Hilary Putnam once suggested that “the actual existence of sets as ‘intangible objects’ suffers… from a generalization of a problem first pointed out by Paul Benacerraf… are sets a kind of function or are functions a sort of set?” Sadly, he did not elaborate; my aim, here, is to do so on his behalf. There are well-known methods for treating sets as functions and functions as sets. But these do not raise any obvious philosophical or foundational puzzles. For that, we (...) first need to provide a full-fledged function theory. I supply such a theory: it axiomatizes the iterative notion of function in exactly the same sense that ZF axiomatizes the iterative notion of set. Indeed, this function theory is synonymous with ZF. It might seem that set theory and function theory present us with rival foundations for mathematics, since they postulate different ontologies. But appearances are deceptive. Set theory and function theory provide the very same judicial foundation for mathematics. They do not supply rival metaphysical foundations; indeed, if they supply metaphysical foundations at all, then they supply the very same metaphysical foundations. (shrink)

This paper argues that we should solve paradoxes for propositions (such as the Russell–Myhill paradox) in essentially the same way that we solve Russellian paradoxes for sets. That is, the standard, iterative approach to sets is extended to include properties, and then the resulting hierarchy of sets and properties is used to construct propositions. Propositions on this account are structured in the sense of mirroring the sentences that express them, and they would seem to serve the needs of philosophers (...) of language and metaphysicians who rely on such propositions. The resulting account has limitations, comparable to those faced by the iterative approach to sets, but it is argued to be in important ways preferable to others that have been proposed. (shrink)

The Question of Iterated Grounding (QIG) asks what grounds the grounding facts. Although the question received a lot of attention in the past few years, it is usually discussed independently of another important issue: the connection between metaphysical explanation and the relation or relations that supposedly “back” it. I will show that once we get clear on the distinction between metaphysical explanation and the relation(s) backing it, we can distinguish no fewer than four questions lumped under QIG. I will also (...) argue that given some plausible assumptions about what it would take for a relation to back metaphysical explanation, many salient views about grounding allow us to give “easy” answers to these questions—easy in the sense that we can straightforwardly derive them from the respective conception of grounding without getting into the sorts of complexities that typically inform answers to QIG. The paper's main upshot is that we cannot expect to make much progress on QIG without first addressing the difficult issue of how exactly grounding is related to metaphysical explanation. (shrink)

Why are natural theories pre-well-ordered by consistency strength? In previous work, an approach to this question was proposed. This approach was inspired by Martin's Conjecture, one of the most prominent conjectures in recursion theory. Fixing a reasonable subsystem $T$ of arithmetic, the goal was to classify the recursive functions that are monotone with respect to the Lindenbaum algebra of $T$. According to an optimistic conjecture, roughly, every such function must be equivalent to an iterate $\mathsf{Con}_T^\alpha$ of the consistency operator ``in (...) the limit'' within the ultrafilter of sentences that are true in the standard model. In previous work the author established the first case of this optimistic conjecture; roughly, every recursive monotone function is either as weak as the identity operator in the limit or as strong as $\mathsf{Con}_T$ in the limit. Yet in this note we prove that this optimistic conjecture fails already at the next step; there are recursive monotone functions that are neither as weak as $\mathsf{Con}_T$ in the limit nor as strong as $\mathsf{Con}_T^2$ in the limit. In fact, for every $\alpha$, we produce a function that is cofinally equivalent to $\mathsf{Con}^\alpha_T$ yet cofinally equivalent to $\mathsf{Con}_T$. (shrink)

