
74812.070144
Let’s suppose someone says that Gödel is the man who proved the incompleteness of arithmetic. . . . In the case of Gödel that’s practically the only thing many people have heard about him—that he discovered the incompleteness of arithmetic. Does it follow that [for such people] whoever discovered the incompleteness of arithmetic is the referent of ‘Godel’? . . . Suppose that Gödel was not in fact the author of this theorem. A man named ‘Schmidt’, whose body was found in Vienna under mysterious circumstances many years ago, actually did the work in question. His friend Gödel somehow got hold of the manuscript and it was thereafter attributed to Gödel. On the view in question, then, . . . since the man who discovered the incompleteness of arithmetic is in fact Schmidt, we [who have heard nothing else about Gödel], when we talk about ‘Gödel’, are in fact always referring to Schmidt. But it seems to me that we are not. We simply are not. (Kripke, 1980, pp. 83–4) The judgement Kripke reports here is often regarded as a paradigmatic case of an appeal to ‘philosophical intuition’, and such appeals have been the subject of much recent debate. This particular one attracted the attention, some years ago, of Machery, Mallon, Nichols, and Stich (MMN&S), who were then at the leading edge of the emerging ‘experimental philosophy’ movement. Their paper “Semantics, CrossCultural Style” reported the results of experiments that show, or so they claimed, that such intutions vary crossculturally. In particular, although ‘Westerners’ do tend to agree with Kripke, ‘East Asians’ tend to disagree.

138985.070215
This paper presents an account of the semantic content and conventional discourse effects of a range of sentence types in English, namely falling declaratives, polar interrogatives, and certain kinds of rising declaratives and tag interrogatives. The account aims to divide the labor between compositional semantics and conventions of use in a principled way. We argue that falling declaratives and polar interrogatives are unmarked sentence types. On our account, differences in their conventional discourse effects follow from independently motivated semantic differences combined with a single convention of use, which applies uniformly to both sentence types. As a result, the Fregean ‘illocutionary force operators’ Assertion and Question become unnecessary. In contrast, we argue that rising declaratives and tag interrogatives are marked sentence types. On our account, their conventional discourse effects consist of the effects that are dictated by the basic convention of use that is common to all sentence types considered here, augmented with special effects that are systematically connected to their formal properties. Thus, a central feature of our approach is that it maintains a parallelism between unmarked and marked sentence types on the one hand, and basic and complex discourse effects on the other.

194813.070237
There is a familiar philosophical position – sometimes called the doctrine of the open future – according to which future contingents (claims about underdetermined aspects of the future) systematically fail to be true. For instance: supposing that there are ways things could develop from here in which Trump is impeached, and in which he is not, it is not now true that Trump will be impeached, and not now true that Trump will not be impeached. For well over 2000 years, however, open futurists have been accused of denying certain logical laws – bivalence, excluded middle, or both – for entirely ad hoc reasons, most notably, that their denials are required for the preservation of something we hold dear. In a recent paper, however, I sought to argue that this deeply entrenched narrative ought to be overturned. My thought was this: given a popular, plausible approach to the semantics of future contingents, we can reduce the question of their status to the Russell/Strawson debate concerning presupposition failure, definite descriptions, and bivalence. In that case, we will see that open futurists in fact needn’t deny bivalence (Russell), or, if they do, they will do so for perfectly general (Strawsonian) reasons – reasons for which we all must deny bivalence. Of course, the metaphysical objections to the open futurist’s model of the future will remain just as they were. However, the millenniaold “semantic” or “logical” objections to the doctrine would be answered.

202487.070261
In this paper I investigate whether certain substructural theories are able to dodge paradox while at the same time containing what might be viewed as a naive validity predicate. To this end I introduce the requirement of internalization, roughly, that an adequate theory of validity should prove that its own metarules are validitypreserving. The main point of the paper is that substructural theories fail this requirement in various ways.

209161.070303
It’s been a long time since I’ve blogged about the Complex Adaptive System Composition and Design Environment or CASCADE project run by John Paschkewitz. For a reminder, read these:
• Complex adaptive system design (part 1), Azimuth, 2 October 2016. …

308146.070339
The need for expressing temporal constraints in conceptual models is wellknown, but it is unclear which representation is preferred and what would be easier to understand by modellers. We assessed five different modes of representing temporal constraints, being the formal semantics, Description logics notation, a codingstyle notation, temporal EER diagrams, and (pseudo)natural language sentences. The same information was presented to 15 participants in an experimental evaluation. Principally, it showed that 1) there was a clear preference for diagrams and natural language versus a dislike for other representations; 2) diagrams were preferred for simple constraints, but the natural language rendering was preferred for more complex temporal constraints; and 3) a multimodal modelling tool will be needed for the data analysis stage to be effective.

