The portrait of a lady by Correggio in the Hermitage Museum, St Petersburg, has long attracted the attention of scholars. While the attribution to Antonio Allegri has been established beyond doubt, the identification of the young woman remains in dispute. The principal aim of this essay is to explore the ways in which the painting interacts with classical literature, and in turn with the ideas permeating northern Italy in the early sixteenth century. In particular, the paper contends that the composition (...) ought to be thought of in the context of humanist interpretations of Homer’s Odyssey, iv.221, around the time it was painted. (shrink)

On many currently live interpretations, quantum mechanics violates the classical supposition of value definiteness, according to which the properties of a given particle or system have precise values at all times. Here we consider whether either metaphysical supervaluationist or determinable-based approaches to metaphysical indeterminacy can accommodate quantum metaphysical indeterminacy (QMI). We start by discussing the standard theoretical indicator of QMI, and distinguishing three seemingly different sources of QMI (S1). We then show that previous arguments for the conclusion that metaphysical supervaluationism (...) cannot accommodate QMI, due to Darby 2010 and Skow 2010, are unsuccessful, in leaving open several supervaluationist responses. We go on to provide more comprehensive argumentation for the negative conclusion. Here, among other results, we establish that the problems for supervaluationism extend far beyond the concern that is the focus of Darby's and Skow's discussions (according to which a supervaluationist approach is incompatible with the orthodox interpretation, in light of the Kochen-Specker theorem) to also attach to common understandings of other interpretations on which there is QMI (S2). We then argue that a determinable-based account can successfully accommodate all three varieties of QMI (S3). We close by observing the positive mutual bearing of our results on the coherence and intelligibility of both quantum mechanics and metaphysical indeterminacy (S4). (shrink)

This paper explores quantum indeterminacy, as it is operative in the failure of value‐definiteness for quantum observables. It first addresses questions about its existence, its nature, and its relations to extant quantum interpretations. Then, it provides a critical discussions of the main accounts of quantum indeterminacy.

In Calosi and Wilson (Phil Studies 2019/2018), we argue that on many interpretations of quantum mechanics (QM), there is quantum mechanical indeterminacy (QMI), and that a determinable-based account of metaphysical indeterminacy (MI), as per Wilson 2013 and 2016, properly accommodates the full range of cases of QMI. Here we argue that this approach is superior to other treatments of QMI on offer, both realistic and deflationary, in providing the basis for an intelligible explanation of the interference patterns in the double-slit (...) experiment. We start with a brief overview of the motivations for QMI and for a determinable-based account of MI (§1). We then apply a developed 'glutty' implementation of determinable-based QMI to the superposition-based QMI present in the double-slit experiment, and positively compare the associated explanation of double-slit interference with that available on a metaphysical supervaluationist account of QMI (§2). We then present and respond to objections, due to Glick (2017) and Torza (2017), either to QMI (§3) or to our specific account of QMI (§4); in these sections we also positively compare our treatment of double-slit interference to that available on Glick's deflationary treatment of QMI. We conclude with some dialectical observations (§5). (shrink)

Monism is roughly the view that there is only one fundamental entity. One of the most powerful argument in its favor comes from quantum mechanics. Extant discussions of quantum monism are framed independently of any interpretation of the quantum theory. In contrast, this paper argues that matters of interpretation play a crucial role when assessing the viability of monism in the quantum realm. I consider four different interpretations: modal interpretations, Bohmian mechanics, many worlds interpretations, and wavefunction realism. In particular, I (...) extensively argue for the following claim: several interpretations of QM do not support monism at a more serious scrutiny, or do so only with further problematic assumptions, or even support different versions of it. (shrink)

The paper address the question of whether quantum mechanics (QM) favors Priority Monism, the view according to which the Universe is the only fundamental object. It develops formal frameworks to frame rigorously the question of fundamental mereology and its answers, namely (Priority) Pluralism and Monism. It then reconstructs the quantum mechanical argument in favor of the latter and provides a detailed and thorough criticism of it that sheds furthermore new light on the relation between parthood, composition and fundamentality in QM.

