What can rational deliberation indicate about belief? Belief clearly influences deliberation. The principle that rational belief is stake-invariant rules out at least one way that deliberation might influence belief. The principle is widely, if implicitly, held in work on the epistemology of categorical belief, and it is built into the model of choice-guiding degrees of belief that comes to us from Ramsey and de Finetti. Criticisms of subjective probabilism include challenges to the assumption of additive values (the package (...) principle) employed by defenses of probabilism. But the value-interaction phenomena often cited in such challenges are excluded by stake-invariance. A comparison with treatments of categorical belief suggests that the appeal to stake-invariance is not ad hoc. Whether or not to model belief as stake-invariant is a question not settled here. (shrink)

The idea that beliefs may be stake-sensitive is explored. This is the idea that the strength with which a single, persistent belief is held may vary and depend upon what the believer takes to be at stake. The stakes in question are tied to the truth of the belief—not, as in Pascal’s wager and other cases, to the belief’s presence. Categorical beliefs and degrees of belief are considered; both kinds of account typically exclude the idea and treat belief (...) as stake-invariant , though an exception is briefly described. The role of the assumption of stake-invariance in familiar accounts of degrees of belief is also discussed, and morals are drawn concerning finite and countable Dutch book arguments. (shrink)

The value of knowledge can vary in that knowledge of important facts is more valuable than knowledge of trivialities. This variation in the value of knowledge is mirrored by a variation in evidential standards. Matters of greater importance require greater evidential support. But all knowledge, however trivial, needs to be evidentially certain. So on one hand we have a variable evidential standard that depends on the value of the knowledge, and on the other, we have the invariant standard of (...) evidential certainty. This paradox in the concept of knowledge runs deep in the history of philosophy. We approach this paradox by proposing a bet settlement theory of knowledge. Degrees of belief can be measured by the expected value of a bet divided by stake size, with the highest degree of belief being probability 1, or certainty. Evidence sufficient to settle the bet makes the expectation equal to the stake size and therefore has evidential probability 1. This gives us the invariant evidential certainty standard for knowledge. The value of knowledge relative to a bet is given by the stake size. We propose that evidential probability can vary with stake size, so that evidential certainty at low stakes does not entail evidential certainty at high stakes. This solves the paradox by allowing that certainty is necessary for knowledge at any stakes, but that the evidential standards for knowledge vary according to what is at stake. We give a Stake Size Variation Principle that calculates evidential probability from the value of evidence and the stakes. Stake size variant degrees of belief are probabilistically coherent and explain a greater range of preferences than orthodox expected utility theory, namely the Ellsberg and Allais preferences. The resulting theory of knowledge gives an empirically adequate, rationally grounded, unified account of evidence, value and probability. (shrink)

What is a duty of justice? And how is it different from a duty of beneficence? We need a clear account of the contrast. Unfortunately, there is no consensus in the philosophical literature as to how to characterize it. Different articulations of it have been provided, but it is hard to identify a common core that is invariant across them. In this paper, I propose an account of how to understand duties of justice, explain how it contrasts with several (...) proposals as to how to distinguish justice and beneficence, respond to some objections and suggest further elaborations of it. The conceptual exploration pursued in this paper has practical stakes. A central aim is to propose and defend a capacious concept of justice that makes a direct discussion of important demands of justice (domestic and global) possible. Duties of justice can be positive besides negative, they can be imperfect as well as perfect, they can range over personal besides institutional contexts, they can include multiple associative reasons such us non-domination, non-exploitation and reciprocity, and they can even go beyond existing national, political, and economic associative frameworks to embrace strictly universal humanist concerns. We should reject ideological abridgments of the concept of justice that render these possibilities, and the important human interests and claims they may foster, invisible. (shrink)

Thomas Blackson argues that interest-relative epistemologies cannot explain the irrationality of certain choices when the agent has three possible options. I argue that his examples only refute a subclass of interest-relative theories. In particular, they are good objections to theories that say that what an agent knows depends on the stakes involved in the gambles that she faces. But they are not good objections to theories that say that what an agent knows depends on the odds involved in the gambles (...) that she faces. Indeed, the latter class of theories does a better job than interest-invariant epistemologies of explaining the phenomena he describes. (shrink)

