This article critically examines a recent philosophical debate on the role of values in climate change forecasts, such as those found in assessment reports of the Intergovernmental Panel on Climate Change. On one side, several philosophers insist that the argument from inductive risk, as developed by Rudner and Douglas among others, applies to this case. AIR aims to show that ethical value judgments should influence decisions about what is sufficient evidence for accepting scientific hypotheses that have implications for policy issues. (...) Advocates of extending AIR to climate science claim that values are deeply... (shrink)

Second-order uncertainty, also known as model uncertainty and Knightian uncertainty, arises when decision-makers can (partly) model the parameters of their decision problems. It is widely believed that subjective probability, and more generally Bayesian theory, are ill-suited to represent a number of interesting second-order uncertainty features, especially “ignorance” and “ambiguity”. This failure is sometimes taken as an argument for the rejection of the whole Bayesian approach, triggering a Bayes vs anti-Bayes debate which is (...) in many ways analogous to what the classical vs non-classical debate used to be in logic. This paper attempts to unfold this analogy and suggests that the development of non-standard logics offers very useful lessons on the contextualisation of justified norms of rationality. By putting those lessons to work I will flesh out an epistemological framework suitable for extending the expressive power of standard Bayesian norms of rationality to second- order uncertainty in a way which is both formally and foundationally conservative. Contents. (shrink)

You have higher-order uncertainty iff you are uncertain of what opinions you should have. I defend three claims about it. First, the higher-order evidence debate can be helpfully reframed in terms of higher-order uncertainty. The central question becomes how your first- and higher-order opinions should relate—a precise question that can be embedded within a general, tractable framework. Second, this question is nontrivial. Rational higher-order uncertainty is pervasive, and lies at the foundations (...) of the epistemology of disagreement. Third, the answer is not obvious. The Enkratic Intuition---that your first-order opinions must “line up” with your higher-order opinions---is incorrect; epistemic akrasia can be rational. If all this is right, then it leaves us without answers---but with a clear picture of the question, and a fruitful strategy for pursuing it. (shrink)

The last 20 years or so has seen an intense search carried out within Dempster–Shafer theory, with the aim of finding a generalization of the Shannon entropy for belief functions. In that time, there has also been much progress made in credal set theory—another generalization of the traditional Bayesian epistemic representation—albeit not in this particular area. In credal set theory, sets of probability functions are utilized to represent the epistemic state of rational agents instead of the single probability function of (...) traditional Bayesian theory. The Shannon entropy has been shown to uniquely capture certain highly intuitive properties of uncertainty, and can thus be considered a measure of that quantity. This article presents two measures developed with the purpose of generalizing the Shannon entropy for (1) unordered convex credal sets and (2) possibly non-convex credal sets ordered by second order probability, thereby providing uncertainty measures for such epistemic representations. There is also a comparison with the results of the measure AU developed within Dempster–Shafer theory in a few instances where unordered convex credal set theory and Dempster–Shafer theory overlap. (shrink)

The first round about ‘The myth of ASCOT and its rival ASCO2.T: tech-noetic vs. techno-logic’ exposed the hazard in colliding obsolete disciplinary categories under outdated procedures. The orthodox jurisdiction of Ars Electronica and CERN in Collide@CERN, one of the most prominent ongoing programmes of this kind, does not eliminate the risk of missing the target by operating with categories of artists and scientists. Art is one of those disciplines with a long expired warranty, but with decay on its periphery that (...) is turning into fertile forefront territories. Fresh temporary categories are marking and spreading over these uncharted territories and sensibly interconnecting with peripheries of other disciplines. The ex-artist that is reborn in this peripheral transdisciplinary zone can be provisionally categorized as a polyphibian for its features to be carefully studied. Like amphibians, a polyphibian can coherently transcend from one medium to another, in between and beyond the disciplines. In order to research the implications of such ‘categorical’ mutations, a readymade was submitted to the organization of Collide@CERN under the licence of R. Mutt. Namely, the readymade ASCOTT (Apparatus with Super COnducting Thought Transduction) dubbed also ASCO2.T is needed as the second-order upgrade of the existing plan for ASCOT (Apparatus with Super COnducting Toroids) invented by the scientists for CERN. As is expected from the reputation of R. Mutt’s readymades – this submission was ignored and refused in just the same quiet manner as his most notorious one. But if society would not provide salons for the refused artists (Salon des Refuses) right next to the salons under the scrutiny of academically established artists, there would be no mutations and no evolution in art. Such mutations of the artist into a ‘complex and widely distributed system’ at the dispersing fringes of decomposing art was already predicted by R. Ascott. Polyphibians are the species surviving the ripening metamorphosis of disciplines by taking refuge in the unexplored transdisciplinary buffer zone. This is the only zone where a confrontation of ASCOT technology with tech-noetics of ASCO2.T is possible. The refused unknown demands not a Salon but the Interval of Suspended Judgement. In the sequel to the first round of this debate, the Interval of Suspended Judgement will be investigated. (shrink)

