Cantor’s theory of cardinal numbers offers a way to generalize arithmetic from finite sets to infinite sets using the notion of one-to-one association between two sets. As is well known, all countable infinite sets have the same ‘size’ in this account, namely that of the cardinality of the natural numbers. However, throughout the history of reflections on infinity another powerful intuition has played a major role: if a collectionAis properly included in a collectionBthen the ‘size’ ofAshould be less than the (...) ‘size’ ofB(part–whole principle). This second intuition was not developed mathematically in a satisfactory way until quite recently. In this article I begin by reviewing the contributions of some thinkers who argued in favor of the assignment of different sizes to infinite collections of natural numbers (Thabit ibn Qurra, Grosseteste, Maignan, Bolzano). Then, I review some recent mathematical developments that generalize the part–whole principle to infinite sets in a coherent fashion (Katz, Benci, Di Nasso, Forti). Finally, I show how these new developments are important for a proper evaluation of a number of positions in philosophy of mathematics which argue either for the inevitability of the Cantorian notion of infinite number (Gödel) or for the rational nature of the Cantorian generalization as opposed to that, based on the part–whole principle, envisaged by Bolzano (Kitcher). (shrink)

The COVID-19 pandemic is an unprecedented event entailing long-term consequences on population health and welfare. Those who contracted the coronavirus may have suffered from both physical and mental health issues that unfold the need for tailored intervention strategies. Hence, our study aims to investigate the psychological and social consequences of COVID-19 on a sample of 86 participants, encompassing 43 patients recruited from Bari University Hospital, 19 of whom were hospitalized due to the disease. The remaining 43 were individuals not fallen (...) ill with COVID-19 to date. The investigation yielded significant gender differences in post-traumatic stress symptoms, depression, and representation of interpersonal distance, evaluated through the IES-R, the BDI-II, and the IVAS task, respectively. This pattern of results was not replicated in the control group. In general, participants who reported having experienced the most intense post-traumatic symptoms also presented a greater mood deflection and, more specifically, within the clinical group women obtained the highest scores on both scales. Women reported higher IES-R and BDI-II scores compared to men, that could indicate that women who have contracted COVID-19 are more exposed to post-traumatic and depressive symptoms. Our results also showed a significant effect of COVID-19 on IPD with a tendency of disease-experienced individuals to increase their preferred IPD from adults, children, and elderly people. Regarding gender differences in mood and proxemic behavior, a correlation between depressive symptoms and probable PTSD and a further correlation between probable PTSD and greater IPD were found in women from both clinical and control group. Overall, these findings might contribute to a better understanding of gender-based implications of the current pandemic on mental health, also leading to the development of integrated yet personalized intervention strategies. (shrink)

Scientific literature on particular themes in ontology is extremely abundant, but it is often very hard for freshmen or sophomores to find a red thread between the various proposals. This text is an opinionated introduction, a preliminary text to research in ontology from the so called standard approach to ontological commitment, that is from the particular point of view that connects ontological questions to quantificational questions. It offers a survey of this viewpoint in ontology together with their possible applications through (...) a broad array of examples and open problems and, at the same time, essential references to the classics of philosophy, so as to allow non-specialists to understand the terms and analysis procedures characterizing the discipline. Its result is a wide-ranging overview of the issued tackled by ontology, with a particular focus on the most relevant problems of contemporary debate. (shrink)

We review several of de Finetti’s fundamental contributions where these have played and continue to play an important role in the development of imprecise probability research. Also, we discuss de Finetti’s few, but mostly critical remarks about the prospects for a theory of imprecise probabilities, given the limited development of imprecise probability theory as that was known to him.