This paper provides the first thorough assessment of a physics-based answer, the Bound State Answer, to the Special Composition Question. According to the BSA some objects compose something if they are in a common bound state. The reasons to endorse such an answer, in particular, motivations coming from empirical adequacy and conservativeness, precision, simplicity, and parsimony, are critically addressed. I then go on to compare the BSA to other moderate answers to the SCQ and consider whether objections raised against such (...) answers can be raised against the BSA as well. I finally relate the discussion with mereological pluralism. (shrink)

According to the Determinable Based Account of metaphysical indeterminacy, there is MI when there is an indeterminate state of affairs, roughly a state of affairs in which a constituent object x has a determinable property but fails to have a unique determinate of that determinable. There are different ways in which x might have a determinable but no unique determinate: x has no determinate—gappy MI, or x has more than one determinate—glutty MI. Talk of determinables and determinates is usually constructed (...) as relative to levels of determination. In this paper I first provide a formal construction for determinables and determinates that pays crucial attention to intermediate levels of determination, and then explore the consequences for the DBA of introducing such intermediate levels. In particular, I argue that intermediate levels of determination highlight crucial differences between gappy and glutty cases of MI, and allow one to introduce a third way of indeterminacy, glappy MI. (shrink)

Among the most egregious and discouraging problems of conservation is the rapidly escalating human‐caused species extinction rate. “De‐extinction” refers to the application of certain cutting‐edge techniques for the supposed recovery of lost species and gives the impression that scientists, enlightened and empowered by the miracles of technology, are coming to the rescue. “De‐extinction” is the latest example of a long play of language that has given conservation efforts a tragically false sense of accomplishment and has worsened the conservation crisis. De‐extinction (...) is the tip of an intellectual iceberg that sits atop of a host of profoundly questionable value systems, expectations, attitudes, and priorities that elude and bewitch critical reflection. It gives the impression that extinction is reversible and, thus, diminishes the gravity of the human annihilation of species. Here, we examine how the language of de‐extinction influences attitudes, shapes thoughts and imagination, and creates ethical blindness. The language developing around “de‐extinction” reveals what is in fact a profound intellectual crisis at the foundation of conservation. The underlying challenge is to find the language that will articulate and inspire the radical and indispensable change needed to come to grips with the value of nature. (shrink)

For some of us, the defeasibility theory of knowledge remains the most plausible approach to the Gettier Problem. Epistemological fashion and faded memories notwithstanding, persuasive objections to the theory are very hard to find. The most impressive of those objections to the theory that have hitherto gone unanswered are examined and rejected here. These are objections put forward by Richard Feldman, Richard Foley, and John Turri. While these are all interesting, the objection recently put forward by Turri is, we think, (...) by far, the most serious threat to the theory that we have seen in a long time. A successful reply to it requires a surprising amount of care, as it turns out. If tenable, Turri's objection deals a devastating blow to the theory developed by Roderick Chisholm, Keith Lehrer, Peter Klein, Marshall Swain, Risto Hilpinen, John Pollock, and Paul Moser, among others. Under scrutiny, however, the threat proves illusory. It results from inattention to a crucial, but relatively subtle, aspect of.. (shrink)

Super-substantivalism (of the type we’ll consider) roughly comprises two core tenets: (1) the physical properties which we attribute to matter (e.g. charge or mass) can be attributed to spacetime directly, with no need for matter as an extraneous carrier “on top of” spacetime; (2) spacetime is more fundamental than (ontologically prior to) matter. In the present paper, we revisit a recent argument in favour of super-substantivalism, based on General Relativity. A critique is offered that highlights the difference between (various accounts (...) of) fundamentality and (various forms of) ontological dependence. This affords a metaphysically more perspicuous view of what super-substantivalism’s tenets actually assert, and how it may be defended. We tentatively propose a re-formulation of the original argument that not only seems to apply to all classical physics, but also chimes with a standard interpretation of spacetime theories in the philosophy of physics. (shrink)

The present study investigated the mediating role of conceptions of learning in the relationship between metacognition and academic outcomes among middle school students. The self-report ‘Learning Conceptions Questionnaire’ (LCQ) and ‘Metacognitive questionnaire on the method of study’ (QMS) were administered to 136 middle school students and their academic outcomes were collected. Correlation analyses revealed that within metacognition only self-assessment was positively correlated with academic outcomes. Mediation analysis indicated that a conception of learning as internal attribution of success and failure was (...) significantly involved as mediator in the relationship between metacognition and academic achievements. The present study permitted to advance our knowledge about the relationship between metacognition and academic achievements and it opened the way to practical implications. (shrink)