Over the years I’ve written many papers defending an idiosyncratic version of interest-relative epistemology. This book collects and updates the views I’ve expressed over those papers. -/- Interest-relative epistemologies all start in roughly the same way. A big part of what makes knowledge important is that it rationalises action. But for almost anything we purportedly know, there is some action that it wouldn’t rationalise. I know what I had for breakfast, but I wouldn’t take a bet at billion to one (...) odds about it. Knowledge has practical limits. The first idiosyncratic feature of my version of interest-relative epistemology is how those limits are identified. Other interest-relative philosophers typically say that the limits have to do with stakes; in high stakes situations knowledge goes away. That’s no part of my view. I think knowledge goes away in long odds situations. High stakes situations are almost always are long odds situations, for reasons to do with the declining marginal utility of money. But the converse isn’t true. On my view, knowledge often goes away in cases where it is trivial to check before action. This idea, that interests matter in long odds cases, and not just in high stakes cases, is the main constant in what I’ve written on interest-relativity over the years. -/- But there are three other respects in which the view I’m going to set out and defend in this book is very different from the view I set out in older papers. -/- I used to identify the practical limits on knowledge with cases where relying on the purported knowledge would get the wrong answer. I focused, that is, on the outputs of inquiry. Knowledge goes away if relying on it would lead one to make a mistake. I now think I was looking at the wrong end of inquiry. Knowledge goes away if the thinker starts conducting an inquiry where the purported knowledge is an inappropriate starting point, and inappropriate for the special reason that it might be false. Now one way we can tell that something is a bad starting point is that starting there will mean we end up at the wrong place. But it’s not the only way. Sometimes a bad starting point will lead to the right conclusion for the wrong reasons. As the Nyāya philosophers argued, rational inquiry starts with knowledge. If it would be irrational to start this inquiry with a particular belief, that belief isn’t knowledge. -/- Not all inquiries are practical inquiries, but many are. And practical inquiries are usually going to be at the center of attention in this book. But what is someone trying to figure out when they conduct a practical inquiry? I used to think that they were trying to figure out which option maximised expected utility, and to a first approximation identified knowledge with those things one could conditionalise on without changing the option that maximised expected utility. As noted in the previous paragraph, I no longer think that we can identify knowledge with what doesn’t change our verdicts. But more importantly, I no longer think that expected utility maximisation is as central to practical inquiry as I once did. There are some theoretical reasons from game theory that raise some doubts about expected utility maximisation. Weak dominance reasoning is part of our theory of rational choice, and can’t be modelled as expected utility maximisation. Perhaps some kinds of equilibrium seeking are parts of practical inquiry, and can’t be modelled as expected utility maximisation. But there are also very practical reasons to think that practical inquiry doesn’t aim at expected utility maximisation. When there are a lot of very similar options - think about selecting a can from a supermarket shelf - and it’s more trouble than it’s worth to figure out which of them maximises expected utility, it’s best to ignore the differences between them and just pick. As I’ll argue in Chapter 6, this makes a big difference to how interests and knowledge interact. -/- In the version of interest-relativity that I’m defending here, everything in epistemology is interest-relative. Knowledge, rational belief, and evidence are all interest-relative. But they are all interest-relative in slightly different ways. The main aim here is to defend the interest-relativity of knowledge. A common objection to interest-relative theories of knowledge is that they can’t be extended into theories of all the things we care about in epistemology. Here I try to meet that challenge. The way I do so is a little messy. It would be nice if there was some part of epistemology that’s interest-invariant, as I used to think, or if all the interest-relative notions were interest-relative in the same way, as other interest-relative epistemologists argue. For better or worse, that’s not the view I’m defending. Interests matter throughout epistemology, and we just have to go case by case to figure out how and why they matter. (shrink)

Although the invariance criterion of logicality first emerged as a criterion of a purely mathematical interest, it has developed into a criterion of considerable linguistic and philosophical interest. In this paper I compare two different perspectives on this criterion. The first is the perspective of natural language. Here, the invariance criterion is measured by its success in capturing our linguistic intuitions about logicality and explaining our logical behavior in natural-linguistic settings. The second perspective is more theoretical. Here, the invariance criterion (...) is used as a tool for developing a theoretical foundation of logic, focused on a critical examination, explanation, and justification of its veridicality and modal force. (shrink)

Properties and relations in general have a certain degree of invariance, and some types of properties/relations have a stronger degree of invariance than others. In this paper I will show how the degrees of invariance of different types of properties are associated with, and explain, the modal force of the laws governing them. This explains differences in the modal force of laws/principles of different disciplines, starting with logic and mathematics and proceeding to physics and biology.