In the last decades, Systems Biology (including cancer research) has been driven by technology, statistical modelling and bioinformatics. In this paper we try to bring biological and philosophical thinking back. We thus aim at making diferent traditions of thought compatible: (a) causality in epidemiology and in philosophical theorizing—notably, the “sufcient-component-cause framework” and the “mark transmission” approach; (b) new acquisitions about disease pathogenesis, e.g. the “branched model” in cancer, and the role of biomarkers in this process; (c) the burgeoning of omics (...) research, with a large number of “signals” and of associations that need to be interpreted. In the paper we summarize frst the current views on carcinogenesis, and then explore the relevance of current philosophical interpretations of “cancer causes”. We try to ofer a unifying framework to incorporate biomarkers and omic data into causal models, referring to a position called “evidential pluralism”. According to this view, causal reasoning is based on both “evidence of diference-making” (e.g. associations) and on “evidence of underlying biological mechanisms”. We conceptualize the way scientists detect and trace signals in terms of information transmission, which is a generalization of the mark transmission theory developed by philosopher Wesley Salmon. Our approach is capable of helping us conceptualize how heterogeneous factors such as micro and macro-biological and psycho-social—are causally linked. This is important not only to understand cancer etiology, but also to design public health policies that target the right causal factors at the macro-level. (shrink)

This article begins by examining the status of “difference” in representations of perspectivist cosmologies, which are themselves often represented as radically different to Euro-American cosmologi...

This article is both a comment on Neyland’s ‘On organizing algorithms’ and a supplementary note to our ‘The concept of algorithm as an interpretative key of modern rationality’. In the first part we discuss the concepts of algorithm and recursive function from a different perspective from that of our previous article. Our cultural reference for these concepts is once again computability theory. We give additional arguments in support of the idea that a culture informed by an algorithmic logic has promoted (...) modern rationality both in science and in society. We stress again the importance of distinguishing between algorithms applied to quantifiable entities such as space, time and value and those applied to ontological entities such as human actions. In the second case, the algorithm is applied outside its domain of definition and leads to social disaggregation. (shrink)

Constrained coherence is compared to coherence and its role in the behavioural interpretation of coherence is discussed. The equivalence of these two notions is proven for coherent conditional previsions, showing that the same course of reasoning applies to several similar concepts developed in the realm of imprecise probability theory.

Since the microbiological revolution, most infectious diseases have been defined and classified according to an etiologic criterion, i.e. the identification of single, external necessary causes (for example, Mycobacterium for tuberculosis). This is not the case with cancer. Not only external necessary causes of cancer have not been identified, but also the morphological classification cannot be based on univocal criteria. Although neoplasia and anaplasia appear to be universal attributes of cancer, these events are only quantitative. Neoplastic growth can be fast or (...) slow (development may take weeks or years), and tissue pathologies are difficult to detect from normal tissue in some cancers but are obvious in others. Common special properties of anaplasia appear to be concealed in the wide range of morphologies. In the absence of a coherent morphological definition, and of external necessary causes (such as bacteria for infectious diseases), a mechanistic definition could be adopted. However, unless molecular biology discovers specific mechanistic steps in carcinogenesis, which indicate the existence of necessary events in carcinogenesis, we cannot adopt a univocal (monothetic) definition of cancer. The alternative is to use a polythetic definition, according to Wittgenstein's model of a long rope twisted together out of many shorter fibres. (shrink)

The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity of second and higher-order logic. However, the epistemological significance of such investigations has not received much attention in the contemporary foundational debate.We discuss Girard’s normalization proof for second order type theory or System F and compare it with two faulty consistency arguments: the one given by Frege for the logical system of the Grundgesetze and (...) the one given by Martin-Löf for the intuitionistic type theory with a type of all types.The comparison suggests that the question of the circularity of second order logic cannot be reduced to Russell’s and Poincaré’s 1906 “vicious circle” diagnosis. Rather, it reveals a bunch of mathematical and logical ideas hidden behind the hazardous idea of impredicative quantification, constituting a vast domain for foundational research. (shrink)

More than any other philosopher, Duns Scotus and Simondon both gave extensive consideration to the relation between what is primarily common and what is primarily singular. Pointing to certain resonances between their ideas can help us to develop a theoretical model to decipher the mode of being of the contemporary multitude. This article deals with: 1. The critique that Duns Scotus and Simondon address to everyone who believes that the matter form pair can account for the process of individuation; 2. (...) The gap separating the notion of the « universal » from that of the « common », and therefore, the need to precisely define the ontological and logical status of the « common » without any surreptitious use of categories linked to the « universal 1); 3. The paradoxical relation involving both addition and subtraction - between the individuated individual and « common nature »; and 4. The question of angels , a source of enduring fame in school textbooks for Duns Scotus, re-examined here in the light of Simondon ’s concepts of « transindividuality » and of « collective individuation ». (shrink)

Journal Name: Philologus Issue: Ahead of print.

