-/- A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. -/- Kalish-Montague proposed using vbtos to formalize definite descriptions, set abstracts {x: F}, minimalization in recursive function theory, etc. However, they gave no sematics for vbtos. Hatcher gave a semantics but one that has flaws. We give a correct (...) semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture was later proved independently by the authors and by Newton da Costa. -/- The expression (vy:F) is called a variable bound term (vbt). In case F has only y free, (vy:F) has the syntactic propreties of an individual constant; and under a suitable interpretation of the language vy:F) denotes an individual. By a semantic analysis of vbtos we mean a proposal for amending the standard notions of (1) "an interpretation o f a first -order language" and (2) " the denotation of a term under an interpretation and an assignment", such that (1') an interpretation o f a first -order language associates a set-theoretic structure with each vbto and (2') under any interpretation and assignment each vb t denotes an individual. (shrink)

Giordano Bruno’s interest in magic was not a marginal aspect of his philosophy. In the magical works written in 1589 and 1591, Bruno carried out his project of a cultural reform, which he also conceived as a pratical renovatio. In De magia naturali Bruno undertook a careful theoretical reexamination of Renaissance magic in order to ground its "experimental data" on physical foundation. Some traditional notions , which Bruno found in his sources and made use of, are analyzed in his paper (...) to show the deep change they underwent in the light of Bruno’s new ontology and cosmology. (shrink)

The general theory of variable binding term operators is an interesting recent development in logic. It opens up a rich class of semantic and model-theoretic problems. In this paper we survey the recent literature on the topic, and offer some remarks on its significances and on its connections with other branches of mathematical logic.

It is a well known empirical observation that natural axiomatic theories are pre-well-ordered by consistency strength. For any natural theory $T$, the next strongest natural theory is $T+\mathsf{Con}_T$. We formulate and prove a statement to the effect that the consistency operator is the weakest natural way to uniformly extend axiomatic theories.

Vita e pensiero di A. Rosmini -- Introduzione alla filosofia -- Nuovo saggio sull'origine delle idee -- Logica -- Teosofia -- Antropologia in servizio della scienza morale -- Psicologia -- Principi della scienza morale -- Trattato della coscienza morale -- Scritti pedagogici -- La società e il suo fine -- Filosofia del diritto -- Tesari filosofici (sintesi delle opere).

This article is meant to give psychotherapists a glimpse of the clinical implications of Merleau-Ponty's approach to unconscious thought and insight. Freud found evidence of consciousness and intentionality in processes that were understood in terms of coincidence or biological automata. Phenomenology has demonstrated that intentionality is an attribute of the entire embodied subjectivity. Both approaches point to the fact that the sphere of lived intentions is much larger than that of conscious thought. The article includes clinical examples.

Dans cet article nous étudions trois notes de M. Fréchet sur les opérations linéaires et leur rôle dans l’émergence de l’analyse fonctionnelle au début du XXème siècle. Dans un premier temps nous mettons en évidence les processus de sélection, d’extraction et de réinterprétation mis en oeuvre par Fréchet à partir de matériaux publiés antérieurement. A partir de cette analyse nous nous attachons à montrer comment la progression vers une vision plus générale met en jeu des éléments structurels fondamentaux dans la (...) constitution d’un champ nouveau des mathématiques. Notre étude permet finalement de préciser le concept de structure dans son rôle central dans l’émergence de l’analyse fonctionnelle. (shrink)

These are notes designed to bring the beginning student of the philosophy of quantum mechanics 'up to scratch' on the mathematical background needed to understand elementary finite-dimensional quantum theory. There are just three chapters: Ch. 1 'Vector Spaces'; Ch. 2 'Inner Product Spaces'; and Ch. 3 'Operators on Finite-Dimensional Complex Inner Product Spaces'. The notes are entirely self-contained and presuppose knowledge of only high school level algebra.

