Conditionals,probability, and non-triviality

We show that the implicational fragment of intuitionism is the weakest logic with a non-trivial probabilistic semantics which satisfies the thesis that the probabilities of conditionals are conditional probabilities. We also show that several logics between intuitionism and classical logic also admit non-trivial probability functions which satisfy that thesis. On the other hand, we also prove that very weak assumptions concerning negation added to the core probability conditions with the restriction that probabilities of conditionals are conditional probabilities are sufficient to trivialize the semantics.     

Reasoning About Uncertain Conditionals

There is a long tradition in formal epistemology and in the psychology of reasoning to investigate indicative conditionals. In psychology, the propositional calculus was taken for granted to be the normative standard of reference. Experimental tasks, evaluation of the participants’ responses and psychological model building, were inspired by the semantics of the material conditional. Recent empirical work on indicative conditionals focuses on uncertainty. Consequently, the normative standard of reference has changed. I argue why neither logic nor standard probability theory provide appropriate rationality norms for uncertain conditionals. I advocate coherence based probability logic as an appropriate framework for investigating uncertain conditionals. Detailed proofs of the probabilistic non-informativeness of a paradox of the material conditional illustrate the approach from a formal point of view. I survey selected data on human reasoning about uncertain conditionals which additionally support the plausibility of the approach from an empirical point of view.     

Indicative conditionals,conditional probabilities,and the “defective truth-table”: A request for more experiments

While there is now considerable experimental evidence that, on the one hand, participants assign to the indicative conditional as probability the conditional probability of consequent given antecedent and, on the other, they assign to the indicative conditional the “defective truth-table” in which a conditional with false antecedent is deemed neither true nor false, these findings do not in themselves establish which multi-premise inferences involving conditionals participants endorse. A natural extension of the truth-table semantics pronounces as valid numerous inference patterns that do seem to be part of ordinary usage. However, coupled with something the probability account gives us—namely that when conditional-free ? entails conditional-free ψ, “if ? then ψ” is a trivial, uninformative truth—we have enough logic to derive the paradoxes of material implication. It thus becomes a matter of some urgency to determine which inference patterns involving indicative conditionals participants do endorse. Only thus will we be able to arrive at a realistic, systematic semantics for the indicative conditional.     

Rational belief change,popper functions and counterfactuals

This paper uses Popper's treatment of probability and an epistemic constraint on probability assignments to conditionals to extend the Bayesian representation of rational belief so that revision of previously accepted evidence is allowed for. Results of this extension include an epistemic semantics for Lewis' theory of counterfactual conditionals and a representation for one kind of conceptual change.     

A process model of the understanding of uncertain conditionals

To build a process model of the understanding of conditionals we extract a common core of three semantics of if-then sentences: (a) the conditional event interpretation in the coherencebased probability logic, (b) the discourse processingtheory of Hans Kamp, and (c) the game-theoretical approach of Jaakko Hintikka. The empirical part reports three experiments in which each participant assessed the probability of 52 if-then sentencesin a truth table task. Each experiment included a second task: An n-back task relating the interpretation of conditionals to working memory, a Bayesian bookbag and poker chip task relating the interpretation of conditionals to probability updating, and a probabilistic modus ponens task relating the interpretation of conditionals to a classical inference task. Data analysis shows that the way in which the conditionals are interpreted correlates with each of the supplementary tasks. The results are discussed within the process model proposed in the introduction.     

Defending a Possible-Worlds Account of Indicative Conditionals

One very popular kind of semantics for subjunctive conditionals is aclosest-worlds account along the lines of theories given by David Lewisand Robert Stalnaker. If we could give the same sort of semantics forindicative conditionals, we would have a more unified account of themeaning of ``if ... then ...' statements, one with manyadvantages for explaining the behaviour of conditional sentences. Such atreatment of indicative conditionals, however, has faced a battery ofobjections. This paper outlines a closest-worlds account of indicativeconditionals that does better than some of its cousins in explaining thebehaviour of such conditionals. The paper then discusses objectionsoffered by Dorothy Edgington and Frank Jackson to closest-worldsaccounts of indicative conditionals, and shows that these objections canbe met by the account outlined.     

On the Logic of Nonmonotonic Conditionals and Conditional Probabilities: Predicate Logic

In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional interpretation of quantifiers in crucial ways, and show that Field's approach is closely related to the usual objectual semantics. One of Field's quantifier rules, however, must be significantly modified to be adapted to nonmonotonic conditional semantics. And this modification suggests, in turn, an alternative quantifier rule for probabilistic semantics.     

