Defining answer classes using resolution refutation

Resolution theorem proving provides a useful paradigm for the exploration of question answering. A partition of the clauses generated during resolution refutation based on their syntactic structure is presented. The three classes comprising this partition correspond to semantically intuitive types of answers. This work encompasses and expands upon previous work on question answering in a theorem proving paradigm, which began with the association of answers with proofs. A complete, formal definition of what is meant by answer in the context of resolution theorem proving is presented. In this context, clauses that are relevant are all identified as answers, where relevance is determined with respect to a question and knowledge base: any clause descended from the clause form of a negated question is deemed relevant. This definition of relevance is not in and of itself novel; rather, it is the way in which the set of relevant clauses is partitioned that provides the key to interpreting clauses as answers. The three answer classes identified are: specific, generic, and hypothetical. These classes are formally distinguished by the way in which literals in a clause share variables, with class membership based on a property termed the closure of variable sharing of a literal. The results presented provide a foundation for further work by establishing a context-independent logical pragmatics of question answering.     

Modalising Plurals

There has been very little discussion of the appropriate principles to govern a modal logic of plurals. What debate there has been has accepted a principle I call (NecInc); informally if this is one of those then, necessarily: this is one of those. On this basis Williamson has criticised the Boolosian plural interpretation of monadic second-order logic. I argue against (NecInc), noting that it isn’t a theorem of any logic resulting from adding modal axioms to the plural logic PFO+, and showing that the most obvious formal argument in its favour is question begging. I go on to discuss the behaviour of natural language plurals, motivating a case against (NecInc) by developing a case that natural language plural terms are not de jure rigid designators. The paper concludes by developing a model theory for modal PFO+ which does not validate (NecInc). An Appendix discusses (NecInc) in relation to counterpart theory.     

Explanation and Understanding Revisited: Bohman and the New Philosophy of Social Science

James Bohman has succeeded in reinvigorating the old debate over explanation and understanding by situating it within contemporary discussions about sociological indeterminacy and complexity. I argue that Bohman's preference for a paradigm based on Habermas's theory of communicative action is justifiable given the explanatory deficiencies of ethnomethodological, rational choice, rule-based, and functionalist methodologies. Yet I do not share his belief that the paradigm is preferable to less formalized models of interpretation.     

On A Neglected Path to Intuitionism

According to Quine, in any disagreement over basic logical laws the contesting parties must mean different things by the connectives or quantifiers implicated in those laws; when a deviant logician ‘tries to deny the doctrine he only changes the subject’. The standard (Heyting) semantics for intuitionism offers some confirmation for this thesis, for it represents an intuitionist as attaching quite different senses to the connectives than does a classical logician. All the same, I think Quine was wrong, even about the dispute between classicists and intuitionists. I argue for this by presenting an account of consequence, and a cognate semantic theory for the language of the propositional calculus, which (a) respects the meanings of the connectives as embodied in the familiar classical truth-tables, (b) does not presuppose Bivalence, and with respect to which (c) the rules of the intuitionist propositional calculus are sound and complete. Thus the disagreement between classicists and intuitionists, at least, need not stem from their attaching different senses to the connectives; one may deny the doctrine without changing the subject. The basic notion of my semantic theory is truth at a possibility, where a possibility is a way that (some) things might be, but which differs from a possible world in that the way in question need not be fully specific or determinate. I compare my approach with a previous theory of truth at a possibility due to Lloyd Humberstone, and with a previous attempt to refute Quine’s thesis due to John McDowell.     

The Virtue of Epistemological Dualism

The article tries to answer the following question: what is the most promising epistemological strategy if my objective is the construction of a theory which gives me the opportunity to decrease the risk of getting to what is actually absolute, that is, to irreversible negative actions (irreversible as a theory might not be, but as an action often is)? The answer proposed is a form of epistemological dualism which means that I metaphysically believe (that is, I programmatically and systematically believe, without certainly knowing it) that the epistemological relationship between any theory and any reality is dualistic. More specifically, I metaphysically believe that the epistemological relationship between any theory and any reality is not saturated: in any theory there is an ideal error, because there is no theory which is totally saturated by reality, and any reality can actualize the ideal error, because there is no reality which is totally saturated by theory.     

On a Promise or on the Game: What's Wrong with Selling Consent?

Is selling sex a service like any other? Philosophers have given a range of answers to this question: (a) sex has a specific value that is debased by commercial markets in sex; (b) sex work is a service like any other; (c) markets in sex perpetuate structural systems of inequality. This article takes seriously the suggestion that there is something special about sex itself which raises a specific set of concerns when traded for money. The challenge is to explain this without drawing on contentious essentialist claims about the value of sex. It proceeds by analysing a parallel between sexual promises and selling sexual consent. On an expectational theory of promising, commercial agreements to sex generate obligations in a way that is normatively analogous to sexual promises. Understanding the normative release conditions for such assurance-providing agreements provides a way of analysing the justifiability of various ways of enforcing such agreements. I argue that the release conditions for agreements involving sex are not conducive to being codified under typical forms of service contract. As such, regulation aimed at legitimising sex work must provide adequate protections to workers without codifying it under typical forms of service contract.     

