What does it mean to ‘give’ the value of a variable in an algebraic context, and how does giving the value of a variable differ from merely describing it? I argue that to answer this question, we need to examine the role that giving the value of a variable plays in problem-solving practice. I argue that four different features are required for a statement to count as giving the value of a variable in the context of solving an elementary algebra (...) problem: the variable must be in the scope opened by the problem statement; the values given must be in the range of the variable, which is determined by the problem; the statement giving the values must represent a complete solution; and it must be in a canonical form. This account helps us better understand elementary algebra itself, as well as the use of algebraic tools to analyze phenomena in natural language. (shrink)

Normative explanations, which specify why things have the normative features they do, are ubiquitous in normative theory and ordinary thought. But there is much less work on normative explanation than on scientific or metaphysical explanation. Skow (2016) argues that a complete answer to the question why some fact Q occurs consists in all of the reasons why Q occurs. This paper explores this theory as a case study of a general theory that promises to offer us a grip on normative (...) explanation which is independent of particular normative theories. I first argue that the theory doesn’t give an adequate account of certain enablers of reasons which are important in normative explanation. I then formulate and reject three responses on behalf of the theory. But I suggest that since theories of this general sort have the right kind of resources to illuminate how normative explanation might be similar to and different from explanations in other domains, they nonetheless merit further exploration by normative theorists. (shrink)

THIS IS AN EARLY DRAFT OF MY PAPER "RESEARCH PROBLEMS" PUBLISHED IN BJPS IN 2021. PLEASE REFER TO THAT PAPER INSTEAD OF THIS ONE. -/- Philosophers increasingly study how scientists conduct actual scientific projects and the goals they pursue. But as of yet, there are few accounts of goals that can be used to identify different kinds, and specific instances, of goals pursued by scientists. I propose that there are at least four distinct kinds of goals pursued by scientists: ameliorating (...) problems, addressing questions, satisfying values, and achieving epistemic aims. I focus on the first two kinds, and I provide tools to help conceptualize, distinguish, and identify the problems and questions pursued by scientists. This paper illustrates the use of those tools with two examples. (shrink)

Frege famously held that numbers play the role of objects in our language and thought, and that this role is on display when we use sentences like "The number of Jupiter's moons is four". I argue that this role is an example of a general pattern that also encompasses persons, times, locations, reasons, causes, and ways of appearing or acting. These things are 'objects' simply in the sense that they are answers to questions: they are the sort of thing we (...) search for and specify during investigation or inquiry. I support this epistemological conception of objects by studying specificational sentences, a class of sentences which includes Frege's original example. I defend an analysis of such sentences as question-answer pairs, and show how to formally represent this analysis using game-theoretical semantics. (shrink)

Orthodoxy has it that knowledge is absolute—that is, it cannot come in degrees. On the other hand, there seems to be strong evidence for the gradability of know-how. Ascriptions of know-how are gradable, as when we say that one knows in part how to do something, or that one knows how to do something better than somebody else. When coupled with absolutism, the gradability of ascriptions of know-how can be used to mount a powerful argument against intellectualism about know-how—the view (...) that know-how is a species of propositional knowledge. This essay defends intellectualism from the argument of gradability. It is argued that the gradability of ascriptions of know-how should be discounted as a rather superficial linguistic phenomenon, one that can be explained in a way compatible with the absoluteness of the state reported. (shrink)

It was something of a dogma for much of the twentieth century that one cannot validly derive an ought from an is. More generally, it was held that non-normative propositions do not entail normative propositions. Call this thesis about the relation between the natural and the normative Natural-Normative Autonomy. The denial of Autonomy involves the entanglement of the natural with the normative. Naturalism entails entanglement—in fact it entails the most extreme form of entanglement—but entanglement does not entail naturalism. In a (...) ground-breaking paper “The autonomy of ethics” Arthur Prior constructed some intriguing counterexamples to Autonomy. While his counterexamples have convinced few, there is little agreement on what is wrong with them. I present a new analysis of Autonomy, one which is grounded in a general and independently plausible account of subject matters. While Prior’s arguments do establish shallow natural-normative entanglement, this is a consequence of simple logical relationships that hold between just about any two subject matters. It has nothing special to do with the logical structure of normativity or its relation to the natural. Prior’s arguments leave the fundamental idea behind natural-normative Autonomy intact. I offer a new argument for deep entanglement. I show that in any framework adequate for dealing with the natural and the normative spheres, a purely natural proposition entails a purely normative proposition, and vice-versa. But this is no threat to non-naturalist moral realism. In fact it helps ameliorate the excesses of an extreme non-naturalism, delivering a more palatable and plausible position. (shrink)