The standard rule of single privative modification replaces privative modifiers by Boolean negation. This rule is valid, for sure, but also simplistic. If an individual a instantiates the privatively modified property (MF) then it is true that a instantiates the property of not being an F, but the rule fails to express the fact that the properties (MF) and F have something in common. We replace Boolean negation by property negation, enabling us to operate on contrary rather than contradictory properties. (...) To this end, we apply our theory of intensional essentialism, which operates on properties (intensions) rather than their extensions. We argue that each property F is necessarily associated with an essence, which is the set of the so-called requisites of F that jointly define F. Privation deprives F of some but not all of its requisites, replacing them by their contradictories. We show that properties formed from iterated privatives, such as being an imaginary fake banknote, give rise to a trifurcation of cases between returning to the original root property or to a property contrary to it or being semantically undecidable for want of further information. In order to determine which of the three forks the bearers of particular instances of multiply modified properties land upon we must examine the requisites, both of unmodified and modified properties. Requisites underpin our presuppositional theory of positive predication. Whereas privation is about being deprived of certain properties, the assignment of requisites to properties makes positive predication possible, which is the predication of properties the bearers must have because they have a certain property formed by means of privation. (shrink)

If $U$ is a normal ultrafilter on a measurable cardinal $\kappa$, then the intersection of the $\omega$ first iterated ultrapowers of the universe by $U$ is a Prikry generic extension of the $\omega$th iterated ultrapower.

According to the iterative conception of set, each set is a collection of sets formed prior to it. The notion of priority here plays an essential role in explanations of why contradiction-inducing sets, such as the Russell set, do not exist. Consequently, these explanations are successful only to the extent that a satisfactory priority relation is made out. I argue that attempts to do this have fallen short: understanding priority in a straightforwardly constructivist sense threatens the coherence of the (...) empty set and raises serious epistemological concerns; but the leading realist interpretations---ontological and modal interpretations of priority---are deeply problematic as well. I conclude that the purported explanatory virtues of the iterative conception are, at present, unfounded. (shrink)

This paper argues that two widely accepted principles about the indicative conditional jointly presuppose the falsity of one of the most prominent arguments against epistemological iteration principles. The first principle about the indicative conditional, which has close ties both to the Ramsey test and the “or‐to‐if” inference, says that knowing a material conditional suffices for knowing the corresponding indicative. The second principle says that conditional contradictions cannot be true when their antecedents are epistemically possible. Taken together, these principles entail that (...) it is impossible to be in a certain kind of epistemic state: namely, a state of ignorance about which of two partially overlapping bodies of knowledge corresponds to one's actual one. However, some of the more popular “margin for error” style arguments against epistemological iteration principles suggest that such states are not only possible, but commonplace. I argue that the tension between these views runs deep, arising just as much for non‐factive attitudes like belief, presupposition, and certainty. I also argue that this is worse news for those who accept the principles about the indicative conditional than it is for those who reject epistemological iteration principles. (shrink)

In a single-iteration fake barn case, the agent correctly identifies an object of interest on the first try, despite the presence of nearby lookalikes that could have mislead her. In a multiple-iteration fake barn case, the agent first encounters several fakes, misidentifies each of them, and then encounters and correctly identifies a genuine item of interest. Prior work has established that people tend to attribute knowledge in single-iteration fake barn cases, but multiple-iteration cases have not been tested. However, some theorists (...) contend that multiple-iteration cases are more important and will elicit a strong tendency to deny knowledge. Here I report a behavioural experiment investigating knowledge judgments in multiple-iteration fake barn cases. The main finding is that people tend to attribute knowledge in these cases too. Ironically, the results indicate that the presence of fakes could prevent iterated errors from lowering knowledge attributions. The results also provide evidence that ordinary knowledge attributions are based on attributions of cognitive ability. (shrink)

Let an iterated essentialist statement be a statement of the form 'It lies in the nature of x1,x2,... that it lies in the nature of y1,y2,... that φ'. Let Iteration be the thesis that there are true iterated essentialist statements. Iteration has recently been disputed by Dasgupta (2014) and Glazier (2017). Both authors take the falsity of Iteration to be central to the explanatory role of essentialist truths. An important consequence that is not explicitly noted by them is that the (...) falsity of Iteration would entail that metaphysical necessity is not reducible to essence in the manner suggested by Fine (1994). This paper defends Iteration against these challenges, drawing attention to some features of the collective essences of properties, propositions, and logical operations that have been largely neglected in discussions about essence. (shrink)

