The Probabilities of Conditionals Revisited

According to what is now commonly referred to as “the Equation” in the literature on indicative conditionals, the probability of any indicative conditional equals the probability of its consequent of the conditional given the antecedent of the conditional. Philosophers widely agree in their assessment that the triviality arguments of Lewis and others have conclusively shown the Equation to be tenable only at the expense of the view that indicative conditionals express propositions. This study challenges the correctness of that assessment by presenting data that cast doubt on an assumption underlying all triviality arguments.     

The rhetoric of the reasoned social scientific fact

An analysis is provided for one possible practical link between rhetorical and social scientific inquiry. That link is found in the rhetoric of the reasoned social scientific fact. Understanding this point of intersection involves grounding a rhetorical theory of how to create and to evaluate arguments (a rhetorical theory of invention and judgment) in the practical problems that confront contemporary social scientists during their efforts to construct reasoned social facts. The applicability of this invention and judgment framework to analysis of the rhetoric of social science is illustrated with reference to a controversy over the legitimacy of rules theoretic explanations of human communication processes. Implications of the practical link between rhetorical and social scientific inquiry are then drawn out.     

Against the Compositional View of Facts

It is commonly assumed that facts would be complex entities made out of particulars and universals. This thesis, which I call Compositionalism, holds that parthood may be construed broadly enough so that the relation that holds between a fact and the entities it ‘ties’ together counts as a kind of parthood. I argue, first, that Compositionalism is incompatible with the possibility of certain kinds of fact and universal, and, second, that such facts and universals are possible. I conclude that Compositionalism is false. What all these kinds of fact and universal have in common is a violation of supplementation principles governing any relation that may be intelligibly regarded as a kind of parthood. Although my arguments apply to Compositionalism generally, I focus on recent work by David Armstrong, who is a prominent and explicit Compositionalist.     

Setting the Facts Straight

Substantial facts (or states of affairs) are not well-understood entities. Many philosophers object to their existence on this basis. Yet facts, if they can be understood, promise to do a lot of philosophical work: they can be used to construct theories of property possession and truthmaking, for example. Here, I give a formal theory of facts, including negative and logically complex facts. I provide a theory of reduction similar to that of the typed λ-calculus and use it to provide identity conditions for facts. This theory validates truthmaker maximalism: it provides truthmakers for all truths. I then show how the usual truth-in-a-model relation can be replaced by two relations: one between models and facts, saying that a given fact obtains relative to the model, and the other between facts and propositions: the truthmaking relation.     

Grounding,physicalism and necessity

Recent work on metaphysical grounding has suggested that physicalism can be characterised in terms of the mental facts being grounded in physical facts. It is often assumed that the full grounds of a fact metaphysically necessitate that fact. Therefore, it seems that if the physical grounds the mental, then the physical facts metaphysically necessitate the mental facts. Stefan Leuenberger argues that such a version of physicalism would be vulnerable to counterexamples. I shall outline a characterisation of grounding which appeals to a relation between grounding and the essences of properties instantiated in the grounded facts or in their grounds. If a grounded fact is such that its constituent property is essentially related to the properties instantiated in its grounds, or vice versa, then the grounded fact will be metaphysically necessitated by its full grounds. This characterisation of grounding not only avoids Leuenberger’s counterexamples, but has broader implications for characterising physicalism in terms of grounding.     

Resolving arguments by different conceptual traditions of realization

There is currently a significant amount of interest in understanding and developing theories of realization. Naturally arguments have arisen about the adequacy of some theories over others. Many of these arguments have a point. But some can be resolved by seeing that the theories of realization in question fall under different conceptual traditions with different but compatible goals. The arguments I will discuss fit a general pattern. A philosopher argues that one theory of realization is better than another because it provides a better explanation for a particular range of phenomena, say, accounting for common sense cases, or cases within the sciences, when in fact the theories in question are not genuine competitors. I will first describe three different conceptual traditions that are implicated by the arguments under discussion. I will then examine the arguments, from an older complaint by Norman Malcolm against a familiar functional theory to a recent argument by Thomas Polger against an assortment of theories that traffic in inherited causal powers, showing how they can be resolved by situating the theories under their respective conceptual traditions.     

Direct Arguments for the Truth-Condition Theory of Meaning

The truth-condition theory of meaning is, naturally, thought of an as explanatory theory whose explananda are the meaning facts. But there are at least two deductive arguments that purport to establish the truth of the theory irrespective of its explanatory virtues. This paper examines those arguments and concludes that they succeed.     