This paper argues that questions have an important role to to play in logic, both semantically and proof-theoretically. Semantically, we show that by generalizing the classical notion of entailment to questions, we can capture not only the standard relation of logical consequence, which holds between pieces of information, but also the relation of logical dependency, which holds between information types. Proof-theoretically, we show that questions may be used in inferences as placeholders for arbitrary information of a given type; by manipulating (...) such placeholders, we may construct formal proofs of dependencies. Finally, we show that such proofs have a specific kind of constructive content: they do not just witness the existence of a certain dependency, but actually encode a method for transforming information of the types described by the assumptions into information of the type described by the conclusion. (shrink)

There are many ways of understanding the nature of philosophical questions. One may consider their morphology, semantics, relevance, or scope. This article introduces a different approach, based on the kind of informational resources required to answer them. The result is a definition of philosophical questions as questions whose answers are in principle open to informed, rational, and honest disagreement, ultimate but not absolute, closed under further questioning, possibly constrained by empirical and logico-mathematical resources, but requiring noetic resources to be answered. (...) The article concludes with a discussion of some of the consequences of this definition for a conception of philosophy as the study (or “science”) of open questions, which uses conceptual design to analyse and answer them. (shrink)

It is argued that Heidegger should be seen as something of a Kantian Idealist. Like Kant, Heidegger distinguishes two standpoints (transcendental and empirical) which we can occupy when we ask the question whether natural things depend on us. He agrees with Kant that from the empirical or human standpoint we are justified in saying that natural things do not depend on us. But in contrast with Kant, Heidegger argues that from the transcendental standpoint we can say neither that natural things (...) do depend on us, nor that they do not. His reasons for saying this, however, represent an attempt to rework both Kant's temporal idealism and his temporal interpretation of the concept of an object (which shows up in Heidegger as a temporal interpretation of being). Heidegger suggests that Kant was led astray into a transcendental idealism about natural entities, because he did not understand the implications of transcendental idealism about being. (shrink)

Much of the extant discussion focuses on the question of whether contextualism resolves skeptical paradoxes. Understandably. Yet there has been less discussion as to the internal structure of contextualist theories. Regrettably. Here, for instance, are two questions that could stand further discussion: (i) what is the linguistic basis for contextualism and (ii) what is the parameter that shifts with context?

Does G. E. Moore know that he has hands? Yes, says the dogmatist: Moore’s hands are right before his eyes. No, says the skeptic: for all Moore knows he could be a brain-in-a-vat. Yes and no, says the contrastivist: yes, Moore knows that he has hands rather than stumps; but no, Moore does not know that he has hands rather than vat-images of hands. The dogmatist and the skeptic suppose that knowledge is a binary, categorical relation: s knows that p. (...) The contrastivist says that knowledge is a ternary, contrastive relation: s knows that p rather than q. (shrink)

The concept of search scenario is explicated in terms of erotetic logic, i.e., the logic of questions. Different kinds of erotetic search scenarios are characterized. The basic logical properties of erotetic search scenarios are analyzed.

