In this article, we analyse the ontological import of adding classes to set theories. We assume that this increment is well represented by going from ZF system to NBG. We thus consider the standard techniques of reducing one system to the other. Novak proved that from a model of ZF we can build a model of NBG (and vice versa), while Shoenfield have shown that from a proof in NBG of a set-sentence we can generate a proof in ZF of (...) the same formula. We argue that the first makes use of a too strong metatheory. Although meaningful, this symmetrical reduction does not equate the ontological content of the theories. The strong metatheory levels the two theories. Moreover, we will modernize Shoenfields proof, emphasizing its relation to Herbrands theorem and that it can only be seen as a partial type of reduction. In contrast with symmetrical reductions, we believe that asymmetrical relations are powerful tools for comparing ontological content. In virtue of this, we prove that there is no interpretation of NBG in ZF, while NBG trivially interprets ZF. This challenges the standard view that the two systems have the same ontological content. (shrink)

Interpretations are generally regarded as the formal representation of the concept of translation.We do not subscribe to this view. A translation method must indeed establish relative consistency or have some uniformity. These are requirements of a translation. Yet, one can both be more strict or more flexible than interpretations are. In this article, we will define a general scheme translation. It should incorporate interpretations but also be compatible with more flexible methods. By doing so, we want to account for methods (...) that seem to imply a sense of translation but are not reducible to interpretations. The main example will be the relative consistent proof between ZF and NBG given by Novak (1950). Further, we will explore a way of combining interpretations. This should account for truth conditions discarded by interpretations in translated theories. (shrink)

In this article, instead of taking a particular method as translation, we ask: what does one expect to do with a translation? The answer to this question will reveal, though, that none of the first order methods are capable of fully represent the required transference of ontological commitments. Lastly, we will show that this view on translation enlarge considerably the scope of translatable, and, therefore, ontologically comparable theories.

Is consistency the sort of thing that could provide a guide to mathematical ontology? If so, which notion of consistency suits this purpose? Mark Balaguer holds such a view in the context of platonism, the view that mathematical objects are non-causal, non-spatiotemporal, and non-mental. For the purposes of this paper, we will examine several notions of consistency with respect to how they can provide a platon-ist epistemology of mathematics. Only a Gödelian notion, we suggest, can provide a satisfactory guide to (...) a platonist ontology. Is consistency the sort of thing that could provide a guide to mathematical ontology? If so, which notion of consistency suits this purpose? Mark Bala-guer holds such a view in the context of platonism, the view that mathematical objects are non-causal, non-spatiotemporal, and non-mental. Balaguer's version of Platonism, Full-Blooded Platonism (FBP), is the view that "there are as many abstract mathematical objects as there could be-i.e., there actually exist abstract mathematical objects of all possible kinds" (Balaguer, 2017, p. 381). He continues: Since FBP says that there are abstract mathematical objects of all possible kinds, it follows that if FBP is true, then every purely mathematical theory that could be true-i.e., that is internally consistent-accurately describes some collection of actually existing abstract objects. Thus it follows from FBP that in order to acquire knowledge of abstract objects, all we have to do is come up with an internally consistent purely mathematical theory (and know that it is internally consistent). (Balaguer, 2017, p. 381) * To be published in 43rd International Wittgenstein Symposium proceedings. (shrink)

Often ZF practice includes the use of the meta-theoretical notion of classes as shorthand expressions or in order to simplify the understanding of conceptual resources. NBG theory expresses formally the internalization of this feature in set theory; in this case, classes, before used metatheoretically, will also be captured by quantifiers of the first order theory. Never- theless there is a widespread opinion that this internalization of classes is harmless. In this context, it is common to refer to the conservativeness of (...) NBG in relation to ZF as a sufficient condition to understand those theories as “equivalent”, attributing a sense of virtuality to the use of classes quantified in NBG. We believe, however, that a technique used to estab- lish relationships between theories is not necessarily neutral in relation to its results - so a conservativeness established through models have different meaning and depth of that rela- tionship established by finitary interpretations. We believe, therefore, that the way in which relationships between theories are established influences the analysis result. In the case of the relationship between NBG and ZF, since NBG is finitely axiomatizible and ZF not, we believe that we have sufficient reasons to assert that the use of different analysis tools may re- veal differences such as expressiveness, ontological commitment and logical conservativeness. Therefore, this project aims to clarify the relationship between these two theories through triangulations between them and the different analysis tools. The use of finitary techniques, in this case, may prove greater expressiveness and ontological commitment of NBG in relation to ZF - relation obscured by an infinitary approach. We believe that, through this research, we can contribute to the debate on the basis of mathematics, denaturalizing the supposedly “equivalent” use of NBG and ZF for this purpose. (shrink)

