
396772.86539
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, pp.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]. In this paper, I put forward a paradoxical feature of the severity score as a measure of evidence. To do this, I create a scenario where a frequentist statistician S is interested in finding out if there is a difference between the means of two normally distributed random variables. The null hypothesis (H0) states that there is no difference between the two means.

522055.865474
Today’s Virtual Colloquium is “Global and Local Atheisms” by Jeanine Diller. Dr. Diller received her PhD from the University of Michigan and is currently an assistant professor in the Department of Philosophy and Program on Religious Studies of the University of Toledo in Ohio. …

569727.865509
I propose a new definition of identification in the limit (also called convergence to the truth), as a new success criterion that is meant to complement, rather than replacing, the classic definition due to Gold (1967). The new definition is designed to explain how it is possible to have successful learning in a kind of scenario that Gold’s classic account ignores—the kind of scenario in which the entire infinite data stream to be presented incrementally to the learner is not presupposed to completely determine the correct learning target. From a purely mathematical point of view, the new definition employs a convergence concept that generalizes net convergence and sits in between pointwise convergence and uniform convergence. Two results are proved to suggest that the new definition provides a success criterion that is by no means weak: (i) Between the new identification in the limit and Gold’s classic one, neither implies the other. (ii) If a learning method identifies the correct target in the limit in the new sense, any Ushaped learning involved therein has to be redundant and can be removed while maintaining the new kind of identification in the limit. I conclude that we should have (at least) two success criteria that correspond to two senses of identification in the limit: the classic one and the one proposed here. They are complementary: meeting any one of the two is good; meeting both at the same time, if possible, is even better.

627328.865529
In this work we present a dynamical approach to quantum logics. By changing the standard formalism of quantum mechanics to allow nonHermitian operators as generators of time evolution, we address the question of how can logics evolve in time. In this way, we describe formally how a nonBoolean algebra may become a Boolean one under certain conditions. We present some simple models which illustrate this transition and develop a new quantum logical formalism based in complex spectral resolutions, a notion that we introduce in order to cope with the temporal aspect of the logical structure of quantum theory.

627344.865545
We discuss generalized pobabilistic models for which states not necessarily obey Kolmogorov’s axioms of probability. We study the relationship between properties and probabilistic measures in this setting, and explore some possible interpretations of these measures.

834872.86556
There was a period in the 1970’s when the admissions data for the UC–Berkeley graduate school (hereafter, BGS) exhibited some (prima facie) peculiar statistical correlations. Specifically, a strong negative correlation was observed between being female and being accepted into BGS. This negative correlation (in the overall population of BGS applicants) was (initially) a cause for some concern regarding the possibility of gender bias in the admissions process at BGS. However, closer scrutiny of the BGS admissions data from this period revealed that no individual department’s admissions data exhibited a negative correlation between being female and being admitted. In fact, every department reported a positive correlation between being female and being accepted. In other words, a correlation that appears at the level of the general population of BGS applicants is reversed in every single department of BGS. This sort of correlation reversal is known as Simpson’s Paradox. Because admissions decisions at BGS are made (autonomously) by each individual department, the lack of departmental correlations seems to ruleout the gender bias hypothesis as the best (causal) explanation of the observed correlations in the data. As it happens, there was a strong positive correlation between being female and applying to a department with a (relatively) high rejection rate.

1075380.865575
It was, I think, till recently broadly assumed among working analytic metaphysicians that metaphysics, or at least that branch of it called ontology, is concerned with issues of existence, and that one’s known arguments that one can resist positing Meinongian unreal objects by accepting his theory of descriptions. However, it would be a mistake to read Russell as nothing more than a protoQuinean. This will no doubt already be conceded for the period of Russell’s career in which he thought there were notions of “existence” not explicable by means of the existential quantifier, or embraced a distinction between existence and mere being or subsistence (e.g., PoM §427, Papers 4, 486–89, PP 100). However, in what follows I want to argue that this is true even for mature Russell, during the period (starting roughly 1913) in which he officially held the position that all existence claims are to be understood quantificationally. In particular, metaphysical position is more or less exhausted by one’s position on while mature Russell understood “Fs exist” as expressing p(∃v)Fvq, the question of what entities there are, or what entities exist. This he would not have taken the truth of this claim necessarily to setlikely stemmed from Quine’s wellknown paper “On What There Is”, tle the metaphysical or ontological status of Fs. Russell had, runviews is determined by what things its quantifiers range over: “To be is to be the value of a variable,” as he succinctly put it (Quine 1948, 15). Of course, Quine’s views were never universal, but at least most ning alongside his account of existence, a conception of belonging to what is, as he variously put it, “ultimate,” “fundamental”, the “bricks of the universe”, the “furniture of the world”, something “really there”.

