conceptual

  One might think that this is obviously true: Two expressions are synonyms if they have the same content and having the same content is a transitive relation. This is a direct corollary from a more general principle that if we define a relation by an identity (or in general, we have a relation that is equivalent to some identity), the relation will inherent from the relevant identity its structural features, including transitivity. In other words, for every R if there is an F that R(x,y) =def F(x)=F(y) then R is transitive. This applies not only to the definition of synonym as sameness of meaning, but also to the definition of synonym as substitution salva veritate : φ is cognitively synonym to ψ if and only if, for all allowed sentential  contexts χ[. . .], we have χ[φ] iff χ[ψ]. Here, the double conditional in the final equation hides also an identity (of truth value). This can be made explicit thus: φ is cognitively synonym to ψ if and only if, for all allowed senten...

There are some problematic cases for defenders of the hypothesis that logical form is topic-transparent, i.e. the claim that two statements that differ only in the logical composition off its atomic components cannot differ in topic:  On the one hand, many people, myself included, claim that tautologies are not about anything in the content of the atomic components that occur in them, but about the logical operators themselves. Presumably, sentences of the form ( P → ( Q → P )) are not about whatever P and Q are about, but about material implication: in particular, they tell us that if the consequent of an implication is true, the whole implication is true as well. The basic argument for this later claim is that whatever P and Q are about makes no difference to the content of the tautology.  Based on Wittgenstein, Lazerowitz and Ambrose, and myself , we have argued that even though sentences like “Triangles are my favorite geometrical figures” are about triangles, i...

¿En qué sentido se habla de "relevancia" en las lógicas relevantes? ¿Qué relación tienen con el lenguaje natural, si alguno? Trato de responder estas y otras preguntas en esta entrevista.

Notes on Franz Berto’s first talk of the 2023 Cátedra Gaos Just as to be an intentionalist (like Kripke, but unlike Quine) is to take extentionality to be too coarse as tool for philosophically analyzing some phenomena, to be a hyperintentionalist (like Dunn and Restall, Berto, Chalmers, Yablo, Fine, etc. but unlike Lewis (sometimes), Stalker   (sometimes) , Montague, etc.) is to take intensionality (traditional modality) to be too coarse as tool for philosophically analyzing some phenomena. Intentionality is to material equivalence as hyper-intentionality is to necessary equivalence, but this can be extended ad infinitum, at least in principle, thus: Let R be an equivalence relation on a representational domain D , then H is a hyper-R operator iff not- R(H(p), H(q)) in spite of R(p, q) . In this schema, intentionality is hyper-extensionality, and hyper-intentionality is, well, hyper-intentionality. Thus, there can be hyper-hyper-intentionality and hyper-hyper-hyp...

What I saw at Marco Panza and collaborators’ Euclid session at Chapman University this Friday October 13th: Looking, right now at mathematicians workshop looking for a non-standard model to a formal system of axioms, it is very interesting to see how the whiteboard is used. For example, by explicitly writing out the formulas, it raises the salience of the operations involved. Thus, once it was shown, by explicitly writing the relevant formula, that a certain parameter was being calculated by a quadratic equation, this immediately suggested the use of irrationals to find the desired non-standard model.  Similarly, using ad-hoc formulas i.e. displays that belong to no actual standardized formal language but share a superficial grammar with them, for example, at some time Marco Panza wrote “SAS : Ang → Sea” to represent the fact that, in Euclid, the so-called Segment-Angle-Segment axiom (which they never called that way, always using the acronym “SAS”) states that, given c...

One of the basic problem of grounding  theory originates from an assumed fundamental asymmetry between the ultimate explanans and explananda of metaphysical explanation. While explananda can be composed of other facts in several ways, by disjunction, negation, conjunction, quantification, etc., the fundamental facts that constitute the explanans are supposed to be simple in themselves and total explanans can only be composed in of these simple facts in a straightforward aggregative way. In other words, while we need to find a metaphysical explanation to disjunctive, negative, quantified truth-bearers, etc., Neo-Aristotelian metaphysics resists the acceptance of fundamental negative, disjunctive or quantified facts. Thus, it faces the significant challenge of having to find adequate non-disjunctive grounds for disjunctive facts, positive grounds for negative facts, non-quantified grounds for quantified fact, non-modal grounds for modal facts, etc. So far, this task had proved elusiv...

In Euclid, parallelism is defined negatively by the absence of an intersection. But, even if they are not explicitly mentioned in this definition, the phenomenon of parallelism is ultimately about angles, because line intersection is also ultimately about angles (in particular, about the angle thus determined) – this is common sense, I think –; thus, in the end, parallelism is not about the angle between the parallel lines themselves (which does not exist) but about the angles produced by other, non-parallel, lines (otherwise, as I just mentioned, there would be no angles). In this context, we can think of axiom SAS as an extreme, simpler case of how to answer a more general question: how are angles are parallels related?  The other extreme is to say that they are completely independent, which is what José Gil is currently exploring. But there is an ample space between one extreme and the other. Remember that, according to SAS, if two straight lines (well, to be historically accura...

