
299511.476825
Higherorder evidence is, roughly, evidence of evidence. The idea is that evidence comes in levels. At the lowest level is evidence of the familiar type —evidence concerning some proposition that is not itself about evidence. At a higher level the evidence concerns some proposition about evidence at a lower level. Only in recent years has this less familiar type been the subject of epistemological focus, and the work on it remains relegated to a small circle of authors—far disproportionate to the attention it deserves. It deserves to occupy center stage for several reasons. First, higherorder evidence frequently arises in a diverse range of contexts, including testimony, disagreement, empirical observation, introspection, and memory, among others. Second, such evidence often plays a crucial epistemic role in these contexts. Third, the role it plays is complex, yields interesting epistemological puzzles, and therefore remains controversial and not yet fully understood. Although the ultimate goal of an investigation into higherorder evidence is to produce an account of its epistemic significance, my present concern is more fundamental. I have two primary sets of goals here. The first is expositional: to serve as an introduction for readers new to the topic. The second is argumentative: to establish that the existing characterizations of the concept of higherorder evidence and various related concepts are in dire need of refinement, to demonstrate that this lack of refinement is the source of major errors in the literature, and to provide the needed refinement to set the stage for further progress.

301156.476893
This paper concerns an investigation of the conceptual spaces account of graded membership in the case of gradable adjectives. Douven and collaborators have shown that the degree of membership of an item intermediate between two color categories (green vs. blue) or two shape categories (vase vs. bowl) can be derived from the categories’ typical instances. An issue left open is whether the conceptual spaces approach can account for graded membership in more abstract categories. In this paper we consider dimensional adjectives such as tall and expensive, for which the notion of prototypicality is more problematic. We present the results of an empirical study showing that the account can be extended successfully to that class, taking advantage of systematic relations of antonymy in those adjectives. The approach’s assumption that typical instances of a category are equally typical and its ability to account for interindividual differences in degree membership are discussed.

315409.476932
Consider this Thomisticstyle doctrine:
God’s believing that a contingent entity x exists is the cause of x’s existing. Let B be God’s believing that I exist. Then, either
B exists in all possible worlds
or
B exists in all and only the worlds where I exist. …

402084.476964
Stephen Senn
Stephen Senn
Head of Competence Center for Methodology and Statistics (CCMS)
Luxembourg Institute of Health
Twitter @stephensenn
Automatic for the people? Not quite
What caught my eye was the estimable (in its nonstatistical meaning) Richard Lehman tweeting about the equally estimable John Ioannidis. …

595841.477
Analogical reasoning addresses the question how evidence from various phenomena can be amalgamated and made relevant for theory development and prediction. In the first part of my contribution, I review some influential accounts of analogical reasoning, both historical and contemporary, focusing in particular on Keynes, Carnap, Hesse, and more recently Bartha. In the second part, I sketch a general framework. To this purpose, a distinction between a predictive and a conceptual type of analogical reasoning is introduced. I then take up a common intuition according to which (predictive) analogical inferences hold if the differences between source and target concern only irrelevant circumstances. I attempt to make this idea more precise by addressing possible objections and in particular by specifying a notion of causal irrelevance based on difference making in homogeneous contexts.

595877.477034
This paper provides a critical guide to the literature concerning the answer to the question: when does a quantum experiment have an result? This question was posed and answered by Rovelli (Rovelli [1998]) and his proposal was critiqued by Oppenheim, Reznick and Unruh (Oppenheim et al. [2000]), who also suggest another approach that (as they point out) leads to the quantum Zeno effect. What these two approaches have in common is the idea that a question about the time at which an event occurs can be answered through the instantaneous measurement of a projector (in Rovelli’s case, a single measurement; in that of Oppenheim et al. [2000], a repeated measurement). However, the interpretation of a projection as an instantaneous operation that can be performed on a system at a time of the experimenter’s choosing is problematic, particularly when it is the time of the outcome of the experiment that is at issue.