368394.070357
There’s a new paper on the arXiv that claims to solve a hard problem:
• Norbert Blum, A solution of the P versus NP problem. Most papers that claim to solve hard math problems are wrong: that’s why these problems are considered hard. …

368397.070373
We owe to Frege in Begriffsschrift our modern practice of taking unrestricted quantification (in one sense) as basic. I mean, he taught us how to rephrase restricted quantifications by using unrestricted quantifiers plus connectives in the now familiar way, so that e.g. …

700360.070392
In models for paraconsistent logics, the semantic values of sentences and their negations are less tightly connected than in classical logic. In “American Plan” logics for negation, truth and falsity are, to some degree, independent. The truth of ∼p is given by the falsity of p, and the falsity of ∼p is given by the truth of p. Since truth and falsity are only loosely connected, p and ∼p can both hold, or both fail to hold. In “Australian Plan” logics for negation, negation is treated rather like a modal operator, where the truth of ∼p in a situation amounts to p failing in certain other situations. Since those situations can be different from this one, p and ∼p might both hold here, or might both fail here.

702653.070407
The main goal of this article is to defend nonmetacognitive interpretations of both the questionasking and questionanswering behavior of young children. Rather than manifesting awareness of their own states of knowledge or ignorance (as many in the field assume), such behavior is best seen as dependent upon a set of firstorder (nonmetacognitive) questioning attitudes, such as curiosity. In addition, the role of such attitudes in other aspects of development is briefly considered.

876823.070422
Nelson Goodman has certainly been one of the most influential figures
in contemporary aesthetics and analytic philosophy in general (in
addition to aesthetics, his contributions cover the areas of applied
logic, metaphysics, epistemology, and philosophy of science). His
Languages of Art (first published in 1968 [Goodman 1976]),
together with Ernst Gombrich’s Art and Illusion (1960)
and Richard Wollheim’s Art and Its Objects (1968),
represents a fundamental turning point in the analytic approach to
artistic issues in AngloAmerican philosophy. His often unorthodox
take on art is part of a general approach to knowledge and reality,
and is always pervasively informed by his cognitivism, nominalism,
relativism, and constructivism.

931082.070437
We give a precise semantics for a proposed revised version of the Knowledge Interchange Format. We show that quantification over relations is possible in a firstorder logic, but sequence variables take the language beyond firstorder.

1010433.070452
We report on progress and an unsolved problem in our attempt to obtain a clear rationale for relevance logic via semantic decomposition trees. Suitable decomposition rules, constrained by a natural parity condition, generate a set of directly acceptable formulae that contains all axioms of the wellknown system R, is closed under substitution and conjunction, satisfies the lettersharing condition, but is not closed under detachment. To extend it, a natural recursion is built into the procedure for constructing decomposition trees. The resulting set of acceptable formulae has many attractive features, but it remains an open question whether it continues to satisfy the crucial lettersharing condition.

1043813.070467
J. D. Hamkins and O, “The modal logic of settheoretic potentialism and the potentialist maximality principles.” (manuscript in preparation)
Citation arχiv
@ARTICLE{HamkinsLinnebo:Modallogicofsettheoreticpotentialism,
author = {Joel David Hamkins and {\O}ystein Linnebo},
title = {The modal logic of settheoretic potentialism and the potentialist maximality principles},
journal = {},
year = {},
volume = {},
number = {},
pages = {},
month = {},
note = {manuscript in preparation},
abstract = {},
keywords = {},
source = {},
eprint = {1708.01644},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/settheoreticpotentialism},
doi = {},
}
Abstract. …

1049693.070481
The medieval name for paradoxes like the famous Liar Paradox
(“This proposition is false”) was “insolubles”
or insolubilia,
^{[ 1 ]}
though besides semantic paradoxes, they included epistemic paradoxes,
e.g., “You do not know this proposition”. From the
latetwelfth century to the end of the Middle Ages and beyond, such
paradoxes were discussed at length by an enormous number of authors. Yet, unlike twentieth century interest in the paradoxes, medieval
interest seems not to have been prompted by any sense of theoretical
“crisis”. The history of the medieval discussions can be divided into three main
periods: (a) an early stage, from the latetwelfth century to the
1320s; (b) a period of especially intense and original work, during
roughly the second quarter of the fourteenth century; (c) a late
period, from about 1350 on.