Reichenbach, induction, and discovery

Conclusion I have applied a fairly general, learning theoretic perspective to some questions raised by Reichenbach's positions on induction and discovery. This is appropriate in an examination of the significance of Reichenbach's work, since the learning-theoretic perspective is to some degree part of Reichenbach's reliabilist legacy. I have argued that Reichenbach's positivism and his infatuation with probabilities are both irrelevant to his views on induction, which are principally grounded in the notion of limiting reliability. I have suggested that limiting reliability is still a formidable basis for the formulation of methodological norms, particularly when reliability cannot possibly be had in the short run, so that refined judgments about evidential support must depend upon measure-theoretic choices having nothing to do in the short run with the truth of the hypothesis under investigation. To illustrate the generality of Reichenbach's program, I showed how it can be applied to methods that aim to solve arbitrary assessment and discovery problems in various senses. In this generalized Reichenbachian setting, we can characterize the intrinsic complexity of reliable inductive inference in terms of topological complexity. Finally, I let Reichenbach's theory of induction have the last say about hypothetico-deductive method.     

Contingency in Nature

Contingencies in Nature may be explained, but such explanations refer to other contingencies (pt. I). Is there a way to “explain away” all contingencies? The first physical theory of modern times, Newton’s theory of gravitation, was received in a way that leaves this question open (pt. II), while Kepler’s theory of cosmological harmony arrived at a positive solution (pt. III). However, later developments in science outdated Kepler’s approach (pt. IV).     

(Un)touchability: Disclosure and the Ethics of Loss

In this lyrical essay, I attempt to unravel the complexity behind new modes of HIV prevention and the rise of segregation among people of different antibody status in queer communities. In particular, I question the ease with which disclosure of HIV status is equated with safe sex. Because disclosure often reproduces the power dynamics of confession, I try to imagine an ethics of reciprocity in bearing witness. The essay is perforated by poetic fragments, the way all bodies are perforated, infected or not.     

Experiment and theory building

I examine the role of inference from experiment in theory building. What are the options open to the scientific community when faced with an experimental result that appears to be in conflict with accepted theory? I distinguish, in Laudan’s (1977), Nickels’s (1981), and Franklin’s (1993) sense, between the context of pursuit and the context of justification of a scientific theory. Making this distinction allows for a productive middle position between epistemic realism and constructivism. The decision to pursue a new or a revised theory in response to the new evidence may not be fully rationally determined. Nonetheless, it is possible to distinguish the question of whether there is reason to pursue a theory from the question of whether that theory, once it has been pursued over time, solves a problem of interest to science. I argue that, in this context, there is a solid way to distinguish between the contexts of pursuit and of justification, on the basis of a theory’s evidential support and problem-solving ability.     

Answering the Ethical Question

Many philosophers have attempted to answer the ‘ethical question’: can the ethical value of an artwork ever contribute to its aesthetic value, and if so, how? In this paper, I consider a methodological question that arises out of this discussion: should attempts to address the ethical question use analytic tools found in contemporary philosophical literature, art criticism, or some combination of the two? I concur with arguments proposed elsewhere, which suggest that art criticism has an important role to play in addressing the ethical question. However, I argue that any fruitful attempt to answer the question must defend some particular way of understanding the ethical value of artworks, which suggests that we should address what I label the ‘art question’: what is the role and importance of art? This question, I suggest, is one with which philosophers can usefully engage. This division of labour offers a way forward in addressing this important issue.     

Problems with the ‘physical’ in physicalism

Hempel's Dilemma is a challenge that has to be met by any formulation of physicalism that specifies the physical by reference to a particular physical theory. It poses the problem that if one's specification of the physical is ‘current’ physical theory, then the physicalism which depends on it is false because current physics is false; and if the specification of the physical is a future or an ideal physics, the physicalism based on it would be trivial as it would be tautologously true, or because very little (if anything at all) can be inferred from or about a physics that does not yet exist. I review the reasons for thinking that the dilemma is a perpetual problem for currentist specifications of the physical, then introduce the argument that the standard positions on the specification question are wanting because they lack a generality which physicalism is generally accepted to have. I end with a suggestion for a way forward for physicalism.     

A vehicular theory of corporeal qualia (a gift to computationalists)

I have argued elsewhere that non-sentential representations that are the close kin of scale models can be, and often are, realized by computational processes. I will attempt here to weaken any resistance to this claim that happens to issue from those who favor an across-the-board computational theory of cognitive activity. I will argue that embracing the idea that certain computers harbor nonsentential models gives proponents of the computational theory of cognition the means to resolve the conspicuous disconnect between the sentential character of the data structures they posit and the nonsentential qualitative character of our perceptual experiences of corporeal (i.e., spatial, kinematic, and dynamic) properties. Along the way, I will question the viability of some externalist remedies for this disconnect, and I will explain why the computational theory put forward here falls quite clearly beyond the useful bounds of the Chinese-Room argument.     

