Why contextualists cannot know they are right: Self-refuting implications of contextualism

Conversational contextualism in epistemology is characterized by four main theses: 1. the indexicality of knowledge claims thesis; 2. the attributor contextualism thesis; 3. the conversational contextualism thesis, and 4. the main thesis of contextualism according to which a knowledge claim can be true in one context and false in another context in which more stringent standards for knowledge are operant. It is argued that these theses taken together generate problems for contextualism. In particular, it is shown that there is no context in which the contextualist can truthfully claim to know her theory is true. Since these results were obtained only with principles the contextualist cannot give up—like the principle of epistemic closure and the principle that knowledge implies truth—it seems that contextualism is in need of a thoroughgoing revision if it is to become a successful epistemic theory.     

Contextualist theories of knowledge

Contextualist theories of knowledge offer a semantic hypothesis to explain the observed contextual variation in what people say they know, and the difficulty people have resolving skeptical paradoxes. Subject or speaker relative versions make the truth conditions of “S knows that p” depend on the standards of either the knower’s context (Hawthorne and Stanley) or those of the speaker’s context (Cohen and DeRose). Speaker contextualism avoids objections to subject contextualism, but is implausible in light of evidence that “know” does not behave like an indexical. I deepen and extend these criticisms in light of recent defenses by contextualists (including Ludlow). Another difficulty is that whether certain standards are salient or intended does not entail that they are the proper standards. A normative form of contextualism on which the truth of a knowledge claim depends on the proper standards for the context is more promising, but still unsatisfactory whether the view is speaker or subject relative. I defend alternative explanations for the observed linguistic and psychological data: a pragmatic account for some cases and a cognitive account for others.¹ I presented this paper at the 2004 Bled Conference on Contextualism, sponsored by Mirabor and Northern Illinois Universities.     

Contextualism on a pragmatic,not a skeptical,footing

Contextualism is supposed to explain why the following argument for skepticism seems plausible: (1) I don’t know that I am not a bodiless brain-in-a-vat (BIV); (2) If I know I have hands, then I know I am not a bodiless BIV; (3) Therefore, I do not know I have hands. Keith DeRose claims that (1) and (2) are “initially plausible.” I claim that (1) is initially plausible only because of an implicit argument that stands behind it; it is not intuitively plausible. The argument DeRose offers is based on the requirement of sensitivity, that is, on the idea that if you know something then you would not believe it if it were false. I criticize the sensitivity requirement thereby undercutting its support for (1) and the skeptical data that contextualism is meant to explain. While skepticism is not a plausible ground for contextualism, I argue that certain pragmatic considerations are. It’s plausible to think that to know something more evidence is required when more is at stake. The best way to handle skepticism is to criticize the arguments for it. We should not adopt contextualism as a means of accommodating skepticism even if there are other pragmatic reasons for being a contextualist about knowledge.     

Scepticism,context and modal reasoning

I analyze some classical solutions of the skeptical argument and some of their week points (especially the contextualist solution). First I have proposed some possible improvement of the contextualist solution (the introduction of the explicit-implicit belief and knowledge distinction beside the differences in the relevance of some counter-factual alternatives). However, this solution does not block too fast jumps of the everyday context (where empirical knowledge is possible) into skeptical context (where empirical knowledge is impossible). Then I analyze some formal analogies between some modal arguments on the contingency of empirical facts (and the world as whole) and the skeptical arguments against empirical knowledge. I try to show that the skeptical conclusion “Empirical knowledge does not exist” is logically coherent with the thesis that they are empirical facts and that we have true belief on them. In order to do that without contradictions I have to accept a non-classical definition of knowledge: S knows that p:= S is not justified to allow that non-p. Knowledge and justified allowance function here as some pseudo-theoretical concepts which allow only some partial and conditional definitions by some “empirical” terms and logical conditions.     

