We introduce a new axiom scheme for constructive set theory, the Relation Reflection Scheme . Each instance of this scheme is a theorem of the classical set theory ZF. In the constructive set theory CZF–, when the axiom scheme is combined with the axiom of Dependent Choices , the result is equivalent to the scheme of Relative Dependent Choices . In contrast to RDC, the scheme RRS is preserved in Heyting-valued models of CZF– using set-generated frames. We give an (...) application of the scheme to coinductive definitions of classes. (shrink)

Action is not always guided by conscious deliberation; in many circumstances, we act intuitively rather than reflectively. Tamar Gendler (2014) contends that because intuitively guided action can lead us away from our reflective commitments, it limits the power of knowledge to guide action. While I agree that intuition can diverge from reflection, I argue that this divergence does not constitute a restriction on the power of knowledge. After explaining my view of the contrast between intuitive and reflective thinking, this (...) paper argues against the conclusions Gendler draws from empirical work on implicit bias. (shrink)

Human decisions are increasingly supported by decision support systems (DSS). Humans are required to remain “on the loop,” by monitoring and approving/rejecting machine recommendations. However, use of DSS can lead to overreliance on machines, reducing human oversight. This paper proposes “reflection machines” (RM) to increase meaningful human control. An RM provides a medical expert not with suggestions for a decision, but with questions that stimulate reflection about decisions. It can refer to data points or suggest counterarguments that are (...) less compatible with the planned decision. RMs think against the proposed decision in order to increase human resistance against automation complacency. Building on preliminary research, this paper will (1) make a case for deriving a set of design requirements for RMs from EU regulations, (2) suggest a way how RMs could support decision-making, (3) describe the possibility of how a prototype of an RM could apply to the medical domain of chronic low back pain, and (4) highlight the importance of exploring an RM’s functionality and the experiences of users working with it. (shrink)

How should you take into account the opinions of an advisor? When you completely defer to the advisor's judgment, then you should treat the advisor as a guru. Roughly, that means you should believe what you expect she would believe, if supplied with your extra evidence. When the advisor is your own future self, the resulting principle amounts to a version of the Reflection Principle---a version amended to handle cases of information loss. When you count an advisor as an (...) epistemic peer, you should give her conclusions the same weight as your own. Denying that view---call it the ``equal weight view''---leads to absurdity: the absurdity that you could reasonably come to believe yourself to be an epistemic superior to an advisor simply by noting cases of disagreement with her, and taking it that she made most of the mistakes. Accepting the view seems to lead to another absurdity: that one should suspend judgment about everything that one's smart and well-informed friends disagree on, which means suspending judgment about almost everything interesting. But despite appearances, the equal weight view does not have this absurd consequence. Furthermore, the view can be generalized to handle cases involving not just epistemic peers, but also epistemic superiors and inferiors. (shrink)

Gödel initiated the program of finding and justifying axioms that effect a significant reduction in incompleteness and he drew a fundamental distinction between intrinsic and extrinsic justifications. Reflection principles are the most promising candidates for new axioms that are intrinsically justified. Taking as our starting point Tait’s work on general reflection principles, we prove a series of limitative results concerning this approach. These results collectively show that general reflection principles are either weak ) or inconsistent. The philosophical (...) significance of these results is discussed. (shrink)

Individuals’ propensity not to override the first answer that comes to mind is thought to be a crucial cause behind many failures in reasoning. In the present study, we aimed to explore the strategies used and the abilities employed when individuals solve the cognitive reflection test, the most widely used measure of this tendency. Alongside individual differences measures, protocol analysis was employed to unfold the steps of the reasoning process in solving the CRT. This exploration revealed that there are (...) several ways people solve or fail the test. Importantly, 77% of the cases in which reasoners gave the correct final answer in our protocol analysis, they started their response with the correct answer or with a line of thought which led to the correct answer. We also found that 39% of the incorrect responders reflected on their first response. The findings indicate that the suppression of the first answer may not be the only crucial feature of reflectivity in the CRT and that the lack of relevant knowledge is a prominent cause of the reasoning errors. Additionally, we confirmed that the CRT is a multi-faceted construct: both numeracy and reflectivity account for performance. The results can help to better apprehend the “whys and whens” of the decision errors in heuristics and biases tasks and to further refine existing explanatory models. (shrink)