Ontological individualism reconsidered

The thesis of methodological individualism in social science is commonly divided into two different claims—explanatory individualism and ontological individualism. Ontological individualism is the thesis that facts about individuals exhaustively determine social facts. Initially taken to be a claim about the identity of groups with sets of individuals or their properties, ontological individualism has more recently been understood as a global supervenience claim. While explanatory individualism has remained controversial, ontological individualism thus understood is almost universally accepted. In this paper I argue that ontological individualism is false. Only if the thesis is weakened to the point that it is equivalent to physicalism can it be true, but then it fails to be a thesis about the determination of social facts by facts about individual persons. Even when individualistic facts are expanded to include people’s local environments and practices, I shall argue, those still underdetermine the social facts that obtain. If true, this has implications for explanation as well as ontology. I first consider arguments against the local supervenience of social facts on facts about individuals, correcting some flaws in existing arguments and affirming that local supervenience fails for a broad set of social properties. I subsequently apply a similar approach to defeat a particularly weak form of global supervenience, and consider potential responses. Finally, I explore why it is that people have taken ontological individualism to be true.     

The possibility of morality

Despite much discussion over the existence of moral facts, metaethicists have largely ignored the related question of their possibility. This paper addresses the issue from the moral error theorist’s perspective, and shows how the arguments that error theorists have produced against the existence of moral facts at this world, if sound, also show that moral facts are impossible, at least at worlds non-morally identical to our own and, on some versions of the error theory, at any world. So error theorists’ arguments warrant a stronger conclusion than has previously been noticed. This may appear to make them vulnerable to counterarguments that take the possibility of moral facts as a premise. However, I show that any such arguments would be question-begging.     

Upward Grounding

Realists about universals face a question about grounding. Are things how they are because they instantiate the universals they do? Or do they instantiate those universals because they are how they are? Take Ebenezer Scrooge. You can say that (i) Scrooge is greedy because he instantiates greediness, or you can say that (ii) Scrooge instantiates greediness because he is greedy. I argue that there is reason to prefer the latter to the former. I develop two arguments for the view. I also respond to some concerns one might have about the view defended. I close by showing that analogous views regarding the truth of propositions (that if the proposition that p is true, then it is true because p) and the existence of facts (that if the fact that p exists, then it exists because p) are supported by analogs of one of these arguments.     

Equality in Law and Philosophy

This article discusses various arguments for and against treating equality as a fundamental norm in law and political philosophy, combining prior arguments to the effect that equality is essentially an empty idea with arguments that treat it as a non‐empty but mistaken value that should be rejected. After concluding that most of the arguments for treating equality as a fundamental value fall victim to one or both of these arguments, it considers more closely arguments made by philosophers such as Ronald Dworkin and Thomas Nagel that base a duty of promoting equality on the fact that governments impose a legal order on persons without their consent. It concludes that these arguments are mistaken: if the legal order imposed by government is justified then imposing it is not wrongful and generates no duty of equal treatment, while if that order is not justified no requirement of equality of treatment would cure the lack of justification. It concludes that equality should not be a value in law or political theory, but in some cases other considerations (such as alleviating poverty and distress, promoting accuracy and substantive justice, avoiding arbitrariness, and other values) may justify particular rules that are sometimes mistakenly thought to be based on equality.     

The argument from agreement: How universal values undermine moral realism

The most popular argument against moral realism is the argument from disagreement: if there are mind‐independent moral facts, then we would not expect to find as much moral disagreement as we in fact do; therefore, moral realism is false. In this paper, I develop the flipside of this argument. According to this argument from agreement, we would expect to find lots of moral disagreement if there were mind‐independent moral facts. But we do not, in fact, find much moral disagreement; therefore, moral realism is false. I defend the argument, explain the empirical evidence that supports it, and show what makes this challenge novel and powerful.     

Conditionals, Comparative Probability, and Triviality: The Conditional of Conditional Probability Cannot Be Represented in the Object Language

In this paper we examine the thesis that the probability of the conditional is the conditional probability. Previous work by a number of authors has shown that in standard numerical probability theories, the addition of the thesis leads to triviality. We introduce very weak, comparative conditional probability structures and discuss some extremely simple constraints. We show that even in such a minimal context, if one adds the thesis that the probability of a conditional is the conditional probability, then one trivializes the theory. Another way of stating the result is that the conditional of conditional probability cannot be represented in the object language on pain of trivializing the theory.     

ARGUMENTS FROM CONCEIVABILITY1

What can be inferred from the fact that something is, or is not, conceivable? In this paper I argue, contrary to some deflationary remarks in recent literature, that arguments which use such facts as their starting point may have significant philosophical import. I use Strawson's results from the first chapter of Individuals in order to show that Galileo's arguments in favour of the distinction between primary and secondary qualities, which are based on premises concerning conceivability, should not be dismissed: they are the first step towards recognising an important conceptual truth.     

