Against Barnett (2012), I argue that the theory I advance in DeRose 2010 is best construed as one on which ‘"were"ed-up’ future-directed conditionals like ‘If the house were not to be painted, it would soon look quite shabby’ are, in ways important to how they function in deliberation, different in literal content from their ‘straightforward’ counterparts like ‘If the house is not painted, it will soon look quite shabby’. I also defend my way of classifying future-directed conditionals against an attack (...) by Barnett by defending a standard (among philosophers) approach to the basic structure of some conditionals. Finally, I counter Barnett’s charge that by using the concept of deliberation in my account of the meaning of future-directed conditionals, I put an implausibly demanding constraint on what it takes to understand such sentences. (shrink)

Recent work on the interpretation of counterfactual conditionals has paid much attention to the role of causal independencies. One influential idea from the theory of Causal Bayesian Networks is that counterfactual assumptions are made by intervention on variables, leaving all of their causal non-descendants unaffected. But intervention is not applicable across the board. For instance, backtracking counterfactuals, which involve reasoning from effects to causes, cannot proceed by intervention in the strict sense, for otherwise they would be equivalent to their consequents. (...) We discuss these and similar cases, focusing on two factors which play a role in determining whether and which causal parents of the manipulated variable are affected: Speakers' need for an explanation of the hypothesized state of affairs, and differences in the ‘resilience’ of beliefs that are independent of degrees of certainty. We describe the relevant theoretical notions in some detail and provide experimental evidence that these factors do indeed affect speakers' interpretation of counterfactuals. (shrink)

Modus ponens is the argument from premises of the form If A, then B and A to the conclusion B. Nearly all participants agree that the modus ponens conclusion logically follows when the argument appears in this Basic form. However, adding a further premise can lower participants’ rate of agreement—an effect called suppression. We propose a theory of suppression that draws on contemporary ideas about conditional sentences in linguistics and philosophy. Semantically, the theory assumes that people interpret an indicative conditional (...) as a context-sensitive strict conditional: true if and only if its consequent is true in each of a contextually determined set of situations in which its antecedent is true. Pragmatically, the theory claims that context changes in response to new assertions, including new conditional premises. Thus, the conclusion of a modus ponens argument may no longer be accepted in the changed context. Psychologically, the theory describes people as capable of reasoning about broad classes of possible situations, ordered by typicality, without having to reason about individual possible worlds. The theory accounts for the main suppression phenomena, and it generates some novel predictions that new experiments confirm. (shrink)

It is argued that expressivists can solve their problems in accounting for the unity and autonomy of logic – logic is topic independent and does not derive from a general ‘logic’ of mental states – by adopting an analysis of the logical connectives that takes logically complex sentences to express complex combinations of simple attitudes like belief and disapproval and dispositions to form such simple attitudes upon performing suppositional acts, and taking acceptance and rejection of sentences to be the common (...) mental denominator in descriptive and evaluative discourse, and structural requirements governing these to be the basis for logic. Such an account requires that attitudes like belief, intention and disapproval can come in hypothetical mode – plausibly linked to the capacity to mentally simulate or emulate one's own attitudes – and, if correct, suggests that these form the basic building blocks for our capacity to understand logically complex sentences. (shrink)

This paper explores the possibility that causal decision theory can be formulated in terms of probabilities of conditionals. It is argued that a generalized Stalnaker semantics in combination with an underlying branching time structure not only provides the basis for a plausible account of the semantics of indicative conditionals, but also that the resulting conditionals have properties that make them well-suited as a basis for formulating causal decision theory. Decision theory (at least if we omit the frills) is not an (...) esoteric science, however unfamiliar it may seem to an outsider. Rather it is a systematic exposition of the consequences of certain well-chosen platitudes about belief, desire, preference and choice. It is the very core of our common-sense theory of persons, dissected out and elegantly systematized. (David Lewis, Synthese 23:331–344, 1974, p. 337). A small distortion in the analysis of the conditional may create spurious problems with the analysis of other concepts. So if the facts about usage favor one among a number of subtly different theories, it may be important to determine which one it is. (Robert Stalnaker, A Defense of Conditional Excluded Middle, pp. 87–104, 1980, p. 87). (shrink)