The basic theory of scientific understanding presented in Sections 1–2 exploits three main ideas.First, that to understand a phenomenonP (for a given agent) is to be able to fitP into the cognitive background corpusC (of the agent).Second, that to fitP intoC is to connectP with parts ofC (via arguments in a very broad sense) such that the unification ofC increases.Third, that the cognitive changes involved in unification can be treated as sequences of shifts of phenomena inC. How the theory fits (...) typical examples of understanding and how it excludes spurious unifications is explained in detail. Section 3 gives a formal description of the structure of cognitive corpuses which contain descriptive as well as inferential components. The theory of unification is then refined in the light of so called puzzling phenomena, to enable important distinctions, such as that between consonant and dissonant understanding. In Section 4, the refined theory is applied to several examples, among them a case study of the development of the atomic model. The final part contains a classification of kinds of understanding and a discussion of the relation between understanding and explanation. (shrink)

Following Dretske (1977), there has been a considerable body of literature on the role of contrastive stress in causal claims. Following van Fraassen (1980), there has been a considerable body of literature on the role of contrastive stress in explanations and explanation-requesting why-questions. Amazingly, the two bodies of literature have remained almost entirely disjoint. With an understanding of the contrastive nature of ordinary causal claims, and of the linguistic roles of contrastive stress, it is possible to provide a unified account (...) of both phenomena. I provide such an account from within the framework of a probabilistic theory of causation. Relations of screening-off, long familiar to researchers in probabilistic causality, play a central role in this account. (shrink)

Problem solving has recently become a central topic both in the philosophy of science and in cognitive science. This paper integrates approaches to problem solving from these two disciplines and discusses the epistemological consequences of such an integration. The paper first analyzes problem solving as getting a true answer to a question. It then explores some stages of cognitive activity relevant to question answering that have been delineated by historians and philosophers of science and by cognitive psychologists and artificial intelligencers. (...) The traditional opposition between discovery and justification is challenged. It is suggested that epistemology may be conceptualized, in part, as the critical assessment of problem-solving strategies. (shrink)

Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.

The concept of erotetic argument is introduced. Two relations between sets of declarative sentences and questions are analysed; and two classes of erotetic arguments are characterized.

A number of logicians and philosophers have turned their attention in recent years to the problem of developing a logic of interrogatives. Their work has thrown a great deal of light on the formal properties of questions and question-sentences and has led also to interesting innovations in our understanding of the structures of performatives in general and, for example, in the theory of presuppositions. When, however, we examine the attempts of logicians such as Belnap or Åqvist to specify what, precisely, (...) a question is, or what it is to ask or raise a question, then what we are offered is somewhat less illuminating. Two alternative reductionist accounts seem in particular to have gained most favor: questions are identified either as special sorts of statements, or as special sorts of requests. As we hope will become clear in what follows, neither of these accounts is even nearly adequate; and matters are not improved if questions are identified, by force majeure, as combinations of statements and requests. (shrink)

Contextualism treats ‘knows’ as an indexical that denotes different epistemic properties in different contexts. Contrastivism treats ‘knows’ as denoting a ternary relation with a slot for a contrast proposition. I will argue that contrastivism resolves the main philosophical problems of contextualism, by employing a better linguistic model. Contextualist insights are best understood by contrastivist theory.

Imperatives cannot be true or false, so they are shunned by logicians. And yet imperatives can be combined by logical connectives: "kiss me and hug me" is the conjunction of "kiss me" with "hug me". This example may suggest that declarative and imperative logic are isomorphic: just as the conjunction of two declaratives is true exactly if both conjuncts are true, the conjunction of two imperatives is satisfied exactly if both conjuncts are satisfied—what more is there to say? Much more, (...) I argue. "If you love me, kiss me", a conditional imperative, mixes a declarative antecedent ("you love me") with an imperative consequent ("kiss me"); it is satisfied if you love and kiss me, violated if you love but don't kiss me, and avoided if you don't love me. So we need a logic of three -valued imperatives which mixes declaratives with imperatives. I develop such a logic. (shrink)

causal relevance, a three-place relation between event types, and circumstances, and argue for a logical independence condition on properties standing in the causal relevance relation relative to circumstances. In section 3, I apply these results to show that functionally defined states are not causally relevant to the output or state transitions in terms of which they are defined. In section 4, I extend this result to what that output in turn causes and to intervening mechanisms. In section 5, I examine (...) the implications of this result for functional theories of mental states. In section 6, I distinguish between functional descriptions of properties and functional definitions of properties, and argue the former present no obstacle to mental states being causally relevant to behavior, but that this is so because they do not treat mental states as functional states. In section 7, I examine the nature of explanations that appeal to functional states or properties. section 8 identifies some difficulties that arise in thinking about specifically conscious mental states as functional states. section 9 is a brief conclusion. (shrink)