Philosophers of perception frequently assume that we see actual states of affairs, or facts. Call this claim factualism. In his book, William Fish suggests that factualism is supported by phenomenological observation as well as by experimental studies on multiple object tracking and dynamic feature-object integration. In this paper, I examine the alleged evidence for factualism, focusing mainly on object detection and tracking. I argue that there is no scientific evidence for factualism. This conclusion has implications for studies on the phenomenology (...) and epistemology of visual perception. (shrink)

The sensorimotor theory of vision and visual consciousness is often described as a radical alternative to the computational and connectionist orthodoxy in the study of visual perception. However, it is far from clear whether the theory represents a significant departure from orthodox approaches or whether it is an enrichment of it. In this study, I tackle this issue by focusing on the explanatory structure of the sensorimotor theory. I argue that the standard formulation of the theory subscribes to the same (...) theses of the dynamical hypothesis and that it affords covering-law explanations. This however exposes the theory to the mere description worry and generates a puzzle about the role of representations. I then argue that the sensorimotor theory is compatible with a mechanistic framework, and show how this can overcome the mere description worry and solve the problem of the explanatory role of representations. By doing so, it will be shown that the theory should be understood as an enrichment of the orthodoxy, rather than an alternative. (shrink)

Ang kakayahan ng mga mag-aaral sa paggamit ng wikang Filipino ay nararapat lamang na malinang nang lubusan ng mga tagapagturong may sapat na kasanayan. Ang pag-aaral na ito ay gumamit ng pagsusuring palarawan, upang malinaw na makita ang saloobin ng mga mag-aaral sa paggamit ng Filipino sa paraan na pagpapahayag ng kanilang saloobin. Nilayon ng pag-aaral na ito na malaman ang saloobin ng mga mag-aaral hinggil sa paggamit ng Filipino sa mga piling asignatura ng GEC (General Education Subject) kabilang dito (...) ang GEC 5 (Purposive Communication), GEC 2 (Readings in Philippine History), GEC 1 (Understanding The Self) at GEM 14 (The Life and Works of Rizal). Sinusuri rin dito ang mga uri ng pag-uulat, mga sulatin at proyekto sa naging negatibong saloobin ng mga mag-aaral sa paggamit ng wikang Filipino. At bilang midyum sa mga piling asignatura, 33 o 27.50% ng mga mag-aaral ay may negatibong tugon samantalang (87 o 72.50%) karamihan ay nagsabi na kailangan, mahalaga, nakatutulong, madaling gamitin, at gamitin pa sa ibang asignatura. Ang mga respondent ay napatunayan na batid nila na ang paggamit ng Filipino ay isa sa mga wikang panturo sa mga piling asignatura sa antas tersarya at ang walang pagkakaibang saloobin ng mga mag-aaral sa paggamit ng Filipino ay nagpapakita ng kanilang positibong pagtanggap sa Filipino ay kinakailangan sa kanilang pagkatuto. Batay sa kinalabasan ng pag-aaral, ang mga mag-aaral ay kailangang mabigyan ng mga kaukulang gawain kaugnay sa wika upang mapahalagahan ang kanilang saloobin at lalong magamit ang wikang Filipino bilang unang wika sa paraang pasulat at pasalita. (shrink)

Cognitive representations are typically analysed in terms of content, vehicle and format. While current work on formats appeals to intuitions about external representations, such as words and maps, in this paper we develop a computational view of formats that does not rely on intuitions. In our view, formats are individuated by the computational profiles of vehicles, i.e., the set of constraints that fix the computational transformations vehicles can undergo. The resulting picture is strongly pluralistic, it makes space for a variety (...) of different formats, and is intimately tied to the computational approach to cognition in cognitive science and artificial intelligence. (shrink)

The aim of this work is to expose the Cartesian Model of the mind in Cognitive Archaeology and point out how it relates to the questions behind this branch of archaeology. Based on this, some of the premises assumed by the Cartesian Model and how they influence the formulation to the problem of epistemological relativism in the branch are explained. According to this problem, since there is no way to evaluate hypotheses in this research area, the investigations on cognition, based (...) on archaeological evidence, are unjustified. Finally, some alternative approaches to the Cartesian Model and its research agendas are summarized. (shrink)