603660.477066
Today’s Virtual Colloquium is “God’s Standing to Forgive” by Brandon Warmke. Dr. Warmke received his PhD in philosophy from the University of Arizona in 2014 and is currently Assistant Professor of Philosophy at Bowling Green State University in Ohio. …

653522.477093
The popular impression of Bohmian mechanics is that it is standard quantum mechanics with the addition of some extra gadgets— exact particle positions and a guiding equation for particle trajectories— the advantages being that the gadgets pave the way for a resolution of the measurement problem that eschews state vector reduction while restoring the determinism lost in standard quantum mechanics. In fact, the Bohmian mechanics departs in signi…cant ways from standard quantum mechanics. By itself this is not a basis for criticism; indeed, it makes Bohmian mechanics all the more interesting. But Bohmian mechanics is not, as the popular impression would have it, empirically equivalent to standard quantum mechanics in terms of probabilistic predictions for the outcomes of measurements of quantum observables. Indeed, in physically important applications to systems for which standard quantum mechanics delivers empirically wellcon…rmed probabilistic predictions, the sophisticated form of Bohmian mechanics designed to prove the global existence of Bohmian particle trajectories fails to deliver unequivocal predictions— of even a probabilistic variety— for the future behavior of said systems. Possible responses to this lacuna are discussed.

653539.477107
The idea that the quantum probabilities are best construed as the personal/subjective degrees of belief of Bayesian agents is an old one. In recent years the idea has been vigorously pursued by a group of physicists who ‡y the banner of quantum Bayesianism (QBism). The present paper aims to identify the prospects and problems of implementing QBism, and it critically assesses the claim that QBism provides a resolution (or dissolution) of some of the long standing foundations issues in quantum mechanics, including the measurement problem and puzzles of nonlocality.

659018.477132
How do you determine the answer to the question of how likely it is that H is true? To answer it, you will need to do at least two things. First, you will need to figure out what evidence is in your possession. And second, you will need to figure out how likely H is to be true, given that totality of evidence. Most of the efforts of confirmation theory have been dedicated to understanding the second of these two tasks, i.e., explaining the confirmation relations between any arbitrary evidence set and any arbitrary hypothesis. But in the past two decades, many epistemologists have tried to understand the first of the two tasks, viz., determining what evidence is in your possession.

834212.477156
Neyman April 16, 1894 – August 5, 1981
For my final Jerzy Neyman item, here’s the post I wrote for his birthday last year:
A local acting group is putting on a short theater production based on a screenplay I wrote: “Les Miserables Citations” (“Those Miserable Quotes”) [1]. …

861623.477188
Here are two technical problems with consciousness causes collapse (ccc) interpretations of quantum mechanics. In both, suppose a quantum experiment with two possible outcomes, A and B, of equal probability 1/2. …

884320.477219
In his article “Reassurance via Translation” Marcel Crabbe proposed a formalism to obtain reassurance and classical recapture in the setting of minimal F DE. His formalism proved to be general enough to be extended in order to formalize other forms of nonmonotonic systems based on preference relations. It is the aim of this article to show how his result can be extended in a natural way by combining two different reasoning systems, namely minimal F DE and circumscription, in order to get a paraconsistent and paracomplete version of circumscription, which we will call paracomplistent circumscription, which has the advantages of F DE and circumscription but is neither explosive nor lacks modus ponens in consistent contexts. Furthermore, we will complete a proof Crabbe left unfinished.

934604.477251
Much recent work in modal epistemology assumes a kind of modal realism according to which reality includes basic modal elements—basic capacities, essences, counterfactuals, etc., which are simply out there, waiting to be discovered. Alternative views of modality put modal epistemology in a very different light. On the reductionist Humean view championed by Lewis (e.g. [Lewis 1986b], [Lewis 1986a], [Lewis 1994]), modal statements express ultimately nonmodal propositions concerning the spatiotemporal distribution of categorical properties, and thus modal knowledge is not knowledge of special modal facts. On conventionalist accounts (like [Ayer 1936] or [Sidelle 1989]), modal knowledge is presumably knowledge of linguistic conventions. On projectivist accounts (like [Skyrms 1980] or [Blackburn 1986]), modal knowledge is not knowledge of genuine objective facts at all.