Humans have distinctive powers of reflection: no other animal seems to have anything like our capacity for self-examination. Many philosophers hold that this capacity has a uniquely important guiding role in our cognition; others, notably Hilary Kornblith, draw attention to its weaknesses. Kornblith chiefly aims to dispel the sense that there is anything ‘magical’ about second-order mental states, situating them in the same causal net as ordinary first-order mental states. But elsewhere he goes further, suggesting that there is something (...) deeply misleading about reflection’s first-person view of cognition. This chapter takes a closer look at the conditions under which reflection is misleading. Even if humans are the only reflective animals, we are no longer the only creatures that can be questioned about their claims. Chatbots can also be asked to explain themselves, and by studying the conditions under which they produce clarification as opposed to confabulation, we can develop a non-skeptical account of the epistemic value of reflection. I argue that this capacity naturally supports the distribution of complex problem solving among multiple agents. (shrink)

This paper explores an initially attractive principle connecting beliefs in general with beliefs about what beliefs are rational. The principle turns out to be violated by intuitively rational beliefs in some situations. The paper lays out some options for reacting to this fact.

In their Basic Logic, Sambin, Battilotti and Faggian give a foundation of logical inference rules by reference to certain reflection principles. We investigate the relationship between these principles and the principle of Definitional Reflection proposed by Hallnäs and Schroeder-Heister.

A common line of thought claims that we are responsible for ourselves and our actions, while less sophisticated creatures are not, because we are, and they are not, self-aware. Our self-awareness is thought to provide us with a kind of control over ourselves that they lack: we can reflect upon ourselves, upon our thoughts and actions, and so ensure that they are as we would have them to be. Thus, our capacity for reflection provides us with the control over (...) ourselves that grounds our responsibility. I argue that this thought is subtly, but badly, confused. It uses, as its model for the control that grounds our responsibility, the kind of control we exercise over ordinary objects and over our own voluntary actions: we represent to ourselves what to do or how to change things, and then we bring about that which we represent. But we cannot use this model to explain our responsibility for ourselves and our actions: if there is a question about why or how we are responsible for ourselves and our actions, it cannot be answered by appeal to a sophisticated, self-directed action. There must be some more fundamental account of how or why we are responsible. I replace the usual account with a novel but natural view: responsible mental activity can be modeled, not as an ordinary action, but as the settling of a question. This shift will require abandoning the tempting but troublesome thought that responsible activity involves discretion and awareness—which, I argue, we must abandon in any case. (shrink)

Diachronic Dutch book arguments seem to support both conditionalization and Bas van Fraassen's Reflection principle. But the Reflection principle is vulnerable to numerous counterexamples. This essay addresses two questions: first, under what circumstances should an agent obey Reflection, and second, should the counterexamples to Reflection make us doubt the Dutch book for conditionalization? In response to the first question, this essay formulates a new "Qualified Reflection" principle, which states that an agent should obey Reflection (...) only if he or she is certain that he or she will conditionalize on veridical evidence in the future. Qualified Reflection follows from the probability calculus together with a few idealizing assumptions. The essay then formulates a "Distorted Reflection" principle that approximates Reflection even in cases where the agent is not quite certain that he or she will conditionalize on veridical evidence. In response to the second question, the essay argues that contrary to a common misconception, not all Dutch books dramatize incoherence—some dramatize a less blameworthy sort of epistemic frailty that the essay calls "self-doubt." The distinction between Dutch books that dramatize incoherence and those that dramatize self-doubt cross-cuts the distinction between synchronic and diachronic Dutch books. The essay explains why the Dutch book for conditionalization reveals true incoherence, whereas the Dutch book for Reflection reveals only self-doubt. (shrink)

In this paper we review the most common forms of reflection and introduce a new form which we call sharp‐generated reflection. We argue that sharp‐generated reflection is the strongest form of reflection which can be regarded as a natural generalization of the Lévy reflection theorem. As an application we formulate the principle sharp‐maximality with the corresponding hypothesis. The statement is an analogue of the (Inner Model Hypothesis, introduced in ) which is compatible with the existence (...) of large cardinals. (shrink)