In March 2016, an interdisciplinary group met for two days and two evenings to explore the implications for policy making of second-order science. The event was sponsored by SITRA, the Finnish Parliament's Innovation Fund. Their interest arose from their concern that the well-established ways, including evidence-based approaches, of policy and decision making used in government were increasingly falling short of the complexity, uncertainty, and urgency of needed decision making. There was no assumption that second-order science (...) or second-order cybernetics would reveal any practical possibilities at this early stage of enquiry. On the other hand, some members of the group are practioners in both policy and in facilitating change in sectors of society. Thus, the intellectual concepts were strongly grounded in experience. This is an account of the deliberations of that group and some reflections on what came out of the various shared contributions and ensuing dialogues. The overall conclusion of the event is that there definitely are possibilities that are worthy of further research and exploration. (shrink)

This paper presents a systematic study of the prehistory of the traditional subsystems of second-order arithmetic that feature prominently in the reverse mathematics program of Friedman and Simpson. We look in particular at: (i) the long arc from Poincar\'e to Feferman as concerns arithmetic definability and provability, (ii) the interplay between finitism and the formalization of analysis in the lecture notes and publications of Hilbert and Bernays, (iii) the uncertainty as to the constructive status of principles equivalent (...) to Weak K\"onig's Lemma, and (iv) the large-scale intellectual backdrop to arithmetical transfinite recursion in descriptive set theory and its effectivization by Borel, Lusin, Addison, and others. (shrink)

Context: This conceptual paper tries to tackle the advantages and the limitations that might arise from including second-order science into global climate change sciences, a research area that traditionally focuses on first-order approaches and that is currently attracting a lot of media and public attention. Problem: The high profile of climate change research seems to provoke a certain dilemma for scientists: despite the slowly increasing realization within the sciences that our knowledge is temporary, tentative, uncertain, and far (...) from stable, the public expectations towards science and scientific knowledge are still the opposite: that scientific results should prove to be objective, reliable, and authoritative. As a way to handle the uncertainty, scientists tend to produce “varieties of scenarios” instead of clear statements, as well as reports that articulate different scientific opinions about the causes and dynamics of change for this specific field of research. (shrink)

System security is essential for the operation of the island microgrid. However, the system security is generally threatened due to the presence of physical uncertainties and cyber attacks. In this article, a novel sliding mode load control strategy is proposed for the microgrid to mitigate cyber attacks and physical uncertainties. Firstly, a high-order disturbance observer is designed to estimate the unmeasurable factors in the microgrid. Secondly, a HODO-based sliding mode control strategy is proposed where the estimated value observed by (...) the HODO is applied to the sliding mode surface and control law. It can better guarantee the security of the isolated microgrid. Then, the stability of the HODO-based SMC is demonstrated by Lyapunov stability theory. Finally, simulation results show that the proposed control strategy has excellent control performance. (shrink)

We are often unsure about what we ought to do. This can be because we lack empirical knowledge, such as the extent to which future generations will be harmed by climate change. It can also be because we lack normative knowledge, such as the relative moral importance of the interests of present people and the interests of future people. However, though the question of how one ought to act under empirical uncertainty has been addressed extensively by both economists and (...) philosophers---with expected utility theory providing the standard formal framework---the question of how one ought to act under normative uncertainty is comparatively neglected. My thesis attempts to address this gap. -/- In my thesis I develop a view that I call metanormativism: that there are second-order norms that govern action that are relative to a decision-maker's uncertainty about first-order norms. -/- In the first part of the thesis, I defend one specific metanormative view: that under normative uncertainty decision-makers should maximise expected choice-worthiness, treating normative uncertainty analogously with empirical uncertainty. Drawing on the analogy between decision-making under normative uncertainty and social choice theory, I defend this view at length in response to the problem of merely ordinal theories and the problem of intertheoretic value comparisons. -/- In the second part of the thesis, I explore the implications of metanormativism for other philosophical issues. I argue that it has important consequences regarding the theory of rational action in the face of incomparable values, the causal/evidential debate in decision-theory, and our assessment of the value of moral philosophy. (shrink)

Most ethical decisions are conditioned by formidable uncertainty. Decision makers may lack reliable information about relevant facts, the consequences of actions, and the reactions of other people. Resources for dealing with uncertainty are available from standard forms of decision theory, but successful application to decisions under risk requires a great deal of quantitative information: point-valued probabilities of states and point-valued utilities of outcomes. When this information is not available, this paper recommends the use of a form of decision (...) theory that operates on a bare minimum of information inputs: comparative plausibilities of states and comparative utilities of outcomes. In addition, it proposes a comparative strategy for dealing with second-order uncertainty. The paper illustrates its proposal with reference to a well-known ethical dilemma: Kant’s life-saving lie. (shrink)