Adams’s Thesis, the claim that the probabilities of indicative conditionals equal the conditional probabilities of their consequents given their antecedents, has proven impossible to accommodate within orthodox possible-world semantics. This essay proposes a modification to the orthodoxy that removes this impossibility. The starting point is a proposal by Jeffrey and Stalnaker that conditionals take semantic values in the unit interval, interpreting these (à la McGee) as their expected truth-values at a world. Their theories imply a false principle, namely, that the (...) probability of a conditional is independent of any proposition inconsistent with its antecedent. But they also point to something important, namely, that our uncertainty about conditionals is not confined to uncertainty about the facts (what the actual world is like) but also expresses uncertainty about the counterfacts (what the world would be like if one or another supposition were true). To capture this observation, this essay proposes that the semantic contents of conditionals be treated as sets of vectors of possible worlds, not singleton worlds, with the coordinates of each specifying the world that is or would be true under the supposition that it represents. The probabilities of truth for conditionals will then depend on the joint probabilities of the facts and counterfacts, the latter in turn depending on the mode of supposition. The implication of this treatment is that the probabilities of conditionals are conditional probabilities whenever the mode of supposition is evidential. (shrink)

The Desire-as-Belief thesis (DAB) states that any rational person desires a proposition exactly to the degree that she believes or expects the proposition to be good. Many people take David Lewis to have shown the thesis to be inconsistent with Bayesian decision theory. However, as we show, Lewis's argument was based on an Invariance condition that itself is inconsistent with the (standard formulation of the) version of Bayesian decision theory that he assumed in his arguments against DAB. The aim of (...) this paper is to explore what impact the rejection of Invariance has on the DAB thesis. Without assuming Invariance, we first refute all versions of DAB that entail that there are only two levels of goodness. We next consider two theses according to which rational desires are intimately connected to expectations of (multi-levelled) goodness, and show that these are consistent with Bayesian decision theory as long as we assume that the contents of 'value propositions' are not fixed. We explain why this conclusion is independently plausible, and show how to construct such propositions. (shrink)

According to the Ramsey Test hypothesis the conditional claim that if A then B is credible just in case it is credible that B, on the supposition that A. If true the hypothesis helps explain the way in which we evaluate and use ordinary language conditionals. But impossibility results for the Ramsey Test hypothesis in its various forms suggest that it is untenable. In this paper, I argue that these results do not in fact have this implication, on the grounds (...) that similar results can be proved without recourse to the Ramsey test hypothesis. Instead they show that a number of well entrenched principles of rational belief and belief revision do not apply to conditionals. (shrink)

Adams' famous thesis that the probabilities of conditionals are conditional probabilities is incompatible with standard probability theory. Indeed it is incompatible with any system of monotonic conditional probability satisfying the usual multiplication rule for conditional probabilities. This paper explores the possibility of accommodating Adams' thesis in systems of non-monotonic probability of varying strength. It shows that such systems impose many familiar lattice theoretic properties on their models as well as yielding interesting logics of conditionals, but that a standard complementation operation (...) cannot be defined within them, on pain of collapsing probability into bivalence. (shrink)

In this paper, I consider a variant of the ancient Idle Argument involving so‐called “unconditionals” with interrogative antecedents. This new Idle Argument provides an ideal setting for probing the logic of these close relatives of if‐conditionals, which has been comparatively underexplored. In the course of refuting the argument, I argue that contrary to received wisdom, many unconditionals do not entail their main clauses, yet modus ponens is still unrestrictedly valid for this class of expressions. I make these lessons precise in (...) a formal system drawing on recent work in inquisitive semantics. My larger aim is to challenge standard truth preservation accounts of logic and deductive argumentation. (shrink)