There is conflicting experimental evidence about whether the “stakes” or importance of being wrong affect judgments about whether a subject knows a proposition. To date, judgments about stakes effects on knowledge have been investigated using binary paradigms: responses to “low” stakes cases are compared with responses to “high stakes” cases. However, stakes or importance are not binary properties—they are scalar: whether a situation is “high” or “low” stakes is a matter of degree. So far, no experimental work has investigated the (...) scalar nature of stakes effects on knowledge: do stakes effects increase as the stakes get higher? Do stakes effects only appear once a certain threshold of stakes has been crossed? Does the effect plateau at a certain point? To address these questions, we conducted experiments that probe for the scalarity of stakes effects using several experimental approaches. We found evidence of scalar stakes effects using an “evidence seeking” experimental design, but no evidence of scalar effects using a traditional “evidence-fixed” experimental design. In addition, using the evidence-seeking design, we uncovered a large, but previously unnoticed framing effect on whether participants are skeptical about whether someone can know something, no matter how much evidence they have. The rate of skeptical responses and the rate at which participants were willing to attribute “lazy knowledge”—that someone can know something without having to check—were themselves subject to a stakes effect: participants were more skeptical when the stakes were higher, and more prone to attribute lazy knowledge when the stakes were lower. We argue that the novel skeptical stakes effect provides resources to respond to criticisms of the evidence-seeking approach that argue that it does not target knowledge. (shrink)

Many philosophers are baffled by necessity. Humeans, in particular, are deeply disturbed by the idea of necessary laws of nature. In this paper I offer a systematic yet down to earth explanation of necessity and laws in terms of invariance. The type of invariance I employ for this purpose generalizes an invariance used in meta-logic. The main idea is that properties and relations in general have certain degrees of invariance, and some properties/relations have a stronger degree of invariance than others. (...) The degrees of invariance of highly-invariant properties are associated with high degrees of necessity of laws governing/describing these properties, and this explains the necessity of such laws both in logic and in science. This non-mysterious explanation has rich ramifications for both fields, including the formality of logic and mathematics, the apparent conflict between the contingency of science and the necessity of its laws, the difference between logical-mathematical, physical, and biological laws/principles, the abstract character of laws, the applicability of logic and mathematics to science, scientific realism, and logical-mathematical realism. (shrink)

The presence of symmetries in physical theories implies a pernicious form of underdetermination. In order to avoid this theoretical vice, philosophers often espouse a principle called Leibniz Equivalence, which states that symmetry-related models represent the same state of affairs. Moreover, philosophers have claimed that the existence of non-trivial symmetries motivates us to accept the Invariance Principle, which states that quantities that vary under a theory’s symmetries aren’t physically real. Leibniz Equivalence and the Invariance Principle are often seen as part of (...) the same package. I argue that this is a mistake: Leibniz Equivalence and the Invariance Principle are orthogonal to each other. This means that it is possible to hold that symmetry-related models represent the same state of affairs whilst having a realist attitude towards variant quantities. Various arguments have been presented in favour of the Invariance Principle: a rejection of the Invariance Principle is inter alia supposed to cause indeterminism, undetectability or failure of reference. I respond that these arguments at best support Leibniz Equivalence. (shrink)

Contextualists and Subject Sensitive Invariantists often cite the knowledge norm of assertion as part of their argument. They claim that the knowledge norms in conjunction with our intuitions about when a subject is properly asserting in low or high stakes contexts provides strong evidence that what counts as knowledge depends on practical factors. In this paper, I present new data to suggest they are mistaken in the way they think about cases involving high and low stakes and I show how (...) insensitive invariantists can explain the data. I exploit recent work done on the distinction between flouting a norm and being blamed for that violation to formulate a rigorous theory of rational expected blameworthiness that allows insensitive invariantists to explain the data cited. (shrink)

This paper has three main objectives: (a) Discuss the formal analogy between some important symmetry-invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether’s theorem in physics, the maximum entropy principle in probability theory, and de Finetti-type theorems in Bayesian statistics; (b) Discuss the epistemological and ontological implications of these theorems, as they are interpreted in physics and statistics. Specifically, we will focus on the positivist (in physics) or subjective (in statistics) interpretations vs. objective interpretations that (...) are suggested by symmetry and invariance arguments; (c) Introduce the cognitive constructivism epistemological framework as a solution that overcomes the realism-subjectivism dilemma and its pitfalls. The work of the physicist and philosopher Max Born will be particularly important in our discussion. (shrink)

It is now standard to interpret symmetry-related models of physical theories as representing the same state of affairs. Recently, a debate has sprung up around the question when this interpretational move is warranted. In particular, Møller-Nielsen :1253–1264, 2017) has argued that one is only allowed to interpret symmetry-related models as physically equivalent when one has a characterisation of their common content. I disambiguate two versions of this claim. On the first, a perspicuous interpretation is required: an account of the models’ (...) common ontology. On the second, stricter, version of this claim, a perspicuous formalism is required in addition: one whose mathematical structures ‘intrinsically’ represent the physical world, in the sense of Field. Using Dewar’s :485–521, 2019) distinction between internal and external sophistication as a case study, I argue that the second requirement is decisive. This clarifies the conditions under which it is warranted to interpret symmetry-related models as physically equivalent. (shrink)

