Online research in philosophy

This is a short critique of sufficiency views.

(Canadian Journal of Philosophy 37 (2007), pp. 111-127) A popular view about why death is bad for the one who dies is that death deprives its subject of the good things in life. This is the “deprivation account” of the evil of death. There is another view about death that seems incompatible with the deprivation account: the view that a person’s death is less bad if she has lived a good life. I give some arguments against this view and defend (...) the deprivation account. Penultimate draft posted with kind permission of the Canadian Journal of Philosophy; please use published version for citations. (shrink)

This paper revisits Carnap’s theory of degree of confirmation, identifies certain shortcomings, and argues that a new approach based on objective Bayesian epistemology can overcome these shortcomings.

How ought we learn causal relationships? While Popper advocated a hypothetico-deductive logic of causal discovery, inductive accounts are currently in vogue. Many inductive approaches depend on the causal Markov condition as a fundamental assumption. This condition, I maintain, is not universally valid, though it is justifiable as a default assumption. In which case the results of the inductive causal learning procedure must be tested before they can be accepted. This yields a synthesis of the hypothetico-deductive and inductive accounts, which forms (...) the focus of this paper. I discuss the justification of this synthesis and draw an analogy between objective Bayesianism and the account of causal learning presented here. (shrink)

Inductive logic admits a variety of semantics (Haenni et al., 2011, Part 1). This paper develops semantics based on the norms of Bayesian epistemology (Williamson, 2010, Chapter 7). §1 introduces the semantics and then, in §2, the paper explores methods for drawing inferences in the resulting logic and compares the methods of this paper with the methods of Barnett and Paris (2008). §3 then evaluates this Bayesian inductive logic in the light of four traditional critiques of inductive logic, arguing (i) (...) that it is language independent in a key sense, (ii) that it admits connections with the Principle of Indifference but these connections do not lead to paradox, (iii) that it can capture the phenomenon of learning from experience, and (iv) that while the logic advocates scepticism with regard to some universal hypotheses, such scepticism is not problematic from the point of view of scientific theorising. (shrink)

Bayesians hold that probability is a mental notion: saying that the probability of rain is 0.7 is just saying that you believe it will rain to degree 0.7. Degrees of belief are themselves cashed out in terms of bets—in this case you consider 7 : 3 to be fair odds for a bet on rain. There are two extreme Bayesian positions. Strict Subjectivists think that an agent can adopt whatever degrees of belief she likes, as long as they satisfy the (...) axioms of probability. Thus your degree of belief in rain and degree of belief in no rain must sum to one but are otherwise unconstrained. At the other extreme, objectivists claim that an agent’s background knowledge considerably narrows down the choice of appropriate degrees of belief. In particular, if you know only that the frequency of rain is 0.7 then you should believe it will rain to degree 0.7; if you know absolutely nothing about the weather then you should set your degree of belief in rain to be 0.5; in neither of these cases is there room for subjective choice of degree of belief. In this book, Jeffrey advocates what is sometimes called empirically-based subjectivism, a position that lies between the two extremes of strict subjectivism and objectivism. According to this position, knowledge of frequencies constrains degree of belief, but lack of knowledge does not impose any constraints, so that if you know nothing about the weather you may adopt any degree of belief in rain you like.1 The aim of the book isn’t so much to justify this point of view as to provide a comprehensive exposition of probability theory from the perspective that it offers. The book succeeds admirably: Jeffrey presents a broad range of standard topics concerning Bayesianism, including the betting interpretation of degrees of belief, a discussion of objective chance, the application of Bayesianism to scientific reasoning, conditionalisation, expectation, exchangeability and decision theory. Naturally much of the discussion of these topics focuses on Jeffrey’s own multifarious contributions to the subject.. (shrink)