Many artists, art critics, and poets suggest that an aesthetic appreciation of artworks may modify our perception of the world, including quotidian things and scenes. I call this Art-to-World, AtW. Focusing on visual artworks, in this paper I articulate an empirically-informed account of AtW that is based on content-related views of aesthetic experience, and on Goodman’s and Elgin’s concept of exemplification. An aesthetic encounter with artworks demands paying attention to its aesthetic, expressive, or design properties that realize its purpose. Attention (...) to these properties make percipients better able to spot them in other entities and scenes as well. The upshot is that an aesthetic commerce with artworks enlarges the scope of what we are able to see and has therefore momentous epistemic consequences. (shrink)

En el artículo se defiende que si se acepta la superación entre fundacionismo y coherentismo que plantea Ernest Sosa y se sostiene una teoría de la justificación epistémica basada en el ejercicio de virtudes intelectuales, esta no es condición suficiente para usar el razonamiento analógico en la investigación arqueológica. Por ende, aunque se puede sostener su necesidad para utilizar la analogía, no es suficiente a menos que se recurra a la virtud de la responsabilidad (Code) como eje de la justificación (...) epistémica. Finalmente se discute su viabilidad e importancia para el caso de la arqueología en México. (shrink)

Introduction to the topical collection "The Structure of Perceptual Objects"—with contributions by Mohan Matthen, EJ Green, Alisa Mandrigin, Blazej Skrzypulec, and Anna Drożdżowicz.

Many artists, art critics, and poets suggest that an aesthetic appreciation of artworks may modify our perception of the world, including quotidian things and scenes. I call this Art-to-World, AtW. Focusing on visual artworks, in this paper I articulate an empirically-informed account of AtW that is based on content related views of aesthetic experience, and on Goodman’s and Elgin’s concept of exemplification. An aesthetic encounter with artworks demands paying attention to its aesthetic, expressive, or design properties that realize its purpose. (...) Attention to these properties make percipients better able to spot them in other entities and scenes as well. The upshot is that an aesthetic commerce with artworks enlarges the scope of what we are able to see and has therefore momentous epistemic consequences. (shrink)

At the beginning of the 20th century, Gestalt psychologists put forward the concept of psychoneural isomorphism, which was meant to replace Fechner’s obscure notion of psychophysical parallelism and provide a heuristics that may facilitate the search for the neural correlates of the mind. However, the concept has generated much confusion in the debate, and today its role is still unclear. In this contribution, I will attempt a little conceptual spadework in clarifying the concept of psychoneural isomorphism, focusing exclusively on conscious (...) visual perceptual experience and its neural correlates. Firstly, I will outline the history of our concept, and its alleged metaphysical and epistemic roles. Then, I will clarify the nature of isomorphism and rule out its metaphysical role. Finally, I will review some epistemic roles of our concept, zooming in on the work of Jean Petitot, and suggest that it does not play a relevant heuristic role. I conclude suggesting that psychoneural isomorphism might be an indicator of robustness for certain mathematical descriptions of perceptual content. (shrink)

Tras analizar sucintamente las consecuencias científicas y filosóficas de la identidad mente-cerebro, se señalan argumentos a favor y en contra de mantener el debate mente-cerebro. En particular se consideran las nuevas técnicas de exploración del cerebro como argumento en contra de tal debate. Las deficiencias e insuficiencias de tales técnicas aconsejan mantener el debate mente-cerebro y no asumir el materialismo.

According to the sensorimotor account, vision does not imply theconstruction of internally generated representations of the environment, butit isthe skillful exercise of the sensorimotor contingencies obeying sense-specific laws. In this short study, I focus on the notion of “sensorimotor law” and characterize the kind of explanation providedby the sensorimotor theory as a form of covering law model. I then question the nature of such sensorimotor laws and describe them as mechanisms. I show that a mechanistic interpretation provides a better account (...) of the sensorimotor invariances, which fosters us to rebalance the explanatory burden of sensorimotor action and information. Finally, I show that the question of the roleof representations within the sensorimotor theory should be reconsidered. (shrink)