Righting the early history of computing,or how sausage was made

The short answer to the question just posed seems to be, “Not much.” Since I have given “the long answer” elsewhere,¹² I can summarize it here. Berg could see no point in writing Bromley. What could he write to someone he believed guilty of plagiarism? What could such a letter accomplish? He did, however, write to New York University Press; to all the universities involved, and to the Works’ English publisher (Pickering and Chatto), who said they passed the letter on to Campbell-Kelly (30 June 1990); to a great many professional societies in Australia, England, and the United States; to a great many governmental agencies and some politicians in those countries; to some publications, both academic and popular; to the Pope and several cardinals; and to a miscellany of other individuals. Generally, those in the best position to do something—for example, the three universities involved —did not even answer Berg’s letter. Others often did answer, but their answer was generally that they were in no position to do anything. That was how matters stood when I published my first article on “the Berg Affair”.₁₂ Its publication finally roused those best positioned to answer. Late in 1993, Galler, Bromley, and Campbell-Kelly wrote letters to the editor of Accountability in Research criticizing me for not getting their side of the story before I published Berg’s. Campbell-Kelly threatened the journal’s publisher with a lawsuit if I (or it) did not retract. The three also provided some insight into what their explanation of events might be. Bromley, though listed prominently in ads for the Works, claimed to have had only a small part, merely advising Campbell-Kelly on selection and arrangement of the papers printed in Volumes 2 and 3. Campbell-Kelly confirmed that Bromley took no part in the detailed editing or in the provision of documents. That work was performed by one C.J.D. (“Jim”) Roberts, a “London-based independent scholar” who was “editorial consultant to the Works” (and, apparently, worked directly under Campbell-Kelly). Roberts seems to deserve more public credit than he has so far received. According to Campbell-Kelly, it was Roberts who, making a systematic search for unknown holdings of Babbage, turned up the original of the letter to Quetelet by writing the Royal Library (one “tiny triumph” among many). Campbell-Kelly also claimed that neither he nor Roberts knew of Berg’s prior discovery.     

Expressing and Describing Experiences. A Case of Showing Versus Saying

Experiences are interpreted as conscious mental occurrences that are of phenomenal character. There is already a kind of (weak) intentionality involved with this phenomenal interpretation. A stricter conception of experiences distinguishes between purely phenomenal experiences and intentional experiences in a narrow sense. Wittgenstein’s account of psychological (experiential) verbs is taken over: Usually, expressing mental states verbally is not describing them. According to this, “I believe” can be seen as an expression of one’s own belief, but not as an expression of a belief about one’s belief. Hence, the utterance “I believe it is raining” shows that I believe that it is raining, although it is not said by these words that I believe that it is raining. Thinking thoughts such as “I believe it is raining, but it is not raining” (a variant of Moore’s paradox) is an absurdity between what is already said by silently uttering “It is not raining” and what is shown by silently uttering “I believe it is raining.” The paper agrees with a main result of Wittgenstein’s considerations of Moore’s paradox, namely the view that logical structure, deducibility, and consistency cannot be reduced solely to propositions—besides a logic of propositions, there is, for example, a logic of assertions and of imperatives, respectively.     

A Note on Belief Reports and Context Dependence

The aim of this paper is to pose a problem for theories that claim that belief reports are context dependent. Firstly, I argue that the claim (interpreted in the spirit of moderate contextualism) is committed to verbalism, a theory that derives the context sensitivity of belief reports from the context sensitivity of the psychological verbs used in such reports. Secondly, I argue that verbalism is not an attractive theoretical option because it is in conflict with the non-proto-rigidity of verbs like ‘believe’. Finally, I describe various consequences that the argument has for invariantism and moderate contextualism.     

What Mary’s Aboutness Is About

The aim of this paper is to reinforce anti-physicalism by extending the “hard problem” to a specific kind of intentional states. For reaching this target, I investigate the mental content of the new intentional states of Jackson’s Mary. I proceed in the following way: I start analyzing the knowledge argument, which highlights the “hard problem” tied to phenomenal consciousness. In a second step, I investigate a powerful physicalist reply to this argument: the phenomenal concept strategy. In a third step, I propose a constitutional account of phenomenal concepts that captures the Mary scenario adequately, but implies anti-physicalist referents. In a last step, I point at the ramifications constitutional phenomenal concepts have on the constitution of Mary’s new intentional states. Therefore, by focusing the attention on phenomenal concepts, the so-called “hard problem” of consciousness will be carried over to the alleged “easy problem” of intentional states as well.     

Phenomena in Inverse Stackelberg Games,Part 2: Dynamic Problems

Games are considered in which the role of the players is a hierarchical one. Some players behave as leaders, others as followers. Such games are named after Stackelberg. In the current paper, a special type of these games is considered, known in the literature as inverse Stackelberg games. In such games, the leader (or: leaders) announces his strategy as a mapping from the follower (or: followers) decision space into his own decision space. Arguments for studying such problems are given. The routine way of analysis, leading to a study of composed functions, is not very fruitful. Other approaches are given, mainly by studying specific examples. Phenomena in problems with more than one leader and/or follower are studied within the context of the inverse Stackelberg concept. As a side issue, expressions like “two captains on a ship” and “divide and conquer” are given a mathematical foundation.     