1077455.070504
We propose an investigation of the ways in which speakers’ subjective perspectives are likely to affect the meaning of gradable adjectives like tall or heavy. We present the results of a study showing that people tend to use themselves as a yardstick when ascribing these adjectives to human figures of variable measurements: subjects’ height and weight requirements for applying tall and heavy are found to be positively correlated with their personal measurements. We draw more general lessons regarding the definition of subjectivity and the ways in which a standard of comparison and a significant deviation of that standard are specified.

1077503.070536
Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin’s [16] semantic consequence relation for a language with epistemic modals and indicative conditionals. In the other direction, the formal semantics for indicative conditionals due to Kolodny and MacFarlane [9] gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane’s indicative conditional via a full and faithful computable translation from their logic to the modal logic K45.

1222819.07057
In 1986 David Gauthier proposed an arbitration scheme for two player cardinal bargaining games based on interpersonal comparisons of players’ relative concessions. In Gauthier’s original arbitration scheme, players’ relative concessions are defined in terms of Raiffanormalized cardinal utility gains, and so it cannot be directly applied to ordinal bargaining problems. In this paper I propose a relative benefit equilibrating bargaining solution (RBEBS ) for two and nplayer ordinal and quasiconvex ordinal bargaining problems with finite sets of feasible basic agreements based on the measure of players’ ordinal relative individual advantage gains. I provide an axiomatic characterization of this bargaining solution and discuss the conceptual relationship between RBEBS and ordinal egalitarian bargaining solution (OEBS ) proposed by Conley and Wilkie (2012). I show the relationship between the measurement procedure for ordinal relative individual advantage gains and the measurement procedure for players’ ordinal relative concessions, and argue that the proposed arbitration scheme for ordinal games can be interpreted as an ordinal version of Gauthier’s arbitration scheme.

1330045.070603
This article offers an overview of inferential role semantics. We aim to provide a map of the terrain as well as challenging some of the inferentialist’s standard commitments. We begin by introducing inferentialism and placing it into the wider context of contemporary philosophy of language. §2 focuses on what is standardly considered both the most important test case for and the most natural application of inferential role semantics: the case of the logical constants. We discuss some of the (alleged) benefits of logical inferentialism, chiefly with regards to the epistemology of logic, and consider a number of objections. §3 introduces and critically examines the most influential and most fully developed form of global inferentialism: Robert Brandom’s inferentialism about linguistic and conceptual content in general. Finally, in §4 we consider a number of general objections to IRS and consider possible responses on the inferentialist’s behalf.

1332313.070634
Suszko’s problem is the problem of finding the minimal number of truth values needed to semantically characterize a syntactic consequence relation. Suszko proved that every Tarskian consequence relation can be characterized using only two truth values. Malinowski showed that this number can equal three if some of Tarski’s structural constraints are relaxed. By so doing, Malinowski introduced a case of socalled mixed consequence, allowing the notion of a designated value to vary between the premises and the conclusions of an argument. In this paper we give a more systematic perspective on Suszko’s problem and on mixed consequence.

1332802.070666
Rational choice theorists and deontic logicians both study actions, yet using very different approaches and tools. This paper introduces some choicetheoretic concepts – feasible options, choice contexts, choice functions, rankings of options, and reasons structures – into deontic logic. These concepts are used to define a simple ‘choicetheoretic’ language for deontic logic, and four ‘choicetheoretic’ semantics for that language, called basic, behavioural, rankingbased and reasonbased semantics, respectively. We compare these semantics in terms of the strength of their entailment relations, and characterize precisely the ‘gaps’ in strength between weaker and stronger ones of these semantics.

1337826.070698
Plato (429?–347 B.C.E.) is, by any reckoning, one of the most
dazzling writers in the Western literary tradition and one of the most
penetrating, wideranging, and influential authors in the history of
philosophy. An Athenian citizen of high status, he displays in his
works his absorption in the political events and intellectual movements
of his time, but the questions he raises are so profound and the
strategies he uses for tackling them so richly suggestive and
provocative that educated readers of nearly every period have in some
way been influenced by him, and in practically every age there have
been philosophers who count themselves Platonists in some important
respects.