Wigner's quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincaré group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase spaces at fixed energy, and show that in order for a classical massless particle to be physically sensible, its phase space must feature a classical-particle counterpart of electromagnetic gauge invariance. By examining the connection between massless and massive particles in the massless limit, we also derive a classical-particle (...) version of the Higgs mechanism. (shrink)

In the remainder of this article, we will disarm an important motivation for epistemic contextualism and interest-relative invariantism. We will accomplish this by presenting a stringent test of whether there is a stakes effect on ordinary knowledge ascription. Having shown that, even on a stringent way of testing, stakes fail to impact ordinary knowledge ascription, we will conclude that we should take another look at classical invariantism. Here is how we will proceed. Section 1 lays out some limitations of previous (...) research on stakes. Section 2 presents our study and concludes that there is little evidence for a substantial stakes effect. Section 3 responds to objections. The conclusion clears the way for classical invariantism. (shrink)

This note contains a corrective and a generalization of results by Borsboom et al. (2008), based on Heesen and Romeijn (2019). It highlights the relevance of insights from psychometrics beyond the context of psychological testing.

We explore depth substitution invariance, or hyperformalism, and extend known results in this realm to justification logics extending weak relevant logics. We then examine the surprising invariance of justifications over formulas and restrict our attention to the substitution of proofs in the original relevant logic. The results of this paper indicate that depth invariance is a recalcitrant feature of the logic and that proof structures in hyperformal logics are quite inflexible.

It is widely accepted that our initial intuitions regarding knowledge attributions in stakes-shifting cases (e.g., Cohen’s Airport) are best explained by standards variantism, the view that the standards for knowledge may vary with contexts in an epistemically interesting way. Against standards variantism, I argue that no prominent account of the standards for knowledge can explain our intuitions regarding stakes-shifting cases. I argue that the only way to preserve our initial intuitions regarding such cases is to endorse position variantism, the view (...) that one’s epistemic position may vary with contexts in an epistemically interesting way. Some had argued that epistemic position is incompatible with intellectualism. In reply, I point out that position variantism and intellectualism are compatible, if one’s truth-relevant factors with respect to p can vary with contexts in an epistemically interesting way. (shrink)

Some philosophers say that in special relativity, four-dimensional stuff is invariant in some sense that three-dimensional stuff is not. I show that this claim is false.

According to the fallibilist, it is possible for us to know things when our evidence doesn't entail that our beliefs are correct. Even if there is some chance that we're mistaken about p, we might still know that p is true. Fallibilists will tell you that an important virtue of their view is that infallibilism leads to skepticism. In this paper, we'll see that fallibilist impurism has considerable skeptical consequences of its own. We've missed this because we've focused our attention (...) on the high-stakes cases that they discuss in trying to motivate their impurism about knowledge. We'll see this once we think about the fallibilist impurist's treatment of low-stakes cases. (shrink)

What is a logical constant? The question is addressed in the tradition of Tarski's definition of logical operations as operations which are invariant under permutation. The paper introduces a general setting in which invariance criteria for logical operations can be compared and argues for invariance under potential isomorphism as the most natural characterization of logical operations.

A number of papers have applied the CNI model of moral judgments to investigate deontological and consequentialist response tendencies (Gawronski et al., 2017). A controversy has emerged concerning the methodological assumptions of the CNI model (Baron & Goodwin, 2020, 2021; Gawronski et al. 2020). In this paper, we contribute to this debate by extending the CNI paradigm with a skip option. This allows us to test an invariance assumption that the CNI model shares with prominent process-dissociation models in cognitive and (...) social psychology (Klauer et al., 2015). Like for these models, the present experiments found violations of the invariance assumption for the CNI model. In Experiment 2, we replicate these results and selectively influence the new parameter for the skip option. In addition, structural equation modeling reveals that previous findings for the relationship between gender and the CNI parameters are completely mediated by the association of gender with primary psychopathy. (shrink)

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement. A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. It should be equated to (...) a well-ordered set after measurement and thus requires the axiom of choice. Quantum invariance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information. Quantum invariance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity. (shrink)

I provide a theory of causation within the causal modeling framework. In contrast to most of its predecessors, this theory is model-invariant in the following sense: if the theory says that C caused (didn't cause) E in a causal model, M, then it will continue to say that C caused (didn't cause) E once we've removed an inessential variable from M. I suggest that, if this theory is true, then we should understand a cause as something which transmits deviant (...) or non-inertial behavior to its effect. (shrink)

“Pragmatic encroachers” about knowledge generally advocate two ideas: (1) you can rationally act on what you know; (2) knowledge is harder to achieve when more is at stake. Charity Anderson and John Hawthorne have recently argued that these two ideas may not fit together so well. I extend their argument by working out what “high stakes” would have to mean for the two ideas to line up, using decision theory.

