e.g., believing p to some degree x), with the latter explicable as theoretical constructs designed to facilitate reasoning about patterns within systems of comparative beliefs that exist under special conditions. In this paper, I fi rst outline several varieties of comparativism, including two `Ramseyan' varieties which generalise the standard `probabilistic' approaches. I then provide a general critique that applies (...) to any and all comparativist views. Ultimately, there are too many things that we ought to be able to say about partial beliefs that comparativism renders unintelligible. Moreover, there are alternative ways to account for the measurement of belief that need not face the same expressive limitations. (shrink)

Over the past 50 years, philosophers and psychologists have perennially argued for the existence of analog mental representations of one type or another. This study critically reviews a number of these arguments as they pertain to three different types of mental representation: perceptual representations, imagery representations, and numerosity representations. Along the way, careful consideration is given to the meaning of “analog” presupposed by these arguments for analog mental representation, and to open avenues for future research.

The science of logic has occupied an important role in Islamic history. Especially when al-Gazali 505-1111 has come and claimed that who learned Islamic sciences, without learning the Logic we cannot trust in his knowledge. From this time The science of logic has been flourished and quietly began to include in many sciences even Tefsir and Fiqh. After that, Al-razzi 606/1210 has established a big school in Islamic philosophy in general and in logic in particular. al-Khonaji 646/1248 one of his (...) important students. Who moved from Iran to Egypt and became Qadi al-Qudat (Chief Islamic justice). He has improved The science of logic by his books; like Keshf al-Asrar. In the sixth/twelfth one of his books has been spread in Muslim world and became the first step for who wanted to learn Logic. Beside that we have a lot of scholars has made commentaries on this book. In this article we focused on (Metn al-Jumal) by al-Konaji with his spreading in the Sixth. Seventh h.centuries. (shrink)

A work on the philosophy of mathematics (2017) -/- ‘Number’, such a simple idea, and yet it fascinated and absorbed the greatest proportion of human geniuses over centuries, not to mention the likes of Pythagoras, Euclid, Newton, Leibniz, Descartes and countless maths giants like Euler, Gauss and Hilbert, etc.. Einstein thought of pure maths as the poetry of logical ideas, the exactitude of which, although independent of experience, strangely seems to benefit the study of the objects of reality. And, interestingly (...) as well as surprisingly we are nowhere near any clear understandings of numbers despite discoveries of many productive usages of numbers. This is - rightly or wrongly - a humble attempt to approach the subject from an angle hitherto unthought-of. (shrink)

This paper is concerned with a version of Kamp and Partee's account of graded membership that relies on the conceptual spaces framework. Three studies are reported, one to construct a particular shape space, one to detect which shapes representable in that space are typical for certain sorts of objects, and one to elicit degrees of category membership for the various shapes from which the shape space was constructed. Taking Kamp and Partee's proposal as given, the first two studies allowed us (...) to predict the degrees to which people would judge shapes representable in the space to be members of certain categories. These predictions were compared with the degrees that were measured in the third study. The comparison yielded a test of the account of graded membership at issue. The outcome of this test was found to support the conceptual spaces version of Kamp and Partee's account of graded membership. (shrink)

Gentzen’s height measure of the 1938 consistency proof is a cumulative complexity measure for sequents that is measured bottom-up in a derivation. By a factorisation of the ordinal assignment a top-down ordinal assignment can be given that does not depend on information occurring below the sequent to which the ordinal is assigned. Furthermore, an ordinal collapsing function is defined in order to collapse the top-down ordinal to the one assigned by Gentzen’s own ordinal assignment. A direct definition of the factorised (...) assignment follows as a corollary. This extraction of an ordinal collapsing function hopes to provide a formal or conceptual clarification of Gentzen’s ordinal assignment and its height-line argument. (shrink)

I discuss ethical aspects of behavioural policies in domestic energy usage, recycling, food waste and transportation.