Opinion

The calculus sequence is a juggernaut and there are strong indications that we are heading for the 1500-page text. If enough mathematicians are willing to devote their energies to writing one-year texts that include standard topics decided on by a national committee and if major publishers with a large fixed focus can be found to promote such texts, there is a chance of reversing the trend toward mammoth books. However, it is important to avoid a “consensus text”; we need several competing books, each with a stamp of its author or authors. Negating the influence of publishers will be difficult, and I have no idea how to bring it about. The calculus market is enormous, and the commercial firms active in it will continue to attempt to gain an advantage any way they can. It would be helpful if all TA’s were required to have at least one course in physics so that topics with applications could be discussed with authority. For example, one of the most beautiful applications of integration is that of computing areas and volumes of irregularly shaped objects. Yet this topic is not considered an “application,” because students are not convinced they will ever have to calculate such an area or volume. It is hard to find real applications of calculus that students can identify as important. Finally, how do we change the study habits of the average student? Or should we try? The organization of most texts works against change; unless we develop another system we will be locked into the one we have.     

On duality gap in linear conic problems

In their paper “Duality of linear conic problems” Shapiro and Nemirovski considered two possible properties (A) and (B) for dual linear conic problems (P) and (D). The property (A) is “If either (P) or (D) is feasible, then there is no duality gap between (P) and (D)”, while property (B) is “If both (P) and (D) are feasible, then there is no duality gap between (P) and (D) and the optimal values val(P) and val(D) are finite”. They showed that (A) holds if and only if the cone K is polyhedral, and gave some partial results related to (B). Later Shapiro conjectured that (B) holds if and only if all the nontrivial faces of the cone K are polyhedral. In this note we mainly prove that both the “if” and “only if” parts of this conjecture are not true by providing examples of closed convex cone in \mathbbR⁴{\mathbb{R}^{4}} for which the corresponding implications are not valid. Moreover, we give alternative proofs for the results related to (B) established by Shapiro and Nemirovski.     

The sweet mystery of compatibilism

Any satisfactory account of freedom must capture, or at least permit, the mysteriousness of freedom—a “sweet” mystery involving a certain kind of ignorance rather than a “sour” mystery of unintelligibility, incoherence, or unjustifiedness. I argue that compatibilism can capture the sweet mystery of freedom. I argue first that an action is free if and only if a certain “rationality constraint” is satisfied, and that nothing in standard libertarian accounts of freedom entails its satisfaction. Satisfaction of this constraint is consistent with the universal causal predetermination of action (UCP). If UCP is true and the rationality constraint satisfied, there’s a sense in which our actions are explanatorily (though not necessarily causally) overdetermined. While it seems plausible (given UCP) that our actions are so overdetermined, it seems utterly mysterious why they should be so overdetermined. Compatibilism’s capacity to accommodate this mystery is a mark in its favor.     

Conditional lexicographic orders in constraint satisfaction problems

The lexicographically-ordered CSP (“lexicographic CSP” or “LO-CSP” for short) combines a simple representation of preferences with the feasibility constraints of ordinary CSPs. Preferences are defined by a total ordering across all assignments, such that a change in assignment to a given variable is more important than any change in assignment to any less important variable. In this paper, we show how this representation can be extended to handle conditional preferences in two ways. In the first, for each conditional preference relation, the parents have higher priority than the children in the original lexicographic ordering. In the second, the relation between parents and children need not correspond to the importance ordering of variables. In this case, by obviating the “overwhelming advantage” effect with respect to the original variables and values, the representational capacity is significantly enhanced. For problems of the first type, any of the algorithms originally devised for ordinary LO-CSPs can also be used when some of the domain orderings are dependent on assignments to “parent” variables. For problems of the second type, algorithms based on lexical orders can be used if the representation is augmented by variables and constraints that link preference orders to assignments. In addition, the branch-and-bound algorithm originally devised for ordinary LO-CSPs can be extended to handle CSPs with conditional domain orderings.     

Stochastic programming: Potential hazards when random variables reflect market interaction

There are two types of random phenomena modeled in stochastic programs. One type is what we may term “external” or “natural” random variables, such as temperature or the roll of a dice. But in many other cases, random variables are used to reflect the behavior of other market participants. This is the case for such as price and demand of a product. Using simple game theoretic models, we demonstrate that stochastic programming may not be appropriate in these cases, as there may be no feasible way to replace the decisions of others by a random variable, and arrive at the correct decision. Hence, this simple note is a warning against certain types of stochastic programming models. Stochastic programming is unproblematic in pure forms of monopoly and perfect competition, and also with respect to external random phenomena. But if market power is involved, such as in oligopolies, the modeling may not be appropriate.     