Landauer's principle, often regarded as the basic principle of the thermodynamics of information processing, holds that any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment. Conversely, it is generally accepted that any logically reversible transformation of information can in principle be accomplished by an appropriate physical mechanism operating in a (...) thermodynamically reversible fashion. These notions have sometimes been criticized either as being false, or as being trivial and obvious, and therefore unhelpful for purposes such as explaining why Maxwell's Demon cannot violate the second law of thermodynamics. Here I attempt to refute some of the arguments against Landauer's principle, while arguing that although in a sense it is indeed a straightforward consequence or restatement of the Second Law, it still has considerable pedagogic and explanatory power, especially in the context of other influential ideas in nineteenth and twentieth century physics. Similar arguments have been given by Jeffrey Bub. (shrink)

In philosophy and rhetorical studies, self-knowledge inscribes the absolutely indivisible line that separates “the human” from “the animal.” Autodeixis, the self-reflexive power of the I, is the condition both for language acquisition and for reason; it names an exceptional sort of auto–affection in which a being demonstrates the capacity to step back from itself enough to recognize itself and so to refer to itself as itself. What I propose in this article, however, is that autodeixis involves not a specifically human (...) power to disclose an ontological as such but the extrahuman operations of an allegorical as if. The presumption of self-knowledge is not an innate quality of “the human” but the already relational condition for any living being that must repeat itself to be itself. A kind of preoriginary rhetoricity, I argue, is the very condition for the singularity and functioning of any living being. (shrink)

A proof by Allan Gibbard (Ifs: Conditionals, beliefs, decision, chance, time. Reidel, Dordrecht, 1981) seems to demonstrate that if indicative conditionals have truth conditions, they cannot be stronger than material implication. Angelika Kratzer's theory that conditionals do not denote two-place operators purports to escape this result [see Kratzer (Chic Linguist Soc 22(2):1–15, 1986, 2012)]. In this note, I raise some trouble for Kratzer’s proposed method of escape and then show that her semantics avoids this consequence of Gibbard’s proof by (...) denying modus ponens. I also show that the same holds for Anthony Gillies’ semantics (Philos Rev 118(3):325–349, 2009) and argue that this consequence of these theories is not obviously prohibitive—hence, both remain viable theories of indicative conditionals. (shrink)

Dasgupta :35–67, 2009) has argued that material individuals, such as particles and laptops, are metaphysically objectionable and must be eliminated from our fundamental theories of the world. He proposes to eliminate them by redescribing all the fundamental facts of the world in a variant of predicate functor logic. We study the status, on this theory, of a putative fact particularly recalcitrant to a formulation within predicate functor logic: his own claim that there are no fundamental or primitive material individuals. We (...) consider three regimentations of the denial of primitive individuals and show that—under some plausible hypotheses about fundamental truths and the fundamentality operator—they cannot be consistently translated in predicate functor logic by Dasgupta’s usual strategy. We conclude by discussing two approaches to salvage Generalism, in the absence of such a translation. (shrink)

Cette note devait introduire à un public anglophone la traduction de la « Lettre de Louis Althusser datée du 18 mars 1966 et adressée au Comité central du PCF », elle est ici enrichie dans une version livrée au public français. Elle apporte le contexte historique et théorique nécessaire à la compréhension des interventions « anti-humanistes » de Louis Althusser qui questionne les choix politiques opérés par le PCF au cours des années 1960. Nulle part ailleurs, dans les écrits (...) publiés d’Althusser, nous ne voyons aussi clairement les enjeux politiques imbriqués dans son projet philosophique, ni comment ce projet évolua progressivement d’une entreprise « théoriciste » à la recherche d’une philosophie en lien plus étroit avec la pratique. Cette lettre nous paraît de la plus haute importance pour les spécialistes de l’œuvre d’Althusser, les historiens de la pensée marxiste, mais aussi plus largement à tous ceux qui s’intéressent à l’importance que peut revêtir le travail d’Althusser dans les débats actuels dans le champ de la philosophie marxiste. (shrink)

The notion of a bilattice was rst introduced by Ginsburg (see Gin]) as a general framework for a diversity of applications (such as truth maintenance systems, default inferences and others). The notion was further investigated and applied for various purposes by Fitting (see Fi1]- Fi6]). The main idea behind bilattices is to use structures in which there are two (partial) order relations, having di erent interpretations. The two relations should, of course, be connected somehow in order for the mathematical structure (...) to be useful. It is not clear, however, what this connection should be. Ginsberg, for example, has made the connection through an extra operation of negation. Fitting, on the other hand, has investigated connections in the form of conditions on the structure (such as being interlaced { see below). These conditions are independent of the existence, or even the possibility to de ne, operations like Ginsberg's negation.* Fitting de nes, accordingly, notions like \an interlaced bilattice", \a distributive bilattice", \a bilattice with negation" and others. He does not provide, however, any de nition of the notion of bilattice itself (without an extra modi er). I was unable to nd anywhere, in fact, a de nition which will cover all the structures which were called \bilattice" in the literature. (shrink)

This short note is on the question whether the intersection of all fixed points of a positive arithmetic operator and the intersection of all its closed points can proved to be equivalent in a weak fragment of second order arithmetic.

Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic Analysis of (...) Variable Binding Term Operators” (Co-author John Herring), Logique et Analyse 55, 646–57. MR0307874 (46 #6989). A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. Kalish-Montague 1964 proposed using vbtos to formalize definite descriptions “the x: x+x=2”, set abstracts {x: F}, minimization in recursive function theory “the least x: x+x>2”, etc. However, they gave no semantics for vbtos. Hatcher 1968 gave a semantics but one that has flaws described in the 1971 paper and admitted by Hatcher. In 1971 we give a correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture, proved in this paper with Hatcher’s help, was proved independently about the same time by Newton da Costa. (shrink)

Two questions frame this response to Amin’s article ‘The Remainders of Race’. It first introduces an epistemological question that recognizes the impossibility of separating ontology and epistemology in modern thought and asks why contemporary studies of racial subjugation so infrequently consider the concept of race’s onto-epistemological function. The second, methodological, question necessarily follows. Acknowledging that ‘the what of race’ cannot be separated from the ‘how of race’ makes it crucial to ask why the former is no longer considered in most (...) analyses of the latter. There follows a mapping of the context of emergence of political-symbolic strategies that carve out racial difference and cultural difference as human attributes. The article shows that, rather than an extraneous notion or a referent of a natural human attribute, the concept of race is the modern ethico-political device that refigures the workings of scientific universality in political and ethical texts. What this does is to enable the argument that, instead of manifestations of human ‘sorting’ instincts, the operatives of raciality proliferating in the global present consist of biopolitical architectures, mechanisms and procedures designed and assembled with the main tools of racial power/knowledge, namely racial and cultural difference. (shrink)

With any structural inference rule A/B, we associate the rule $${(A \lor p)/(B \lor p)}$$, providing that formulas A and B do not contain the variable p. We call the latter rule a join-extension ( $${\lor}$$ -extension, for short) of the former. Obviously, for any intermediate logic with disjunction property, a $${\lor}$$ -extension of any admissible rule is also admissible in this logic. We investigate intermediate logics, in which the $${\lor}$$ -extension of each admissible rule is admissible. We prove that (...) any structural finitary consequence operator (for intermediate logic) can be defined by a set of $${\lor}$$ -extended rules if and only if it can be defined through a set of well-connected Heyting algebras of a corresponding quasivariety. As we exemplify, the latter condition is satisfied for a broad class of algebraizable logics. (shrink)

Contemporary art is increasingly reverting to notions of the index to image the slow changes and catastrophic destructions caused by climate breakdown. Looking at Gideon Mendel’s photo series Watermarks (since 2011), Tomonari Nishikawa’s short film sound of a million insects, light of a thousand stars (2014), and Santiago Sierra’s installation 52 Canvases Exposed to Mexico City’s Air (2019), the essay analyzes three positions that employ analog techniques of direct exposure to the elements and to toxicity. They use the index to (...) create artworks that function as collaborative testimonies of human and non-human witnessing work, prompting a re-reading of Rosalind Krauss’ two-part essay “Notes on the Index” (1977) for the present. Central to such a re-reading is the form the testimonies take on. I describe them as indexical abstractions, seeing in them images that are materially connected to the world yet expressing that involvement in non-mimetic ways. The works cite the idiom of abstract art not only to show that modernism has put the planet into distress but to also find a pictorial code operating beyond the confines of linear perspective. By doing so, they give expression to what Timothy Morton has called the hyperobject of climate change, creating pictures that combine image and imagination, thereby asking viewers to approach them – and the world they index – with care. (shrink)

Witnessed Gödel logics are based on the interpretation of () by minimum instead of supremum . Witnessed Gödel logics appear for many practical purposes more suited than usual Gödel logics as the occurrence of proper infima/suprema is practically irrelevant. In this note we characterize witnessed Gödel logics with absoluteness operator w.r.t. witnessed Gödel logics using a uniform translation.