A popular view is that we create our own identities and values. An attractive version of this is the thesis that the creation of values follows from the creation of identities. The thesis is best supported by a conception of identity in terms of projects and a conception of values that are internal to projects: in creating my projects, I create values internal to them; so I create those values. This paper argues that the thesis faces a dilemma: it is (...) either true but uninteresting or interesting by false. The dilemma persists whether the values in question are conceived as purpose-relative, as moral, or as both purpose-relative and moral. (shrink)

This paper first provides a brief survey of a possibilistic handling of default rules. A set of default rules of the form, "generally, from α deduce β", is viewed as the family of possibility distributions satisfying constraints expressing that the situation where α and β is true has a greater plausibility than the one where α and ⇁β is true. When considering only the subset of linear possibility distributions, the well-known System P of postulates proposed by Kraus, Lehmann and Magidor, (...) has been obtained. We also present two rational extensions: one based on the minimum specificity principle and the other is based on the lexicographic ordering. The second part of the paper presents an empirical study of three desirable properties for a consequence relation that capture default reasoning: Rationality, Property Inheritance and Ambiguity Preservation. An experiment is conducted to investigate 13 patterns of inference for the test of these properties. Our experimental apparatus confirms previous results on the relevance of System P, and enforces the psychological relevance of the studied properties. (shrink)

Let us call a statement of the form ‘If A was, is, or will be the case, then C was, is, or will be the case’ an indicative conditional. And let us call a statement of the form ‘If A had been, were, or were to be the case, then C would have been, would be, or would come to be the case’ a subjunctive, or counterfactual, conditional.

I aim to show that standard theories of counterfactuals are mistaken, not in detail, but in principle, and I aim to say what form a tenable theory must take. Standard theories entail a categorical interpretation of counterfactuals, on which to state that, if it were that A, it would be that C is to state something, not relative to any supposition or hypothesis, but categorically. On the rival suppositional interpretation, to state that, if it were that A, it would be (...) that C is to state that it would be that C relative to the supposition that it were that A. The two interpretations make incompatible predictions concerning the correct evaluation of counterfactuals. I argue that the suppositional interpretation makes the correct prediction. (shrink)

We defend a set of acceptance rules that avoids the lottery paradox, that is closed under classical entailment, and that accepts uncertain propositions without ad hoc restrictions. We show that the rules we recommend provide a semantics that validates exactly Adams’ conditional logic and are exactly the rules that preserve a natural, logical structure over probabilistic credal states that we call probalogic. To motivate probalogic, we first expand classical logic to geo-logic, which fills the entire unit cube, and then we (...) project the upper surfaces of the geo-logical cube onto the plane of probabilistic credal states by means of standard, linear perspective, which may be interpreted as an extension of the classical principle of indifference. Finally, we apply the geometrical/logical methods developed in the paper to prove a series of trivialization theorems against question-invariance as a constraint on acceptance rules and against rational monotonicity as an axiom of conditional logic in situations of uncertainty. (shrink)

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context are explored.

We define a semantics for conditionals in terms of stochastic graphs which gives a straightforward and simple method of evaluating the probabilities of conditionals. It seems to be a good and useful method in the cases already discussed in the literature, and it can easily be extended to cover more complex situations. In particular, it allows us to describe several possible interpretations of the conditional and to formalize some intuitively valid but formally incorrect considerations concerning the probabilities of conditionals under (...) these two interpretations. It also yields a powerful method of handling more complex issues. The stochastic graph semantics provides a satisfactory answer to Lewis’s arguments against the PC = CP principle, and defends important intuitions which connect the notion of probability of a conditional with the notion of conditional probability. It also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues. (shrink)