Reversible stopping (“switching”) implies super contact

This note shows that the second derivative of the value function exists (across a stopping threshold, short “super contact”) if reversibly stopping and entering involves no cost, called “switching”. This holds for discrete (real option) as well as for continuous stochastic control problems and proves particularly suitable in real option set ups since it provides the lacking boundary condition. However, super contact does not hold in dynamic games. A simple example documents the applicability of this condition. This paper was written during my visit of the University of Technology, Sydney (UTS) and I am grateful for the hospitality of and the stimulus at the School of Finance and Economics, in particular to Carl Chiarella. I also acknowledge many helpful discussions with Thomas Dangl on related issues, valuable suggestions from a referee and last but not least encouragement by Josef Kallrath     

On trees covering chains or stars

In this paper, in the context of the “dessins d’enfants” theory, we give a combinatorial criterion for a plane tree to cover a tree from the classes of “chains” or “stars.” We also discuss some applications of this result that are related to the arithmetical theory of torsion on curves. Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 6, pp. 207–215, 2007.     

Study on “double dawn”

The ancient record, “During the first year of King Yi, the day dawned twice at Zheng”, has provided important clues to early Chinese chronicles. The astronomical conditions and visible area distributions related to such a “double dawn” event are discussed, and the precision and current problems in the calculations of ancient astronomical phenomena are shown. On such a basis, all the solar eclipses from 1000 BC to 840 BC are calculated and their associated “double dawn” features investigated. The conclusion that the “double dawn” was a solar eclipse occurring on April 21st, 899 BC is corfirmed to be the most reasonable. Project supported by the Xia-Shang-Zhou Chronology Project and Director Foundation of the Chinese Academy of Sciences.     

The Pepsi Putnam Challenge

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Cohn Adam’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be hannless.     

Fermats ?ad?quare? – und kein Ende?

In his papers on the determination of maxima and minima and on the calculation of tangents Pierre Fermat uses two different Latin verbs, ?quare and ad?quare, which do not differ semantically but are used by him obviously in different meanings. While ?quabitur is used unambiguously in the sense of “is equal” the meaning of ad?quabitur is disputed by the experts since Tannery’s French translation (Œuvres complètes de Fermat, Vol. III, 1896). Herbert Breger (Arch. Hist. Exact Sci. 46, 193–219, (1994), p. 197 f), for instance, holds the view that Fermat used the word ad?quare in the sense of “to put equal” and adds: In a mathematical context, the only difference between “?quare” and “ad?quare” (if there is any) seems to be that the latter gives more stress on the fact that the equality is achieved. In contrast to this Michael Mahoney holds the thesis that ad?quare describes a counterfactual equality (Mahoney, M.S.: Fermat, Pierre de. In: Dictionary of Scientific Biography, vol. IV (1971), p. 569) or a pseudo-equality (Mahoney, M.S.: The Mathematical Career of Pierre de Fermat (1601–1665), (1973), p. 164), whatever that may mean. This viewpoint has been taken up again recently by Enrico Giusti (Ann. Fac. Sci. Toulouse, Math. (6), 18 fascicule spécial, 59–85 (2009)) in order to bring arguments to bear against Breger. In contrast to these (and other) authors, I show that Fermat makes a subtle logical distinction between the words ?quare and ad?quare. The same distinction is made by Nicolas Bourbaki introducing his ?théorie égalitaire?. Notwithstanding: both verbs stand for a ?relation d’égalité?. On this premiss, I describe—using six selected examples—that Fermat’s “method” may be justified right down to the last detail, even from the view of today’s mathematical knowledge.     

Junctions of singularly degenerating domains with different limit dimensions 1

The asymptotic series for solutions of the mixed boundary-value problem for the Poisson equation in a domain, which is a junction of singularly degenerating domains, are constructed. In this paper, which is the first part of the publication, the three-dimensional problem (“wheel hub with spokes”) and the analogous two-dimensional problems are considered. The methods of matched and compound asymptotic expansions are used. It is shown that a special self-adjoint extension of the operator of the limit problem in the “hub” supplied by the straight-line segments (“limits of spokes”) can be chosen as an asymptotical model of the problem in question; the extension parameters are to be some integral characteristics of the boundary-layer problems. Bibliography: 39 titles. Translated from Trudy Seminara imeni I. G. Petrovskogo. No. 18, pp. 3–78, 1995.