Innovative research on decision making under ‘deep uncertainty’ is underway in applied fields such as engineering and operational research, largely outside the view of normative theorists grounded in decision theory. Applied methods and tools for decision support under deep uncertainty go beyond standard decision theory in the attention that they give to the structuring (also called framing) of decisions. Decision structuring is an important part of a broader philosophy of managing uncertainty in decision making, and normative decision theorists can both (...) learn from, and contribute to, the growing deep uncertainty decision support literature. (shrink)

Many edusemiotic writers have begun to closely align edusemitoics to biosemiotics; the basic logic being that, if the life process can be defined through the criterion of semiotic engagement, so can the learning process :373–387, 2006). Thus, the ecological concept of umwelt has come to be a central area of investigation for edusemiotics; allowing theorists to address learning and living concurrently, from the perspective of meaning and significance. To address the conceptual and experiential foundations of the edusemiotic perspective, this paper (...) will focus its attention on the basic semiosic processes that sustain the learner’s primary modelling system or umwelt—the world of meaning and sensory engagement that the organism is immersed in. This focus enables us to identify and explore four basic principles that an ecologically concerned edusemiotic perspective can be said to rest upon; the Iconicity Hypothesis, the Principle of Suprasubjective Relation, the Natural Learning Flow Principle, and the Continuity Principle. The identification and elaboration of these basic philosophical orientations will help establish the importance and relevance of the edusemiotic perspective for educational philosophy and theory in general. This task requires the methodological framework of Sebeok and Danesi’s Modelling Systems Theory, which; provides a biosemiotically grounded approach to understanding the diversity of modelling phenomena across all species, and; contextualizes the specific focus of this study within the broader forms of learning and knowing encompassed by a semiotic theory of learning. Hopefully such attention to the foundational doctrina of this new perspective will encourage more educational research to take what Semetsky has called the edusemiotic turn. (shrink)

This paper considers the foundational role of the contagium vivum fluidum—first proposed by the Dutch microbiologist Martinus Beijerinck in 1898—in the history of virology, particularly in shaping the modern virus concept, defined in the 1950s. Investigating the cause of mosaic disease of tobacco, previously shown to be an invisible and filterable entity, Beijerinck concluded that it was neither particulate like the bacteria implicated in certain infectious diseases, nor soluble like the toxins and enzymes responsible for symptoms in others. He offered (...) a completely new explanation, proposing that the agent was a “living infectious fluid” whose reproduction was intimately linked to that of its host cell. Difficult to test at the time, the contagium vivum fluidum languished in obscurity for more than three decades. Subsequent advances in technologies prompted virus researchers of the 1930s and 1940s—the first to separate themselves from bacteriologists—to revive the idea. They found in it both the seeds for their emerging virus concept and a way to bring hitherto opposing thought styles about the nature of viruses and life together in consensus. Thus, they resurrected Beijerinck as the founding father, and contagium vivum fluidum as the core concept of their discipline. (shrink)

According to Richard Jeffrey’s value-free ideal, scientists should avoid making value judgments about inductive risks by offering explicit representations of scientific uncertainty to decision-makers, who can use these to make decisions according to their own values. Some philosophers have responded by arguing that higher-order inductive risks arise in the process of producing representations of uncertainty. This chapter explores this line of argument and its limits, arguing that the Jeffreyan value-free ideal is achievable in contexts where methodological decisions introduce minimal higher-order (...) uncertainty and where communications of uncertainty are unlikely to be manipulated or misunderstood by scientists or decision-makers. This chapter illustrates the limits of the Jeffreyan ideal with reference to climate science and argues that the context of climate science is not conducive to the Jeffreyan ideal, so the argument that climate modeling is value-laden due to higher-order inductive risks withstands recent criticisms. (shrink)

This paper discusses ethical issues surrounding Integrated Assessment Models (IAMs) of the economic effects of climate change, and how climate economists acting as policy advisors ought to represent the uncertain possibility of catastrophe. Some climate economists, especially Martin Weitzman, have argued for a precautionary approach where avoiding catastrophe should structure climate economists’ welfare analysis. This paper details ethical arguments that justify this approach, showing how Weitzman’s “fat tail” probabilities of climate catastrophe pose ethical problems for widely used IAMs. The main (...) claim is that economists who ignore or downplay catastrophic risks in their representations of uncertainty likely fall afoul of ethical constraints on scientists acting as policy advisors. Such scientists have duties to honestly articulate uncertainties and manage (some) inductive risks, or the risks of being wrong in different ways. (shrink)

I illustrate with three classical examples the mistakes arising from using a modal operator admitting multiple interpretations in the same argument; the flaws arise especially easily if no attention is paid to the range of propositional variables. Premisses taken separately might seem convincing and a substitution for a propositional variable in a modal context might seem legitimate. But there is no single interpretation of the modal operators involved under which all the premisses are plausible and the substitution successful.