949446.477279
April 16, 1894 – August 5, 1981
I’ll continue to post Neymanrelated items this week in honor of his birthday. This isn’t the only paper in which Neyman makes it clear he denies a distinction between a test of statistical hypotheses and significance tests. …

1007091.477316
J. D. Hamkins and M. Kikuchi, “The inclusion relations of the countable models of set theory are all isomorphic.” (manuscript under review)
Citation arχiv
@ARTICLE{HamkinsKikuchi:Theinclusionrelationsofthecountablemodelsofsettheoryareallisomorphic,
author = {Joel David Hamkins and Makoto Kikuchi},
title = {The inclusion relations of the countable models of set theory are all isomorphic},
journal = {},
editor = {},
year = {},
volume = {},
number = {},
pages = {},
month = {},
doi = {},
note = {manuscript under review},
eprint = {1704.04480},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/inclusionrelationsareallisomorphic},
abstract = {},
keywords = {},
source = {},
}
Abstract. …

1039274.477347
Today is Jerzy Neyman’s birthday. I’ll post various Neyman items this week in honor of it, starting with a guest post by Aris Spanos. Happy Birthday Neyman! A. Spanos
A Statistical Model as a Chance Mechanism
Aris Spanos
Jerzy Neyman (April 16, 1894 – August 5, 1981), was a Polish/American statistician[i] who spent most of his professional career at the University of California, Berkeley. …

1166524.477378
I was just reading a paper by Martin and Liu (2014) in which they allude to the “questionable logic of proving H0 false by using a calculation that assumes it is true”(p. 1704). They say they seek to define a notion of “plausibility” that
“fits the way practitioners use and interpret pvalues: a small pvalue means H0 is implausible, given the observed data,” but they seek “a probability calculation that does not require one to assume that H0 is true, so one avoids the questionable logic of proving H0 false by using a calculation that assumes it is true“(Martin and Liu 2014, p. 1704). …

1172608.477412
In philosophy of statistics, Deborah Mayo and Aris Spanos have championed the following epistemic principle, which applies to frequentist tests: Severity Principle (full). Data x (produced by process G) provides good evidence for hypothesis H (just) to the extent that test T severely passes H with x . (Mayo and Spanos 2011, p.162). They have also devised a severity score that is meant to measure the strength of the evidence by quantifying the degree of severity with which H passes the test T (Mayo and Spanos 2006, 2011; Spanos 2013). That score is a real number defined on the interval [0,1]. That score is particularly high for hypotheses that are substantially different from the nullhypothesis when a significant result is obtained by using an underpowered test. This means that such hypotheses are very well supported by the evidence according to that measure. However, it is now well documented that significant tests with low power display inflated effect sizes. They systematically show departures from the null hypothesis H0 that are much greater than they really are:”theoretical considerations prove that when true discovery is claimed based on crossing a threshold of statistical significance and the discovery study is underpowered, the observed effects are expected to be inflated”(Ioannidis 2008, p.640) This is problematic in research contexts where the differences between H0 and H1 is particularly small and where the sample size is also small. See(Button et al. 2013; Ioannidis 2008; Gelman and Carlin 2014) for examples).

1335486.477442
Many accounts of structural rationality give a special role to logic. This paper reviews the problem case of cleareyed logical uncertainty. An account of rational norms on belief that does not give a special role to logic is developed: doxastic probabilism.

1337593.477475
This paper provides a new argument for a natural view in distributive ethics: that the interests of the relatively worse off matter more than the interests of the relatively better off, in the sense that it is more important to give some benefit to those that are worse off than it is to give that same benefit to those that are better off, and that it is sometimes (but not always) more important to give a smaller benefit to the worse off than to give a larger benefit to those better off. I will refer to this position as relative prioritarianism. The formal realization of this position is known as weightedrank utilitarianism or the Gini social welfare function, and it is typically classified as an egalitarian view, though for reasons I will mention that classification may be misleading.

1411070.477507
This paper shows how to conservatively extend theories formulated in nonclassical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s ˙= fA(¯t) and A(¯t, s) even though A( ¯x, y) determines the extension of a function.