A challenge faced by defenders of the precautionary principle is to clarify when the evidence that a harmful event might occur suffices to regard this prospect as a real possibility. Plausible versions of the principle must articulate some epistemic threshold, orde minimisrequirement, which specifies when precautionary measures are justified. Critics have argued that formulating such a threshold is problematic in the context of the precautionary principle. First, this is because the precautionary principle appears to be ambiguous about the distinction between (...) risk and uncertainty: should the principle merely be invoked when evidential probabilities are absent, or also when probabilities have low epistemic credentials? Secondly, defenders of the precautionary principle face an aggregation puzzle: in judging whether or not thede minimisrequirement has been met, how should first-order evidential probabilities and their second-order epistemic standing be aggregated? This article argues that the ambiguity can be resolved, and the epistemological puzzle can be solved. Focusing on decisions in the context of climate uncertainty, I advance a version of the precautionary principle that serves as a plausible decision rule, to be adopted in situations where its main alternative—cost–benefit analysis—does not deliver. (shrink)

In ‘Patients, doctors and risk attitudes,’ Makins argues that, when physicians must decide for, or act on behalf of, their patients they should defer to patient risk attitudes for many of the same reasons they defer to patient values, although with a caveat: physicians should defer to the higher-order desires of patients when considering their risk attitudes. This modification of what Makins terms the ‘deference principle’ is primarily driven by potential counterexamples in which a patient has a first-order (...) desire with one risk attitude (either risk-seeking or averse) and a second-order desire that this risk attitude not be effective in guiding their choices.1 There are two reasons we might think people with obsessive–compulsive disorder (OCD) are particularly relevant patients for evaluating Makins’ proposal. Not only might their first-order risk attitudes be irrational, but many people with OCD also judge their own OCD behaviours to be excessive or unwarranted making them structurally similar to the counterexamples outlined above. Yet, I argue that recent research about risk and decision-making under uncertainty for those with OCD complicates Makins’ proposal by raising questions of whether and to what degree their risk attitudes are irrational such that they should not play a part in the surrogate decisions made by physicians. This places more …. (shrink)

Two types of measures of probabilistic uncertainty are introduced and investigated. Dispersion measures report how diffused the agent’s second-order probability distribution is over the range of first-order probabilities. Robustness measures reflect the extent to which the agent’s assessment of the prior (objective) probability of an event is perturbed by information about whether or not the event actually took place. The properties of both types of measures are investigated. The most obvious type of robustness measure is shown (...) to coincide with one of the major candidates for a dispersion measure, the mean square deviation measure. (shrink)

Our uncertainty about matters of fact can often be adequately represented by probabilities, but there are also cases in which we, intuitively speaking, know too little even to assign meaningful probabilities. In many of these cases, other formal representations can be used to capture some of the prominent features of our uncertainty. This is a non-technical overview of some of these representations, including probability intervals, belief functions, fuzzy sets, credal sets, weighted credal sets, and second order (...) probabilities. (shrink)

Should you always be certain about what you should believe? In other words, does rationality demand higher-order certainty? First answer: Yes! Higher-order uncertainty can’t be rational, since it breeds at least a mild form of epistemic akrasia. Second answer: No! Higher-order certainty can’t be rational, since it licenses a dogmatic kind of insensitivity to higher-order evidence. Which answer wins out? The first, I argue. Once we get clearer about what higher-order certainty is, a (...) view emerges on which higher-order certainty does not, in fact, license any kind of insensitivity to higher-order evidence. The view as I will describe it has plenty of intuitive appeal. But it is not without substantive commitments: it implies a strong form of internalism about epistemic rationality, and forces us to reconsider standard ways of thinking about the nature of evidential support. Yet, the view put forth promises a simple and elegant solution to a surprisingly difficult problem in our understanding of rational belief. (shrink)

A challenge faced by defenders of the precautionary principle is to clarify when the evidence that a harmful event might occur suffices to regard this prospect as a real possibility. Plausible versions of the principle must articulate some epistemic threshold, or de minimis requirement, which specifies when precautionary measures are justified. Critics have argued that formulating such a threshold is problematic in the context of the precautionary principle. First, this is because the precautionary principle appears to be ambiguous about the (...) distinction between risk and uncertainty: should the principle merely be invoked when evidential probabilities are absent, or also when probabilities have low epistemic credentials? Secondly, defenders of the precautionary principle face an aggregation puzzle: in judging whether or not the de minimis requirement has been met, how should first-order evidential probabilities and their second-order epistemic standing be aggregated? This article argues that the ambiguity can be resolved, and the epistemological puzzle can be solved. Focusing on decisions in the context of climate uncertainty, I advance a version of the precautionary principle that serves as a plausible decision rule, to be adopted in situations where its main alternative—cost–benefit analysis—does not deliver. (shrink)

I argue that in order to account for normative uncertainty, an expressivist theory of normative language and thought must accomplish two things: Firstly, it needs to find room in its framework for a gradable conative attitude, degrees of which can be interpreted as representing normative uncertainty. Secondly, it needs to defend appropriate rationality constraints pertaining to those graded attitudes. The first task – finding an appropriate graded attitude that can represent uncertainty – is not particularly problematic. (...) I tackle the second task by exploring whether we can devise expressivist versions of the standard arguments used to support rationality constraints on degrees of uncertainty, Dutch book arguments and accuracy-dominance arguments. I show that we can do so, but that the resulting arguments don’t support the same rationality constraints as the original versions of the arguments. (shrink)