Machamer, Darden and Craver: ‘Mechanisms are entities and activities organized such that they are productive of regular changes from start or set-up to finish or termination conditions.’ (Machamer, Darden and Craver 2000 p3.) Glennan: ‘A mechanism for a behavior is a complex system that produces that behavior by the interaction of a number of parts, where the interactions between parts can be characterized by direct, invariant, change-relating generalizations.’ (Glennan 2002b pS344.) Bechtel and Abrahamsen: ‘A mechanism is a structure performing a (...) function in virtue of its component parts, component operations, and their organization. The orchestrated functioning of the mechanism is responsible for one or more phenomena.’ (Bechtel and Abrahamsen 2005 p423.). (shrink)

Practical reasoning requires decision—making in the face of uncertainty. Xenelda has just left to go to work when she hears a burglar alarm. She doesn’t know whether it is hers but remembers that she left a window slightly open. Should she be worried? Her house may not be being burgled, since the wind or a power cut may have set the burglar alarm off, and even if it isn’t her alarm sounding she might conceivably be being burgled. Thus Xenelda can (...) not be certain that her house is being burgled, and the decision that she takes must be based on her degree of certainty, together with the possible outcomes of that decision. (shrink)

this paper we argue that the formalism can also be applied to modelling the hierarchical structure of physical mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations are vital for prediction, explanation and control respectively, a recursive Bayesian net can be applied to all these tasks. We show how a Recursive Bayesian Net can be used to model mechanisms in cancer science. (...) The highest level of the proposed model will contain variables at the clinical level, while a middle level will map the structure of the DNA damage response mechanism and the lowest level will contain information about gene expression. (shrink)

In this chapter I discuss connections between machine learning and the philosophy of science. First I consider the relationship between the two disciplines. There is a clear analogy between hypothesis choice in science and model selection in machine learning. While this analogy has been invoked to argue that the two disciplines are essentially doing the same thing and should merge, I maintain that the disciplines are distinct but related and that there is a dynamic interaction operating between the two: a (...) series of mutually beneficial interactions that changes over time. I will introduce some particularly fruitful interactions, in particular the consequences of automated scientific discovery for the debate on inductivism versus falsificationism in the philosophy of science, and the importance of philosophical work on Bayesian epistemology and causality for contemporary machine learning. I will close by suggesting the locus of a possible future interaction: evidence integration. (shrink)

This introduction to the volume begins with a manifesto that puts forward two theses: first, that the sciences are the best place to turn in order to understand causality; second, that scientifically-informed philosophical investigation can bring something to the sciences too. Next, the chapter goes through the various parts of the volume, drawing out relevant background and themes of the chapters in those parts. Finally, the chapter discusses the progeny of the papers and identifies some next steps for research into (...) causality in the sciences. (shrink)

Bayesian theory now incorporates a vast body of mathematical, statistical and computational techniques that are widely applied in a panoply of disciplines, from artificial intelligence to zoology. Yet Bayesians rarely agree on the basics, even on the question of what Bayesianism actually is. This book is about the basics e about the opportunities, questions and problems that face Bayesianism today.

The paper argues that, although a distinction between a priori and a posteriori knowledge (or justification) can be drawn, it is a superficial one, of little theoretical significance. The point is not that the distinction has borderline cases, for virtually all useful distinctions have such cases. Rather, it is argued by means of an example, the differences even between a clear case of a priori knowledge and a clear case of a posteriori knowledge may be superficial ones. In both cases, (...) experience plays a role that is more than purely enabling but less than strictly evidential. It is also argued that the cases at issue are not special, but typical of a wide range of others, including knowledge of axioms of set theory and of elementary logical truths. Attempts by Quine and others to make all knowledge a posteriori (‘empirical’) are repudiated. The paper ends with a call for a new framework to be developed for analysing the epistemology of cognitive uses of the imagination. (shrink)

The Linguistic Turn is the title of an influential anthology edited by Richard Rorty, published in 1967. In his introduction, Rorty explained: The purpose of the present volume is to provide materials for reflection on the most recent philosophical revolution, that of linguistic philosophy. I shall mean by “linguistic philosophy” the view that philosophical problems are problems which may be solved (or dissolved) either by reforming language, or by understanding more about the language we presently use. (1967: 3) ‘The linguistic (...) turn’ has subsequently become a standard vague phrase for a diffuse event — some regard it as the event — in twentieth century philosophy, one not confined to signed-up linguistic philosophers in Rorty’s sense. For those who took the turn, language was somehow the central theme of philosophy. There is an increasingly widespread sense that the linguistic turn is past. In this essay I ask how far the turn has been, or should be, reversed. (shrink)