I argue for a manipulationist-mechanistic framework for content-NCC research in the case of visual consciousness (Bechtel 2008; Neisser 2012). Reference to mechanisms is common in the NCC research. Furthermore, recent developments in non-invasive brain stimulation techniques (NIBS) lend support to a manipulationist standpoint. The crucial question is to understand what is changed after manipulation of a brain mechanism. In the second part of the paper I review the literature on intentionalism, and argue that intervention on the neural mechanism is likely (...) to change the intentional content of consciousness. This urges us to shift from content-NCC to what I call “intentional mechanisms”. Such mechanisms, it is argued, should be understood as neural prerequisites of conscious visual experience. (shrink)

This paper is aimed to indicate two new possible Descartes’ sources. As far as the Cartesian theory of free creation of eternal truths is concerned, this doctrine has often been considered as a reaction to the thought of Francisco Suárez. In this article, we tried to demonstrate that there is the possibility of extending the domain of Cartesian references. In this regard, we have focused on Pedro da Fonseca and the Coimbra Commentaries, trying to point out some additional sources in (...) the Cartesian reflection. (shrink)

discussion of contemporary theories of self-consciousness.

Contemporary theories of consciousness are based on widely different concepts of its nature, most or all of which probably embody aspects of the truth about it. Starting with a concept of consciousness indicated by the phrase “the feeling of what happens” (the title of a book by Antonio Damásio), we attempt to build a framework capable of supporting and resolving divergent views. We picture consciousness in terms of Reality experiencing itself from the perspective of cognitive agents. Each conscious experience is (...) regarded as composed of momentary feeling events that are combined by recognition and evaluation into extended conscious episodes that bind cognitive contents with a wide range of apparent durations (0.1 secs to 2 or more secs, for us humans, depending on circumstances and context). Three necessary conditions for the existence of consciousness are identified: a) a ground of Reality, envisaged as an universal field of potentiality encompassing all possible manifestations, whether material or 'mental'; b) a transitional zone, leading to; c) a manifest world with its fundamental divisions into material, 'informational' and quale-endowed aspects. We explore ideas about the nature of these necessary conditions, how they may relate to one another and whether our suggestions have empirical implications. (shrink)

Nesta comunicação pretende-se desenvolver a relação entre violência e política enquadrada no pensamento de Hannah Arendt e a partir de duas obras fundamentais, On Revolution (1963) e On Violence (1970). Investigando-se sobre o que constitui cada experiência em particular, a da violência (ainda que sob a forma da guerra ou da revolução) e a da política, esta relação permitirá equacionar criticamente as possibilidades e os limites das sociedades democráticas actuais como o resultado da tradição política e das revoluções da modernidade.

This study examines the impact of Islamic Work Ethic on organizational citizenship behaviors and knowledge-sharing behaviors among university employees in Pakistan. A total of 215 respondents from public sector educational institutions participated in this research. The findings suggest that IWE has a positive effect on OCBs. In other words, individuals with high IWE demonstrate more citizenship behaviors than those with low IWE. The findings also suggest a positive effect of IWE on KSBs. Individuals with high IWE exhibit more KSBs than (...) those with low IWE. The paper also discusses the theoretical and practical implications of these findings. (shrink)

This study focused on determining the attitudes and academic performance of engineering students in Technological University of the Philippines-Manila. A total of 139 male engineering and 47 female engineering students were the respondents of the study. This only dwell on the attitude in learning English Language Vocabulary in terms of their behavioral aspects, cognitive aspects, and emotional aspects. This is a quantitative study utilized by descriptive and inferential method as the research design. Based on the findings, academic grades strongly correlate (...) with their attitude in learning English vocabulary which is a negative correlation coefficient in all its components with r value of -0.3695 in behavioral, -0.5261 in Cognitive, and -0.4332 in emotional aspect. Their P values is less than .00001 which is significant at p<0.05. Thus, the null hypothesis where there is no significant relationship between their ALEV and academic performance is rejected. The researcher recommends that teachers should enhance creativity in teaching vocabulary which inculcate the positive attitudes and motivation towards learning process. Teachers and parents should encourage the learners to read and watch educational related materials. (shrink)

The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the relativity of mathematical languages used to describe the Turing machines. A deep investigation is performed on the interrelations between mechanical computations and their mathematical descriptions emerging when a human (the researcher) starts to describe a Turing machine (the object of the study) by (...) different mathematical languages (the instruments of investigation). Together with traditional mathematical languages using such concepts as ‘enumerable sets’ and ‘continuum’ a new computational methodology allowing one to measure the number of elements of different infinite sets is used in this paper. It is shown how mathematical languages used to describe the machines limit our possibilities to observe them. In particular, notions of observable deterministic and non-deterministic Turing machines are introduced and conditions ensuring that the latter can be simulated by the former are established. (shrink)