In debates about rationalizing action explanation causalists assume that the psychological states that explain an intentional action have both causal and rational features. I scrutinize the presuppositions of those who seek and offer rationalizing action explanations. This scrutiny shows, I argue, that where rational features play an explanatory role in these contexts, causal features play only a presuppositional role. But causal features would have to play an explanatory role if rationalizing action explanation were a species of causal explanation. Consequently, we (...) should conclude that action explanation is not a species of causal explanation. (shrink)

How should the contrastivist formulate closure? That is, given that knowledge is a ternary contrastive state Kspq (s knows that p rather than q), how does this state extend under entailment? In what follows, I will identify adequacy conditions for closure, criticize the extant invariantist and contextualist closure schemas, and provide a contrastive schema based on the idea of extending answers. I will conclude that only the contrastivist can adequately formulate closure.

Inferential erotetic logic and inquisitive semantics give accounts of questions and model various aspects of questioning. In this paper we concentrate upon connections between inquisitiveness, being the core concept of INQ, and question raising, characterized in IEL by means of the concepts of question evocation and erotetic implication. We consider the basic system InqB of INQ, remain at the propositional level and show, inter alia, that: a disjunction of all the direct answers to an evoked question is always inquisitive; a (...) formula is inquisitive if, and only if it evokes a yes–no question whose affirmative answer expresses a possibility for the formula; inquisitive formulas evoke questions whose direct answers express all the possibilities for the formulas, and each question erotetically implies a question whose direct answers express the possibilities for the direct answers to the implying question. (shrink)

Recently, it has become a custom to treat questions as a game between two subjects. Unfortunately, one rarely goesbeyond the scheme of Questioner-Scientist and Answerer-Nature, althoughthe Interlocutor so conceived displays some undesirable features. This paperargues for the idea that logic of questions can be build as a logic of the gamebetween “knowledge resources” persons or theories, rather than errant Scientist and omniscient Nature. To this end the concept of epistemically-possibleworlds is discussed, which is conceived as analogous to that of possible (...) worldsin modal logic. And, furthermore, the concepts of relation of epistemic alternativeness and of epistemically-alternative worlds are introduced. On thisbasis a version of semantics for propositional, three-valued logic of questionsis offered and semantic proofs of some theses are given. (shrink)

John Dewey's ideas on politics derive from his epistemology of inquiry as practical problem-solving. Dewey's philosophy is important for democratic theory because it emphasizes deliberation through questioning. However, Dewey's philosophy shares with positivism the same conception of answering as exclusively the dissolution of questions. While Dewey's ideas are distinct from positivism in important respects, he rejects a constitutive role for questioning by constructing knowledge as problem-solving via experience. The problem-solving ideal lends itself to a scientific conception of politics. Applying Michel (...) Meyer's philosophy of questioning, problematology, to Dewey's logic, reveals that Dewey's theory of inquiry is itself the product of an inquiry, confirming that questioning plays a constitutive role in knowledge. This suggests a problematological reconstruction of knowledge which extends Dewey's ideas by affirming an enhanced status for questioning. Grounding knowledge in the principle of questioning provides the basis for extending the rhetorical analysis of politics. (shrink)

Do you know who you are? If the question seems unclear, it might owe to the notion of ‘knowing-wh’ (knowing-who, knowing-what, knowing-when, etc.). Such knowledge contrasts with ‘knowing-that’, the more familiar topic of epistemologists. But these days, knowing-wh is receiving more attention than ever, and here we will survey three current debates on the nature of knowing-wh. These debates concern, respectively, (1) whether all knowing-wh is reducible to knowing-that (‘generalized intellectualism’), (2) whether all knowing-wh is relativized to a contrast proposition (...) (‘contrastivism about knowing-wh’), and (3) whether the context-sensitivity of knowing-wh is a semantic or purely pragmatic phenomenon (‘contextualism vs. invariantism about knowing-wh’). (shrink)