Relativity Theory by Albert Einstein has been so far littleconsidered by cognitive scientists, notwithstanding its undisputedscientific and philosophical moment. Unfortunately, we don't have adiary or notebook as cognitively useful as Faraday's. But physicshistorians and philosophers have done a great job that is relevant bothfor the study of the scientist's reasoning and the philosophy ofscience. I will try here to highlight the fertility of a `triangulation'using cognitive psychology, history of science and philosophy of sciencein starting answering a clearly very complex question:why (...) did Einstein discover Relativity Theory? Here we arenot much concerned with the unending question of precisely whatEinstein discovered, that still remains unanswered, for we have noconsensus over the exact nature of the theory's foundations. We are mainly interested in starting to answer the`how question', and especially the following sub-question: what were his goals and strategies in hissearch? I will base my argument on fundamental publications ofEinstein, aiming at pointing out a theory-specific heuristic, settingboth a goal and a strategy: covariance/invariance.The result has significance in theory formation in science, especiallyin concept and model building. It also raises other questions that gobeyond the aim of this paper: why was he so confident in suchheuristic? Why didn't many other scientists use it? Where did he keep? such a heuristic? Do we have any other examples ofsimilar heuristic search in other scientific problemsolving? (shrink)

Metaphysicians who are aware of modern physics usually follow Putnam (1967) in arguing that Special Theory of Relativity is incompatible with the view that what exists is only what exists now or presently. Partisans of presentism (the motto ‘only present things exist’) had very difficult times since, and no presentist theory of time seems to have been able to satisfactorily counter the objection raised from Special Relativity. One of the strategies offered to the presentist consists in relativizing existence to inertial (...) frames. This unfashionable strategy has been accused of counterfeiting, since the meaning of the concept of existence would be incompatible with its relativization. Therefore, existence could only be relativistically invariant. In this paper, I shall examine whether such an accusation hits its target, and I will do this by examining whether the different criteria of existence that have been suggested by the Philosophical Tradition from Plato onwards imply that existence cannot be relativized. (shrink)

One class of central debates between normative realists appears to concern whether we should be naturalists or reductionists about the normative. However, metaethical discussion of naturalism and reduction is often inconsistent, murky, or uninformative. This can make it hard to see why commitments relative to these metaphysical categories should matter to normative realists. This paper aims to clarify the nature of these categories, and their significance in debates between normative realists. I develop and defend what I call the joint-carving taxonomy, (...) which builds on David Lewis’ notion of elite properties. I argue that this taxonomy is clear and metaphysically interesting, and answers to distinctive taxonomic interests of normative realists. I also suggest that it has important implications for the project of adjudicating debates among normative realists. (shrink)

Historical patterns of discrimination seem to present us with conflicts between what morality requires and what we epistemically ought to believe. I will argue that these cases lend support to the following nagging suspicion: that the epistemic standards governing belief are not independent of moral considerations. We can resolve these seeming conflicts by adopting a framework wherein standards of evidence for our beliefs to count as justified can shift according to the moral stakes. On this account, believing a paradigmatically racist (...) belief reflects a failure to not only attend to the epistemic risk of being wrong, but also a failure to attend to the distinctively moral risk of wronging others given what we believe. (shrink)

A violation of procedure invariance in preference measurement is that the predominant or prominent attribute looms larger in choice than in a matching task. In Experiment 1, this so-called prominence effect was demonstrated for choices between pairs of options, choices to accept single options, and preference ratings of single options. That is, in all these response modes the prominent attribute loomed larger than in matching. The results were replicated in Experiment 2, in which subjects chose between or rated their preference (...) for pairs of options which were matched to be equally attractive either in the same session or 1 week earlier. On the basis of these and previous results, it is argued that the prominence effect is a reliable phenomenon. However, none of several cognitive explanations which have been offered appears to be completely viable. (shrink)

This paper investigates whether practical interests affect knowledge attributions in cases of testimony. It is argued that stakes impact testimonial knowledge attributions by increasing or decreasing the requirements for hearers to trust speakers and thereby gain the epistemic right to acquire knowledge via testimony. Standard, i.e. invariantist, reductionism and non-reductionism fail to provide a plausible account of testimony that is stakes sensitive, while non- invariantist versions of both traditional accounts can remedy this deficiency. Support for this conceptual analysis of stakes (...) is found through a review of the experimental philosophy literature on stakes effects on knowledge attribution. Finally, a diagnosis is offered for what is needed to provide a more robust defense of the paper’s primary claims in terms of future experimental study. (shrink)