1312550.86559
We consider a naturallanguage sentence that cannot be formally represented in a firstorder language for epistemic twodimensional semantics. We also prove this claim in the appendix. It turns out, however, that the most natural ways to repair the expressive inadequacy of the firstorder language render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal. In this paper we investigate some questions concerning the expressive power of a firstorder modal language with twodimensional operators. In particular, a language endowed with a twodimensional semantics intended to provide a logical analysis of the discourse involving a priori knowledge. We consider a naturallanguage sentence that cannot be formally represented in such a language. This was firstly conjectured in Lampert (manuscript), but here we present a proof. It turns out, however, that the most natural ways to repair this expressive inadequacy render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal.

1376496.865605
Traditional monotheism has long faced logical puzzles (omniscience, omnipotence, and more) [10, 11, 13, 14]. We present a simple but plausible ‘gappy’ framework for addressing these puzzles. By way of illustration we focus on God’s alleged stone problem. What we say about the stone problem generalizes to other familiar ‘paradoxes of omni properties’, though we leave the generalization implicit. We assume familiarity with the proposed (subclassical) logic but an appendix is offered as a brief review.

1551240.86562
Is part of a perfectly natural, or fundamental, relation? Philosophers have been hesitant to take a stand on this issue. One of reason for this hesitancy is the worry that, if parthood is perfectly natural, then the perfectly natural properties and relations are not suitably “independent” of one another. (Roughly, the perfectly natural properties are not suitably independent if there are necessary connections among them.) In this paper, I argue that parthood is a perfectly natural relation. In so doing, I argue that this “independence” worry is unfounded. I conclude by noting some consequences of the naturalness of parthood.

1557459.865635
We prove that under some technical assumptions on a general, nonclassical probability space, the probability space is extendible into a larger probability space that is common cause closed in the sense of containing a common cause of every correlation between elements in the space. It is argued that the philosophical significance of this common cause completability result is that it allows the defence of the Common Cause Principle against certain attempts of falsification. Some open problems concerning possible strengthening of the common cause completability result are formulated.

1564115.86565
Let me tell you about the game Buckets of fish. This is a twoplayer game played with finitely many buckets in a line on the beach, each containing a finite number of fish. There is also a large supply of additional fish available nearby, fresh off the boats. …

1876767.865665
We offer a defense of one aspect of Paul Horwich’s response to the Liar paradox—more specifically, of his move to preserve classical logic. Horwich’s response requires that the full intersubstitutivity of ‘ ‘A’ is true’ and A be abandoned. It is thus open to the objection, due to Hartry Field, that it undermines the generalization function of truth. We defend Horwich’s move by isolating the grade of intersubstitutivity required by the generalization function and by providing a new reading of the biconditionals of the form “ ‘A’ is true iff A.”

1953189.865683
This paper offers a unified semantic explanation of two observations that prove to be problematic for classical analyses of modals, conditionals, and disjunctions: (i) the fact that disjunctions scoping under possibility modals give rise to the free choice effect and (ii) the fact that counterfactuals license simplification of disjunctive antecedents. It shows that the data are well explained by a dynamic semantic analysis of modals and conditionals that uses ideas from the inquisitive semantic tradition in its treatment of disjunction. The analysis explains why embedding a disjunctive possibility under negation reverts disjunction to its classical behavior, is general enough to predict less studied simplification patterns, and also makes progress toward a unified perspective on the distinction between informative, inquisitive, and attentive content.

2363330.865699
Dependence logic is an extension of firstorder logic which adds to it
dependence atoms, that is, expressions of the form
\(\eqord(x_1 \ldots x_n, y)\) which assert that the value of \(y\) is
functionally dependent on (in other words, determined by) the values
of \(x_1 \ldots x_n\). These atoms permit the specification of
nonlinearly ordered dependency patterns between variables,
much in the same sense of IFLogic slashed quantifiers; but,
differently from IFlogic, dependence logic separates quantification
from the specification of such dependence/independence conditions.