Recent work on the philosophy of modality has tended to pass over questions about iterated modalities in favour of constructing ambitious metaphysical theories of possibility and necessity, despite the central importance of iterated modalities to modal logic. Yet there are numerous unresolved but fundamental issues involving iterated modalities: Chandler and Salmon have provided forceful arguments against the widespread assumption that all necessary truths are necessarily necessary, for example. The current paper examines a range of ways in which one might seek (...) to identify limited regions within which some of the most well-known principles featuring iterated modalities may safely be assumed. (shrink)

Rondo Keele makes a foray into what he calls 'applied logic', investigating a complex argument strategy employed against Ockham by his greatest contemporary opponent, Walter Chatton. Chatton conceives a two-part strategy which attempts to force a kind of iteration of conceptual analysis, together with an infinite explanatory regress, in order to establish that one particular philosophical analysis is ultimately dependent on another. Chatton uses this strategy against Ockham in order to show that the latter's reductionist metaphysics depends ultimately upon a (...) deeper level of realist assumptions that he can neither evade nor explain away. Keele then shows how, earlier in his career, Chatton found himself on the receiving end of this same strategy, defending his own highly original solution to the problem of future contingents from the very iteration-regress attack he would subsequently use on Ockham. Keele concludes with an examination of Chatton's attempts to avoid the consequences of his own strategy, and draws some connections between this argument strategy and modal collapse in modern logics. (shrink)

The conclusion of this chapter is that higher-order vagueness is universal: no sentence whatsoever is definitely true, definitely definitely true, definitely definitely definitely true, and so on ad infinitum. The argument, of which there are several versions, turns on the existence of Sorites sequences of possible worlds connecting the actual world to possible worlds where a given sentence is used in such a way that its meaning is very different. The chapter attempts to be neutral between competing accounts of the (...) nature of vagueness and definiteness. (shrink)

The present paper argues that there is a knowledge norm for conversational implicature: one may conversationally implicate p only if one knows p. Linguistic data about the cancellation behavior of implicatures and the ways they are challenged and criticized by speakers is presented to support the thesis. The knowledge norm for implicature is then used to present a new consideration in favor of the KK thesis. It is argued that if implicature and assertion have knowledge norms, then assertion requires not (...) only knowledge but iterated knowledge: knowing that you know that you know that... you know. Such a condition on permissible assertion is argued to be plausible only if the KK thesis is true. (shrink)

You omega know p when you possess every iteration of knowledge of p. This book argues that omega knowledge plays a central role in philosophy. In particular, the book argues that omega knowledge is necessary for permissible assertion, action, inquiry, and belief. Although omega knowledge plays this important role, existing theories of omega knowledge are unsatisfying. One theory, KK, identifies knowledge with omega knowledge. This theory struggles to accommodate cases of inexact knowledge. The other main theory is skeptical, claiming that (...) we do not omega know any ordinary claims about the world. This book develops and critically compares three new theories of omega knowledge. (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)

After a number of decades of research into the dynamics of rational belief, the belief revision theory community remains split on the appropriate handling of sequences of changes in view, the issue of so-called iterated revision. It has long been suggested that the matter is at least partly settled by facts pertaining to the results of various single revisions of one’s initial state of belief. Recent work has pushed this thesis further, offering various strong principles that ultimately result in a (...) wholesale reduction of iterated to one-shot revision. The present paper offers grounds to hold that these principles should be significantly weakened and that the reductionist thesis should ultimately be rejected. Furthermore, the considerations provided suggest a close connection between the logic of iterated belief change and the logic of evidential relevance. (shrink)

Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we give the (...) lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the notions of disjunction and iterated conditioning and we show that the usual probabilistic properties still hold. (shrink)