Plato on False Judgment in the  Theaetetus Axel Barceló-Aspeitia  ,  Edgar González-Varela Journal of the History of Philosophy Johns Hopkins University Press Volume 61, Number 3, July 2023 pp. 349-372 10.1353/hph.2023.a902875 Abstract Under what conditions would it be paradoxical to consider the possibility of false judgment? Here we claim that in the initial puzzle of  Theaetetus  187e5–188c9, where Plato investigates the question of what could psychologically cause a false judgment, the paradoxical nature of this question derives from certain constraints and restrictions about causal explanation, in particular, from the metaphysical principle that opposites cannot cause opposites. Contrary to all previous interpretations, this metaphysical approach does not attribute to Plato any controversial epistemological assumptions and fits better with the text and its role within the dialectic of the dialogue.

  Factores que pueden justificar la adopción y mantenimiento de una creencia: Evidenciales Directa Empírica Por intuición racional Indirecta ¿Puede ser inferida de manera adecuado de otras creencias sobre el mismo tema? ¿Quién mas (qué otros agentes individuales y colectivos) creen y/o afirman lo mismo o lo contrario y en qué circunstancias? Lo que está en juego: Efectos que tendría la adopción de la creencia En el agente (individual o colectivo) que la adopta y en los demás Materialmente o en su auto-percepción Independientemente de que sea verdadera o no Si acertáramos y fuera verdadera Si nos equivocáramos y no fuera verdadera

 Hace unos días en el desayuno, mi novia y yo nos topamos con esta paradoja que, por lo menos yo, no había visto en otro lado. Parte de cuatro premisas que me parecen poco controversiales: Los objetos del conocimiento proposicional son proposiciones [Primera Premisa] Para saber de manera singular (es decir, de manera directa, no descriptiva) de un objeto  a  que es F,  es necesario conocer a a . (Como Platón ya argumentaba en el Teeteto ) [Segunda Premisa] El conocimiento es fáctico: solo se pueden conocer proposiciones verdaderas. [Tercera Premisa] El escepticismo es falso: existe por lo menos un sujeto epistémico S  y una proposición p  tal que S  sabe que p. [Cuarta Premisa] Por un poco de reflexión, S  puede llegar a saber de no- p  que es falsa [de 4 y un poco de lógica]. S  conoce a no -p  [de 5 y 2] no- p  es verdadera [de 6, 3 y 1] p  es verdadera [de 3 y 4] p  y no- p son ambas verdaderas. [Contradicción] ¿Al...

I take this to be a fundamental logical principle of rationality: that whatever you are already committed to believing restricts what else you can believe (without revising what you are already committed to believing). This is enough to derive some version of the principle of non-contradiction, all that is required is recognizing that this relation be recognized as being none other but what we call “negation”. The basis motivation behind the main and only premise of this argument is that rationality has to do not only with what one ought to believe or not ex nihilo , but what one ought to believe or not given what we already do believe or not. This basic principle can be decomposed in four different principles: What one believes restricts what one can believe or not What one believes restricts what one ought to believe or not What one does not believe restricts what one can believe or not What one does not believe restricts what one ought to believe or not Let us focus on the first on...

  Entre las muchas metáforas desafortunadas que plagan la escritura de Ludwig Wittgenstein, tal vez una de las peores sea la de “límite”, como en “los límites de mi lenguaje son los límites de mi mundo” y pasajes similares. Wittgenstein usa la palabra “límite” para hablar de lo que, en otros contextos teóricos llamaríamos las condiciones de posibilidad o presupuestos de algo, es decir, aquello que define un espacio desde afuera. Por ejemplo, de qué tipo de objeto hablemos delimita qué podemos decir de él. De un objeto abstracto, por ejemplo, no podemos preguntarnos de qué color es. Así dicho, el término “límite” parece ser muy adecuado.   Desfortunadamente, la noción de límite tiene también la connotación, muy notoria, de establecer una frontera entre dos espacios que, de otra manera, serían uniformes. En otras palabras, lo que está mas allá del límite  suele ser un espacio del mismo tipo que aquel que se está delimitando. Por ejemplo, mas allá de las fronteras de nuest...

Let's call theories of grounding according to which (i) grounding necessitation is false and (ii)   “grounds aren't the only facts that might be difference-makers” (Muñoz 2020)  disjuctivist  theories of grounding. In (2015) I defended a disjunctivist account of truth-making as a defeasible relation and Muñoz (2020) recognizes this work as an antecedent to his own disjunctivism. Another important form of disjunctivism is conditional grounding theories like those of Badder or  Van Oordt Faller. The main difference between conditional theories and accounts like Muñoz or mine is that while   Badder and Van Oordt Faller recognize that besides grounds, there are also enabling conditions, Muñoz and I recognize also/instead disabling or defeating conditions. Disjunctivist accounts have recently been criticized by the likes of  Fatema  Amijee, who writes:   “The best candidate for such a view – and the onl...

  I. Introduction Before he reached his mature metaphysical view of being as gradual in the  Republic   (Allen 1961) , Plato claims that neither can negative facts explain positive facts, nor vice versa  ( Phaedo  103b) (this is very likely a corollary of  his principle of opposites  according to which if  A  and  B  are of opposite ontological categories,  A  cannot explain  B  ( González-Varela and Barceló  2 023 ). Paulo Sergio Méndoza just informed me (on January 2024) that Kant held a similar ontological principle in his A  New  Explanation  of the  First  Principles of Metaphysical Knowledge   (September 27, 1755). Yet, it seems obvious that we explain positive facts by appealing to negative facts and vice versa, all the time. We say things like " Pat must be sick, because she would not have missed the party otherwise", "The Plant died because we forgot to water it", " The...