1452939.47754
At least since Aristotle’s famous ‘seabattle’ passages in On Interpretation 9, some substantial minority of philosophers has been attracted to what we might call the doctrine of the open future. Open future views (of the sort in question) maintain that future contingent statements— roughly, statements saying of causally undetermined events that they will happen—are never true. Some such views have it that future contingents are neither true nor false; others maintain that they are instead simply false. Both views, however, face a problem: prima facie, they seem inconsistent with what John MacFarlane has called the determinacy intuition—the intuition, roughly, that if something has happened, then (looking backwards) it was the case that it would happen (MacFarlane 2014: Ch. 9). According to MacFarlane, the indeterminacy intuition has it that, looking forwards, future contingents are never true—but the determinacy intuition has it that, looking backwards, they were. This tension forms, in large part, what might be called the problem of future contingents.

1461056.477571
We provide a sufficient frametheoretic condition for a superbiintuitionistic logic to have Maksimova’s variable separation property. We conclude that biintuitionistic logic enjoys the property. Furthermore, we offer an algebraic characterization of the superbiintuitionistic logics with Maksimova’s property.

1461074.477601
This paper reflects on metametaphysics and as such develops a metametametaphysical view: that quietist metametaphysics requires dialetheism, and in turn a paraconsistent logic. I demonstrate this using Carnap’s metametaphysical position in his ‘Empiricism, Semantics and Ontology’ (1950) as an example, with regard to how it exhibits selfreference and results in inconsistency. I show how applying Carnap’s position to itself produces a dilemma, both horns of which lead to a contradiction. Such inconsistency commonly arises from metatheories with global scope, as the ‘meta’ approach aims to transcend the scope of that which it is theorizing about, whilst the global nature will place itself back within the scope of that which it is theorizing about, which together result in the theory referring to itself whilst refuting itself. I argue that any global metametaphysical theory that draws a limit to thought will face selfreference problems leading to contradictory realms. My conclusion is conditional: If we want to metaphilosophize in such a way and treat quietist metatheories as being true, then we need to be dialetheist and utilize a paraconsistent logic in order to accommodate the contradictions that result from such theorizing.

1461112.477632
A theorem from Archimedes on the area of a circle is proved in a setting where some inconsistency is permissible, by using paraconsistent reasoning. The new proof emphasizes that the famous method of exhaustion gives approximations of areas closer than any consistent quantity. This is equivalent to the classical theorem in a classical context, but not in a context where it is possible that there are inconsistent infinitesimals. The area of the circle is taken ‘up to inconsistency’. The fact that the core of Archimedes’s proof still works in a weaker logic is evidence that the integral calculus and analysis more generally are still practicable even in the event of inconsistency.

1461172.477663
This paper investigates the use of neighborhood frames as a semantics for the logics of unknown truths and related nonnormal epistemic systems, including the logic of false beliefs. However, the interest in these logics is not restricted to epistemic settings. As such, this paper is perhaps better viewed as a continuation of the study of reflexiveinsensitive logics (we borrow this terminology from [3]) that was initiated in [5] and further developed in [7] and [3]. In addition to this more systematic motive, it is also our desire to further elucidate (and exploit, in some cases) the connections between these logics and provability logics.

1461238.477693
Circular definitions have primarily been studied in revision theory in the classical scheme. I present systems of circular definitions in the Strong Kleene and supervaluation schemes and provide complete proof systems for them. One class of definitions, the intrinsic definitions, naturally arises in both schemes. I survey some of the features of this class of definitions.

1461260.477722
In recent years, two nonclassical views about negation have gained considerable traction in the philosophical literature. The paracomplete view holds that excluded middle (EM) is invalid, while the paraconsistent view holds that explosion (EX) is invalid. Both run contrary to classical logic in distinct but dual ways.

1525866.477751
If $M$ is a model of ZFC set theory, let $I$ be the definable cut of its ordinals, the collection of ordinals that are below an ordinal $\delta$ of $M$ that is definable in $M$ without parameters. This would include all the ordinals of $M$, if the definable ordinals happen to be unbounded in $M$, but one can also construct examples where the definable cut is bounded in $M$. …