1. As John Hawthorne and Maria Lasonen-Aarnio appreciate, some of the central issues raised in their ‘Knowledge and Objective Chance’ arise for all but the most extreme theories of knowledge. In a wide range of cases, according to very plausible everyday judgments, we know something about the future, even though, according to quantum mechanics, our belief has a small but nonzero chance (objective probability) of being untrue. In easily constructed examples, we are in that position simultaneously with respect to many (...) different propositions about the future that are equiprobable and probabilistically independent of each other, at least to a reasonable approximation. (shrink)

Some systems of modal logic, such as S5, which are often used as epistemic logics with the ‘necessity’ operator read as ‘the agent knows that’, are problematic as general epistemic logics for agents whose computational capacity does not exceed that of a Turing machine because they impose unwarranted constraints on the agent’s theory of non-epistemic aspects of the world, for example by requiring the theory to be decidable rather than merely recursively axiomatizable. To generalize this idea, two constraints on an (...) epistemic logic are formulated: r.e. conservativeness, that any recursively enumerable theory R in the sublanguage without the epistemic operator is conservatively extended by some recursively enumerable theory in the language with the epistemic operator which is permitted by the logic to be the agent’s overall theory; the weaker requirement of r.e. quasi-conservativeness is similar except for applying only when R is consistent. The logic S5 is not even r.e. quasiconservative; this result is generalized to many other modal logics. However, it is also proved that the modal logics S4, Grz and KDE are r.e. quasi-conservative and that K4, KE and the provability logic GLS are r.e. conservative. Finally, r.e. conservativeness and r.e. quasiconservativeness are compared with related non-computational constraints. (shrink)

by living organisms to process chemical comchemical reactions. Understanding metabolism is an impounds in order to take energy and eliminate portant problem for biology, pharmacology (in particular..

The theory of belief revision and merging has recently been applied to judgement aggregation. In this paper I argue that judgements are best aggregated by merging the evidence on which they are based, rather than by directly merging the judgements themselves. This leads to a threestep strategy for judgement aggregation. First, merge the evidence bases of the various agents using some method of belief merging. Second, determine which degrees of belief one should adopt on the basis of this merged evidence (...) base, by applying objective Bayesian theory. Third, determine which judgements are appropriate given these degrees of belief by applying a decision-theoretic account of rational judgement formation. (shrink)

ϕ1, . . . , ϕn |≈ ψ? Here ϕ1, . . . , ϕn, ψ are premisses of some formal language, such as a propositional language or a predicate language. |≈ is an entailment relation: the entailment holds if all models of the premisses also satisfy the conclusion, where the logic provides some suitable notion of ‘model’ and ‘satisfy’. Proof theory is normally invoked to answer a question of this form: one tries to prove the conclusion from the premisses (...) in a finite sequence of steps, where at each step one invokes an axiom or applies a rule of inference. (shrink)

How should we reason with causal relationships? Much recent work on this question has been devoted to the theses (i) that Bayesian nets provide a calculus for causal reasoning and (ii) that we can learn causal relationships by the automated learning of Bayesian nets from observational data. The aim of this book is to..

By identifying and pursuing analogies between causal and logical influence I show how the Bayesian network formalism can be applied to reasoning about logical deductions.

This chapter addresses two questions: what are causal relationships? how can one discover causal relationships? I provide a survey of the principal answers given to these questions, followed by an introduction to my own view, epistemic causality, and then a comparison of epistemic causality with accounts provided by Judea Pearl and Huw Price.