Resumen: En este artículo presentamos a san Agustín como punto de partida de la reflexión de Husserl respecto del tiempo y la correlación entre memoria y Erinnerung. La investigación fenomenológica de Husserl acerca de la conciencia interna del tiempo parte de la reflexión de san Agustín por el mismo problema. En estas obras, el tiempo se puede medir porque hay una distentio animi. En Husserl, Die Erinnerung nos coloca ante una conexión infinita de “antes”, pues toda percepción se encuentra en (...) una relación de multiplicidad de percepciones. Ambos pensadores están unidos por la vocación de dar cuenta de la propia inmanencia.: This article presents Saint Agustin as a starting point for Husserl’s reflection on time and the correlation between memory and Erinnerung. Husserl’s phenomenological research on the internal consciousness of time starts from the reflection of St. Augustine on the same problem. In this works, time can be measured because there is distentio animi. In Husserl, Die Erinnerung places us in the face of an infinite “before” connection, because all perceptions are to be found on a relationship of multiplicity of perceptions. Both thinkers are united by the vocation to account for their own immanence. (shrink)

La reflexión de Friederich Schleiermacher sobre la universidad se centra en las dificultades que observa para superar el estancamiento de la educación alemana a principios del siglo XIX y establece, en ella, dos niveles: por un lado, la excesiva burocratización de la vida universitaria, que le quita lo que tiene precisamente de vital y, por otro, desde la perspectiva propiamente del profesor, la imposibilidad de cultivar el talento de los alumnos mediante clases farragosas, en las que se repite lo que (...) ya está escrito y en las que la memoria es la única medida del conocimiento. La mayoría de los profesores se encuentran en esta situación porque los conocimientos se perciben de manera fragmentaria y, por lo tanto, se transmiten sin el contenido de su unidad profunda. La Facultad de Filosofía tiene el cometido de construir el camino hacia la unidad de conocimiento y fundamentar el sentido profundo de la vida universitaria. Por ello, los cimientos de la universidad moderna descansan sobre el profesor que investiga y transmite en sus clases el pathos de aquella tarea; también descansan sobre el alumno, a quien hay que ayudar a comprender la dimensión de su talento y desde allí, emprender la tarea de la auto-educación. (shrink)

The relation between noise and disturbance is investigated within the general framework of Galois connections. Within this framework, we introduce the notion of leak of information, mathematically defined as one of the two closure maps arising from the observable-channel compatibility relation. We provide a physical interpretation for it, and we give a comparison with the analogous closure maps associated with joint measurability and simulability for quantum observables.

Although recent work has been done on the Barnes Foundation and its philosophical and pedagogical background, almost all the research effort has been focused on the friendship and intellectual link between John Dewey and Albert C. Barnes. Unfortunately, to the best of our knowledge, the impact of George Santayana’s philosophy on the Foundation has not been systematically examined. The hypothesis that we present and develop in this article is that Santayana’s thought is essential for the aesthetic theories elaborated within the (...) framework of the Barnes Foundation: Barnes’ theory of art criticism; Dewey’s aesthetic theory, and even Lawerence Buermeyer’s aesthetic theory. This article is a first approximation with the purpose of clarifying these philosophical, theoretical and historical relationship so as to start to fill the existing gap in contemporary literature on the topic. (shrink)

BackgroundCerebral Visual Impairment is a very common finding in children affected by Cerebral Palsy. In this paper we studied the characteristics of CVI of a large group of children with CP and CVI, describing their neurovisual profiles according to three different age subgroups.MethodsWe enrolled 180 subjects with CP and CVI for the study. We carried out a demographic and clinical data collection, neurological examination, developmental or cognitive assessment, and a video-recorded visual function assessment including an evaluation of ophthalmological characteristics, oculomotor (...) functions, and basic visual functions. In school-aged children, we also performed an evaluation of their cognitive-visual profiles.ResultsThere were signs of CVI in all the three subgroups. Subgroup 1 and subgroup 2 were different for fixation, visual acuity and contrast sensitivity, being more frequently impaired in younger children. Comparing subgroup 2 with subgroup 3, the older children presented more frequently myopia while the younger ones esotropia and alteration in smooth pursuit and saccades. Furthermore, fixation, smooth pursuit, visual acuity, contrast sensitivity and visual filed were more frequently impaired in younger children compared to the older ones. Multiple correspondence analysis confirmed the different neurovisual profiles according to age: younger children with CP showed more signs of CVI compared to the older ones. 34 out of 68 children belonging to subgroup 3 underwent the cognitive visual evaluation; an impairment of cognitive visual skills was detected in 21 subjects.ConclusionYounger children with CP showed more signs of CVI compared to the older ones, likely for the physiological maturation of visual system and mechanisms of neuroplasticity. In this direction, we suggest an early neurovisual evaluation to detect any weak visual functions. (shrink)