It is raining but you don’t believe that it is raining. Imagine accepting this claim. Then you are committed to saying ‘It is raining but I don’t believe that it is raining’. This would be an ‘absurd’ thing to claim or assert, yet what you say might be true. It might be raining, while at the same time, you are completely ignorant of the state of the weather. But how can it be absurd of you to assert something about yourself (...) that might be true of you? This is Moore’s paradox as it occurs in speech. What is the source of the absurdity? And why does it strike us that a contradiction is somehow at work when there is no contradiction in the content of what is asserted? In Section 2, I describe Moore’s formulation of the paradox and evaluate his own solutions. In Section 3, I discuss Wittgenstein’s inf luence in solving the paradox. In Section 4, I discuss Shoemaker’s priority thesis that once the absurdity in belief has been explained, then this will translate into an explanation of the absurdity in assertion. In Section 5, I discuss work on omissive and commissive Moore-paradoxical assertions, i.e. those of the forms p & I don’t believe that p and p & I believe that not-p. In Section 6, I discuss work on assertions of the form p & I don’t know that p. (shrink)

I outline and motivate a way of implementing a closest world theory of indicatives, appealing to Stalnaker's framework of open conversational possibilities. Stalnakerian conversational dynamics helps us resolve two outstanding puzzles for a such a theory of indicative conditionals. The first puzzle -- concerning so-called 'reverse Sobel sequences' -- can be resolved by conversation dynamics in a theoryneutral way: the explanation works as much for Lewisian counterfactuals as for the account of indicatives developed here. Resolving the second puzzle, by contrast, (...) relies on the interplay between the particular theory of indicative conditionals developed here and Stalnakerian dynamics. The upshot is an attractive resolution of the so-called "Gibbard phenomenon" for indicative conditionals. (shrink)

The standard semantics for counterfactuals ensures that any counterfactual with a true antecedent and true consequent is itself true. There have been many recent attempts to amend the standard semantics to avoid this result. I show that these proposals invalidate a number of further principles of the standard logic of counterfactuals. The case against the automatic truth of counterfactuals with true components does not extend to these further principles, however, so it is not clear that rejecting the latter should be (...) a consequence of rejecting the former. Instead I consider how one might defuse putative counterexamples to the truth of true-true counterfactuals. (shrink)

In this paper, I stress the utility of employing test-driven development (TDD) for conceiving logical systems. TDD, originally invented in the context of Extreme Programming, is a methodology widely used by software engineers to conceive and develop programs. Its main principle is to design the tests of the expected properties of the system before the development phase. I argue that this methodology is especially convenient in conceiving applied logics. Indeed, this technique is efficient with most decidable logics having a software (...) implementation. Having a clear list of the desired inferences right from the beginning makes it possible to refine the properties of the system step by step until its completion. I distinguish and detail seven advantages of the usage of TDD for the conception of a logical theory. Most importantly, this methodology increases the predictability of the inferential power of the theory. A second important benefit is that the time required for the conception of the logic goes down dramatically. This methodology will change both ideas and practices. Logic is no longer considered to be a formal science, but rather to be an empirical one. Research in the field is geared toward specific and concrete goals. Programs are considered tools used to verify the conformity of formal theories. To sum up, I defend the view that, in some situations, this way of designing a formal system brings significant benefits, and that the construction of new logics can be conducted similarly to the development of open source software. (shrink)

Systems of logico-probabilistic (LP) reasoning characterize inference from conditional assertions interpreted as expressing high conditional probabilities. In the present article, we investigate four prominent LP systems (namely, systems O, P, Z, and QC) by means of computer simulations. The results reported here extend our previous work in this area, and evaluate the four systems in terms of the expected utility of the dispositions to act that derive from the conclusions that the systems license. In addition to conforming to the dominant (...) paradigm for assessing the rationality of actions and decisions, our present evaluation complements our previous work, since our previous evaluation may have been too severe in its assessment of inferences to false and uninformative conclusions. In the end, our new results provide additional support for the conclusion that (of the four systems considered) inference by system Z offers the best balance of error avoidance and inferential power. Our new results also suggest that improved performance could be achieved by a modest strengthening of system Z. (shrink)