While some form of evaluation has always been employed in science (e.g. peer review, hiring), formal systems of evaluation of research and researchers have recently come to play a more prominent role in many countries because of the adoption of new models of governance. According to such models, the quality of the output of both researchers and their institutions is measured, and issues such as eligibility for tenure or the allocation of public funding to research institutions crucially depends on the (...) outcomes of such measures. However, concerns have been raised over the risk that such evaluation may be threatening epistemic pluralism by penalizing the existent heterodox schools of thought and discouraging the pursuit of new ones. It has been proposed that this may happen because of epistemic bias favouring mainstream research programmes. In this paper, I claim that (1) epistemic pluralism is desirable and should be preserved; (2) formal evaluation exercises may threaten epistemic pluralism because they may be affected by some form of epistemic bias; therefore, (3) to preserve epistemic pluralism, we need some strategy to actively dampen epistemic bias. (shrink)

There are three slogans in the history of Socialism that are very close in wording, viz. the famous Cabet-Blanc-Marx slogan: "From each according to his ability; To each according to his needs"; the earlier Saint-Simon-Pecqueur slogan: "To each according to his ability; To each according to his works"; and the later slogan in Stalin’s Soviet Constitution: "From each according to his ability; To each according to his work." We will consider the following questions regarding these slogans: a) What are the (...) earliest occurrences of each of these slogans? b) Where does the inspiration for each half of each slogan come from? c) What do the Saint-Simonians mean by “To each according to his ability”? d) What do they mean by “To each according to his works”? e) What motivates the shift from “To each according to his ability” to “From each according to his ability”? f) How should we envisage the progression toward “To each according to his needs”? g) What is the distinction between from “To each according to his works” and “To each according to his work”? (shrink)

This response to Shankman’s 2018 concedes some points, corrects others, and emphasizes the importance of error to the progress of science.

Utilitarianism, it has been said, is not sensitive to the distribution of welfare. In making risky decisions for others there are multiple sensitivities at work. I present examples of risky decision-making involving drug allocations, charitable giving, breast-cancer screening and C-sections. In each of these examples there is a different sensitivity at work that pulls away from the utilitarian prescription. Instances of saving fewer people at a greater risk to many is more complex because there are two distributional sensitivities at work (...) that pull in opposite directions from the utilitarian calculus. I discuss objections to these sensitivities and conclude with some reflections on the value of formal modelling in thinking about societal risk. (shrink)

Many liberals and secularists believe that religious schooling should not be publicly funded or that it should simply be banned. Challenging those views, I claim that although liberal states may refuse to fund and may even ban certain illiberal separate religious schools, it is impermissible, for distinctively liberal reasons, to completely ban publicly funded religious schooling. I will however argue that providing religious instruction within common public schools is more desirable than having separate religious schools. I argue that providing religious (...) instruction within common public schools is a better way to balance the educational interests of parents, children and society than banning religious schooling altogether; authorizing it but refusing to fund it; or having publicly funded separate religious schools. (shrink)

This article presents the promising framework for educational decision makers developed by Brighouse, Ladd, Loeb, and Swift. The framework consists of an account of the educational goods, distributional principles and independent values at stake in education, and a method for making policy decisions on the basis of these and solid social science. I present three criticisms of this approach. The first says that the derivation of educational goods proceeds on the basis of a too narrow conception of values. I suggest (...) that this foundation should consist of an overlapping consensus, rather than flourishing. The second criticism has to do with the way that the distributive principles are characterized. I argue that BLLS’s characterization of distributive principles should be complemented with accounts of what domains of social life these principles regulate and a specification of whether the distributive principles should be understood as applying over time or at specific instances. The final criticism is that BLLS’s conception of independent values focuses solely on values that constrain the pursuit of educational goods. I claim that this part of the framework should be revised to include aspects of values that also support this pursuit. I conclude arguing that the BLLS frameworks should be further developed rather than rejected. (shrink)

Predicate approaches to modality have been a topic of increased interest in recent intensional logic. Halbach and Welch :71–100, 2009) have proposed a new formal technique to reduce the necessity predicate to an operator, demonstrating that predicate and operator methods are ultimately compatible. This article concerns the question of whether Halbach and Welch’s approach can provide a uniform formal treatment for intensionality. I show that the monotonicity constraint in Halbach and Welch’s proof for necessity fails for almost all possible-worlds theories (...) of knowledge. The nonmonotonicity results demonstrate that the most obvious way of emulating Halbach and Welch’s rapprochement of the predicate and operator fails in the epistemic setting. (shrink)