The knowledge account of assertion - roughly: one should not assert what one does not know - can explain a variety of Moorean conjunctions, a fact often cited as evidence in its favor. David Sosa ("Dubious Assertions," Phil Studies, 2009) has objected that the account does not generalize satisfactorily, since it cannot explain the infelicity of certain iterated conjunctions without appealing to the controversial "KK" principle. This essay responds by showing how the knowledge account can handle such conjunctions without use (...) of the KK principle. (shrink)

This theory aims to describe what time iteration is. That is the property of time that it repeats itself. This paper focuses on the repetition of orbital motions of objects in space and gives us three postulates that describe what time will be with different relations of objects and their surroundings. This paper will help to make us understand how everything in our universe which is orbiting something if repeats its orbital motion again and again no matter in what time (...) it completes its one rotation, time do exists for that orbital motion but the motion of that time for the motion of that object is moving in both directions. So I conclude that repetition of orbital motion of objects is in time equilibrium position that we shall discuss in this paper. (shrink)

I give an account of the absurdity of Moorean beliefs of the omissive form(om) p and I don’t believe that p,and the commissive form(com) p and I believe that not-p,from which I extract a definition of Moorean absurdity. I then argue for an account of the absurdity of Moorean assertion. After neutralizing two objections to my whole account, I show that Roy Sorensen’s own account of the absurdity of his ‘iterated cases’(om1) p and I don’t believe that I believe that (...) p,and(com1) p and I believe that I believe that not-p,is unsatisfactory. I explain why it is less absurd to believe or assert (om1) or (com1) than to believe or assert (om) or (com) and show that despite appearances, subsequent iterations of (om1) or (com1) do not decrease the absurdity of believing or asserting them. (shrink)

This study draws a comparative framework between deconstructive reading of texts and jazz standards. It will be argued that both are defined by the constant play of tradition and innovation. On the one hand, the repetition of a set of rules and dominant understanding of texts/tunes that generates tradition. On the other hand, invention and improvisation that take on that tradition and generate innovation. The act of reading/playing becomes also an act of invention/improvisation that manifests a constant tension between the (...) old that is handed down through writing/recording and the new that is generated by the reader/musician. (shrink)

The iterative conception of set is typically considered to provide the intuitive underpinnings for ZFCU (ZFC+Urelements). It is an easy theorem of ZFCU that all sets have a definite cardinality. But the iterative conception seems to be entirely consistent with the existence of “wide” sets, sets (of, in particular, urelements) that are larger than any cardinal. This paper diagnoses the source of the apparent disconnect here and proposes modifications of the Replacement and Powerset axioms so as to allow (...) for the existence of wide sets. Drawing upon Cantor’s notion of the absolute infinite, the paper argues that the modifications are warranted and preserve a robust iterative conception of set. The resulting theory is proved consistent relative to ZFC + “there exists an inaccessible cardinal number.”. (shrink)

A discussion of a view, defended by Robert Adams and Boris Kment, according to which contingent existence requires rejecting many standard principles of propositional modal logic involving iterated modal operators.

Letters exchanged by scientists are a crucial source by which to trace the process that accompanies their scientific evolution. In this paper -accomplished through a historical approach- I aim to throw new light on Leibniz's continuing interest in classical geometry and to stress the significance of his correspondence with the Italian mathematician Vitale Giordano.

This paper argues for several related theses. First, the epistemological position that knowledge requires safe belief can be motivated by views in the philosophy of science, according to which good explanations show that their explananda are robust. This motivation goes via the idea—recently defended on both conceptual and empirical grounds—that knowledge attributions play a crucial role in explaining successful action. Second, motivating the safety requirement in this way creates a choice point—depending on how we understand robustness, we'll end up with (...) different conceptions of safety in epistemology. Lastly, and most controversially, there's an attractive choice at this point that will not vindicate some of the most influential applications of the safety-theoretic framework in epistemology, e.g., Williamson's arguments against the KK principle, and luminosity. (shrink)