McGee argues that it is sometimes reasonable to accept both x and x-> without accepting y->z, and that modus ponens is therefore invalid for natural language indicative conditionals. Here, we examine McGee's counterexamples from a Bayesian perspective. We argue that the counterexamples are genuine insofar as the joint acceptance of x and x-> at time t does not generally imply constraints on the acceptability of y->z at t, but we use the distance-based approach to Bayesian learning to show that applications (...) of modus ponens are nevertheless guaranteed to be successful in an important sense. Roughly, if an agent becomes convinced of the premises of a modus ponens argument, then she should likewise become convinced of the argument's conclusion. Thus we take McGee's counterexamples to disentangle and reveal two distinct ways in which arguments can convince. Any general theory of argumentation must take stock of both. (shrink)

The paper focuses on interpreting ceteris paribus conditions as normal conditions. After discussing six basic problems for the explication of normal conditions and seven interpretations that do not well solve those problems I turn to what I call the epistemic account. According to it the normal is, roughly, the not unexpected. This is developed into a rigorous constructive account of normal conditions, which makes essential use of ranking theory and in particular allows to explain the phenomenon of multiply exceptional conditions. (...) Finally, this static account is extended to a schematic dynamic model of how we may learn about those normal and exceptional conditions. (shrink)

Conditionals somehow express conditional beliefs. However, conditional belief is a bi-propositional attitude that is generally not truth-evaluable, in contrast to unconditional belief. Therefore, this article opts for an expressivistic semantics for conditionals, grounds this semantics in the arguably most adequate account of conditional belief, that is, ranking theory, and dismisses probability theory for that purpose, because probabilities cannot represent belief. Various expressive options are then explained in terms of ranking theory, with the intention to set out a general interpretive scheme (...) that is able to account for the most variegated usage of conditionals. The Ramsey test is only the first option. Relevance is another, familiar, but little understood item, which comes in several versions. This article adds a further family of expressive options, which is able to subsume also counterfactuals and causal conditionals, and indicates at the end how this family allows for partial recovery of truth conditions for conditionals. (shrink)

This paper explores the possibility of supplementing the suppositional view of indicative conditionals with a corresponding view of epistemic modals. The most striking feature of the suppositional view consists in its claim that indicative conditionals are to be evaluated by conditional probabilities. On the basis of a natural link between indicative conditionals and epistemic modals, a corresponding thesis about the probabilities of statements governed by epistemic modals can be derived. The paper proceeds by deriving further consequences of this thesis, in (...) particular, the logic of epistemic modals and their logical interaction with indicative conditionals are studied. (shrink)

Systems of logico-probabilistic reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems _O, P_, _Z_, and _QC_. These systems differ in the number of inferences they licence _. LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of drawing more false or uninformative conclusions. In the first part of the paper, we (...) present the four systems and extend each of them by theorems that allow one to compute almost-tight lower-probability-bounds for the conclusion of an inference, given lower-probability-bounds for its premises. In the second part of the paper, we investigate by means of computer simulations which of the four systems provides the best balance of reward versus risk. Our results suggest that system _Z_ offers the best balance. (shrink)

In the first part I argue that normic laws are the phenomenological laws of evolutionary systems. If this is true, then intuitive human reasoning should be fit in reasoning from normic laws. In the second part I show that system P is a tool for reasoning with normic laws which satisfies two important evolutionary standards: it is probabilistically reliable, and it has rules of low complexity. In the third part I finally report results of an experimental study which demonstrate that (...) intuitive human reasoning is in well accord with basic argument patterns of system P. (shrink)

David Lewis’s semantics for counterfactuals remains the standard view. Yet counter-examples have emerged, which suggest a need to invoke causal independence, and thus threaten conceptual circularity. I will review some of these counter-examples (§§1–2), illustrate how causal independence proves useful (§3), and suggest that any resulting circularity is unproblematic (§4).

The pattern of credences we are inclined to assign to counterfactuals challenges standard accounts of counterfactuals. In response to this problem, the paper develops a semantics of counterfactuals in terms of the epsilon-operator. The proposed semantics stays close to the standard account: the epsilon-operator substitutes the universal quantifier present in standard semantics by arbitrarily binding the open world-variable. Various applications of the suggested semantics are explored including, in particular, an explanation of how the puzzling credences in counterfactuals come about.