1337872.070729
In his seminal address delivered in 1945 to the Royal Society Gilbert Ryle considers a special case of knowinghow, viz., knowing how to reason according to logical rules. He argues that knowing how to use logical rules cannot be reduced to a propositional knowledge. We evaluate this argument in the context of two different types of formal systems capable to represent knowledge and support logical reasoning: Hilbertstyle systems, which mainly rely on axioms, and Gentzenstyle systems, which mainly rely on rules. We build a canonical syntactic translation between appropriate classes of such systems and demonstrate the crucial role of Deduction Theorem in this construction. This analysis suggests that one’s knowledge of axioms and one’s knowledge of rules under appropriate conditions are also mutually translatable. However our further analysis shows that the epistemic status of logical knowinghow ultimately depends on one’s conception of logical consequence: if one construes the logical consequence after Tarski in modeltheoretic terms then the reduction of knowinghow to knowingthat is in a certain sense possible but if one thinks about the logical consequence after Prawitz in prooftheoretic terms then the logical knowledgehow gets an independent status. Finally we extend our analysis to the case of extralogical knowledgehow representable with Gentzenstyle formal systems, which admit constructive meaning explanations. For this end we build a typed sequential calculus and prove for it a “constructive” Deduction Theorem interpretable in extralogical terms. We conclude with a number of open questions, which concern translations between knowledgehow and knowledgethat in this more general semantic setting.

1337992.070758
According to the iterative conception of sets, standardly formalized by ZFC, there is no set of all sets. But why is there no set of all sets? A simpleminded, though unpopular, “minimal” explanation for why there is no set of all sets is that the supposition that there is contradicts some axioms of ZFC. In this paper, I first explain the core complaint against the minimal explanation, and then argue against the two main alternative answers to the guiding question. I conclude the paper by outlining a close alternative to the minimal explanation, the conceptionbased explanation, that avoids the core complaint against the minimal explanation.

1338084.070775
The periodic table of elements represents and organizes all known chemical elements on the basis of their properties. While the importance of this table in chemistry is uncontroversial the role that it plays in scientific reasoning remains heavily disputed. Many philosophers deny the explanatory role of the periodic table, while insisting that it is “merely” classificatory (Shapere 1977, 5345) (Scerri 1997a, 239). In particular, it has been claimed that the table doesn’t figure in causal explanation because it “does not reveal causal structure” (Woody 2014, 143). This paper argues that the modern periodic table does reveal causal structure in the sense of containing causal information that figures in explanations in chemistry. However, this analysis suggests that the earliest versions of the table did serve more of a classificatory role, as they lack the causal structure present in modern versions.

1340847.07079
There is an argument based on sentences that describe pictures in favor of a viewpointcentered possible worlds semantics for pictures, over a propositional semantics (J. Ross 1997). The argument involves perspectival lexical items such as “front”. We show that when a projective possible worlds semantics for pictures is employed, there is a problem with the argument coming from propositional contents being strong. The argument is reconstructed in a model modal space involving linear worlds, and it is shown that it works there, by computing the possible worlds semantics. The construction involves propositions and centered propositions that are regular sets of strings. Finally, by manipulating the marking parameter in a projective semantics for pictures, the argument is reconstructed also for 3D models.

1341878.070804
A number of philosophers and logicians have argued for the conclusion that maps are logically tractable modes of representation by analyzing them in propositional terms. But in doing so, they have often left what they mean by ‘propositional’ undefined or unjustified. I argue that propositions are characterized by a structure that is digital, universal, asymmetrical, and recursive. There is little positive evidence that maps exhibit these features. Instead, we can better explain their functional structure by taking seriously the observation that maps arrange their constituent elements in a nonhierarchical, holistic structure. This is compatible with the more basic claim advanced by defenders of a propositional analysis: that (many) maps do have a formal semantics and logic.

1353597.070818
What we call the HilbertBernays (HB) Theorem establishes that for any satisfiable firstorder quantificational schema S, there are expressions of elementary arithmetic that yield a true sentence of arithmetic when they are substituted for the predicate letters in S. Our goals here are, first, to explain and defend W. V. Quine’s claim that the HB theorem licenses us to define the firstorder logical validity of a schema in terms of predicate substitution; second, to clarify the theorem by sketching an accessible and illuminating new proof of it; and, third, to explain how Quine’s substitutional definition of logical notions can be modified and extended in ways that make it more attractive to contemporary logicians.

1355553.070849
There is an important link between necessity and apriority which can shed light on our knowledge of the former, but initially plausible attempts to spell out what it is fall victim to counterexamples. …

1355588.070884
A few years ago, I had observed after hearing a talk by Benjamin Rin that the principle of firstorder transfinite recursion for set wellorders is equivalent to the replacement axiom over Zermelo set theory, and thus we may take transfinite recursion as a fundamental settheoretic principle, one which yields full ZFC when added to Zermelo’s weaker theory (plus foundation). …