The problem of probabilities of conditionals is one of the long-standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. -/- Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities of conditionals violate (...) standard probability theory. -/- This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. -/- We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. -/- We address two common objections to Adams' view: that the relevant probabilities are ‘probabilities only in name’, and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. -/- Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. (shrink)

It can often seem like the attitude we hold towards a conditional should be our attitude in the consequent on the supposition of the antecedent. Following by Williamson (Suppose and Tell: The Semantics and Heuristics of Conditionals. Oxford University Press, 2020), we call this The suppositional rule (SR). The Adams-style non-propositional theories of indicatives upholds some key implications of SR, allowing, for instance, our credence in a conditional to be the probability of the consequent given the antecedent. Williamson (Suppose and (...) Tell: The Semantics and Heuristics of Conditionals. Oxford University Press, 2020) has recently provided a series of inconsistency arguments against SR. He thereby intends to undermine non-propositional views as well as other rivals to his favoured material conditional account. I outline a strategy which theorists of all stripes can employ to avoid Williamson’s arguments. I then show how non-propositionalists can implement this strategy. I show how they can uphold SR when it is intuitively compelling, whilst allowing it to fail when it is not. (shrink)

In my thesis, I develop two distinct themes. The first part of my thesis is devoted to indicative conditionals and approaching them from an empirically informed perspective. In the second part, I am developing classical topics of philosophy of science, specifically, scientific objectivity and the role of values in science, in connection to recent methodological developments, revolving around the Replication Crisis.

The chapter is devoted to the probability and acceptability of indicative conditionals. Focusing on three influential theses, the Equation, Adams’ thesis, and the qualitative version of Adams’ thesis, Sikorski argues that none of them is well supported by the available empirical evidence. In the most controversial case of the Equation, the results of many studies which support it are, at least to some degree, undermined by some recent experimental findings. Sikorski discusses the Ramsey Test, and Lewis’s triviality proof, with special (...) attention dedicated to the popular ways of blocking it. Sikorski concludes that the role of the three theses in future studies of conditionals should be re-thought, and he presents alternative proposals. (shrink)

Suppose you’re certain that a claim—say, ‘Frida is tall’—does not have a determinate truth value. What attitude should you take towards it? This is the question of the cognitive role of indeterminacy. This paper presents a puzzle for theories of cognitive role. Many of these theories vindicate a seemingly plausible principle: if you are fully certain that A, you are rationally required to be fully certain that A is determinate. Call this principle ‘Certainty’. We show that Certainty, in combination with (...) some minimal side premises, entails a very implausible claim: whenever you’re certain that it’s indeterminate whether A, it is rationally required that you reject A. This is a surprising result, which requires abandoning at least some intuitive views about indeterminacy and cognitive role. (shrink)

Conditional probability is often used to represent the probability of the conditional. However, triviality results suggest that the thesis that the probability of the conditional always equals conditional probability leads to untenable conclusions. In this paper, I offer an interpretation of this thesis in a possible worlds framework, arguing that the triviality results make assumptions at odds with the use of conditional probability. I argue that these assumptions come from a theory called the operator theory and that the rival restrictor (...) theory can avoid these problematic assumptions. In doing so, I argue that recent extensions of the triviality arguments to restrictor conditionals fail, making assumptions which are only justified on the operator theory. (shrink)