General and Formal Ontology Paolo Valore The word ontology derives from tÕ Ôn ( tò òn), which is the neutral participle of e„m. ...

Was liberalism really an outdated ideology in post-1945 European political systems, as claimed by some scholars? The great success of socialism on one side and various forms of Christian Democracy on the other could make that claim appear reasonable. In fact a closer view shows how postwar constitutions in some countries (Italy, France and Germany) presented once again fundamental liberal values, reformulated in different words. One of the roots of that difference is the gap between the Anglo-Saxon approach to liberalism, (...) which takes into account history and communities, and the continental tradition of liberalism, linked to an abstract philosophical approach and highly dependent on long-standing struggles between Churches and the body politic. (shrink)

We use Shelah's theory of possible cofinalities in order to solve some problems about ultrafilters. Theorem: Suppose that $\lambda$ is a singular cardinal, $\lambda ' \lessthan \lambda$, and the ultrafilter $D$ is $\kappa$ -decomposable for all regular cardinals $\kappa$ with $\lambda '\lessthan \kappa \lessthan \lambda$. Then $D$ is either $\lambda$-decomposable or $\lambda ^+$-decomposable. Corollary: If $\lambda$ is a singular cardinal, then an ultrafilter is ($\lambda$,$\lambda$)-regular if and only if it is either $\operator{cf} \lambda$-decomposable or $\lambda^+$-decomposable. We also give applications to (...) topological spaces and to abstract logics. (shrink)

The paper aims to describe the stakes of a Nietzschean influence on Deleuze's reflections on the transcendental and conversely to highlight the Deleuzian operation of politicising Nietzsche by ‘minorising’ him. In order to further understand such a complex relationship of becoming between Deleuze and Nietzsche, the first objective of the paper is to focus on active and reactive forces, which seem to be the core of this very relation. Thus, the paper suggests that micropolitics has its conditions of possibility in (...) the Nietzschean corpus and, in particular, in the symptomatology of decadence, resentment and nihilism. In this sense, now the title of the paper reveals its meaning: the whole Deleuzian operation could be summarised as the passage from the criticism and questioning of an image of Nietzsche ‘forbidden to minors’, typical of the interpretations of the first half of the twentieth century, to a becoming-minor of these very same Nietzschean concepts. It is precisely through such a becoming-minor that Nietzsche's diagnosis and concepts are translated in a political and emancipatory key, in order to give power to minorities. (shrink)

La struttura a livelli modella il tutto e le sue parti con grande generalità. Lo dimostrano le argomentazioni teoriche (4.3), (4.4) e (4.5), e lo comprova la casistica che è stata aggiunta. Una tale struttura non presenta affatto i problemi a), b) e c) che sono tipici della struttura ad albero. Essa corregge inoltre deviazioni concettuali che sono diffuse nel settore informatico. L’immediatezza deviazioni concettuali che sono diffuse nel settore informatico. L’immediatezza visiva, infine, ne facilita la diffusione sul piano professionale (...) e tecnico.Per concludere, ritengo che la struttura a livelli possa fornire un contributo anche alle ricerche di ontologia e in particolare possa favorire i tentativi di unificazione condotti sia sul piano teorico, sia su quello applicativo [Uschold 1996]. Le difficoltà ed i limiti che la teoria degli insiemi oppone ad un formalismo generale (ad esempio quando riduce la casistica della relazione concetto di livello possiede una valenza estremamente ampia e ciò lo predispone per gli auspicati sviluppi ontologici. (shrink)

Providing individuals with the information necessary to make informed decisions is now considered an ethical standard for health systems and general practitioners.