“What do you see when you look at your face in the mirror?” asks J. David Velleman in introducing his philosophical theory of action. He takes this simple act of self-scrutiny as a model for the reflective reasoning of rational agents: our efforts to understand our existence and conduct are aided by our efforts to make it intelligible. Reflective reasoning, Velleman argues, constitutes practical reasoning. By applying this conception, Practical Reflection develops philosophical accounts of intention, free will, and the (...) foundation of morals. This new edition of Practical Reflection contains the original 1989 text along with a new introduction and is the latest entry in The David Hume Series of Philosophy and Cognitive Science Reissues, which keeps in print previously published indispensable works in the area of cognitive science. (shrink)

I examine the relation between logic and nature in terms of ‘reflection’, the word that Hegel uses at the end of theEncyclopaedia Logicto describe the self-sundering or externalization of the idea into nature. Although nominally the term ‘reflection’ seems to denote a uniquely mental process and is often used so by Hegel in his early critique ofReflexionsphilosophie, in his later writings it also has an irreducibly ontological significance. Hegel describes logic's opening-out to nature as a movement of ‘ (...) class='Hi'>reflection’ [Widerschein] and he follows Kant in describing the shift from the finite to the infinite in the relation between nature and thought as one of reflective judgement. Although Hegel generally considers reflection to be uniquely concerned with finite cognition and the constitution of finite things, I argue that in his embrace of reflective judgement he sees a key role for reflection in the relation of logic, nature and spirit. (shrink)

The ‘family consent’ process has been placed at the centre of Chinese clinical practice. Although there has been critical analysis of how the process functions in relation to the autonomy and rights of patients, there has been little examination of the perceptions and attitude of patients and their families and the medical professionals, in relation to moral dilemmas that arise in real cases in the bioethical discourse. When faced with a consent form in an emergency situation, the family member's capacity (...) to act is reduced, as he/she becomes enmeshed in the hospital structure of tacit, socially-imposed rules. In a questionnaires based on a real death case in 2008, 70.9% of the surveyed medical professionals (n = 3,665) disagreed with performing surgery without the consent of the family even if the patient's life was in danger, while 36.6% of the surveyed patients (n = 1,198) hold the same position. This work demonstrates the weakness of the family consent process as a safeguard of patient's autonomy. Finally, I argue that saving the patient's life should be the overriding obligation rather than the respect for the surrogate's autonomous choice at such a decisive moment. (shrink)

In this paper we introduce a recursive notation system O(Π 3 ) of ordinals. An element of the notation system is called an ordinal diagram. The system is designed for proof theoretic study of theories of Π 3 -reflection. We show that for each $\alpha in O(Π 3 ) a set theory KP Π 3 for Π 3 -reflection proves that the initial segment of O(Π 3 ) determined by α is a well ordering. Proof theoretic study for (...) such theories will be reported in [4]. (shrink)

The current study aimed to verify the multidimensional factor structure of teacher reflection and to examine the psychometric properties of a widely used teacher reflection scale using a large-scale representative dataset of 1,611 practicing Iranian English as a Foreign Language teachers. Furthermore, the measurement invariance of the hypothesized, a priori six-factor model of teacher reflection as measured by the adapted scale was assessed across gender and educational degree in Mplus program. In addition, the differences in latent factor (...) means of the same groups were examined. The result of confirmatory factor analysis revealed that teacher reflection was a multidimensional construct, encompassing six underlying factors. Overall, the adapted teacher reflection scale based on the 6-factor model showed an overall good fit. The results also indicated metric and scalar invariance which manifests that the factors underlying the adapted scale had an identical theoretical structure across educational degree/gender groups. Finally, there were significant factor mean differences in reflection components across gender and educational degree groups. A discussion of the results and their implications ensue. (shrink)

We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary reflection, the strong reflection principle, and the existence of square sequences.

This article gives an epistemological analysis of the reflection process by means of which you can come to know the consistency of a mathematical theory that you already accept. It is argued that this process can result in warranted belief in new mathematical principles without justifying them.