A partir da leitura dos escritos de Ficino dedicados à melancolia, a presente investigação considera o modo como, combinando elementos de diversas fontes, o filósofo florentino contribuiu decisivamente para compreensão dessa condição e para a constituição de um medium terapêutico diferenciado. O enquadramento do De Vita Libri Tres na longa sucessão de teorias médico-‑filosóficas relativas à constituição melancólica revela a sua participação na dimensão incremental de uma densa semântica, mas também, de modo decisivo, a ausência de uma evolução unívoca das (...) ideias de melancolia. Assim o demonstra a recuperação de uma vertente favorável do temperamento melancólico, combinando Ficino a ortodoxia médica relativa ao equilíbrio humoral com a possibilidade, enunciada no Problema XXX, de uma forma superior de equilíbrio. O eclodir da genialidade contemplativa, tida como característica central dos maiores feitos humanos, em particular no domínio dos estudos académicos, tem lugar na forma de êxtase, adaptando Ficino traços da mania [furor] platónica. O papel de Ficino na evolução das conceções de melancolia é também evidenciado na sua exploração das suas formas amorosa e religiosa, indicando uma sensibilidade às condições sociais da individuação, mas também a tentativa de compreender e mitigar as tribulações existenciais associadas ao seu próprio temperamento. Já no que se refere ao manancial terapêutico proposto pelo filósofo florentino, o aspeto mais inovador reside na sua mobilização da astrologia e da magia, pro- curando demonstrar que as mesmas são um recurso natural baseado num conceito de simpatia entre os elementos da hierarquia cósmica e, como tal, distintas da necromancia e da demonologia. (shrink)

The present essay seeks to investigate the physical-vital sensations and feelings resulting from the contact with the artistic form. For this purpose, and from the main constellations that orbit around Nietzsche and Warburg, the essay seeks to inquire whether the work of art, as we conceive it, is capable of serving as a vital tonic or stimulant to life. Understanding sensation as friction, the mark of the organism's bodily contact with the environment, and feeling as the incorporation of this sensation (...) in terms of vital increment or decay, the essay seeks to question whether form would not be the translation in vital terms of physical forces. of the world, and therefore, a physical-biological possibility of adding vital power. In this way, more than serving the aesthetic enjoyment, the work would rather be the materialization of a historical way of life, and, therefore, thirsty for the will to power. Key-words: Form; Body; Power. (shrink)

Accountability is a cornerstone of the governance of artificial intelligence (AI). However, it is often defined too imprecisely because its multifaceted nature and the sociotechnical structure of AI systems imply a variety of values, practices, and measures to which accountability in AI can refer. We address this lack of clarity by defining accountability in terms of answerability, identifying three conditions of possibility (authority recognition, interrogation, and limitation of power), and an architecture of seven features (context, range, agent, forum, standards, process, (...) and implications). We analyse this architecture through four accountability goals (compliance, report, oversight, and enforcement). We argue that these goals are often complementary and that policy-makers emphasise or prioritise some over others depending on the proactive or reactive use of accountability and the missions of AI governance. (shrink)