Heath and Tversky (1991, Journal of Risk and Uncertainty 4:5–28) posed that reaction to ambiguity is driven by perceived competence. Competence effects may be inconsistent with ambiguity aversion if betting on own judgement is preferred to betting on a chance event, because judgemental probabilities are more ambiguous than chance events. This laboratory experiment analyses whether ambiguity affects prices and volumes in a double auction market, and contrasts ambiguity aversion to competence effects. In order to test for the presence (...) of competence effects, in the experiment uncertainty is tied to the realisation of events about which the decision maker is more or less knowledgeable. Two experiments are presented: in the first, knowledge is exogenous, whereas in the second the knowledge judgement is endogenous. Market prices provide evidence in favour of the competence hypothesis only when competence is self-assessed. Comparable volumes are observed in both experiments. (shrink)

In this paper, we argue that the characteristics of digital platforms challenge the fundamental assumptions of value sensitive design (VSD). Traditionally, VSD methods assume that we can identify relevant values during the design phase of new technologies. The underlying assumption is that there is onlyepistemic uncertaintyabout which values will be impacted by a technology. VSD methods suggest that one can predict which values will be affected by new technologies by increasing knowledge about how values are interpreted or understood in context. (...) In contrast, digital platforms exhibit a novel form of uncertainty, namely,ontological uncertainty: even with full information and overview, it cannot be foreseen what users or developers will do with digital platforms. Hence, predictions about which values are affected might not hold. In this paper, we suggest expanding VSD methods to account for value dynamism resulting from ontological uncertainty. Our expansions involve (1) extending VSD to the entire lifecycle of a platform, (2) broadening VSD through the addition of reflexivity, i.e. second-order learning about what values to aim at, and (3) adding specific tools of moral sandboxing and moral prototyping to enhance such reflexivity. While we illustrate our approach with a short case study about ride-sharing platforms such as Uber, our approach is relevant for other technologies exhibiting ontological uncertainty as well, such as machine learning, robotics and artificial intelligence. (shrink)

Hierarchical models are commonly used for modelling uncertainty. They arise whenever there is a `correct' or `ideal' uncertainty model but the modeller is uncertain about what it is. Hierarchical models which involve probability distributions are widely used in Bayesian inference. Alternative models which involve possibility distributions have been proposed by several authors, but these models do not have a clear operational meaning. This paper describes a new hierarchical model which is mathematically equivalent to some of the earlier, possibilistic (...) models and also has a simple behavioural interpretation, in terms of betting rates concerning whether or not a decision maker will agree to buy or sell a risky investment for a specified price. We give a representation theorem which shows that any consistent model of this kind can be interpreted as a model for uncertainty about the behaviour of a Bayesian decision maker. We describe how the model can be used to generate buying and selling prices and to make decisions. (shrink)

The Strategic Choice Approach (SCA) is a method meant to deal with operational decision in a strategic way and to manage different sources of uncertainty in decision-making processes. The paper describes how SCA can deal with the future in the specific realm of urban planning in current cities, which represents a typical example of Wicked Problem, taking into account the three different levels of uncertainties that the method aims to manage (Uncertainties about the working Environment, UE; Uncertainties about Related (...) decisions, UR; Uncertainties about guiding Values, UV). We argue that these three types of uncertainties are referred to the ‘ordinary’ problems of modern and contemporary cities. The project of an architectural/urban transformation has to do with this kind uncertainties and implications – in overcoming a series of approvals of different institutional order – and, with this purpose, takes the form of a contract. Instead, this categorisation doesn’t conceive some new and uncertain challenges of future cities, around climate change, infrastructural disruption, insecurity, pandemics, at local and global scales, that are currently under debate in the cities. In this study we suggest that this character of uniqueness can imply the exploration of a new category of uncertainty in the SCA scheme, the ‘uncertainty about disruptive events (UD)’, a type of catastrophic or just unknown in their effects. First of all, we define the PSMs (Problem Structuring Methods) as methods of structuring the «wicked problems». Secondly, we examine the SCA as «a strategic choice process through time», taking into account the three different levels of uncertainty that the method intends to manage. (shrink)

The European Union (EU) is known as the strongest advocate of the liberal global order. It is invested in the idea of rule-based international order, which forms part of its core identity. This adherence to the principles of the liberal global order is visible in its support for multilateral institutions and norms; open market and liberal trade regimes; approaches to security; emphasis on human rights; and democratic norms and values. With the growing uncertainty in the global (...) order, the EU's commitment to the above stated norms has become much more crucial than before. The objective of the study is to understand the shifting dynamics of the liberal world order as it was established at the end of the Second World War and how the EU is responding to these changes. (shrink)