The thesis explores the question of how should a rational moral agent reason and make choices when he finds himself accepting inconsistent moral judgments. It is argued that it is both conceptually and psychologically justified to describe such an agent as suffering from uncertainty. Such uncertainty, however, is not uncertainty regarding the truth of some descriptive claim, but rather uncertainty regarding the truth of a normative claim. Specifically it is uncertainty regarding the truth of a moral judgement. In the literature (...) this is sometimes called “moral uncertainty”. Two different lines of philosophical literatures that explore the idea of moral uncertainty are discussed. The first line – the one that originated from David Lewis‟ argument against the “Desire as Belief Thesis” – explores the mere possibility of moral uncertainty, while the second line explores the question how ought a rational moral agent choose in face of moral uncertainty. The discussion of these two lines of research leads to the conclusion that a consistent account of moral decision making under conditions of moral uncertainty that will be applicable to the kind of cases that the thesis explores, must make use of degrees of beliefs in comparative moral judgements and of them alone. Specifically, no references to degrees of moral value should be made. An attempt to present such an account in the framework of an extension of Leonard Savage‟s model for decision making is carried out. This attempt leads to a problematic result. Several implications of the result to ethic and meta-ethics are discussed as well as possible ways to avoid it. The conclusion is partly positive and partly negative: While a plausible account of moral decision making under conditions of moral uncertainty is presented, an account of moral reasoning that aims at finding a complete moral theory is shown to be a very difficult – if not impossible - aim to achieve. (shrink)

Stalnaker's Thesis about indicative conditionals is, roughly, that the probability one ought to assign to an indicative conditional equals the probability that one ought to assign to its consequent conditional on its antecedent. The thesis seems right. If you draw a card from a standard 52-card deck, how confident are you that the card is a diamond if it's a red card? To answer this, you calculate the proportion of red cards that are diamonds -- that is, you calculate the (...) probability of drawing a diamond conditional on drawing a red card. Skyrms' Thesis about counterfactual conditionals is, roughly, that the probability that one ought to assign to a counterfactual equals one's rational expectation of the chance, at a relevant past time, of its consequent conditional on its antecedent. This thesis also seems right. If you decide not to enter a 100-ticket lottery, how confident are you that you would have won had you bought a ticket? To answer this, you calculate the prior chance--that is, the chance just before your decision not to buy a ticket---of winning conditional on entering the lottery. The central project of this article is to develop a new uniform theory of conditionals that allows us to derive a version of Skyrms' Thesis from a version of Stalnaker's Thesis, together with a chance-deference norm relating rational credence to beliefs about objective chance. (shrink)

Suppose that you're certain that a certain sentence, e.g. "Frida is tall", lacks a determinate truth value. What cognitive attitude should you take towards it—reject it, suspend judgment, or what else? We show that, by adopting a seemingly plausible principle connecting credence in A and Determinately A, we can prove a very implausible answer to this question: i.e., all indeterminate claims should be assigned credence zero. The result is striking similar to so-called triviality results in the literature on modals and (...) conditionals. (shrink)

A spectre haunts the semantics of natural language — the spectre of Triviality. Semanticists (in particular Rothschild 2013; Khoo and Mandelkern 2018a,b) have entered into a holy alliance to exorcise this spectre. None, I will argue, have yet succeeded.

Many recent theories of epistemic discourse exploit an informational notion of consequence, i.e. a notion that defines entailment as preservation of support by an information state. This paper investigates how informational consequence fits with probabilistic reasoning. I raise two problems. First, all informational inferences that are not also classical inferences are, intuitively, probabilistically invalid. Second, all these inferences can be exploited, in a systematic way, to generate triviality results. The informational theorist is left with two options, both of them radical: (...) they can either deny that epistemic modal claims have probability at all, or they can move to a nonstandard probability theory. (shrink)

KK is the thesis that if you can know p, you can know that you can know p. Though it’s unpopular, a flurry of considerations has recently emerged in its favour. Here we add fuel to the fire: standard resources allow us to show that any failure of KK will lead to the knowability and assertability of abominable indicative conditionals of the form ‘If I don’t know it, p’. Such conditionals are manifestly not assertable—a fact that KK defenders can easily (...) explain. I survey a variety of KK-denying responses and find them wanting. Those who object to the knowability of such conditionals must either deny the possibility of harmony between knowledge and belief, or deny well-supported connections between conditional and unconditional attitudes. Meanwhile, those who grant knowability owe us an explanation of such conditionals’ unassertability—yet no successful explanations are on offer. Upshot: we have new evidence for KK. (shrink)