The paper investigates how the mathematical languages used to describe and to observe automatic computations influence the accuracy of the obtained results. In particular, we focus our attention on Single and Multi-tape Turing machines which are described and observed through the lens of a new mathematical language which is strongly based on three methodological ideas borrowed from Physics and applied to Mathematics, namely: the distinction between the object (we speak here about a mathematical object) of an observation and the instrument (...) used for this observation; interrelations holding between the object and the tool used for the observation; the accuracy of the observation determined by the tool. Results of the observation executed by the traditional and new languages are compared and discussed. (shrink)

¿Llegarán los ordenadores a sustituir a los seres humanos? Lo que hasta hace unas décadas parecía una pregunta de ciencia-ficción, es ahora defendido con seriedad por algunos especialistas en inteligencia artificial. El presente articulo dibuja las más importantes líneas de investigación en este campo y las posiciones más relevantes respecto de la relación hombre-maquina pensante. La conclusión que propone el autor supone una decidida apuesta por un humanismo en el que quepa integrar el desarrollo tecnológico sin perder de vista sus (...) innegables implicaciones éticas. (shrink)

This paper expands on the notion of "moral conversion" (advanced by Bernard Lonergan but underdeveloped in his work) by developing a typology that uses two "cross-hatching" criteria. First, it distinguishes between moral conversions that have to do with a person's relation to moral obligation, good and evil, and between moral conversions that have to do with how a person regards the question of happiness and the meaning of life. Secondly, it distinguishes between conversions regarding the _content_ (what is good/evil or (...) the meaning of life?), regarding _attitude_ (becoming committed to doing good or to the meaning-seeking process), and regarding _coherence_ (conforming one's actual life to what is understood to be right/wrong or meaning-giving). Combining both criteria leaves us with six types of moral conversion. Each type is then illustrated and supported with concrete real-life narratives. I conclude with an attempt at a definition of moral conversion that includes all types. The article is a summary of Chapter 5 of my dissertation (2008) "Narratives of Hope: A Philosophical Study of Moral Conversion.". (shrink)

A Teoria dos Dois Sistemas, proposta por Kahneman (2011), pressupõe que a tomada de decisão no contexto econômico se baseia em dois sistemas, um que é automático, intuitivo e principalmente inconsciente e outro reflexivo, racional e totalmente consciente. Consideramos a abordagem kahnemaniana incompleta na medida em que a concepção dos sistemas 1 e 2 não é suficiente para explicar os processos de tomada de decisão. Neste artigo, nosso desafio é mostrar que, diferentemente dos sistemas de Kahneman, a tomada de decisão (...) está ancorada na percepção direta de affordances e é a base das escolhas conceituais, que envolvem experiências sensório-motoras advindas da reciprocidade entre agente e ambiente. Concluímos este artigo, argumentando que, diferentemente da concepção de sistema 1 kahnemaniano, na perspectiva ecológica, a tomada de decisão advém de experiências não conceituais, da percepção direta, não automática, sem envolver representações mentais e processamento de informações. (shrink)

Kahneman's theory of two systems assumes that human decision making in Economy is based on two cognitive systems, one that is automatic, intuitive and mostly unconscious, and one that is reflexive, rational and fully conscious. The authors consider Kahneman’s approach incomplete and limited in accounting for the creativity of embodied agents grasping the opportunities afforded by physical and social environments. This limitation leads us to argue for the existence of a third system in decision making in Economy, the creative intuition (...) based on direct perception of affordances, addressing not only the dispositions and goals of agents but also the social and environmental responsibility of corporations and governments. The authors argue that the third decision-making system the authors propose implies a concept of intuition that is different from the type of association process discussed by Morewedge and Kahneman [2] and gives an example of the third system operation, the Bolsa Família in Brazil, and finding new options for the funding of similar programs. (shrink)