Particles and photons appear to be total opposites; the former has rest mass which requires space to exist; the latter has kinetic energy which requires time to occur (oscillate). But they do share certain properties (e.g., quantization) that remain invariant when one is transformed (swapped) for the other. This gauge invariance is developed in some detail. The symmetry between particle and photon turns out to be one of inversion. It is the equalities of special relativity that support this inversion (...) and the accompanying invariances: mass transformed to energy; space transformed to time. The great advantage of these symmetries (inversions) is that they provide guidance for an object little understood (the photon) based upon an object well understood (the particle). On this basis, progress can be made in the understanding of some long-standing issues: wave-particle duality, time’s arrow, the constant speed of light and nonlocality. (shrink)

This contribution is an invitation to consider the professional situation in a way that goes beyond a social meaning or a subjective approach. Understood as an intermediate object, the professional situation is studied as a result of tension between invariance and perspective. The data centre on the activity of counselors whose role is to guide farmers confronted with agro-environmental standards. This text brings into question on one hand the attributions qualifying the situation as «professional» and that attest to a form (...) of invariance; and on the other, the counselors’ activity of understanding the «perspective» of the farmers with whom they are in relation. Finally, the article suggests three avenues for future work on the notion of professional situation. Cette contribution invite à considérer la situation professionnelle au-delà d’une acception sociale d’un côté et d’une approche subjective d’autre part. Entendue comme objet intermédiaire, la situation professionnelle est étudiée comme résultant d’une tension entre invariance et perspective. Les données portent sur l’activité de conseillers dont le rôle est d’accompagner les agriculteurs confrontés aux normes agro-environnementales. On s’attache à remettre en question d’une part les attributions qualifiant la situation de « professionnelle » qui témoignent d’une forme d’invariance; d’autre part, l’activité de saisie par les conseillers de la « perspective » des agriculteurs avec qui ils sont en relation. Enfin, on propose trois lignes de travail à venir sur la notion de situation professionnelle. (shrink)

The incompleteness of set theory ZFC leads one to look for natural extensions of ZFC in which one can prove statements independent of ZFC which appear to be "true". One approach has been to add large cardinal axioms. Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski- Grothendieck set theory TG [1]-[3] It is a non-conservative extension of ZFC and is obtaineed from other axiomatic set theories by the inclusion of Tarski's axiom which implies the existence (...) of inaccessible cardinals [1].Non-conservative extension of ZFC based on an generalized quantifiers considered in [4]. In this paper we look at a set theory NC_{∞^{#}}^{#},based on bivalent gyper infinitary logic with restricted Modus Ponens Rule [5]-[8]. In this paper we deal with set theory NC_{∞^{#}}^{#} based on gyper infinitary logic with Restricted Modus Ponens Rule. Set theory NC_{∞^{}}^{} contains Aczel's anti-foundation axiom [9]. We present a new approach to the invariant subspace problem for Hilbert spaces. Our main result will be that: if T is a bounded linear operator on an infinite-dimensional complex separable Hilbert space H,it follow that T has a non-trivial closed invariant subspace. Non-conservative extension based on set theory NC_{∞}^{#} of the model theoretical nonstandard analysis [10]-[12] also is considered. (shrink)

The stakes associated with an algorithmic decision are often said to play a role in determining whether the decision engenders a right to an explanation. More specifically, “high stakes” decisions are often said to engender such a right to explanation whereas “low stakes” or “non-high” stakes decisions do not. While the overall gist of these ideas is clear enough, the details are lacking. In this paper, we aim to provide these details through a detailed investigation of what we will call (...) the “Simple Stakes Thesis”. The Simple Stakes Thesis, as it will turn out, is too simple. For even if the stakes associated with a specific one-off decision are low—and hence does not engender a right to an explanation—such decisions may nevertheless form part of a high stakes pattern or aggregate of decisions. In such cases, we argue, even a low stakes decision may engender a right to explanation. Not only does this show that the right to explanation is more demanding than so far recognized. It also shows that the stakes thesis is significantly harder to apply in practice. (shrink)

David Albert has recently argued that classical electromagnetic theory (EM) is not time reversal invariant (non-TRI), while David Malament rejects this argument and maintains the orthodox result, that EM is TRI. Both Albert's and Malament's arguments are analysed, and both are found wanting in certain respects. It is argued here that the result really depends on the choice of theoretical ontology choosen to interpret EM theory, and there is more than one plausible choice. Albert and Malament have choosen different (...) plausible ontologies; but neither shows that their choice of interpretation is definitive. Deeper principles about this choice are examined. The extension to EM theory with magnetic monopoles is also examined. It is concluded that, despite certain flaws in his account, Albert's analysis does reveal serious problems in the orthodox account, which Malament's response does not adequately address. (shrink)