Theoretical approaches to public opinion are hard to find in the sociological literature, with the exception of the seminal work of Jürgen Habermas. One important alternative, although almost unknown in the English-speaking world, is offered in a few contributions by the systems theoretician Niklas Luhmann. Both critical theory and systems theory start from a historical analysis of the conditions that led to the rise of a public sphere and understand its function as the limitation and control of the arbitrariness of (...) power. Critical theory considers the public sphere as a social space where citizens can participate and discuss freely and without constraints. Thus, it legitimizes political power. Systems theory presents a completely different concept of the public sphere and conceives of it in terms of second-order observation. Through public opinion the modern political system observes itself and stimulates as well as limits its decision-making processes. This paper argues that both approaches share the idea that the political system, like every other social subsystem, must generate a system-specific uncertainty in order to limit its own arbitrariness and to be able to develop its decision-making potential. Both approaches locate this uncertainty in the sphere of public opinion. But they radically differ in the way they conceptualize public opinion’s effects on modern politics. Such differences between critical theory and systems theory are illustrated by an analysis of recent political events. (shrink)

Heath and Tversky (1991, Journal of Risk and Uncertainty 4:5–28) posed that reaction to ambiguity is driven by perceived competence. Competence effects may be inconsistent with ambiguity aversion if betting on own judgement is preferred to betting on a chance event, because judgemental probabilities are more ambiguous than chance events. This laboratory experiment analyses whether ambiguity affects prices and volumes in a double auction market, and contrasts ambiguity aversion to competence effects. In order to test for the presence (...) of competence effects, in the experiment uncertainty is tied to the realisation of events about which the decision maker is more or less knowledgeable. Two experiments are presented: in the first, knowledge is exogenous, whereas in the second the knowledge judgement is endogenous. Market prices provide evidence in favour of the competence hypothesis only when competence is self-assessed. Comparable volumes are observed in both experiments. (shrink)

This paper investigates the antidisturbance formation control problem for a class of cluster aerospace unmanned systems suffering from multisource high-dynamic uncertainties. Firstly, to estimate and compensate the uncertainties existing in CAUS coordinate dynamics, an adaptive antidisturbance formation control law, which is combined by a robust adaptive control law and the second order disturbance observer, has been designed. Secondly, aiming at the adverse influences caused by the nonlinear time-varying nonlinearities existing in the formation flight dynamics, the radial basis function (...) neural network is introduced. Furthermore, considering the rapidly varying characteristics of the aforementioned formation flight nonlinearities, a novel board RBFNN has been constructed and utilized to improve the approximation and compensation performance. In virtue of the fusing of the B-RBFNN and the second-order disturbance observer-based adaptive formation control law, the rapid response rate and the higher control accuracy of the formation control system can be achieved. As a result, a novel B-RBFNN-based intelligence adaptive antidisturbance formation control algorithm has been established for CAUS trajectory coordination and formation flight. Numerical simulation results are proposed to illustrate the effectiveness and advantages of the proposed B-RBFNN-based intelligent adaptive formation control method for the CAUS. (shrink)

In the language of second-order logic, first- and second-order variables are distinguished syntactically and cannot be grammatically substituted. According to a prominent argument for the deployment of these languages, these substitution failures are necessary to block the derivation of paradoxes that result from attempts to generalize over predicate interpretations. I first examine previous approaches which interpret second-order sentences using expressions of natural language and argue that these approaches undermine these syntactic restrictions. I then examine (...) Williamson’s primitivist approach according to which second-order sentences are not offered readings in a previously understood language. I argue that the syntactic restrictions alone do not block the derivation of the paradox, unless they are backed by a principled reason that the language cannot be expanded to allow the grammatical substitution of first- and second- order variables. I argue that there is neither a syntactic nor a semantic principle that prohibits such an expansion. (shrink)

The consistency of a second-order version of Morley’s Theorem on the number of countable models was proved in [EHMT23] with the aid of large cardinals. We here dispense with them.