In this paper, I introduce an iterative method aimed at exploring numbers within the interval [0, 1]. Beginning with a foundational set, S0, a series of algorithms are employed to expand and refine this set. Each algorithm has its designated role, from incorporating irrational numbers to navigating non-deterministic properties. With each successive iteration, our set grows, and after infinite iterations, its cardinality is proposed to align with that of the real numbers. This work is an initial exploration into this (...) approach, and further investigation is encouraged to understand its full implications and potential. (shrink)

To stimulate research and innovation (R&I), to contribute to the solution of societal challenges and to align R&I with societal values, the European Commission has launched the governance framework of Responsible Research and Innovation (RRI). RRI figures in many high-level EU policies as a means to promote smart growth, and a growing community of R&I practitioners from both the public and private sectors appears committed to it. Although debates on what RRI precisely entails have not reached closure yet, RRI provides (...) an interesting avenue to explore ways of making R&I more societally germane. While recognizing the usefulness of keeping critical reflection on RRI’s meaning alive, we suggest that to make the step from theorizing to implementation, RRI could benefit from a clearer conceptualization. This chapter presents the iterative trajectory in conceptualizing RRI followed as part of RRI Tools, one of a number of EC-funded research projects and support acts aimed at fleshing out what RRI can and should be, and the conceptualization of RRI that this led to. It suggests that RRI is best captured if in R&I governance attention is paid to the five p’s of Purpose, Products, Processes, Preconditions and People, and that further elaborations on the meaning of RRI should happen in dialogue with attempts at practicing RRI. (shrink)

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this (...) paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general. (shrink)

Ensemble perception—the encoding of objects by their group properties—is known to be resistant to outlier noise. However, this resistance is somewhat paradoxical: how can the visual system determine which stimuli are outliers without already having derived statistical properties of the ensemble? A simple solution would be that ensemble perception is not a simple, one-step process; instead, outliers are detected through iterative computations that identify items with high deviance from the mean and reduce their weight in the representation over time. (...) Here we tested this hypothesis. In Experiment 1, we found evidence that outliers are discounted from mean orientation judgments, extending previous results from ensemble face perception. In Experiment 2, we tested the timing of outlier rejection by having participants perform speeded judgments of sets with or without outliers. We observed significant increases in reaction time (RT) when outliers were present, but a decrease compared to no-outlier sets of matched range suggesting that range alone did not drive RTs. In Experiment 3 we tested the timing by which outlier noise reduces over time. We presented sets for variable exposure durations and found that noise decreases linearly over time. Altogether these results suggest that ensemble representations are optimized through iterative computations aimed at reducing noise. The finding that ensemble perception is an iterative process provides a useful framework for understanding contextual effects on ensemble perception. (shrink)

In this paper, we propose a methodology to maximize the benefits of interdisciplinary cooperation in AI research groups. Firstly, we build the case for the importance of interdisciplinarity in research groups as the best means to tackle the social implications brought about by AI systems, against the backdrop of the EU Commission proposal for an Artificial Intelligence Act. As we are an interdisciplinary group, we address the multi-faceted implications of the mass-scale diffusion of AI-driven technologies. The result of our exercise (...) lead us to postulate the necessity of a behavioural theory that standardizes the interaction process of interdisciplinary groups. In light of this, we conduct a review of the existing approaches to interdisciplinary research on AI appliances, leading to the development of methodologies like ethics-by-design and value-sensitive design, evaluating their strengths and weaknesses. We then put forth an iterative process theory hinging on a narrative approach consisting of four phases: definition of the hypothesis space, building-up of a common lexicon, scenario-building, interdisciplinary self-assessment. Finally, we identify the most relevant fields of application for such a methodology and discuss possible case studies. (shrink)

The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting from revision (...) by ¬A, we look at ways to define the plausibility ordering over worlds resulting from contracting A in terms of (iii) the initial plausibility ordering, and (iv) the plausibility ordering resulting from revision by ¬A. After noting that the most straightforward such extension leads to a trivialisation of the space of permissible orderings, we provide a family of operators for combining plausibility orderings that avoid such a result. These operators are characterised in our domain of interest by a pair of intuitively compelling properties, which turn out to enable the derivation of a number of iterated contraction postulates from postulates for iterated revision. We finish by observing that a salient member of this family allows for the derivation of counterparts for contraction of some well known iterated revision operators, as well as for defining new iterated contraction operators. (shrink)