How should we understand the notion of moral objectivity? Metaethical positions that vindicate morality’s objective appearance are often associated with moral realism. On a realist construal, moral objectivity is understood in terms of mind-, stance-, or attitude-independence. But realism is not the only game in town for moral objectivists. On an antirealist construal, morality’s objective features are understood in virtue of our attitudes. In this paper I aim to develop this antirealist construal of moral objectivity in further detail, and to (...) make its metaphysical commitments explicit. I do so by building on Sharon Street’s version of “Humean Constructivism”. Instead of the realist notion of attitude-independence, the antirealist account of moral objectivity that I articulate centres on the notion of standpoint-invariance. While constructivists have been criticized for compromising on the issue of moral objectivity, I make a preliminary case for the thesis that, armed with the notion of standpoint-invariance, constructivists have resources to vindicate an account of objectivity with just the right strength, given the commitments of ordinary moral thought and practice. In support of this thesis I highlight recent experimental findings about folk moral objectivism. Empirical observations about the nature of moral discourse have traditionally been taken to give prima facie support to moral realism. I argue, by contrast, that from what we can tell from our current experimental understanding, antirealists can capture the commitments of ordinary discourse at least as well as realists can. (shrink)

This contribution is an invitation to consider the professional situation in a way that goes beyond a social meaning or a subjective approach. Understood as an intermediate object, the professional situation is studied as a result of tension between invariance and perspective. The data centre on the activity of counselors whose role is to guide farmers confronted with agro-environmental standards. This text brings into question on one hand the attributions qualifying the situation as «professional» and that attest to a form (...) of invariance; and on the other, the counselors’ activity of understanding the «perspective» of the farmers with whom they are in relation. Finally, the article suggests three avenues for future work on the notion of professional situation. Cette contribution invite à considérer la situation professionnelle au-delà d’une acception sociale d’un côté et d’une approche subjective d’autre part. Entendue comme objet intermédiaire, la situation professionnelle est étudiée comme résultant d’une tension entre invariance et perspective. Les données portent sur l’activité de conseillers dont le rôle est d’accompagner les agriculteurs confrontés aux normes agro-environnementales. On s’attache à remettre en question d’une part les attributions qualifiant la situation de « professionnelle » qui témoignent d’une forme d’invariance; d’autre part, l’activité de saisie par les conseillers de la « perspective » des agriculteurs avec qui ils sont en relation. Enfin, on propose trois lignes de travail à venir sur la notion de situation professionnelle. (shrink)

Third-party property insurance (TPPI) protects insured drivers who accidentally damage an expensive car from the threat of financial ruin. Perhaps more importantly though, TPPI also protects the victims whose losses might otherwise go uncompensated. Ought responsible drivers therefore take out TPPI? This paper begins by enumerating some reasons for why a rational person might believe that they have a moral obligation to take out TPPI. It will be argued that if what is at stake in taking responsibility is the (...) ability to compensate our possible future victims for their losses, then it might initially seem that most people should be thankful for the availability of relatively inexpensive TPPI because without it they may not have sufficient funds to do the right thing and compensate their victims in the event of an accident. But is the ability to compensate one's victims really what is at stake in taking responsibility? The second part of this paper will critically examine the arguments for the above position, and it will argue that these arguments do not support the conclusion that injurers should compensate their victims for their losses, and hence that drivers need not take out TPPI in order to be responsible. Further still, even if these arguments did support the conclusion that injurers should compensate their victims for their losses, then (perhaps surprisingly) nobody should to be allowed to take out TPPI because doing so would frustrate justice. (shrink)

Prominent critics and champions of Experimental Philosophy (X-Phi) alike have tied its philosophical significance to the philosophical significance of intuition. In this essay, I develop an interpretation of X-Phi which does not require an intuition-driven understanding of traditional philosophy, and the arguments challenged by results in X-Phi. X-Phi's role on this account is primarily dialectical. Its aim is to test the universality of claims which are merely assumed to be true, exploring the limits of our assumptions and showing when a (...) proposition is more controversial than is widely believed. (shrink)

