A Priori knowledge contextualised and Benacerraf’s dilemma

In this article, I discuss Hawthorne’s contextualist solution to Benacerraf’s dilemma. He wants to find a satisfactory epistemology to go with realist ontology, namely with causally inaccessible mathematical and modal entities. I claim that he is unsuccessful. The contextualist theories of knowledge attributions were primarily developed as a response to the skeptical argument based on the deductive closure principle. Hawthorne uses the same strategy in his attempt to solve the epistemologist puzzle facing the proponents of mathematical and modal realism, but this problem is of a different nature than the skeptical one. The contextualist theory of knowledge attributions cannot help us with the question about the nature of mathematical and modal reality and how they can be known. I further argue that Hawthorne’s account does not say anything about a priori status of mathematical and modal knowledge. Later, Hawthorne adds to his account an implausible claim that in some contexts a gettierized belief counts as knowledge.     

In Defense of Epistemic Circularity

In this paper I defend epistemic circularity by arguing that the “No Self-Support” principle (NSS) is false. This principle, ultimately due to Fumerton (1995), states that one cannot acquire a justified belief in the reliability of a source of belief by trusting that very source. I argue that NSS has the skeptical consequence that the trustworthiness of all of our sources ultimately depends upon the trustworthiness of certain fundamental sources – sources that we cannot justifiably believe to be reliable. This is a problem, I claim, because if the trustworthiness of all of our sources depends upon sources that we should not believe to be reliable, then a reflective individual should not trust any of his sources at all. The hidden cost of rejecting epistemic circularity is thus the unacceptable skeptical thesis that reflective individuals like you and I have no justified beliefs whatsoever.     

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.     

Perception and Virtue Reliabilism

In some recent work, Ernest Sosa rejects the “perceptual model” of rational intuition, according to which intuitive beliefs (e.g., that 2 + 2 = 4 2 + 2 = 4 ) are justified by standing in the appropriate relation to a nondoxastic intellectual experience (a seeming-true, or the like), in much the way that perceptual beliefs are often held to be justified by an appropriate relation to nondoxastic sense experiential states. By extending some of Sosa’s arguments and adding a few of my own, I argue that Sosa is right to reject the perceptual model of intuition, and that we should reject the “perceptual model” of perception as well. Rational intuition and perception should both receive a virtue theoretic (e.g., reliabilist) account, rather than an evidentialist one. To this end, I explicitly argue against the Grounds Principle, which holds that all justified beliefs must be based on some adequate reason, or ground.     

Reliabilism and Brains in Vats

According to epistemic internalism, the only facts that determine the justificational status of a belief are facts about the subject’s own mental states, like beliefs and experiences. Externalists instead hold that certain external facts, such as facts about the world or the reliability of a belief-producing mechanism, affect a belief’s justificational status. Some internalists argue that considerations about evil demon victims and brains in vats provide excellent reason to reject externalism: because these subjects are placed in epistemically unfavorable settings, externalism seems unable to account for the strong intuition that these subjects’ beliefs are nonetheless justified. I think these considerations do not at all help the internalist cause. I argue that by appealing to the anti-individualistic nature of perception, it can be shown that skeptical scenarios provide no reason to prefer internalism to externalism.     

Coherentism,Truth, and Witness Agreement

Coherentists on epistemic justification claim that all justification is inferential, and that beliefs, when justified, get their justification together (not in isolation) as members of a coherent belief system. Some recent work in formal epistemology shows that “individual credibility” is needed for “witness agreement” to increase the probability of truth and generate a high probability of truth. It can seem that, from this result in formal epistemology, it follows that coherentist justification is not truth-conducive, that it is not the case that, under the requisite conditions, coherentist justification increases the probability of truth and generates a high probability of truth. I argue that this does not follow.     

The semantics of knowledge attributions

The basic idea of conversational contextualism is that knowledge attributions are context sensitive in that a given knowledge attribution may be true if made in one context but false if made in another, owing to differences in the attributors’ conversational contexts. Moreover, the context sensitivity involved is traced back to the context sensitivity of the word “know,” which, in turn, is commonly modelled on the case either of genuine indexicals such as “I” or “here” or of comparative adjectives such as “tall” or “rich.” But contextualism faces various problems. I argue that in order to solve these problems we need to look for another account of the context sensitivity involved in knowledge attributions and I sketch an alternative proposal.     

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.     

Sequent calculi for branching time temporal logics of knowledge and beliefwith awareness: Completeness and decidability

In this paper, we consider branching time temporal logic CT L with epistemic modalities for knowledge (belief) and with awareness operators. These logics involve the discrete-time linear temporal logic operators “next” and “until” with the branching temporal logic operator “on all paths”. In addition, the temporal logic of knowledge (belief) contains an indexed set of unary modal operators “agent i knows” (“agent i believes”). In a language of these logics, there are awareness operators. For these logics, we present sequent calculi with a restricted cut rule. Thus, we get proof systems where proof-search becomes decidable. The soundness and completeness for these calculi are proved. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 328–340, July–September, 2007.     