A teoria dos dois sistemas (Kahneman, 2011), em suas várias vertentes, assume que a tomada de decisão humana é baseada em dois sistemas cognitivos: um que é automático, rápido, agindo com mínimo esforço cognitivo, intuitivo (no sentido de Morewedge & Kahneman, 2010), e majoritariamente inconsciente; e outro que é reflexivo, lento, atuando com intenso esforço cognitivo, racional e totalmente consciente. Neste trabalho, investigamos a teoria dos dois sistemas e sua aplicação na tomada de decisão econômica em governos democráticos, com ênfase (...) especial na proposta de Kahneman. Consideramos sua abordagem incompleta e limitada na explicação do processo intuitivo que orienta a tomada de decisão. Essa limitação nos leva a defender a existência de um terceiro sistema de tomada de decisão em Economia: a intuição ecológica criativa, baseada no attunement entre affective drives e percepção direta de affordances, abordando não só as disposições e objetivos dos agentes, mas também a responsabilidade socioambiental das empresas e governos. Argumentamos que o terceiro sistema de tomada de decisão que propomos implica um conceito de intuição diferente do associativismo de ideias de Simon (1992), e damos como exemplo do funcionamento do terceiro sistema o processo de tomada de decisão que conduziu à formação do Banco Finapop, no Brasil. (shrink)

We propose that Saussure’s signifiers must be processed in the left brain hemisphere (in right handed people) and the signified may be processed in the right. This proposition has consequences for understanding human cognitive phenomena and their pathologies, and can also be related to the passive and active process of thinking, as described by Karl Jaspers. Saussure studied signifiers and their relationships. He left the signified to be studied by psychologists, but there is no consensus about it. According to some (...) linguists, the signified, or the meaning, is the specific activity or succession of bodily states related to each signifier. Learning is the process of linking a signifier (a represented object) to a signified or meaning (a specific activity). However, human beings can represent signifiers autonomously because words and drawings are easily produced with small movements and have syntactic, referential and logical rules of combination. If they are processed in the left hemisphere, the meaning (the signified) is only found when the right hemisphere is reached. The right hemisphere can also work independently, as for instance, when we imagine a story which has to find the words in the left hemisphere. The complex relationship between the hemispheres through the corpus callosum is decisive for telling stories and having self-consciousness. (shrink)

In epoca medievale si è molto discusso su alcuni concetti chiave come prova o giustificazione. La teoria della prova contenuta nei trattati di logica medievale prende il nome tecnico di consequentia, che è un tipo di ragionamento fondato sul passaggio dalla concessione (o negazione) di uno o più enunciati denominati antecedenti alla concessione (o negazione) di uno o più enunciati denominati conseguenti. Questo tipo di teoria ha avuto un correlato a livello dei singoli termini che compongono l’enunciato all'interno della teoria (...) nota come suppositio terminorum. Prende, infatti, il nome di descensus, la regola che permette la verifica del passaggio da un termine maggiore (un termine comune) ad un termine minore (che denota individui). La stessa definizione di alcune ramificazioni della teoria della suppositio è col-legata alla possibilità di ammettere o meno il descensus cioè questa "discesa" da un termine comune ad una congiunzione o disgiunzione di termini singolari. Il presente lavoro intende descrivere la teoria del descensus come un tipo particolare di consequentia mostrandone le connessioni con le moderne tecniche logiche. I trattati che si affronteranno appartengono al XIV e al XV secolo, cioè ad un periodo caratterizzato da una sistemazione della materia che li rende confrontabili con un quadro teorico unitario. (shrink)

Il volume intende presentare in una prospettiva organica la letteratura medievale sugli Insolubilia. Gli insolubili sono stati definiti come proposizioni autoreferenziali che hanno origine direttamente dalla tradizione del paradosso del mentitore. L’impostazione del presente lavoro vuole essere sia filologica che teorica in modo che da un lato si possano inserire le analisi speculative sugli Insolubilia in un contesto critico–storico più ampio che restituisca la peculiarità della trattazione medievale, e dall’altro, possa essere effettuata una analisi precisa dei tentativi di soluzione proposti (...) anche attraverso gli strumenti della logica moderna (quando possibile e non fuorviante). (shrink)

Since the 1980's, the influence of context-based curricula has been growing in curricula and has been taking place in advance of improving the image of chemistry. This article argues that chemical societies should focus on a better understanding of the negative image of chemistry, by supporting historical and philosophical research. Based on that, chemistry curricula should change.

This was a little course of 4 weeks, in which we tried to develop some basic ideas about the proofs related to the properties of logarithms.

Notes from a quick course of 4 weeks, emphasizing the importance of proofs in an introductory course on logarithm, for high school students.