Assume that it is your evidence that determines what opinions you should have. I argue that since you should take peer disagreement seriously, evidence must have two features. (1) It must sometimes warrant being modest: uncertain what your evidence warrants, and (thus) uncertain whether you’re rational. (2) But it must always warrant being guided: disposed to treat your evidence as a guide. Surprisingly, it is very difficult to vindicate both (1) and (2). But diagnosing why this is so leads to (...) a proposal—Trust—that is weak enough to allow modesty but strong enough to yield many guiding features. In fact, I claim that Trust is the Goldilocks principle—for it is necessary and sufficient to vindicate the claim that you should always prefer to use free evidence. Upshot: Trust lays the foundations for a theory of disagreement and, more generally, an epistemology that permits self-doubt—a modest epistemology. (shrink)

Bradley offers a quick and convincing argument that no Boolean semantic theory for conditionals can validate a very natural principle concerning the relationship between credences and conditionals. We argue that Bradley’s principle, Preservation, is, in fact, invalid; its appeal arises from the validity of a nearby, but distinct, principle, which we call Local Preservation, and which Boolean semantic theories can non-trivially validate.

Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation into conditional connectives may (...) show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory. (shrink)

I present two Triviality results for Kratzer's standard “restrictor” analysis of indicative conditionals. I both refine and undermine the common claim that problems of Triviality do not arise for Kratzer conditionals since they are not strictly conditionals at all.

Some left-nested indicative conditionals are hard to interpret while others seem fine. Some proponents of the view that indicative conditionals have No Truth Values (NTV) use their view to explain why some left-nestings are hard to interpret: the embedded conditional does not express the truth conditions needed by the embedding conditional. Left-nestings that seem fine are then explained away as cases of ad hoc, pragmatic interpretation. We challenge this explanation. The standard reasons for NTV about indicative conditionals (triviality results, Gibbardian (...) standoffs, etc.) extend naturally to NTV about biconditionals. So NTVers about conditionals should also be NTVers about biconditionals. But biconditionals embed much more freely than conditionals. If NTV explains why some left-nested conditionals are hard to interpret, why do biconditionals embed successfully in the very contexts where conditionals do not embed? (shrink)

A triviality result for what Lewis called “the Desire by Necessity Thesis” and Broome : 265–267, 1991) called “the Desire as Expectation Thesis” is presented. The result shows that this thesis and three other reasonable conditions can be jointly satisfied only in trivial cases. Some meta-ethical implications of the result are discussed. The discussion also highlights several issues regarding Lewis ’ original triviality result for “the Desire as Belief Thesis” that have not been properly understood in the literature.

I show that David Lewis’s principal principle is not preserved under Jeffrey conditionalization. Using this observation, I argue that Lewis’s reason for rejecting the desire as belief thesis and Adams’s thesis applies also to his own principal principle. 1 Introduction2 Adams’s Thesis, the Desire as Belief Thesis, and the Principal Principle3 Jeffrey Conditionalization4 The Principal Principles Not Preserved under Jeffrey Conditionalization5 Inadmissible Experiences.

According to so-called epistemic theories of conditionals, the assertability/acceptability/acceptance of a conditional requires the existence of an epistemically significant relation between the conditional’s antecedent and its consequent. This paper points to some linguistic data that our current best theories of the foregoing type appear unable to explain. Further, it presents a new theory of the same type that does not have that shortcoming. The theory is then defended against some seemingly obvious objections.