Crowdfunding is regarded a financing mechanism that could improve the funding opportunities of businesses with a pro-social orientation. Indeed, it is assumed that on digital platforms, citizens are inclined to provide more support to projects with a social benefit than to those without such an orientation, with significant ethical implications for the common good. Yet, extant empirical evidence regarding such a claim is still inconclusive. To advance this discussion, the present paper analyzes the conditions that influence crowd support for projects (...) displaying a pro-social orientation on a reward-based crowdfunding platform. To build our hypotheses, we adopt the lens of framing theory, and we relate it to the digital context. Beginning from the premise that, on crowdfunding platforms, information about projects has a hierarchical structure, we argue that a project’s success crucially depends on how much its proponent emphasizes the pro-social cues within this structure. Moreover, we propose that because pro-social cues demarcate a project over others, the effectiveness of pro-social framing is enhanced when the number of projects on the platform, i.e., its crowdedness, increases. Logit estimates on 8631 Kickstarter projects indicate that pro-social framing is positively associated with success as we expected, yet only when it is moderately emphasized. Further, we find that crowdedness on the platform positively moderates the effect of pro-social orientation on success. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The EU proposal for the Artificial Intelligence Act (AIA) defines four risk categories: unacceptable, high, limited, and minimal. However, as these categories statically depend on broad fields of application of AI, the risk magnitude may be wrongly estimated, and the AIA may not be enforced effectively. This problem is particularly challenging when it comes to regulating general-purpose AI (GPAI), which has versatile and often unpredictable applications. Recent amendments to the compromise text, though introducing context-specific assessments, remain insufficient. To address this, (...) we propose applying the risk categories to specific AI scenarios, rather than solely to fields of application, using a risk assessment model that integrates the AIA with the risk approach arising from the Intergovernmental Panel on Climate Change (IPCC) and related literature. This model enables the estimation of the magnitude of AI risk by considering the interaction between (a) risk determinants, (b) individual drivers of determinants, and (c) multiple risk types. We use large language models (LLMs) as an example. (shrink)

Even though the link between perceived corporate social responsibility fit and corporate reputation has received much attention from scholars, this tradition has ignored that the underpinnings of this association vary depending on the particular characteristics of each industry under study. To delve into this matter, we investigate in the increasingly relevant context of controversial industries how PCSR-fit could enhance corporate reputation and which are the mediating mechanisms of this association. Our academic contribution is twofold. First, we find that controversial sectors (...) indeed can increase corporate reputation through CSR activities. However, we find that to achieve this goal, the nature of PCSR-fit should be different than what extant literature indicates, because companies in these settings should directly focus on avoiding or reducing their inherent controversial harm or impact. Second, we evidence that “CSR initiatives' legitimacy” and “situational skepticism” mediate the PCSR-fit and corporate reputation relationship in CIs. Therefore, we further unravel the underpinnings of this association to advance what we know on the matter and aid practitioners in this particular context. (shrink)

The EU Artificial Intelligence Act (AIA) defines four risk categories for AI systems: unacceptable, high, limited, and minimal. However, it lacks a clear methodology for the assessment of these risks in concrete situations. Risks are broadly categorized based on the application areas of AI systems and ambiguous risk factors. This paper suggests a methodology for assessing AI risk magnitudes, focusing on the construction of real-world risk scenarios. To this scope, we propose to integrate the AIA with a framework developed by (...) the Intergovernmental Panel on Climate Change (IPCC) reports and related literature. This approach enables a nuanced analysis of AI risk by exploring the interplay between (a) risk determinants, (b) individual drivers of determinants, and (c) multiple risk types. We further refine the proposed methodology by applying a proportionality test to balance the competing values involved in AI risk assessment. Finally, we present three uses of this approach under the AIA: to implement the Regulation, to assess the significance of risks, and to develop internal risk management systems for AI deployers. (shrink)

The present article is framed within the biosemiotic glossary project as a way to address common terminology within biosemiotic research. The glossary integrates the view of the members of the biosemiotic community through a standard survey and a literature review. The concept of ‘semiotic threshold’ was first introduced by Umberto Eco, defining it as a boundary between semiotic and non-semiotic areas. We review here the concept of ‘semiotic threshold’, first describing its denotation within semiotics via an examination on the history (...) of the concept, its synonyms, antonyms, etymology, usage in other languages and context in which it is used. Then we present a general overview of the survey among researchers, analyzing the difference in responses for the concept of ‘lower semiotic threshold’ and related concepts. From the answers we also review the difference between the general usage of ‘semiotic threshold’ versus its specific use within biosemiotics, and attempt to make a general synthesis of the concept taking into account what we have learned from the survey and the literature review. (shrink)