One challenge for moderate invariantists is to explain why we tend to deny knowledge to subjects in high stakes when the target propositions seem to be inappropriate premises for practical reasoning. According to an account suggested by Williamson, our intuitive judgments are erroneous due to an alleged failure to acknowledge the distinction between first-order and higher-order knowledge: the high-stakes subject lacks the latter but possesses the former. In this paper, I provide three objections to Williamson’s account: i) his account delivers (...) counterintuitive verdicts about what it is appropriate for a high-stakes subject to do; ii) the high-stakes subject doesn’t need iterated knowledge in order to be regarded as appropriately relying on the relevant proposition in practical reasoning; iii) Williamson’s account doesn’t provide a good explanation of why the high-stakes subject would be blameworthy if she were relying on the relevant proposition in her practical reasoning. (shrink)

Recent accounts of teleological naturalism hold that organisms are intrinsically goaldirected entities. We argue that supporters and critics of this view have ignored the ways in which it is used to address quite different problems. One problem is about biology and concerns whether an organism-centered account of teleological ascriptions would improve our descriptions and explanations of biological phenomena. This is different from the philosophical problem of how naturalized teleology would affect our conception of nature, and of ourselves as natural beings. (...) The neglect of this metatheoretic distinction has made it difficult to understand the criteria we should use for evaluating proposals to naturalize teleology. We argue that a clearer distinction between scientific and philosophical contexts shows that we need more than one set of criteria for evaluating proposals to naturalize teleology, and that taking these into account might advance or dissolve recurring debates in the literature. (shrink)

The main examples of pragmatic encroachment presented by Jason Stanley involve the idea that knowledge ascription occurs more readily in cases where stakes are low rather than high. This is the stakes hypothesis. In this paper an example is presented showing that in some cases knowledge ascription is more readily appropriate where stakes are high rather than low.

This review is a critical discussion of three main claims in Debs and Redhead’s thought-provoking book Objectivity, Invariance, and Convention. These claims are: (i) Social acts impinge upon formal aspects of scientific representation; (ii) symmetries introduce the need for conventional choice; (iii) perspectival symmetry is a necessary and sufficient condition for objectivity, while symmetry simpliciter fails to be necessary.

Why do our intuitive knowledge ascriptions shift when a subject's practical interests are mentioned? Many efforts to answer this question have focused on empirical linguistic evidence for context sensitivity in knowledge claims, but the empirical psychology of belief formation and attribution also merits attention. The present paper examines a major psychological factor (called ?need-for-closure?) relevant to ascriptions involving practical interests. Need-for-closure plays an important role in determining whether one has a settled belief; it also influences the accuracy of one's cognition. (...) Given these effects, it is a mistake to assume that high- and low-stakes subjects provided with the same initial evidence are perceived to enjoy belief formation that is the same as far as truth-conducive factors are concerned. This mistaken assumption has underpinned contextualist and interest-relative invariantist treatments of cases in which contrasting knowledge ascriptions are elicited by descriptions of subjects with the same initial information and different stakes. The paper argues that intellectualist invariantism can easily accommodate such cases. (shrink)

Abstract The Preface Paradox, first introduced by David Makinson (1961), presents a plausible scenario where an agent is evidentially certain of each of a set of propositions without being evidentially certain of the conjunction of the set of propositions. Given reasonable assumptions about the nature of evidential certainty, this appears to be a straightforward contradiction. We solve the paradox by appeal to stake size sensitivity, which is the claim that evidential probability is sensitive to stake size. The argument (...) is that because the informational content in the conjunction is greater than the sum of the informational content of the conjuncts, the stake size in the conjunction is higher than the sum of the stake sizes in the conjuncts. We present a theory of evidential probability that identifies knowledge with value and allows for coherent stake sensitive beliefs. An agent’s beliefs are represented two dimensionally as a bid – ask spread, which gives a bid price and an ask price for bets at each stake size. The bid ask spread gets wider when there is less valuable evidence relative to the stake size, and narrower when there is more valuable evidence according to a simple formula. The bid-ask spread can represent the uncertainty in the first order probabilistic judgement. According to the theory it can be coherent to be evidentially certain at low stakes, but less than certain at high stakes, and therefore there is no contradiction in the Preface. The theory not only solves the paradox, but also gives a good model of decisions under risk that overcomes many of the problems associated with classic expected utility theory. (shrink)

Symmetries have a crucial role in today’s physics. In this thesis, we are mostly concerned with time reversal invariance (T-symmetry). A physical system is time reversal invariant if its underlying laws are not sensitive to the direction of time. There are various accounts of time reversal transformation resulting in different views on whether or not a given theory in physics is time reversal invariant. With a focus on quantum mechanics, I describe the standard account of time reversal and (...) compare it with my alternative account, arguing why it deserves serious attention. Then, I review three known ways to T-violation in quantum mechanics, and explain two unique experiments made to detect it in the neutral K and B mesons. (shrink)