2422593.865714
By “paradox” one usually means a statement claiming
something which goes beyond (or even against) ‘common
opinion’ (what is usually believed or held). Paradoxes form a
natural object of philosophical investigation ever since the origins
of rational thought; they have been invented as part of complex
arguments and as tools for refuting philosophical theses (think of the
celebrated paradoxes credited to Zeno of Elea, concerning motion, the
continuum, the opposition between unity and plurality, or of the
arguments entangling the notions of truth and vagueness, credited to
the Megarian School, and Eubulides of Miletus).

2426834.865733
Mereological universalism
Posted on Thursday, 23 Feb 2017
I used to agree with Lewis that classical mereology, including
mereological universalism, is "perfectly understood, unproblematic,
and certain". …

2559832.865766
Résumé : Cet article cherche à montrer comment la pratique mathématique, particulièrement celle admettant des représentations visuelles, peut conduire à de nouveau résultats mathématiques. L’argumentation est basée sur l’étude du cas d’un domaine des mathématiques relativement récent et prometteur: la théorie géométrique des groupes. L’article discute comment la représentation des groupes par les graphes de Cayley rendit possible la découverte de nouvelles propriétés géométriques de groupes. Abstract: The paper aims to show how mathematical practice, in particular with visual representations can lead to new mathematical results. The argument is based on a case study from a relatively recent and promising mathematical subject—geometric group theory. The paper discusses how the representation of groups by Cayley graphs made possible to discover new geometric properties of groups.

2564667.865803
The slogan ‘Evidence of evidence is evidence’ may sound plausible, but what it means is far from clear. It has often been applied to connect evidence in the current situation to evidence in another situation. The relevant link between situations may be diachronic (White 2006: 538): is present evidence of past or future evidence of something present evidence of that thing? Alternatively, the link may be interpersonal (Feldman 2007: 208): is evidence for me of evidence for you of something evidence for me of that thing? Such interperspectival links have been discussed because they can destabilize interperspectival disagreements. In their own right they have become the topic of a lively recent debate (Fitelson 2012, Feldman 2014, Roche 2014, Tal and Comesaña 2014).

2840495.865841
I give an account of proof terms for derivations in a sequent calculus for classical propositional logic. The term for a derivation δ of a sequent Σ ∆ encodes how the premises Σ and conclusions ∆ are related in δ. This encoding is many–to–one in the sense that different derivations can have the same proof term, since different derivations may be different ways of representing the same underlying connection between premises and conclusions. However, not all proof terms for a sequent Σ ∆ are the same. There may be different ways to connect those premises and conclusions.

2843709.86586
Computational complexity theory is a branch of computer science that is dedicated to classifying computational problems in terms of their difficulty. Unlike computability theory, whose object is to determine what we can compute in principle, the object of complexity theory is to inform us with regards to our practical limits. It thus serves as a natural conceptual bridge between the study of mathematics and the study of technology, in the sense that computational complexity theory

2844927.865875
It is not news that we often make discoveries or find reasons for a mathematical proposition by thinking alone. But does any of this thinking count as conducting a thought experiment? The answer to that question is “yes”, but without refinement the question is uninteresting. Suppose you want to know whether the equation [ 8x + 12y = 6 ] has a solution in the integers. You might mentally substitute some integer values for the variables and calculate. In that case you would be mentally trying something out, experimenting with particular integer values, in order to test the hypothesis that the equation has no solution in the integers. Not getting a solution first time, you might repeat the thought experiment with different integer inputs.

2845127.865891
Hintikka taught us that S5 was the wrong epistemic logic because of the unwarranted powers of negative introspection afforded by the (5) schema, ♦p → ♦p. (Tim Williamson later targeted the (4) schema, and with it S4, but that is another story.) The punchline here is that the problem is really the (B) schema, also known as the Brouwershe schema: (B) p → ♦p. In fact, you should think of the (5) schema within S5 as the best hand to play in a classical modal system with (K) when you are dealt the (B) schema. That is the conclusion of (Wheeler 2015), which is about the logic of information rather than logic for lunatics. The behavior of (B), when interpreted as an epistemic modal rather than as a provability operator, is so bizarre, so unreasonable qua epistemic modal, that epistemic logicians should stop referring to (B) as the Brouwershe schema to avoid sullying Brouwer’s good name. Instead, I recommend hereafter for epistemic logicians to refer to (B) as The Blog Schema.