We present a new framework for combining logic with probability, and demonstrate the application of this framework to breast cancer prognosis. Background knowledge concerning breast cancer prognosis is represented using logical arguments. This background knowledge and a database are used to build a Bayesian net that captures the probabilistic relationships amongst the variables. Causal hypotheses gleaned from the Bayesian net in turn generate new arguments. The Bayesian net can be queried to help decide when one argument attacks another. The Bayesian (...) net is used to perform the prognosis, while the argumentation framework is used to provide a qualitative explanation of the prognosis. (shrink)

How is probability related to logic? Should probability and logic be combined? If so, how? Bayesianism tells us we ought to reason probabilistically. In that sense, probability theory is logic. How then does probability theory relate to classical logic and the various non-classical logics that also stake a claim on normative reasoning? Is probability theory to be preferred over other logics or vice versa? Is probability theory to be used in some situations, and the other logics in other situations? Or (...) should probability be combined with other logics? (shrink)

Evidence can be complex in various ways: e.g., it may exhibit structural complexity, containing information about causal, hierarchical or logical structure as well as empirical data, or it may exhibit combinatorial complexity, containing a complex combination of kinds of information. This paper examines evidential complexity from the point of view of Bayesian epistemology, asking: how should complex evidence impact on an agent’s degrees of belief? The paper presents a high-level overview of an objective Bayesian answer: it presents the objective Bayesian (...) norms concerning the relation between evidence and degrees of belief, and goes on to show how evidence of causal, hierarchical and logical structure lead to natural constraints on degrees of belief. The objective Bayesian network formalism is presented, and it is shown how this formalism can be used to handle both kinds of evidential complexity—structural complexity and combinatorial complexity. (shrink)

This paper is a comparison of how first-order Kyburgian Evidential Probability (EP), second-order EP, and objective Bayesian epistemology compare as to the KLM system-P rules for consequence relations and the monotonic / non-monotonic divide.

Bayesian networks are normally given one of two types of foundations: they are either treated purely formally as an abstract way of representing probability functions, or they are interpreted, with some causal interpretation given to the graph in a network and some standard interpretation of probability given to the probabilities specified in the network. In this chapter I argue that current foundations are problematic, and put forward new foundations which involve aspects of both the interpreted and the formal approaches.

We argue that the health sciences make causal claims on the basis of evidence both of physical mechanisms and of probabilistic dependencies. Consequently, an analysis of causality solely in terms of physical mechanisms, or solely in terms of probabilistic relationships, does not do justice to the causal claims of these sciences. Yet there seems to be a single relation of cause in these sciences—pluralism about causality will not do either. Instead, we maintain, the health sciences require a theory of causality (...) that unifies its mechanistic and probabilistic aspects. We argue that the epistemic theory of causality provides the required unification. (shrink)

How should probabilities be interpreted in causal models in the social and health sciences? In this paper we take a step towards answering this question by investigating the case of cancer in epidemiology and arguing that the objective Bayesian interpretation is most appropriate in this domain.

We consider the use of intervention data for eliminating the underdetermination in statistical modelling, and for guiding extensions of the statistical models. The leading example is factor analysis, a major statistical tool in the social sciences. We first relate indeterminacy in factor analysis to the problem of underdetermination. Then we draw a parallel between factor analysis models and Bayesian networks with hidden nodes, which allows us to clarify the use of intervention data for dealing with indeterminacy. It will be shown (...) that in some cases, the indeterminacy can be resolved by an intervention. In the other cases, the intervention data suggest specific extensions of the model. The upshot is that intervention data can replace theoretical criteria that are typically employed in resolving underdetermination and theory change. (shrink)

How ought we learn causal relationships? While Popper advocated a hypothetico-deductive logic of causal discovery, inductive accounts are currently in vogue. Many inductive approaches depend on the causal Markov condition as a fundamental assumption. This condition, I maintain, is not universally valid, though it is justifiable as a default assumption. In which case the results of the inductive causal learning procedure must be tested before they can be accepted. This yields a synthesis of the hypothetico-deductive and inductive accounts, which forms (...) the focus of this paper. I discuss the justification of this synthesis and draw an analogy between objective Bayesianism and the account of causal learning presented here. (shrink)

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