Given two (positive) equivalence relations ∼ 1 , ∼ 2 on the set ω of natural numbers, we say that ∼ 1 is m-reducible to ∼ 2 if there exists a total recursive function h such that for every x, y ∈ ω, we have $x \sim_1 y \operatorname{iff} hx \sim_2 hy$ . We prove that the equivalence relation induced in ω by a positive precomplete numeration is complete with respect to this reducibility (and, moreover, a "uniformity property" holds). This (...) result allows us to state a classification theorem for positive equivalence relations (Theorem 2). We show that there exist nonisomorphic positive equivalence relations which are complete with respect to the above reducibility; in particular, we discuss the provable equivalence of a strong enough theory: this relation is complete with respect to reducibility but it does not correspond to a precomplete numeration. From this fact we deduce that an equivalence relation on ω can be strongly represented by a formula (see Definition 8) iff it is positive. At last, we interpret the situation from a topological point of view. Among other things, we generalize a result of Visser by showing that the topological space corresponding to a partition in e.i. sets is irreducible and we prove that the set of equivalence classes of true sentences is dense in the Lindenbaum algebra of the theory. (shrink)

For elite athletes seeking a winning advantage, manipulation of their own genetic code has become a realistic possibility. In Genetic Technology and Sport, experts from sports science, genetics, philosophy, ethics, and international sports administration describe the potential applications of the new technology and debate the questions surrounding its use.

This volume serves as a reference on the field of cognitive semantics. It offers a systematic and original discussion of the issues at the core of the debate in semiotics and the cognitive sciences. It takes into account the problems of representation, the nature of mind, the structure of perception, beliefs associated with habits, social cognition, autism, intersubjectivity and subjectivity. The chapters in this volume present the foundation of semiotics as a theory of cognition, offer a semiotic model of cognitive (...) integration that combines Enactivism and the Extended Mind Theory, and investigate the role of imagination as the origin of perception. The author develops an account of beliefs that are associated with habits and meaning, grounded in Pragmatism, testing his Narrative Practice Semiotic Hypothesis on persons with autism spectrum disorders. He also integrates his ideas about the formation of the theory of mind with a theory of subjectivity, understood as self-consciousness which derives from semiotic cognitive abilities. This text appeals to students, professors and researchers in the field. (shrink)

On the basis of arguments showing that none of the most influential analyses of Moore's paradox yields a successful resolution of the problem, a new analysis of it is offered. It is argued that, in attempting to render verdicts of either inconsistency or self-contradiction or self-refutation, those analyses have all failed to satisfactorily explain why a Moore-paradoxical proposition is such that it cannot be rationally believed. According to the proposed solution put forward here, a Moore-paradoxical proposition is one for which (...) the believer can have no non-overridden evidence. The arguments for this claim make use of some of Peter Klein's views on epistemic defeasibility. It is further suggested that this proposal may have important meta-epistemological implications. (shrink)

This commentary draws upon the author's experience in bioethics and as a physician, ordained Rabbi, and certified Mohel (a Jewish professional qualified to perform infant male circumcisions (MC)). People's identity and adherence to a religious belief are frequently cited reasons for deciding whether to circumcise their male children. For Jewish and Muslim males, circumcision is considered essential. In this commentary, the author uses his medical, religious, and bioethical knowledge, expertise, and experience to address common arguments used in opposing nontherapeutic male (...) circumcision of minors. In these narratives, half of the parents agreed with circumcision, and half did not. The parents against circumcision cite human rights violations, security, privacy, and bodily integrity issues and refer to circumcision as genital mutilation, while those who agree argue that circumcision should be done for religious reasons to prevent health issues, promote hygiene and cleanness, avoid cancer, or for later sexual enjoyment. After evaluating the evidence, the author states that parents should be free to either consent or decline MC for a son. Though a reoccurring theme in these narratives was for mothers to leave the circumcision decision up to their male partners, the author concludes that women have considerable power regarding the decision. (shrink)

It is well known that, in Peano arithmetic, there exists a formula Theor (x) which numerates the set of theorems. By Gödel's and Löb's results, we have that Theor (˹p˺) ≡ p implies p is a theorem ∼Theor (˹p˺) ≡ p implies p is provably equivalent to Theor (˹0 = 1˺). Therefore, the considered "equations" admit, up to provable equivalence, only one solution. In this paper we prove (Corollary 1) that, in general, if P (x) is an arbitrary formula built (...) from Theor (x), then the fixed-point of P (x) (which exists by the diagonalization lemma) is unique up to provable equivalence. This result is settled referring to the concept of diagonalizable algebra (see Introduction). (shrink)