Counterfactual antecedent falsity and the epistemic sensitivity of counterfactuals

Why do utterances of counterfactual conditionals typically, but not universally, convey the message that their antecedents are false? I demonstrate that two common theoretical commitments–commitment to the existence of scalar implicature and of informative presupposition—can be supplemented with an independently motivated theory of the presuppositions of competing conditional alternatives to jointly predict this information when and only when it appears. The view works best if indicative and counterfactual conditionals have a closely related semantics, so I conclude by undermining two familiar arguments for a nonunified semantics of indicative and counterfactual conditionals.     

A relevant theory of conditionals

In this paper we set out a semantics for relevant (counterfactual) conditionals. We combine the Routley-Meyer semantics for relevant logic with a semantics for conditionals based on selection functions. The resulting models characterize a family of conditional logics free from fallacies of relevance, in particular counternecessities and conditionals with necessary consequents receive a non-trivial treatment.     

New surprises for the Ramsey Test

In contemporary discussions of the Ramsey Test for conditionals, it is commonly held that (i) supposing the antecedent of a conditional is adopting a potential state of full belief, and (ii) Modus Ponens is a valid rule of inference. I argue on the basis of Thomason Conditionals (such as ‘If Sally is deceiving, I do not believe it’) and Moore’s Paradox that both claims are wrong. I then develop a double-indexed Update Semantics for conditionals which takes these two results into account while doing justice to the key intuitions underlying the Ramsey Test. The semantics is extended to cover some further phenomena, including the recent observation that epistemic modal operators give rise to something very like, but also very unlike, Moore’s Paradox.     

Indicative and Subjunctive Conditionals

In any plausible semantics for conditionals, the semantics for indicatives and subjunctives will resemble each other closely. This means that if we are to keep the possible-worlds semantics for subjunctives suggested by Lewis, we need to find a possible-worlds semantics for indicatives. One reason for thinking that this will be impossible is the behaviour of rigid designators in indicatives. An indicative like 'If the stuff in the rivers, lakes and oceans really is H₃O, then water is H₃O' is non-vacuously true, even though its consequent is true in no possible worlds, and hence not in the nearest possible world where the antecedent is true. I solve this difficulty by providing a semantics for conditionals within the framework of two-dimensional modal logic. In doing so, I show that we can have a reasonably unified semantics for indicative and subjunctive conditionals.     

Rethinking Gibbard’s Riverboat Argument

According to the Principle of Conditional Non-Contradiction (CNC), conditionals of the form “If p, q” and “If p, not q” cannot both be true, unless p is inconsistent. This principle is widely regarded as an adequacy constraint on any semantics that attributes truth conditions to conditionals. Gibbard has presented an example of a pair of conditionals that, in the context he describes, appear to violate CNC. He concluded from this that conditionals lack truth conditions. We argue that this conclusion is rash by proposing a new diagnosis of what is going on in Gibbard’s argument. We also provide empirical evidence in support of our proposal.     

Conditionals As Representative Inferences

According to Adams (Inquiry 8:166–197, 1965), the acceptability of an indicative conditional goes with the conditional probability of the consequent given the antecedent. However, some conditionals seem to be inappropriate, although their corresponding conditional probability is high. These are cases with a missing link between antecedent and consequent. Other conditionals are appropriate even though the conditional probability is low. Finally, we have the so-called biscuit conditionals. In this paper we will generalize analyses of Douven (Synthese 164:19–44, 2008) and others to account for the appropriateness of conditionals in terms of evidential support. Our generalization involves making use of Value, or intensity. We will show how this generalization helps to account for biscuit conditionals and conditional threats and promises. Finally, a link is established between this analysis of conditionals and an analysis of generic sentences.

     

A Peculiarity in Pearl’s Logic of Interventionist Counterfactuals

We examine a formal semantics for counterfactual conditionals due to Judea Pearl, which formalizes the interventionist interpretation of counterfactuals central to the interventionist accounts of causation and explanation. We show that a characteristic principle validated by Pearl’s semantics, known as the principle of reversibility, states a kind of irreversibility: counterfactual dependence (in David Lewis’s sense) between two distinct events is irreversible. Moreover, we show that Pearl’s semantics rules out only mutual counterfactual dependence, not cyclic dependence in general. This, we argue, suggests that Pearl’s logic is either too weak or too strong.     