M. Oaksford and N. Chater presented a Bayesian analysis of the Wason selection task in which they proposed that people choose cards in order to maximize expected information gain as measured by reduction in uncertainty in the Shannon-Weaver information theory sense. It is argued that the EIG measure is both psychologically implausible and normatively inadequate as a measure of epistemic utility. The article is also concerned with the descriptive account of findings in the selection task literature offered by (...) Oaksford and Chater. First, it is shown that their analysis data reported in the recent article of K. N. Kirby is unsound; second, an EIG analysis is presented of the experiments of P. Pollard and J. St. B. T. Evans that provides a strong empirical disconfirmation of the theory. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Second GuessingAnonymous OneThis is difficult for me to write because I have tremendous respect for every doctor that has been involved in my son’s care. I firmly believe that they chose and administered the highest level of care that they assessed as appropriate; that they cared for him both personally and professionally as if he were their own child; and that he was in the care of acknowledged (...) giants in their fields. I write this knowing that I will share this narrative with these doctors, in order that they can better understand the decisions I was faced with and the guilt I must live with feeling that I may not have made the best possible informed choice for my son, because of this trust and relationship.Let me describe my oncologist. I say “my” instead of my son’s whose doctor he really is, because he is mine too in every sense of the word. He cares passionately about his work and about my son specifically; he engenders my trust because he is compassionate, brilliant, and available to me for concerns both great and small. His accomplishments have saved lives and will continue to impact his field. He became the narrow bridge I walk, that is the only thing between me and dangerous water and rocks waiting below; the balancing bar on the tightrope that is the only thing that stands to keep me from falling into the abyss and breaking my neck. And this made it difficult for me to disagree with him and seek a second opinion. Because his unspoken words were, “Don’t you trust me that I will do the best for your child?” and I could not answer then what I would answer now, “Nobody is infallible and sometimes we may miss something that someone else can see despite how much we know or care.”It is ironic, I think, that sometimes a layperson, because of her limited knowledge, can see more clearly where a professional may not.My son was diagnosed at age six with Grade II ependymoma in 2006. He was treated with surgery, a complete resection, and then 33 rounds of conformal radiation. He recurred in 2012, and was diagnosed with anaplastic ependymoma Grade III. He had another surgery, with the same surgeons, who pronounced it another successful total resection. This is where my story begins.The MRI taken the next day showed a sliver of something there. My oncologist, much sought after for his diagnostic abilities in reading MRI’s showed slight concern that it may be residual tumor, but both the surgeons and the MRI report came back negative, identifying the sliver as inflammation. Six [End Page 9] weeks later, 3 days before we were scheduled to leave out of town to receive proton beam radiation, I insisted on another MRI. The sliver was enlarged from the post–op MRI. My oncologist said it was tumor; one surgeon said it was inflammation and the other surgeon abstained from speculation. The MRI report stated it appeared to be recurrent tumor.Now here was my dilemma as a parent. The prognosis today of radiation on residual tumor for ependymomas is very bad, especially with a residual tumor of his size. On the other hand, my oncologist felt that going in for surgery with no guarantee of a total resection anyway, was incurring a risk of damage to my child that may impact severely on his quality of life.My oncologist felt that for many medical reasons, inherent risks of surgery, uncertainty about status of the scan reading, quality versus quantity of life, and—I think—an understandably pessimistic view of the possibility of cure for recurrent anaplastic grade III ependymoma, he was against another surgery, and opted to continue with radiation with the tumor as is.I am part of two support groups on line, one for parents of children with any type of brain tumor and the other specific for ependymoma parents. The clinical and anecdotal knowledge of these groups as a whole is phenomenal because, unfortunately, we have parents who have experienced and researched almost everything about this illness, in all its stages. When I was faced... (shrink)

This article deals with scientific advice to the public where the relevant science is subject to public attention and uncertainty of knowledge. It focuses on a tension in the management and presentation of scientific uncertainty between the uncertain nature of science and the expectation that scientific advisers will provide clear public guidance. In the first part of the paper the tension is illustrated by the presentation of results from a recent interview study with nutrition scientists in Denmark. According (...) to the study, nutrition scientists feel their roles as ‘‘public advisers’’ and ‘‘scientists’’ differ in that the former involves an expectation that they will provide unambiguous advice of the kind that might relegate scientific uncertainty to the background. In the second, more general, part of the paper we provide a normative analysis of different strategies of dealing with the tension. The analysis is structured around the extremes of either total concealment or full openness regarding scientific uncertainty. The result of analysis is that scientific advisers should not simply ‘‘feed’’ scientific conclusions to the public. They should rather attempt to promote the ability and willingness of the public to assess and scrutinize scientific knowledge by displaying uncertainties in the scientific basis of advice. On the other hand, scientific advisers must accommodate the public’s need for guidance. Such guidance should be restricted by careful consideration of what it is relevant for the public to know in order to evaluate scientific advice in practical terms. (shrink)

This paper considers two kinds of stochastic reentrant job shop scheduling problems, i.e., the SRJSSP with the maximum tardiness criterion and the SRJSSP with the makespan criterion. Owing to the NP-complete complexity of the considered RJSSPs, an effective differential evolutionary algorithm combined with two uncertainty handling techniques, namely, DEA_UHT, is proposed to address these problems. Firstly, to reasonably control the computation cost, the optimal computing budget allocation technique is applied for allocating limited computation budgets to assure reliable evaluation and (...) identification for excellent solutions or individuals, and the hypothesis test technique is added to execute a statistical comparison to reduce some unnecessary repeated evaluation. Secondly, a reentrant-largest-order-value rule is designed to convert the DEA’s individual to the SRJSSP’s solution. Thirdly, a conventional active decoding scheme for the job shop scheduling problem is extended to decode the solution for obtaining the criterion value. Fourthly, an Insert-based exploitation strategy and an Interchange-based exploration strategy are devised to enhance DEA’s exploitation ability and exploration ability, respectively. Finally, the test results and comparisons manifest the effectiveness and robustness of the proposed DEA_UHT. (shrink)

Second-order logic and modal logic are both, separately, major topics of philosophical discussion. Although both have been criticized by Quine and others, increasingly many philosophers find their strictures uncompelling, and regard both branches of logic as valuable resources for the articulation and investigation of significant issues in logical metaphysics and elsewhere. One might therefore expect some combination of the two sorts of logic to constitute a natural and more comprehensive background logic for metaphysics. So it is somewhat surprising (...) to find that philosophical discussion of secondorder modal logic is almost totally absent, despite the pioneering contribution of Barcan. (shrink)