This paper clarifies the relationship between the Triviality Results for the conditional and the Restrictor Theory of the conditional. On the understanding of Triviality proposed here, it is implausible—pace many proponents of the Restrictor Theory—that Triviality rests on a syntactic error. As argued here, Triviality arises from simply mistaking the feature a claim has when that claim is logically unacceptable for the feature a claim has when that claim is unsatisfiable. Triviality rests on a semantic confusion—one which some semantic theories, (...) but not others, are prone to making. On the interpretation proposed here, Triviality Results thus play a theoretically constructive role in the project of natural language semantics. (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)

On an influential line of thinking tracing back to Ramsey, conditionals are closely linked to the attitude of supposition. When applied to counterfactuals, this view suggests a subjunctive version of the so-called Ramsey test: the probability of a counterfactual If A, would B ought to be equivalent to the probability of B, under the subjunctive supposition that A. I present a collapse result for any view that endorses the subjunctive version of the Ramsey test. Starting from plausible assumptions, the result (...) shows that one’s rational credence in a would-counterfactual and in the corresponding might-counterfactual have to be identical. (shrink)

ABSTRACT A trivalent theory of indicative conditionals automatically enforces Stalnaker's thesis – the equation between probabilities of conditionals and conditional probabilities. This result holds because the trivalent semantics requires, for principled reasons, a modification of the ratio definition of conditional probability in order to accommodate the possibility of undefinedness. I explain how this modification is motivated and how it allows the trivalent semantics to avoid a number of well-known triviality results, in the process clarifying why these results hold for many (...) bivalent theories. In short, the slew of triviality results published in the last 40-odd years need not be viewed as an argument against Stalnaker's thesis: it can be construed instead as an argument for abandoning the bivalent requirement that indicative conditionals somehow be assigned a truth-value in worlds in which their antecedents are false. (shrink)

Intuition says that choosing to create a miserable person is wrong, but choosing not to create a happy one is not; this is ‘the Asymmetry’. There is a complete theory which agrees – the ‘Harm Minimization’ theory. A well-known objection is that this theory rejects Parfit’s principle of ‘No Difference’. But No Difference has less intuitive support than the Asymmetry, and there seems to be no complete theory which agrees with both. There is, however, a more serious problem for Harm (...) Minimization: it says it is wrong to create happy people if we could have made some of them happier at the expense of others. The purpose of this note is to describe a complete theory which agrees with the Asymmetry and avoids this unacceptable consequence; like Harm Minimization, it rejects No Difference. (shrink)

Case-based reasoning is a familiar method of evaluating sentences. But when applied to conditionals, it seems to lead to implausible conclusions. In this paper I argue that the problem arises from equating the probability of a conditional sentence on the evidential supposition of some condition with the conditional probability of the former, given the latter.

On the basis of impossibility results on probability, belief revision, and conditionals, it is argued that conditional beliefs differ from beliefs in conditionals qua mental states. Once this is established, it will be pointed out in what sense conditional beliefs are still conditional, even though they may lack conditional contents, and why it is permissible to still regard them as beliefs, although they are not beliefs in conditionals. Along the way, the main logical, dispositional, representational, and normative properties of conditional (...) beliefs are studied, and it is explained how the failure of not distinguishing conditional beliefs from beliefs in conditionals can lead philosophical and empirical theories astray. (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)

I present some counterexamples to Adams's Thesis and explain how they undermine arguments that indicative conditionals cannot be truth-evaluable propositions.

Less‐than‐certain conditional judgments pose notorious problems for strict analyses of conditionals: across their various incarnations, these analyses have trouble making sense of how conditionals could have non‐trivial probabilities in the first place; minimal constraints on how such probabilities are to be assigned, moreover, lead to results that seem at odds with a strict outlook on the semantics of conditionals, most notably the validity of Conditional Excluded Middle. I demonstrate that a strict analysis can overcome the trouble if couched in a (...) bilateral dynamic setting that properly extends the familiar Ramsey test for accepting conditionals to other iffy attitudes, most importantly the one of rejecting a conditional. The resulting framework accommodates the appeal of Stalnaker's thesis as well as of Conditional Excluded Middle in a strict setting. A discussion of how to handle the probability of epistemically modalized conditionals and of compounds of conditionals is provided. (shrink)