Could it be the Case that if I am Right My Opponents will be Pleased? A Rejoinder to Johnson-Laird,Byrne and Girotto

I take up the four issues considered by Johnson-Laird, Byrne and Girotto in their reply to Politzer (2007). Based on the conceptual clarification which they adduce, it seems that the disagreement can be settled about the first one (truth functionality) and can be attenuated about the second one (the paradoxes of material implication). However, I maintain and refine my criticisms on the last two (negation and the probability of conditionals), backed up by considerations borrowed from the perspective of the conditional probability semantics for conditionals.     

If-Clauses and Probability Operators

Adams’ thesis is generally agreed to be linguistically compelling for simple conditionals with factual antecedent and consequent. We propose a derivation of Adams’ thesis from the Lewis-Kratzer analysis of if-clauses as domain restrictors, applied to probability operators. We argue that Lewis’s triviality result may be seen as a result of inexpressibility of the kind familiar in generalized quantifier theory. Some implications of the Lewis-Kratzer analysis are presented concerning the assignment of probabilities to compounds of conditionals.     

Counterfactuals for Consequentialists

That all subjunctive conditionals with true antecedents and trueconsequents are themselves also true is implied by every plausibleand popularly endorsed account. But I am wary of endorsing thisimplication. I argue that all presently endorsed accounts fail tocapture the nature of certain subjunctive conditionals in contextsof consequentialist reasoning. I attempt to show that we must allowfor the possibility that some subjunctive conditionals with trueantecedents and true consequents are false, if we are to believethat certain types of straightforward consequentialist reasoningare coherent. I begin by evaluating a pair of morally releventcounterfactuals in a case via David Lewis's account. I then turnto a slight modification of the case, arguing that Lewis'ssemantics fails to generate the correct truth values of thesubjunctive conditionals in the modified case. Finally, I presenta modified version of Lewis's semantics that generates the correctresults in all of the cases.     

NTV观点引发的逻辑哲学问题——直陈条件句能嵌套吗

NTV观点的核心思想是直陈条件句不是命题,它没有真值条件并且无真值,其既不为真也不为假,而只表现为一个相应的概率值。这就引发了一个有争论的逻辑哲学问题——直陈条件句能否嵌套。如果把直陈条件句视为无真值的,那么嵌套后的复合条件句就不能判断其真假（真值表不能使用）。对于直陈条件句能否嵌套的问题,学界有不同的观点,我们认为要完全解决真之条件主义与条件概率主义两者之间的矛盾是非常困难的,然而,完全接受条件概率论题的哲学后果是非常危险的,同样,暗示放弃真之语义观也是非常危险的。     

What we know and what to do

This paper discusses an important puzzle about the semantics of indicative conditionals and deontic necessity modals (should, ought, etc.): the Miner Puzzle (Parfit, ms; Kolodny and MacFarlane, J Philos 107:115–143, 2010). Rejecting modus ponens for the indicative conditional, as others have proposed, seems to solve a version of the puzzle, but is actually orthogonal to the puzzle itself. In fact, I prove that the puzzle arises for a variety of sophisticated analyses of the truth-conditions of indicative conditionals. A comprehensive solution requires rethinking the relationship between relevant information (what we know) and practical rankings of possibilities and actions (what to do). I argue that (i) relevant information determines whether considerations of value may be treated as reasons for actions that realize them and against actions that don’t, (ii) incorporating this normative fact requires a revision of the standard ordering semantics for weak (but not for strong) deontic necessity modals, and (iii) an off-the-shelf semantics for weak deontic necessity modals, due to von Fintel and Iatridou, which distinguishes “basic” and “higher-order” ordering sources, and interprets weak deontic necessity modals relative to both, is well-suited to this task. The prominence of normative considerations in our proposal suggests a more general methodological lesson: formal semantic analysis of natural language modals expressing normative concepts demands that close attention be paid to the nature of the underlying normative phenomena.     

On Bradley’s preservation condition for conditionals

Bradley has argued that a truth-conditional semantics for conditionals is incompatible with an allegedly very weak and intuitively compelling constraint on the interpretation of conditionals. I argue that the example Bradley offers to motivate this constraint can be explained along pragmatic lines that are compatible with the correctness of at least one popular truth-conditional semantics for conditionals.