The Context of Inference

There is an ambiguity in the concept of deductive validity that went unnoticed until the middle of the twentieth century. Sometimes an inference rule is called valid because its conclusion is a theorem whenever its premises are. But often something different is meant: The rule's conclusion follows from its premises even in the presence of other assumptions. In many logical environments, these two definitions pick out the same rules. But other environments are context-sensitive, and in these environments the second notion is stronger. Sorting out this ambiguity has led to profound mathematical investigations with applications in complexity theory and computer science. The origins of this ambiguity and the history of its resolution deserve philosophical attention, because our understanding of logic stands to benefit from their details.

I am eager to examine together with you, Crito, whether this argument will appear in any way different to me in my present circumstances, or whether it remains the same, whether we are to abandon it or believe in it.—Plato Crito, 46d     

Higher Education,Knowledge for Its Own Sake,and an African Moral Theory

I seek to answer the question of whether publicly funded higher education ought to aim intrinsically to promote certain kinds of “blue-sky” knowledge, knowledge that is unlikely to result in “tangible” or “concrete” social benefits such as health, wealth and liberty. I approach this question in light of an African moral theory, which contrasts with dominant Western philosophies and has not yet been applied to pedagogical issues. According to this communitarian theory, grounded on salient sub-Saharan beliefs and practices, actions are right insofar as they respect relationships in which people both share a way of life, or identify with one another, and care for others’ quality of life, or are in solidarity with each other. I argue that while considerations of identity and solidarity each provide some reason for a state university to pursue blue-sky knowledge as a final end, they do not provide conclusive reason for it to do so. I abstain from drawing any further conclusion about whether this provides reason to reject the Afro-communitarian moral theory or the intuition that blue-sky knowledge is a proper final end of public higher education. I do point out, however, that the dominant Western moral theories on the face of it do no better than the African one at accounting for this intuition.     

Strategies for a Logic of Plurals

English has plural terms (e.g., 'Oliver and Smiley', 'the co-authors of this paper') as well as singular terms. But our standard formal languages, e.g., the predicate calculus, feature only singular terms. How can the plural idiom be formalized?'Changing the subject' is by far the most common plurals strategy among both philosophers and linguists: a plural term is replaced by a singular term standing for some complex object (a set or an aggregate) that 'contains' the individuals to which the plural term alludes. For example, one might simply replace 'A, B imply C' with '{A, B} implies [singular] C'. We uncover a surprising variety of ways to change the subject, of ever-increasing complexity and ingenuity. Our question is whether any can made to work.     

Mental,behavioural and physiological nonlocal correlations within the Generalized Quantum Theory framework

Generalized Quantum Theory (GQT) seeks to explain and predict quantum-like phenomena in areas usually outside the scope of quantum physics, such as biology and psychology. It draws on fundamental theories and uses the algebraic formalism of quantum theory that is used in the study of observable physical matter such as photons, electrons, etc. In contrast to quantum theory proper, GQT is a very generalized form that does not allow for the full application of formalism. For instance neither a commutator, such as Planck’s constant, nor any additive operations are defined, which precludes the usage of a full Hilbert-space formalism. But it is a formalized phenomenological theory that is applicable whenever the core element of a quantum theory needs to be captured, namely in the presence of incompatible or non-commuting operations. As a consequence, it also predicts nonlocal, generalized entanglement correlations in systems other than proper quantum systems. In this paper we summarize the specific scientific evidence relating to the quantum-like mental, behavioral and physiological nonlocal correlations. Such non-local, generalized entanglement correlations are expected, both in space and time, between subsystems of a larger system, whenever observables pertaining to the global system are incompatible or complementary to observables pertaining to subsystems, as predicted by GQT. The result is a coherent explanation of a significant amount of controversial and seemingly weird occurrences that cannot be explained by classical physical laws. This review also offers a new perspective of the human mind’s potential.     

Transfer of Warrant, Begging the Question and Semantic Externalism

Martin Davies argues that 'limitation principles' block the transfer of warrant from the premises of a certain kind of argument to its conclusion. The class of arguments in question includes Moore's argument for the existence of the external world, and a popular style of argument which starts from two premises that are warranted by first-person authority and semantic externalism respectively, ending with a conclusion that does not, allegedly, admit of a priori justification. I argue that the relevant class of arguments can be shown to be unconvincing without appealing to any limitation principles, by showing that they beg the question against sceptical opponents. Principles limiting the transfer of warrant are not required in order to rebut the claim that first-person authority and semantic externalism are incompatible.     

An Impossibility Theorem on Beliefs in Games

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell’s Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob’s assumption is wrongThis is formalized to show that any belief model of a certain kind must have a ‘hole.’ An interpretation of the result is that if the analyst’s tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.Special Issue Ways of Worlds II. On Possible Worlds and Related Notions Edited by Vincent F. Hendricks and Stig Andur Pedersen