Leibniz repeatedly states that there is a very close connection between reflection and rationality. In his view, reflective acts somehow lead to self-consciousness, reason, the knowledge of necessary truths, and even to the moral liability of the respective substances. Whereas it might be relatively easy to see how reflective acts lead to self-consciousness, it is much harder to understand how they are connected to rationality. Why should a substance which is able to produce reflective acts therefore be rational? How (...) can the having of reflective acts be responsible for the substance’s ability to reason correctly and to acquire knowledge of necessary and eternal truths? The aim of my paper is to understand better the required mechanisms and to make thus conceivable Leibniz’s bold claim that reflective acts lead to rationality. In order to accomplish this, I will proceed in three steps. First, I will specify what kind of self-consciousness is, according to Leibniz, produced by reflective acts. A substance must recognize itself as a unitary substance bearing perceptions. Second, I will argue that this type of self- consciousness can be seen as the basis for the ability to form judgments. This is possible because the subject-predicate structure of judgments is mirrored by the ontology of substances and their modifications. Third, I will point out that, together with the idea of identity (which we also acquire by reflection), the combination of judgments allows us to make inferences. This ability, in turn, is sufficient for rationality. Thus, I can explain how reflective acts and rationality are connected with each other. (shrink)

Proof-theoretic reflection principles are schemas which attempt to express the soundness of arithmetical theories within their own language, e.g., ${\mathtt{{Prov}_{\mathsf {PA}} \rightarrow \varphi }}$ can be understood to assert that any statement provable in Peano arithmetic is true. It has been repeatedly suggested that justification for such principles follows directly from acceptance of an arithmetical theory $\mathsf {T}$ or indirectly in virtue of their derivability in certain truth-theoretic extensions thereof. This paper challenges this consensus by exploring relationships between (...) class='Hi'>reflection principles and principles of mathematical and transfinite induction as well as the status of the latter with respect to various foundational characterizations of number theory. (shrink)

A common objection to hierarchical approaches to truth is that they fragment the concept of truth. This paper defends hierarchical approaches in general against the objection of fragmentation. It argues that the fragmentation required is familiar and unprob-lematic, via a comparison with mathematical proof. Furthermore, it offers an explanation of the source and nature of the fragmentation of truth. Fragmentation arises because the concept exhibits a kind of failure of closure under reflection. This paper offers a more precise characterization (...) of the reflection involved, first in the setting of formal theories of truth, and then in a more general setting. (shrink)

How far, if at all, do our intrapersonal and our interpersonal epistemic obligations run in parallel? This paper treats the question as addressing the stability of doxastic commitment in the two dimensions. In the background lies an analogy between doxastic and practical commitment. We’ll pursue the question of doxastic stability by coining a doxastic analogue of Gregory Kavka’s much-discussed toxin case. In this new case, you foresee that you will rationally abandon a doxastic commitment by undergoing a shift in the (...) context in which you doxastically deliberate. The case reveals an important stability condition on doxastic commitment that plays no role in cases modeled on Ulysses and the Sirens, the scenario that has shaped previous attempts to draw an analogy between doxastic and practical commitment. The stability condition thereby revealed is not diachronic -- it does not involve a shift in belief -- but we can construct specifically diachronic cases that reveal an important intrapersonal epistemic obligation. This obligation arises when you expect the shift in belief by ‘projecting’ yourself into a future doxastic context -- thus vindicating a restricted, but only this restricted, application of Bas van Fraassen’s Reflection Principle. Despite some important differences, we can use these diachronic cases as a model for interpersonal cases that reveal an important role for doxastic context in the epistemology of disagreement. But the roles played by projection and context in disagreement ensure that there is no general obligation to be responsive to the opinion of an epistemic peer who disagrees with you. (shrink)

This text includes the interventions of Alfred Schutz at the 1955 Conference on Science, Philosophy, and Religion, entitled “Aspects of Human Equality,” to which his paper, later published as “Equality and the Meaning Structure of the Social World,” had been submitted. In Schutz’s reactions to the comments of other conference participants, one can see his views on: the “secularization” of more theoretical philosophical and theological ideas, the need to distinguish levels of abstraction, the importance of self-reflection on one’s own (...) viewpoint, and the significance of common sense. In the end, he recommends that theoreticians return to kindergartens and playgrounds to examine the equality practiced there. (shrink)

We define , a square principle in the context of , and prove its consistency relative to ZFC by a directed-closed forcing and hence that it is consistent to have hold when κ is supercompact, whereas □κ is known to fail under this condition. The new principle is then extended to produce a principle with a non-reflection property. Another variation on is also considered, this one based on a family of club subsets of . Finally, a new square principle (...) for cardinals, denoted , is introduced. This principle is proved consistent with κ being supercompact. It is shown to yield a non-reflection result similar to that given by □κ. (shrink)