I give an account of the compositional semantics of unconditionals that explains their relationship to if -conditionals in the Lewis/Kratzer/Heim tradition. Unconditionals involve an alternative-denoting adjunct that supplies domain restrictions pointwise to a main-clause operator such as a modal. The differences from if -clauses follow from the structure of the adjuncts; both are conditionals in the Lewisian sense. In the course of treating unconditionals, I provide a concrete implementation of conditionals where conditional adjuncts in general are a species of correlative, (...) and show what detaching this hypothesis from if involves. (shrink)

The issue of adequacy of the Turing Test (TT) is addressed. The concept of Turing Interrogative Game (TIG) is introduced. We show that if some conditions hold, then each machine, even a thinking one, loses a certain TIG and thus an instance of TT. If, however, the conditions do not hold, the success of a machine need not constitute a convincing argument for the claim that the machine thinks.

We can characterise thought in two different ways. Which is preferred can have implications for important issues about reasoning and the norms that govern cognition. The first, which owes much to the picture of the mind encountered in Descartes' Meditations, observes that paradigmatic examples of thoughts and inferences are events and processes whose special characteristics stem from their being ‘mental’ occurrences. For example they are conscious or, if unconscious, they stand in some special relation to thought processes that are conscious. (...) They typically involve attitudes towards contents or propositions. In general, thoughts have a distinctive onto-logical status and this status depends upon their being mental and typically conscious. The second emphasises that thought is a kind of activity with a definite function. It involves the use of intelligence to solve problems, answer questions, make plans and so on. Thought should be studied as a kind of goal-directed activity. Those interested in the norms that govern thought should attend to the role of responsible disciplined reflection in carrying out this activity. (shrink)

Although explanation is widely regarded as an important concept in the study of rational inquiry, it remains largely unexplored outside the philosophy of science. This, I believe, is not due to oversight as much as to institutional resistance. In analytic philosophy it is basic that epistemic rationality is a function of justification and that justification is a function of argument. Explanation, however, is not argument nor is belief justification its function. I argue here that the task of incorporating explanation into (...) the theory of rational inquiry poses a serious challenge to our basic concept of epistemic rationality as well as the a priori method of inquiry that still lies at the heart of analytic philosophy. Specifically, it pushes us toward a much stronger form of naturalism than is generally thought necessary, one in which argument and explanation are recognized as distinct and equally fundamental cognitive processes whose dynamic relationship is one of the central issues in the theory of rationality. (shrink)

How should one understand knowledge-wh ascriptions? That is, how should one understand claims such as ‘‘I know where the car is parked,’’ which feature an interrogative complement? The received view is that knowledge-wh reduces to knowledge that p, where p happens to be the answer to the question Q denoted by the wh-clause. I will argue that knowledge-wh includes the question—to know-wh is to know that p, as the answer to Q. I will then argue that knowledge-that includes a contextually (...) implicit question. I will conclude that knowledge is a question-relative state. Knowing is knowing the answer, and whether one knows the answer depends (in part) on the question. (shrink)

Scientific knowledge systems function as effective and specialized apparatus for formulating, analyzing and solving scientific problems. In science, problems become internal parts of the knowledge systems; thus they acquire new forms and properties in comparison with common-sense problems. Definite theoretical structures connected with problems and questions appear in the theory. Among them are erotetic expressions and languages, calculi and algebras of problems. On the basis of the structure-nominative reconstruction of a theory, the unified treatment of these structures is given. Methods (...) of the theory of named sets are used in the logical analysis of problems and their systems. As a consequence a new formalized model of the problem part of theory is constructed. (shrink)

Three semantic relations are analyzed: the relation of implication of a question by a question and a set of declarative sentences, the relation of implication of a question by a question, and the relation of strong implication of a question by a question and a set of declarative sentences. The connections between these concepts and the concepts of relative soundness, partial answerhood and presupposition are examined. The principal results are theorems about, to speak generally, epistemic reducibility of well-posed questions to (...) sequences of implied yes-no questions. (shrink)