Evolutionary applications of game theory present one of the most pedagogically accessible varieties of genuine, contemporary theoretical biology. We present here Oyun (OY-oon, http://charlespence.net/oyun), a program designed to run iterated prisoner’s dilemma tournaments, competitions between prisoner’s dilemma strategies developed by the students themselves. Using this software, students are able to readily design and tweak their own strategies, and to see how they fare both in round-robin tournaments and in “evolutionary” tournaments, where the scores in a given “generation” directly determine contribution (...) to the population in the next generation. Oyun is freely available, runs on Windows, Mac, and Linux computers, and the process of creating new prisoner’s dilemma strategies is both easy to teach and easy for students to grasp. We illustrate with two interesting examples taken from actual use of Oyun in the classroom. (shrink)

There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, $P(\textit{if } A \textit{ then } B)$, is the conditional probability of $B$ given $A$, $P(B|A)$. We identify a conditional which is such that $P(\textit{if } A \textit{ then } B)= P(B|A)$ with de Finetti's conditional event, $B|A$. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of (...) conditional events. In this paper, we illustrate how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds and iterations as conditional random quantities which, given some logical dependencies, may reduce to conditional events. We show how the inference to $B|A$ from $A$ and $B$ can be extended to compounds and iterations of both conditional events and biconditional events. Moreover, we determine the respective uncertainty propagation rules. Finally, we make some comments on extending our analysis to counterfactuals. (shrink)

To stimulate research and innovation (R&I), to contribute to the solution of societal challenges and to align R&I with societal values, the European Commission has launched the governance framework of Responsible Research and Innovation (RRI). RRI figures in many high-level EU policies as a means to promote smart growth, and a growing community of R&I practitioners from both the public and private sectors appears committed to it. Although debates on what RRI precisely entails have not reached closure yet, RRI provides (...) an interesting avenue to explore ways of making R&I more societally germane. While recognizing the usefulness of keeping critical reflection on RRI’s meaning alive, we suggest that to make the step from theorizing to implementation, RRI could benefit from a clearer conceptualization. This chapter presents the iterative trajectory in conceptualizing RRI followed as part of RRI Tools, one of a number of EC-funded research projects and support acts aimed at fleshing out what RRI can and should be, and the conceptualization of RRI that this led to. It suggests that RRI is best captured if in R&I governance attention is paid to the five p’s of Purpose, Products, Processes, Preconditions and People, and that further elaborations on the meaning of RRI should happen in dialogue with attempts at practicing RRI. (shrink)

Philosophy of science and history of science have been unable to integrate in a meaningful fashion. The major difficulty has been the question of how the history of science can inform the philosophy of science. By making several distinctions to characterize the type of philosophy of science relevant for integrated HPS, I show how traditional approaches to integration failed. These include a top-down and a bottom-up philosophical approach to integrated HPS. I then present a more fruitful way of integrating the (...) disciplines, that of iterations. (shrink)

In recent years, it becomes clear that ITER project in France, as one of the largest experimental fusion reactors underway, is far away from achieving net energy production. In this review article, we presented a short communication this week with Robert Neil Boyd, a senior physicist who happens to have his own working design of fusion reactor in the past. We hope that this transcript of our communication with him (as per 15-17th Nov. 2021) may be found useful for younger (...) scientists. (shrink)