2845152.865906
The Univalent Foundations (UF) offer a new picture of the foundations of mathematics largely independent from set theory. In this paper I will focus on the question of whether Homotopy Type Theory (HoTT) (as a formalization of UF) can be justified intuitively as a theory of shapes in the same way that ZFC (as a formalization of settheoretic foundations) can be justified intuitively as a theory of collections. I first clarify what I mean by an “intuitive justification” by distinguishing between formal and preformal “meaning explanations” in the vein of MartinLöf. I then explain why MartinLöf’s original meaning explanation for type theory no longer applies to HoTT. Finally, I outline a preformal meaning explanation for HoTT based on spatial notions like “shape”, “path”, “point” etc. which in particular provides an intuitive justification of the axiom of univalence. I conclude by discussing the limitations and prospects of such a project.

2847348.86595
One of Tarski’s stated aims was to give an explication of the classical conception of truth—truth as ‘saying it how it is’. Many subsequent commentators have felt that he achieved this aim. Tarski’s core idea of defining truth via satisfaction has now found its way into standard logic textbooks. This paper looks at such textbook definitions of truth in a model for standard firstorder languages and argues that they fail from the point of view of explication of the classical notion of truth. The paper furthermore argues that a subtly different definition—also to be found in classic textbooks but much less prevalent than the kind of definition that proceeds via satisfaction—succeeds from this point of view.

4289410.865995
Provability logic is a modal logic that is used to investigate what
arithmetical theories can express in a restricted language about their
provability predicates. The logic has been inspired by developments in
metamathematics such as Gödel’s incompleteness theorems of 1931
and Löb’s theorem of 1953. As a modal logic, provability logic
has been studied since the early seventies, and has had important
applications in the foundations of mathematics. From a philosophical point of view, provability logic is interesting
because the concept of provability in a fixed theory of arithmetic has
a unique and nonproblematic meaning, other than concepts like
necessity and knowledge studied in modal and epistemic logic.

4464556.866031
Computer scientists, logicians and functional programmers have studied continuations in laboratory settings for years. As a result of that work, continuations are now accepted as an indispensable tool for reasoning about control, order of evaluation, classical versus intuitionistic proof, and more. But all of the applications just mentioned concern artificial languages; what about natural languages, the languages spoken by humans in their daily life? Do natural languages get by without any of the marvelous control operators provided by continuations, or can we find continuations in the wild? This paper argues yes: that an adequate and complete analysis of natural language must recognize and rely on continuations. In support of this claim, I identify four independent linguistic phenomena for which a simple CPSbased description provides an insightful analysis.

4640182.86605
Although mathematicians often use it, mathematical beauty is a philosophically challenging concept. How can abstract objects be evaluated as beautiful? Is this related to the way we visualise them? Using a case study from graph theory (the highly symmetric Petersen graph), this paper tries to analyse aesthetic preferences in mathematical practice and to distinguish genuine aesthetic from epistemic or practical judgements. It argues that, in making aesthetic judgements, mathematicians may be responding to a combination of perceptual properties of visual representations and mathematical properties of abstract structures; the latter seem to carry greater weight. Mathematical beauty thus primarily involves mathematicians’ sensitivity to aesthetics of the abstract.

4685991.866065
Scopetaking is one of the most fundamental, one of the most characteristic, and one of the most dramatic features of the syntax and semantics of natural languages. A phrase takes scope over a larger expression that contains it when the larger expression serves as the smaller phrase’s semantic argument.

4763427.86608
Brasoveanu 2011 argues that certain expressions exhibit what he calls “association with distributivity” (AWD for short): (1) a. Every boy read a different poem. b. The boys read a different poem. The claim is that in (1a), different can be anaphorically linked to the distributivity introduced by the quantificational determiner every, in which case (1a) entails that no poem was read by more than one boy. In contrast, in (1b) the plural the boys does not introduce distributivity, which is why (on the AWD account) (1b) does not have the reading just described. Instead, (1b) only has an external reading on which different is anaphoric to some element outside to the sentence.