Recently, Wilcox (JGPS 51: 65–87, 2020) argued against the so-called wide interval view and in favor of the principle of indifference as the correct response to unspecific evidence. Embedded in a formal model of the beliefs of an agent, the former presupposes imprecise probabilities and the latter numerically precise degrees of belief. His argument is illustrated by a thought experiment that comes with a fundamental intuition. According to Wilcox, the wide interval view is incompatible with this intuition and, thus, undermined. (...) In contrast, I show that the intuition behind the thought experiment is, in fact, compatible with the wide interval view if it is embedded into a specific conception of imprecise probabilities as model of belief. This conception is an extension of a framework which I call modified supervaluationism (MSV) and which I recently presented elsewhere (Karge 2021, 175–191). To accommodate the thought experiment’s fundamental intuition, it introduces a notion of second-order beliefs. (shrink)

Stem cell research is a newly emerging technology that promises a wide variety of benefits for humanity. It has, however, also caused much ethical, legal, and theological debate. While some forms of its application were prohibited in the beginning, they have now started to be used in many countries. This fact obliges us to discuss the regulation of stem cell research at national and international level. It is obvious that in order to make regulations and to draw up legislation (...) at national or international levels it helps to know the perspectives of different cultures and faith traditions. In this article the issue is explored from an Islamic perspective. Firstly, some basic information is given about Islam to explain how laws are drawn up and regulations made in this tradition. Secondly, the principles on which the laws and regulations are based are applied to stem cell research, and finally the permitted and prohibited methods of stem cell research are described. The discussions throughout the paper demonstrate that while some ethicists argue that stem cell research is unethical in the Islamic tradition, tradition permits it as long as such research is aimed at improving human health. (shrink)

Both motivational internalism and externalism need to explain why sometimes moral judgments tend to motivate us. In this paper, I argue that Dreier’ second-order desire model cannot be a plausible externalist alternative to explain the connection between moral judgments and motivation. I explain that the relevant second-order desire is merely a constitutive requirement of rationality because that desire makes a set of desires more unified and coherent. As a rational agent with the relevant second-order (...) desire is disposed towards coherence, she will have some motivation to act in accordance with her moral judgments. Dreier’s second-order desire model thus collapses into a form of internalism and cannot be a plausible externalist option to explain the connection between moral judgments and motivation. (shrink)

Quine’s most important charge against second-, and more generally, higher-order logic is that it carries massive existential commitments. The force of this charge does not depend upon Quine’s questionable assimilation of second-order logic to set theory. Even if we take second-order variables to range over properties, rather than sets, the charge remains in force, as long as properties are individuated purely extensionally. I argue that if we interpret them as ranging over properties more reasonably (...) construed, in accordance with an abundant or deflationary conception, Quine’s charge can be resisted. This interpretation need not be seen as precluding the use of model-theoretic semantics for second-order languages; but it will preclude the use of the standard semantics, along with the more general Henkin semantics, of which it is a special case. To that extent, the approach I recommend has revisionary implications which some may find unpalatable; it is, however, compatible with the quite different special case in which the second-order variables are taken to range over definable subsets of the first-order domain, and with respect to such a semantics, some important metalogical results obtainable under the standard semantics may still be obtained. In my final section, I discuss the relations between second-order logic, interpreted as I recommend, and a strong version of schematic ancestral logic promoted in recent work by Richard Heck. I argue that while there is an interpretation on which Heck’s logic can be contrasted with second-order logic as standardly interpreted, when it is so interpreted, its differences from the more modest form of second-order logic I advocate are much less substantial, and may be largely presentational. (shrink)

We examine second order intuitionistic propositional logic, IPC². Let $F_\exists $ be the set of formulas with no universal quantification. We prove Glivenko's theorem for formulas in $F_\exists $ that is, for φ € $F_\exists $ φ is a classical tautology if and only if ¬¬φ is a tautology of IPC². We show that for each sentence φ € $F_\exists $ (without free variables), φ is a classical tautology if and only if φ is an intuitionistic tautology. As (...) a corollary we obtain a semantic argument that the quantifier V is not definable in IPC² from ⊥, V, ^, →. (shrink)

A normative reason for a person to? is a consideration which favours?ing. A motivating reason is a reason for which or on the basis of which a person?s. This paper explores a connection between normative and motivating reasons. More specifically, it explores the idea that there are second-order normative reasons to? for or on the basis of certain first-order normative reasons. In this paper, I challenge the view that there are second-order reasons so understood. I (...) then show that prominent views in contemporary epistemology are committed to the existence of second-order reasons, specifically, views about the epistemic norms governing practical reasoning and about the role of higher-order evidence. If there are no second-order reasons, those views are mistaken. (shrink)