In their unifying theory to model uncertainty, Friedman and Halpern (1995–2003) applied plausibility measures to default reasoning satisfying certain sets of axioms. They proposed a distinctive condition for plausibility measures that characterizes “qualitative” reasoning (as contrasted with probabilistic reasoning). A similar and similarly fundamental, but more general and thus stronger condition was independently suggested in the context of “basic” entrenchment-based belief revision by Rott (1996–2003). The present paper analyzes the relation between the two approaches to formalizing basic notions of plausibility (...) as used in qualitative default reasoning. While neither approach is a special case of the other, translations can be found that elucidate their relationship. I argue that Rott’s notion of plausibility allows for a more modular set-up and has a better philosophical motivation than that of Friedman and Halpern. (shrink)

This paper attempts to set up a probabilistic framework for understanding the notion of causal necessity. What results is a relaxed and relativized probabilistic theory of epsilon-Causal necessity and an explicit attempt to avoid deterministic assumptions. The theory developed emphasizes the notions of partial cause, Causal contribution, And the degree of contribution. Implications for causal overdetermination, Causal preemption, And causal discourse are discussed.

I take up the four issues considered by Johnson -Laird, Byrne and Girotto in their reply to Politzer. Based on the conceptual clarification which they adduce, it seems that the disagreement can be settled about the first one and can be attenuated about the second one. However, I maintain and refine my criticisms on the last two, backed up by considerations borrowed from the perspective of the conditional probability semantics for conditionals.

(No abstract is available for this citation).

Sidney Morgenbesser brought to attention cases of the following form: (MC1) Chump tosses an indeterministic coin and, whilst it is in mid-air, calls heads. The coin lands tails, and Chump loses. His betting was causally independent of the coin’s fall. Chump seems right to say: ‘If I had bet tails, I would have won.’1 (MC2).

We discuss O&C's probabilistic approach from a probability logical point of view. Specifically, we comment on subjective probability, the indispensability of logic, the Ramsey test, the consequence relation, human nonmonotonic reasoning, intervals, generalized quantifiers, and rational analysis.

This position paper advocates combining formal epistemology and the new paradigm psychology of reasoning in the studies of conditionals and reasoning with uncertainty. The new paradigm psychology of reasoning is characterized by the use of probability theory as a rationality framework instead of classical logic, used by more traditional approaches to the psychology of reasoning. This paper presents a new interdisciplinary research program which involves both formal and experimental work. To illustrate the program, the paper discusses recent work on the (...) paradoxes of the material conditional, nonmonotonic reasoning, and Adams’ Thesis. It also identifies the issue of updating on conditionals as an area which seems to call for a combined formal and empirical approach. (shrink)

Recent advances in causal reasoning have given rise to a computational model that emulates the process by which humans generate, evaluate, and distinguish counterfactual sentences. Contrasted with the “possible worlds” account of counterfactuals, this “structural” model enjoys the advantages of representational economy, algorithmic simplicity, and conceptual clarity. This introduction traces the emergence of the structural model and gives a panoramic view of several applications where counterfactual reasoning has benefited problem areas in the empirical sciences.

The aim of this paper is to strengthen the point made by Horty about the relationship between reason holism and moral particularism. In the literature prima facie obligations have been considered as the only source of reason holism. I strengthen Horty’s point in two ways. First, I show that contrary-to-duties provide another independent support for reason holism. Next I outline a formal theory that is able to capture these two sources of holism. While in simple settings the proposed account coincides (...) with Horty’s one, this is not true in more complicated or “realistic” settings in which more than two norms collide. My chosen formalism is so-called input/output logic. A bottom-line example is introduced. It raises the issue of whether the conventional wisdom is right in assuming that normative reasons run parallel to epistemic ones. (shrink)