In this paper we distinguish between various kinds of doxastic theories. One distinction is between informal and formal doxastic theories. AGM-type theories of belief change are of the former kind, while Hintikka’s logic of knowledge and belief is of the latter. Then we distinguish between static theories that study the unchanging beliefs of a certain agent and dynamic theories that investigate not only the constraints that can reasonably be imposed on the doxastic states of a rational agent but also rationality (...) constraints on the changes of doxastic state that may occur in such agents. An additional distinction is that between non-introspective theories and introspective ones. Non-introspective theories investigate agents that have opinions about the external world but no higher-order opinions about their own doxasticnstates. Standard AGM-type theories as well as the currently existing versions of Segerberg’s dynamic doxastic logic (DDL) are non-introspective. Hintikka-style doxastic logic is of course introspective but it is a static theory. Thus, the challenge remains to devise doxastic theories that are both dynamic and introspective. We outline the semantics for truly introspective dynamic doxastic logic, i.e., a dynamic doxastic logic that allows us to describe agents who have both the ability to form higher-order beliefs and to reflect upon and change their minds about their own (higher-order) beliefs. This extension of DDL demands that we give up the Preservation condition on revision. We make some suggestions as to how such a non-preservative revision operation can be constructed. We also consider extending DDL with conditionals satisfying the Ramsey test and show that Gärdenfors’ well-known impossibility result applies to such a framework. Also in this case, Preservation has to be given up. (shrink)

The availability of large digital archives of historical newspaper content has transformed the historical sciences. However, the scale of these archives can limit the direct application of advanced text processing methods. Even if it is computationally feasible to apply sophisticated language processing to an entire digital archive, if the material of interest is a small fraction of the archive, the results are unlikely to be useful. Methods for generating smaller specialized corpora from large archives are required to solve this problem. (...) This article presents such a method for historical newspaper archives digitized using the METS/ALTO XML standard (Veridian Software, n.d.). The method is an ‘iterative bootstrapping’ approach in which candidate corpora are evaluated using text mining techniques, items are manually labelled, and Naïve Bayes text classifiers are trained and applied in order to produce new candidate corpora. The method is illustrated by a case study that investigates philosophical content, broadly construed, in pre-1900 English-language New Zealand newspapers. Extensive code is provided in Supplementary Materials. (shrink)

After the Event Horizon Telescope Collaboration released in April 2019 the first empirical images of a black hole, an astrophysical object previously thought “unseeable,” much of the public discourse has approached these images as straightforward visual depictions of a black hole. This article challenges this view by showing that the first images of a black hole went beyond merely making an invisible cosmic object visible and that the images published in April 2019 were just the first in a series of (...) black hole images the researchers continue producing. Drawing primarily on Sybille Krämer’s concept of the cartographic impulse, the article demonstrates that the Event Horizon Telescope images are, first and foremost, epistemic tools. These epistemic tools enable researchers to actively explore various physical aspects and dynamic properties of a black hole’s immediate environment and test theoretical predictions about it, thus making this elusive environment empirically knowable. To demonstrate this, the article analyses the mapping operations that combined automated algorithmic procedures with expert human judgment and through which these images were produced, read, and interpreted. It also examines how the different Event Horizon Telescope images relate to one another, which particular epistemic functions they fulfil in the research context, under which conditions, and with which limitations, thus tracing how these images facilitate the production of new scientific knowledge about black holes. (shrink)

The spread of the reform found one of its protagonists in the hermit and Cardinal Bishop of Ostia, Peter Damian. An example worthy of case-study is the Gallic mission as apostolic legate in 1063. The most complete report of this journey was written by an anonymous disciple. This perspective allows to observe Damian’s communication strategies and the different methods used referring to the various interlocutors. The cause of the apostolic legation was the help request from Hugh, abbot of Cluny, for (...) the pressures suffered by the Bishop of Macon. The occasion was propitious from the point of view of the cardinal bishop to expand his network of personal and institutional relationships and to legitimize the papal supremacy. He proceeded to France, summoned a council at Chalon-sur-Saône and proved the justice of the contentions of Cluny. Despite the lack of historiographical success, this work remains an extremely useful source for studying a man who made his ars rethorica a powerful weapon in the service of the reform. (shrink)