Some recent views of action have claimed that a correct conceptual account of action must include second-order motivational states. This follows from the fact that first-order motivational states such as desires account for action or mere behavior in which the agent's participation is lacking; thus, first-order motivational states cannot by themselves account for action in which the agent participates, so-called full-blooded action. I argue that representing the agent's participation by means of second-order states is (...) bound to fail because it misrepresents what an agent is doing when acting in the full-blooded sense. I begin by characterizing full-blooded action and explaining the failure of first-order accounts to explain it. I next show that while second-order accounts have some success in explaining full-blooded action, they fail to distinguish it from action which exhibits motivational alienation. I then argue that even if this problem were resolved, the second-order accounts more fundamentally misrepresent full-blooded action by depicting such action in an introverted manner. I conclude by considering a sketch of agency and full-blooded action that does not rely on second-order states and by addressing a primary concern thought to favor the second-order accounts, the concern of agent causation. (shrink)

Intuitionistic dependence logic was introduced by Abramsky and Väänänen [1] as a variant of dependence logic under a general construction of Hodges’ (trump) team semantics. It was proven that there is a translation from intuitionistic dependence logic sentences into second order logic sentences. In this paper, we prove that the other direction is also true, therefore intuitionistic dependence logic is equivalent to second order logic on the level of sentences.

Sellars [1960, ‘Grammar and existence: A preface to ontology’] argues that the truth of a second-order sentence does not incur commitment to there being any sort of abstract entity. This paper begins by exploring the arguments that Sellars offers for the above claim. It then develops those arguments by pointing out places where Sellars has been unclear or ought to have said more. In particular, Sellars's arguments rely on there being a means by which language users could come (...) to understand sentences of a second-order language wherein the truth of second-order existential sentences do not require there to be abstract entities. In addition to this, as Sellars [1979, Naturalism and Ontology] notes, a formal account of quantification is required that does not make use of the apparatus of sequences. Both such a translation of and a formal account of quantification are provided in this article. (shrink)

“Second-order Logic” in Anderson, C.A. and Zeleny, M., Eds. Logic, Meaning, and Computation: Essays in Memory of Alonzo Church. Dordrecht: Kluwer, 2001. Pp. 61–76. -/- Abstract. This expository article focuses on the fundamental differences between second- order logic and first-order logic. It is written entirely in ordinary English without logical symbols. It employs second-order propositions and second-order reasoning in a natural way to illustrate the fact that second-order logic is (...) actually a familiar part of our traditional intuitive logical framework and that it is not an artificial formalism created by specialists for technical purposes. To illustrate some of the main relationships between second-order logic and first-order logic, this paper introduces basic logic, a kind of zero-order logic, which is more rudimentary than first-order and which is transcended by first-order in the same way that first-order is transcended by second-order. The heuristic effectiveness and the historical importance of second-order logic are reviewed in the context of the contemporary debate over the legitimacy of second-order logic. Rejection of second-order logic is viewed as radical: an incipient paradigm shift involving radical repudiation of a part of our scientific tradition, a tradition that is defended by classical logicians. But it is also viewed as reactionary: as being analogous to the reactionary repudiation of symbolic logic by supporters of “Aristotelian” traditional logic. But even if “genuine” logic comes to be regarded as excluding second-order reasoning, which seems less likely today than fifty years ago, its effectiveness as a heuristic instrument will remain and its importance for understanding the history of logic and mathematics will not be diminished. Second-order logic may someday be gone, but it will never be forgotten. Technical formalisms have been avoided entirely in an effort to reach a wide audience, but every effort has been made to limit the inevitable sacrifice of rigor. People who do not know second-order logic cannot understand the modern debate over its legitimacy and they are cut-off from the heuristic advantages of second-order logic. And, what may be worse, they are cut-off from an understanding of the history of logic and thus are constrained to have distorted views of the nature of the subject. As Aristotle first said, we do not understand a discipline until we have seen its development. It is a truism that a person's conceptions of what a discipline is and of what it can become are predicated on their conception of what it has been. (shrink)

It seems natural to think of an unwilling addict as having a pattern of preferences that she does not endorse—preferences that, in some sense, she does not ‘identify’ with. Following Frankfurt (1971), Jeffrey (1974) proposed a way of modeling those features of an agent’s preferences by appealing to preferences among preferences.Th„e addict’s preferences are preferences she does not prefer to have. I argue that this modeling suggestion will not do, for it follows from plausible assumptions that a minimally rational agent (...) must prefer those first-order preferences she actually has. I close by considering two different but related ways to think about the initial phenomenon. (shrink)

This dissertation develops an inferentialist theory of meaning. It takes as a starting point that the sense of a sentence is determined by the rules governing its use. In particular, there are two features of the use of a sentence that jointly determine its sense, the conditions under which it is coherent to assert that sentence and the conditions under which it is coherent to deny that sentence. From this starting point the dissertation develops a theory of quantification as marking (...) coherent ways a language can be expanded and modality as the means by which we can reflect on the norms governing the assertion and denial conditions of our language. If the view of quantification that is argued for is correct, then there is no tension between second-order quantification and nominalism. In particular, the ontological commitments one can incur through the use of a quantifier depend wholly on the ontological commitments one can incur through the use of atomic sentences. The dissertation concludes by applying the developed theory of meaning to the metaphysical issue of necessitism and contingentism. Two objections to a logic of contingentism are raised and addressed. The resulting logic is shown to meet all the requirement that the dissertation lays out for a theory of meaning for quantifiers and modal operators. (shrink)