Moral Explanations of Moral Beliefs

Gilbert Harman and Judith Thomson have argued that moral facts cannot explain our moral beliefs, claiming that such facts could not play a causal role in the formation of those beliefs. This paper shows these arguments to be misguided, for they would require that we abandon any number of intuitively plausible explanations in non-moral contexts as well. But abandoning the causal strand in the argument over moral explanations does not spell immediate victory for the moral realist, since it must still be shown that moral facts do figure in our best global explanatory theory.     

Probabilistic argumentation systems: A new way to combine logic with probability

Probability is usually closely related to Boolean structures, i.e., Boolean algebras or propositional logic. Here we show, how probability can be combined with non-Boolean structures, and in particular non-Boolean logics. The basic idea is to describe uncertainty by (Boolean) assumptions, which may or may not be valid. The uncertain information depends then on these uncertain assumptions, scenarios or interpretations. We propose to describe information in information systems, as introduced by Scott into domain theory. This captures a wide range of systems of practical importance such as many propositional logics, first order logic, systems of linear equations, inequalities, etc. It covers thus both symbolic as well as numerical systems. Assumption-based reasoning allows then to deduce supporting arguments for hypotheses. A probability structure imposed on the assumptions permits to quantify the reliability of these supporting arguments and thus to introduce degrees of support for hypotheses. Information systems and related information algebras are formally introduced and studied in this paper as the basic structures for assumption-based reasoning. The probability structure is then formally represented by random variables with values in information algebras. Since these are in general non-Boolean structures some care must be exercised in order to introduce these random variables. It is shown that this theory leads to an extension of Dempster–Shafer theory of evidence and that information algebras provide in fact a natural frame for this theory.     

Understanding Brute Facts

Brute facts are facts that have no explanation. If we come to know that a fact is brute, we obviously don’t get an explanation of that fact. Nevertheless, we do make some sort of epistemic gain. In this essay, I give an account of that epistemic gain, and suggest that the idea of brute facts allows us to distinguish between the notion of explanation and the notion of understanding.I also discuss Eric Barnes’ (1994) attack on Friedman’s (1974) version of the unification theory of explanation. The unification theory asserts that scientific understanding results from minimizing the number of brute facts that we have to accept in our view of the world. Barnes claims that the unification theory cannot do justice to the notion of being a brute fact, because it implies that brute facts are gaps in our understanding of the world. I defend Friedman’s theory against Barnes’ critique.     

Phenomenal experience and the measure of information

This paper defends the hypothesis that phenomenal experiences may be very complex information states. This can explain some of our most perplexing anti-physicalist intuitions about phenomenal experience. The approach is to describe some basic facts about information in such a way as to make clear the essential oversight involved, by way illustrating how various intuitive arguments against physicalism (such as Frank Jackson’s Knowledge Argument, and Thomas Nagel’s Bat Argument) can be interpreted to show that phenomenal information is not different in kind from physical information, but rather is just more information than we typically attribute to our understanding of a physical theory. I clarify how this hypothesis is distinct from Nagel’s claim that the theory of consciousness may be inconceivable, and then in conclusion briefly describe how these results might suggest a positive and conservative physicalist account of phenomenal experience.     

Focused memory search in fact retrieval

Several studies of fact retrieval have shown that the more facts a person learns about a concept, the longer it takes him or her to retrieve any of these facts. This result has been interpreted to mean that retrieval of a fact about a concept involves a search of all facts stored in memory with that concept. In the present study, it is suggested that retrieval involves not an unfocused search of all facts stored with a concept, but rather a focused memory search that examines relevant stored facts and ignores irrelevant information. This argument is supported by three experiments in which subjects first learned simple facts (e.g., “The banker likes horses”) and then made speeded true-false decisions for test probes le.g., “The banker likes elephants”). Specifically, results suggest that facts stored with a concept may be organized into subsets. For example, a person’s knowledge about Richard Nixon might be organized into subsets concerning Nixon’s resignation, his trips to China, his family, and so on. The data further suggest that a person attempting to retrieve a fact about a concept (e.g., the name of Nixon’s wife) may simply decide which subset is most likely to contain the desired fact (e.g., the subset concerning Nixon’s family) and search that subset. If the sought-for fact is found in this subset, the search process terminates. If, however, the desired information is not located, other subsets of facts may be searched before the retrieval attempt is given up. The notion that memory search focuses on relevant stored facts and ignores irrelevant information may help to explain why experts (i.e., people who know a large number of facts about a topic) do not experience great difficulty in retrieving facts in their areas of expertise.