The paper argues against a commitment to metaphysical necessity, semantic modalities are enough. The best approaches to elucidate the semantic modalities are (still) versions of lingustic ersatzism and fictionalism, even if only developed in parts. Within these necessary properties and the difference between natural and semantic laws can be accounted for. The proper background theory for this is an updated version of Logical Empiricism, which is congenial to recent trends in Structural Realism. The anti-metaphysical attitude of Logical Empiricism deserves revitalization. (...) Another target besides metaphysical necessity are substantial forms of iterated modalities, as used, for instance, in the philosophy of religion. (shrink)

The Problem of Iterated Ground is to explain what grounds truths about ground: if Γ grounds φ, what grounds that Γ grounds φ? This paper develops a novel solution to this problem. The basic idea is to connect ground to explanatory arguments. By developing a rigorous account of explanatory arguments we can equip operators for factive and non-factive ground with natural introduction and elimination rules. A satisfactory account of iterated ground falls directly out of the resulting logic: non- factive grounding (...) claims, if true, are zero-grounded in the sense of Fine. (shrink)

Do sensory measurements deserve the label of “measurement”? We argue that they do. They fit with an epistemological view of measurement held in current philosophy of science, and they face the same kinds of epistemological challenges as physical measurements do: the problem of coordination and the problem of standardization. These problems are addressed through the process of “epistemic iteration,” for all measurements. We also argue for distinguishing the problem of standardization from the problem of coordination. To exemplify our claims, we (...) draw on olfactory performance tests, especially studies linking olfactory decline to neurodegenerative disorders. (shrink)

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...) on the logical conception of set which motivates naive set theory. The accepted solution is to replace this with the iterative conception of set. -/- I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected. (shrink)

This article provides a discussion of the principle of transmission of evidential support across entailment from the perspective of belief revision theory in the AGM tradition. After outlining and briefly defending a small number of basic principles of belief change, which include a number of belief contraction analogues of the Darwiche-Pearl postulates for iterated revision, a proposal is then made concerning the connection between evidential beliefs and belief change policies in rational agents. This proposal is found to be suffcient to (...) establish the truth of a much-discussed intuition regarding transmission failure. (shrink)

In this paper we consider conditional random quantities (c.r.q.’s) in the setting of coherence. Based on betting scheme, a c.r.q. X|H is not looked at as a restriction but, in a more extended way, as \({XH + \mathbb{P}(X|H)H^c}\) ; in particular (the indicator of) a conditional event E|H is looked at as EH + P(E|H)H c . This extended notion of c.r.q. allows algebraic developments among c.r.q.’s even if the conditioning events are different; then, for instance, we can give a (...) meaning to the sum X|H + Y|K and we can define the iterated c.r.q. (X|H)|K. We analyze the conjunction of two conditional events, introduced by the authors in a recent work, in the setting of coherence. We show that the conjoined conditional is a conditional random quantity, which may be a conditional event when there are logical dependencies. Moreover, we introduce the negation of the conjunction and by applying De Morgan’s Law we obtain the disjoined conditional. Finally, we give the lower and upper bounds for the conjunction and disjunction of two conditional events, by showing that the usual probabilistic properties continue to hold. (shrink)

This article argues that various deviations from the basic principles of the scientific ethos – primarily the appearance of pseudoscience in scientific communities – can be formulated and explained using specific models of game theory, such as the prisoner’s dilemma and the iterated prisoner’s dilemma. The article indirectly tackles the deontology of scientific work as well, in which it is assumed that there is no room for moral skepticism, let alone moral anti-realism, in the ethics of scientific communities. Namely, on (...) the basis of the generally accepted dictum of scientific endeavor as the pursuit of knowledge exclusively for knowledge’s sake, scientifically »right« behavior is seen to be clearly defined and distinguishable from scientifically »wrong« behavior. After elucidating the basic principles of game theory, the article illustrates – by using imaginary and real cases, as well as some views from the philosophyof biology (the units of selection debate) – how this sort of reasoning could be applied in an analysis of the functioning of science. (shrink)