Debates about explanation in the social sciences often proceed without any clear idea what an 'account' of explanation should do. In this paper I take a stance - what I will call contextualism - that denies there are purely formal and conceptual constraints on explanation and takes standards of explanation to be substantive empirical claims, paradigmatically claims about causation. I then use this standpoint to argue for position on issues in the philosophy of social science concerning reduction, idealized models, social (...) mechanisms, functional explanations, inference to the best explanation and interpretive understanding. (shrink)

The question of how to arrive at questions is ambiguous. I will concentrate on two readings: (i) How should one set up a formal syntax that accomodates questions? (ii) How does one, while working in a suitable formal language, arrive at a situation where one is allowed to or even must ask a certain question? In other words: How is the asking of questions regulated within a given formal language? I will propose an answer to question (i) and consider the (...) field of possibilities of answering (ii). (shrink)

This paper develops an account of the German discourse particle denn that captures the meaning contribution of this particle in polar questions, wh-questions, and certain conditional antecedents in a unified way. It is shown that the behavior of denn exhibits an asymmetry between polar and wh-interrogatives, which can be captured by treating the particle as sensitive to the property highlighted by its containing clause, in the sense of Roelofsen and Farkas :359–414, 2015). In addition, the paper argues that highlighting-sensitivity should (...) be incorporated in the account of another discourse particle, German überhaupt, and discusses how the proposed account of discourse particle denn may be extended to also cover the use of denn as a causal conjunction. (shrink)

Traditional logical theories are concerned with the characterization of valid reasoning. For such logical theories, the main object of investigation is the notion of entailment, a notion that is construed as a relation between two or more declarative statements, dictating when one of them can be legitimately inferred from the others. In the course of the previous century, however, and especially since the 1970s, the scope of logical theories has become much broader. In particular, logic is no longer only concerned (...) with declarative statements, but also with questions. Accordingly, the field is no longer focusing exclusively on the entailment relation that may hold between two or more statements, but also aims to characterize fundamental relations that may hold between questions, or between questions and statements. For instance, when does a statement resolve a given question? When does a statement evoke a certain question? And when does the resolution of one question depend on the resolu .. (shrink)

Un problème est dit ici «mouvoir» la recherche, quand c'est sur lui que se concentre l'énergie du chercheur et que c'est son traitement qui fait «avancer» la recherche.Une entreprise de recherche, une « e-r »,commej'écrirai souvent, est considérée ici comme une unité individuée et je postule qu'il y a toujours au moins un « niveau » où l'on peut se placer pour qu'il soit légitime de considérer une e-r comme une unité individuée.

Van Fraassen and others have urged that judgements of explanations are relative to why-questions; explanations should be considered good in so far as they effectively answer why-questions. In this paper, I evaluate van Fraassen's theory with respect to mathematical explanation. I show that his theory cannot recognize any proofs as explanatory. I also present an example that contradicts the main thesis of the why-question approach—an explanation that appears explanatory despite its inability to answer the why-question that motivated it. This example (...) shows how explanatory judgements can be context-dependent without being why-question-relative. (shrink)

In a recent paper (Haslanger 2016), Sally Haslanger argues for the importance of structural explanation. Roughly, a structural explana- tion of the behaviour of a given object appeals to features of the struc- tures—physical, social, or otherwise—the object is embedded in. It is opposed to individualistic explanations, where what is appealed to is just the object and its properties. For example, an individualistic explanation of why someone got the grade they did might appeal to features of the essay they wrote—its (...) being well-written, answering the set question, etc. But if the class is graded on a curve, then a better explanation will appeal to features of the class—of the social structure in which the student is embedded. That she wrote a better paper than 90% of the class explains better than that she wrote a well-argued paper. In this paper, I get clear as to various candidate concepts of structure that we might appeal to in structural explanations, argue that Haslanger’s preferred account is lacking, and present an alterna- tive that is more conducive to social structural explanation. (shrink)