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)

There is a renewed debate about modus ponens. Strikingly, the recent counterexamples in Cantwell, Dreier and MacFarlane and Kolodny are generated by restricted readings of the ‘if’-clause. Moreover, it can be argued on general grounds that the restrictor view of conditionals developed in Kratzer and Lewis leads to counterexamples to modus ponens. This paper provides a careful analysis of modus ponens within the framework of the restrictor view. Despite appearances to the contrary, there is a robust sense in which modus (...) ponens is valid, owing to the fact that conditionals do not only allow for restricted readings but have bare interpretations, too. (shrink)

In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.

A proof employing no semantic terms is offered in support of the claim that there can be truths without truthmakers. The logical resources used in the proof are weak but do include the structural rule Contraction.

In this paper I look at indicative nested whether-conditionals, sentences like:If I pass the exam, I will pass whether I pray or not.The behavior of ‘if’ in these examples is to be contrasted with the behavior of ‘if’ in or-to-if conditionals:If Mary is at home or at work, then if she is not at home, she is at work.I argue that no currently available semantics for indicative conditionals can explain both the behavior of ‘if’ in nested whether-conditionals and the behavior (...) of ‘if’ in or-to-ifs. We need a theory that predicts both. While no currently available theory makes the right predictions, one theory comes close—Heim’s rendition of Stalnaker’s semantics :183–221, 1992). I show how to fix Heim’s view to get the right results for all cases. In sum, the paper argues for a particular development of Stalnaker’s semantics, and shows that whether-conditionals cannot be dealt with on other approaches. (shrink)

There is almost a consensus among conditional experts that indicative conditionals are not material. Their thought hinges on the idea that if indicative conditionals were material, A → B could be vacuously true when A is false, even if B would be false in a context where A is true. But since this consequence is implausible, the material account is usually regarded as false. It is argued that this point of view is motivated by the grammatical form of conditional sentences (...) and the symbols used to represent their logical form, which misleadingly suggest a one-way inferential direction from A to B. That conditional sentences mislead us into a directionality bias is a phenomenon that is well-documented in the literature about conditional reasoning. It is argued that this directional appearance is deceptive and does not reflect the underlying truth conditions of conditional sentences. This directional bias is responsible for both the unpopularity of the material account of conditionals and some of the main alternative principles and themes in conditional theory, including the Ramsey’s test, the Equation, Adams’ thesis, conditional-assertion and possible world theories. The directional mindset forgets a hard- earned lesson that made classical logic possible in the first place, namely, that grammatical form of sentences can mislead us about its truth conditions. There is a case to be made for a material account of indicative conditionals when we break the domination of words over the human mind. (shrink)

I argue that we should solve the Lottery Paradox by denying that rational belief is closed under classical logic. To reach this conclusion, I build on my previous result that (a slight variant of) McGee’s election scenario is a lottery scenario (see Lissia 2019). Indeed, this result implies that the sensible ways to deal with McGee’s scenario are the same as the sensible ways to deal with the lottery scenario: we should either reject the Lockean Thesis or Belief Closure. After (...) recalling my argument to this conclusion, I demonstrate that a McGee-like example (which is just, in fact, Carroll’s barbershop paradox) can be provided in which the Lockean Thesis plays no role: this proves that denying Belief Closure is the right way to deal with both McGee’s scenario and the Lottery Paradox. A straightforward consequence of my approach is that Carroll’s puzzle is solved, too. (shrink)

This thesis is about indicative conditionals and apparent counterexamples to classically valid argument forms. Specifically, it applies the following four theories: - material (inspired by Grice (1961, 1975 and 1989)); - possible-worlds (inspired by Stalnaker (1981); Lewis (1976); and Kratzer (2012)), - suppositional (inspired by Adams (1975) and Edgington (1995 and 2014)); and - hybrid (inspired by Jackson (1987)) to try and solve the following two counterexamples: - Vann McGee’s to modus ponens (1985); and - Lewis Carroll’s to modus tollens (...) (1894). I argue that none of the theories I consider can explain – without facing any problems – the three individually plausible but jointly inconsistent theses that give rise to the apparent counterexamples. The three theses of the trilemma are the following: (1) the argument is invalid; (2) the argument is an instance of modus ponens or modus tollens; and (3) modus ponens or modus tollens is valid. (shrink)

Vann McGee has presented a putative counterexample to modus ponens. I show that (a slightly modified version of) McGee’s election scenario has the same structure as a famous lottery scenario by Kyburg. More specifically, McGee’s election story can be taken to show that, if the Lockean Thesis holds, rational belief is not closed under classical logic, including classical-logic modus ponens. This conclusion defies the existing accounts of McGee’s puzzle.