334 research outputs found
Subjunctive Conditionals are Material
The material account claims that indicative conditionals are material. However, the conventional wisdom even among material account enthusiasts is that the material account cannot be extended to subjunctive conditionals. There are mainly three reasons that motivate this consensus: (1) the belief that if subjunctives were material, most subjunctive conditionals would be vacuously true, which is implausible; (2) its inconsistency with Adams pair, which suggest that indicative and subjunctive conditionals have different truth conditions; and (3) the belief that it is an inferior hypothesis compared to the possible world theories. I will argue against (1) that the counterintuitive aspects of vacuously true conditionals can be explained away in a uniform fashion, regardless of whether they are indicatives or subjunctives. I reinforce this assumption by showing that the positive arguments for the material account of indicatives are also intuitively valid for subjunctives. The point mentioned in (2) is resisted by explaining Adams pair as logically equivalent conditionals that can be appropriate at different times, depending of the speaker’s epistemic situation. Finally, (3) is criticised by making the case that the possible world account faces insurmountable problems and that a full-blown material account of indicatives and subjunctives is overall a more elegant solution
Directional Bias
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
Fara's formula and the Supervaluational Thin Red Line
Este artĂculo se centra en un argumento presentado por Fara (2010) en contra del supervaluacionismo en el contexto de la vaguedad. Muestro cĂłmo dicho argumento es igualmente aplicable al supervaluacionismo de tiempo ramificado (presentado por primera vez por Thomason 1970), pero no a la semántica 'STRL' de Malpass y Wawer (2012), que está estrechamente relacionada
Set-Theoretic Completeness for Epistemic and Conditional Logic
The standard approach to logic in the literature in philosophy and
mathematics, which has also been adopted in computer science, is to define a
language (the syntax), an appropriate class of models together with an
interpretation of formulas in the language (the semantics), a collection of
axioms and rules of inference characterizing reasoning (the proof theory), and
then relate the proof theory to the semantics via soundness and completeness
results. Here we consider an approach that is more common in the economics
literature, which works purely at the semantic, set-theoretic level. We provide
set-theoretic completeness results for a number of epistemic and conditional
logics, and contrast the expressive power of the syntactic and set-theoretic
approachesComment: This is an expanded version of a paper that appeared in AI and
Mathematics, 199
Real impossible worlds : the bounds of possibility
Lewisian Genuine Realism (GR) about possible worlds is often deemed unable to accommodate impossible worlds and reap the benefits that these bestow to rival theories. This thesis explores two alternative extensions of GR into the terrain of impossible worlds.
It is divided in six chapters. Chapter I outlines Lewis’ theory, the motivations for
impossible worlds, and the central problem that such worlds present for GR: How can GR
even understand the notion of an impossible world, given Lewis’ reductive theoretical
framework? Since the desideratum is to incorporate impossible worlds into GR without
compromising Lewis’ reductive analysis of modality, Chapter II defends that analysis
against (old and new) objections. The rest of the thesis is devoted to incorporating
impossible worlds into GR. Chapter III explores GR-friendly impossible worlds in the
form of set-theoretic constructions out of genuine possibilia. Then, Chapters IV-VI
venture into concrete impossible worlds. Chapter IV addresses Lewis’ objection against
such worlds, to the effect that contradictions true at impossible worlds amount to true contradictions tout court. I argue that even if so, the relevant contradictions are only ever about the non-actual, and that Lewis’ argument relies on a premise that cannot be nonquestion-
beggingly upheld in the face of genuine impossible worlds in any case. Chapter
V proposes that Lewis’ reductive analysis can be preserved, even in the face of genuine
impossibilia, if we differentiate the impossible from the possible by means of accessibility relations, understood non-modally in terms of similarity. Finally, Chapter VI counters objections to the effect that there are certain impossibilities, formulated in Lewis’ theoretical language, which genuine impossibilia should, but cannot, represent. I conclude that Genuine Realism is still very much in the running when the discussion turns to impossible worlds
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