Life satisfaction is widely considered to be a central aspect of human welfare. Many have identified happiness with it, and some maintain that well-being consists largely or wholly in being satisfied with one’s life. Empirical research on well-being relies heavily on life satisfaction studies. The paper contends that life satisfaction attitudes are less important, and matter for different reasons, than is widely believed. For such attitudes are appropriately governed by ethical norms and are perspectival in ways that make the relationship (...) between life satisfaction and welfare far more convoluted than we tend to expect. And the common identification of life satisfaction with happiness, as well as widespread views about the centrality of life satisfaction for well-being, are problematical at best. The argument also reveals an unexpected way in which philosophical ethics can inform scientific psychology: specifically, ethical reflection can help explain empirical results insofar as they depend on people’s values. (shrink)

This paper argues that Samuelson's criticisms of Sraffa mainly concentrated on Sraffa's claim that the propositions of his book (Sraffa 1960) did not depend on the assumption of constant returns to scale. Garegnani's defence of Sraffa against Samuelson's criticisms remained ineffective because Garegnani's own interpretation of Sraffa's prices as classical 'centre of gravitation' or 'long term' prices requires constant returns to scale assumption. The paper goes on to critique Garegnani's interpretation of Sraffa and the classical economics to show that Garegnani's (...) interpretation of Sraffa and the classical economics is highly problematic and that Samuelson's criticism of Sraffa does not hit the target because Sraffa's prices are not necessarily 'equilibrium' prices and therefore there is no need of returns to scale assumption in his theory. (shrink)

Rescorla explores the relation between Reflection, Conditionalization, and Dutch book arguments in the presence of a weakened concept of sure loss and weakened conditions of self‐transparency for doxastic agents. The literature about Reflection and about Dutch Book arguments, though overlapping, are distinct, and its history illuminates the import of Rescorla's investigation. With examples from a previous debate in the 70s and results about Reflection and Conditionalization in the 80s, I propose a way of seeing the epistemic enterprise (...) in the light of practical requirements to be met by demands for synchronic coherence and probability updating policies. This includes a defense of principles rejected by Rescorla, while allowing for the value of his results in the borderland between theories of cognition and formal epistemology. (shrink)

Background Healthcare leader support and facilitation for ethics work are of great importance for healthcare professionals’ handling of ethical issues, moral distress, and quality care provision. A digital tool for ethical reflection in long-term care was developed in response to the demand for appropriate tools. Research aim This study aimed to explore healthcare leaders’ expectations of using a digital tool for ethical reflection among their home nursing care staff. Research design A qualitative research design with vignettes and focus (...) group interviews was used. The data were analyzed using reflexive thematic analysis. Participants and Research Context The sample comprised ten healthcare leaders from municipal long-term care in Norway. Ethical Considerations Participation was voluntary and based on informed consent. The Norwegian Agency for Shared Services in Education and Research approved this study. Findings The analysis resulted in the development of three themes representing leaders’ expectations of the tool: (i) giving staff a voice, (ii) revealing ethics in practice, and (iii) keeping the pot boiling. Discussion Leaders must be informed about the ethical issues experienced to engage in supportive measures for their staff. Digital channels can increase the democratization, safety, and efficiency of communication between employees and leaders and increase awareness of ethical aspects in daily care work. The leaders had positive expectations of employees’ activities and benefits from using the tool for ethical reflection. However, they admitted that realizing the tool’s potential to ensure continuity in ethics work requires considerable organizational and leader involvement. Conclusions This study shows that healthcare leaders are open to digital solutions for managing ethics work in home nursing care. Both opportunities and important prerequisites for successfully implementing the digital tool were identified. (shrink)

There can be no doubt that Kant thought we should be reflective: we ought to care to make up our own minds about how things are and what is worth doing. Philosophical objections to the Kantian reflective ideal have centred on concerns about the excessive control that the reflective person is supposed to exert over her own mental life, and Kantians who feel the force of these objections have recently drawn attention to Kant’s conception of moral virtue as it is (...) developed in his later work, chiefly the Metaphysics of Morals. Melissa Merritt’s book is a distinctive contribution to this recent turn to virtue in Kant scholarship. Merritt argues that we need a clearer, and textually more comprehensive, account of what reflection is, in order not only to understand Kant’s account of virtue, but also to appreciate how it effectively rebuts long-standing objections to the Kantian reflective ideal. (shrink)

Explores the philosophical theology of Alfred North Whitehead.