In Defense of Brogaard-Salerno Stricture

Brogaard and Salerno (2008) argued that counter-examples to contraposition, strengthening the antecedent, and hypothetical syllogism involving subjunctive conditionals only seem to work because they involve a contextual fallacy where the context assumed in the premise(s) is illicitly shifted in the conclusion. To avoid such counter-examples they have proposed that the context must remain fixed when evaluating an argument for validity. That is the Brogaard-Salerno Stricture. Tristan Haze (2016), however, has recently objected that intuitively valid argumentative forms such as conjunction introduction do not satisfy this constraint. This paper has two goals. First, it argues that the Brogaard-Salerno Stricture is not violated in Haze’s putative counter-example. Second, it argues that since this stricture blocks the usual counter-examples to instances of classical argumentative forms that involve indicative or subjunctive conditionals, it is reasonable to infer that indicative and subjunctive conditionals are material

Some quantitative versions of Ratner's mixing estimates

We give explicit versions for some of Ratner's estimates on the decay of matrix coefficients of SL(2,R)-representations.Comment: 18 pages. Final version based on the referee's suggestion

A Contextualist Defence of the Material Account of Indicative Conditionals

The material account of indicative conditionals faces a legion of counterexamples that are the bread and butter in any entry about the subject. For this reason, the material account is widely unpopular among conditional experts. I will argue that this consensus was not built on solid foundations, since these counterexamples are contextual fallacies. They ignore a basic tenet of semantics according to which when evaluating arguments for validity we need to maintain the context constant, otherwise any argumentative form can be rendered invalid. If we maintain the context fixed, the counterexamples to the material account are disarmed. Throughout the paper I also consider the ramifications of this defence, make suggestions to prevent contextual fallacies, and anticipate some possible misunderstandings and objections

The Triviality Result is not Counter-Intuitive

The Equation (TE) states that the probability of A → B is the probability of B given A. Lewis (1976) has shown that the acceptance of TE implies that the probability of A → B is the probability of B, which is implausible: the probability of a conditional cannot plausibly be the same as the probability of its consequent, e.g., the probability that the match will light given that is struck is not intuitively the same as the probability that it will light. Here I want to counter Lewis’ claim. My aim is to argue that: (1) TE express the coherence requirements implicit in the probability distributions of a modus ponens inference (MP); (2) the triviality result is not implausible because it is a result from these requirements; (3) these coherence requirements measure MP employability, so TE significance is tied to it; (4) MP employability doesn’t provide either the acceptability or the truth conditions of conditionals, since MP employability depends on previous independent reasons to accept the conditional and some acceptable conditionals are not MP friendly. Consequently, TE doesn’t have the logical significance that is usually attributed to it

The Matrix Product Ansatz for integrable U(1)^N models in Lunin-Maldacena backgrounds

We obtain through a Matrix Product Ansatz (MPA) the exact solution of the most general $N$-state spin chain with $U(1)^N$ symmetry and nearest neighbour interaction. In the case N=6 this model contain as a special case the integrable SO(6) spin chain related to the one loop mixing matrix for anomalous dimensions in ${\cal N} = 4$ SYM, dual to type $IIB$ string theory in the generalised Lunin-Maldacena backgrounds. This MPA is construct by a map between scalar fields and abstract operators that satisfy an appropriate associative algebra. We analyses the Yang-Baxter equation in the N=3 sector and the consistence of the algebraic relations among the matrices defining the MPA and find a new class of exactly integrable model unknown up to now

Necessary and Sufficient Conditions are Converse Relations

According to the so-called ‘standard theory’ of conditions, the conditionship relation is converse, that is, if A is a sufficient condition for B, B is a necessary condition for A. This theory faces well-known counterexamples that appeal to both causal and other asymmetric considerations. I show that these counterexamples lose their plausibility once we clarify two key components of the standard theory: that to satisfy a condition is to instantiate a property, and that what is usually called ‘conditionship relation’ is an inferential relation. Throughout the paper this way of interpreting the standard theory is compared favourably over an alternative interpretation that is outlined in causal terms, since it can be applied to all counterexamples without losing its intuitive appeal