Reflective equilibrium and underdetermination in epistemology

The basic aim of Alvin Goldman’s approach to epistemology, and the tradition it represents, is naturalistic; that is, epistemological theories in this tradition aim to identify the naturalistic, nonnormative criteria on which justified belief supervenes (Goldman, 1986; Markie, 1997). The basic method of Goldman’s epistemology, and the tradition it represents, is the reflective equilibrium test; that is, epistemological theories in this tradition are tested against our intuitions about cases of justified and unjustified belief (Goldman, 1986; Markie, 1997). I will argue that the prospect of having to reject their standard methodology is one epistemologists have to take very seriously; and I will do this by arguing that some current rival theories of epistemic justification are in fact in reflective equilibrium with our intuitions about cases of justified and unjustified belief. That is, I will argue that intuition underdetermines theory choice in epistemology, in much the way that observation underdetermines theory choices in empirical sciences. If reflective equilibrium leads to the underdetermination problem I say it leads to, then it cannot satisfy the aims of contemporary epistemology, and so cannot serve as its standard methodology.     

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.     

Future teachers’ general pedagogical knowledge from a comparative perspective: does school experience matter?

General pedagogical knowledge (GPK) is a central component of teacher knowledge. Teacher education programs in many countries therefore provide corresponding opportunities to learn (OTL), and in-school experience is regarded as a core component of OTL fostering knowledge in the area of general pedagogy. However, empirical research on the effectiveness of school experiences during teacher education does not tell us precisely how different kinds of OTL are related to GPK. This paper first reports on the conceptualizing of the GPK test in the context of TEDS-M. Then the relationship between practical in-school OTL of German and US future primary teachers and their GPK is investigated. On the basis of results from Latent-Class Analysis using two core indicators of in-school OTL (the length of time spent on teaching students and the extent of being supported by a mentor or supervisor), three types of future primary teachers in both the US and Germany are distinguished: “starting” (type 1), “autonomous” (type 2), and “balanced” (type 3). In both countries, type 3 future primary teachers reported that they had had OTL to reflect on and improve their teaching to a larger extent than the type 1 teachers. Type 3 teachers also generally achieved better GPK test results than type 1 teachers. Furthermore, there is also a tendency that type 3 future teachers show better results than type 2. Based on these results, we hypothesize that the quality of future teachers’ activities during in-school practicum matters with regard to important outcomes of teacher education, making in-school OTL an effective component of teacher education. Research findings are discussed with regard to the relationship between theory and practice during teacher education.     

Approximate common knowledge revisited

Suppose we replace “knowledge” by “belief with probability p” in standard definitions of common knowledge. Very different notions arise depending on the exact definition of common knowledge used in the substitution. This paper demonstrates those differences and identifies which notion is relevant in each of three contexts: equilibrium analysis in incomplete information games, best response dynamics in incomplete information games, and agreeing to disagree/no trade results.     

Generalizing the Disappearing Act: A Reply to István Aranyosi

In “The Reappearing Act” István Aranyosi postulates a new way of seeing to solve a puzzle posed in “The Disappearing Act;” an object that is exactly shaded can be seen simply by virtue of its contrast with its environment – just like a shadow. This object need not reflect, refract, absorb or block light. To undermine the motive for this heretical innovation, I generalize the puzzle to situations involving inexact shading. Aranyosi cannot extend his solution to these variations because he needs to conserve principles of camouflage. On the bright side, the solution to the puzzle that I propose in my book Seeing Dark Things does extend to these variations.     

The hierarchical approach to modeling knowledge and common knowledge

One approach to representing knowledge or belief of agents, used by economists and computer scientists, involves an infinite hierarchy of beliefs. Such a hierarchy consists of an agent's beliefs about the state of the world, his beliefs about other agents' beliefs about the world, his beliefs about other agents' beliefs about other agents' beliefs about the world, and so on. (Economists have typically modeled belief in terms of a probability distribution on the uncertainty space. In contrast, computer scientists have modeled belief in terms of a set of worlds, intuitively, the ones the agent considers possible.) We consider the question of when a countably infinite hierarchy completely describes the uncertainty of the agents. We provide various necessary and sufficient conditions for this property. It turns out that the probability-based approach can be viewed as satisfying one of these conditions, which explains why a countable hierarchy suffices in this case. These conditions also show that whether a countable hierarchy suffices may depend on the “richness” of the states in the underlying state space. We also consider the question of whether a countable hierarchy suffices for “interesting” sets of events, and show that the answer depends on the definition of “interesting”.     

Towards a new theory of confirmation

Any sequence of events can be “explained” by any of an infinite number of hypotheses. Popper describes the “logic of discovery” as a process of choosing from a hierarchy of hypotheses the first hypothesis which is not at variance with the observed facts. Blum and Blum formalized these hierarchies of hypotheses as hierarchies of infinite binary sequences and imposed on them certain decidability conditions. In this paper we also consider hierarchies of infinite binary sequences but we impose only the most elementary Bayesian considerations. We use the structure of such hierarchies to define “confirmation”. We then suggest a definition of probability based on the amount of confirmation a particular hypothesis (i.e. pattern) has received. We show that hypothesis confirmation alone is a sound basis for determining probabilities and in particular that Carnap’s logical and empirical criteria for determining probabilities are consequences of the confirmation criterion in appropriate limiting cases.     

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.