Nel Tesoro del Duomo di Monza si conservano tre celebri dittici eburnei relativi alla dotazione di suppellettili liturgiche di Berengario del Friuli (inizi X secolo): il dittico di Stilicone e quello del Poeta e della Musa, entrambi tardo antichi; il dittico di re Davide e san Gregorio Magno, di datazione e lettura più controverse (VI secolo ed età carolingia). Primo editore dei pezzi è Anton Francesco Gori nel secondo volume del Thesaurus veterum diptychorum consularium et ecclesiasticorum (1759), corredato di tre (...) tavole di Andrea Scacciati. Pur non avendo mai visionato i manufatti, l’erudito fiorentino dedica ad essi un’ampia disamina critica basandosi essenzialmente sugli acquerelli del pittore Girolamo Ferroni, reclutato dal marchese milanese e prezioso intermediario Alessandro Teodoro Trivulzio. Nel 1794 il padre della storiografia monzese, il canonico Anton Francesco Frisi, risolve di rieditare i dittici in apertura del terzo tomo delle sue Memorie storiche di Monza e sua corte. Consigliato da quel don Carlo Trivulzio erudito e proprietario di un ricco nucleo di avori antichi, supportato dalle modeste incisioni di Giulio Cesare Bianchi, offre una rilettura che puntualizza ed emenda in parte quanto scritto dal Gori, condita da una vena polemica contro «chi non ha esaminati personalmente i Monumenti, sui quali ragiona». Sullo sfondo del contesto culturale dell’epoca e delle personalità che vi presero parte, con l’ausilio della documentazione divisa tra la Veneranda Biblioteca Ambrosiana di Milano, l’Archivio della Fondazione Trivulzio e la Biblioteca Marucelliana di Firenze, il contributo intende proporre una ricostruzione degli avvenimenti con attenzione al rapporto tra originale (i dittici monzesi) e copia (disegni e incisioni che ne scaturirono). (shrink)

What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

The indispensability argument comes in many different versions that all reduce to a general valid schema. Providing a sound IA amounts to providing a full interpretation of the schema according to which all its premises are true. Hence, arguing whether IA is sound results in wondering whether the schema admits such an interpretation. We discuss in full details all the parameters on which the specification of the general schema may depend. In doing this, we consider how different versions of IA (...) can be obtained, also through different specifications of the notion of indispensability. We then distinguish between schematic and genuine IA, and argue that no genuine sound IA is available or easily forthcoming. We then submit that this holds also in the particularly relevant case in which indispensability is conceived as explanatory indispensability. (shrink)

Recent discussions on Fregean and neo-Fregean foundations for arithmetic and real analysis pay much attention to what is called either ‘Application Constraint’ ($AC$) or ‘Frege Constraint’ ($FC$), the requirement that a mathematical theory be so outlined that it immediately allows explaining for its applicability. We distinguish between two constraints, which we, respectively, denote by the latter of these two names, by showing how$AC$generalizes Frege’s views while$FC$comes closer to his original conceptions. Different authors diverge on the interpretation of$FC$and on whether it (...) applies to definitions of both natural and real numbers. Our aim is to trace the origins of$FC$and to explore how different understandings of it can be faithful to Frege’s views about such definitions and to his foundational program. After rehearsing the essential elements of the relevant debate (§1), we appropriately distinguish$AC$from$FC$(§2). We discuss six rationales which may motivate the adoption of different instances of$AC$and$FC$(§3). We turn to the possible interpretations of$FC$(§4), and advance a Semantic$FC$(§4.1), arguing that while it suits Frege’s definition of natural numbers (4.1.1), it cannot reasonably be imposed on definitions of real numbers (§4.1.2), for reasons only partly similar to those offered by Crispin Wright (§4.1.3). We then rehearse a recent exchange between Bob Hale and Vadim Batitzky to shed light on Frege’s conception of real numbers and magnitudes (§4.2). We argue that an Architectonic version of$FC$is indeed faithful to Frege’s definition of real numbers, and compatible with his views on natural ones. Finally, we consider how attributing different instances of$FC$to Frege and appreciating the role of the Architectonic$FC$can provide a more perspicuous understanding of his foundational program, by questioning common pictures of his logicism (§5). (shrink)

Since Saul Kripke’s and Hilary Putnam’s groundbreaking work in the Seventies, the idea has emerged that natural kind terms are semantically special among common nouns. Stephen P. Schwartz, for example, has argued that an artifactual kind term like “pencil” functions very differently from a natural kind term like “tiger.” This, however, blatantly violates a principle that I call Semantic Uniformity. In this paper, I defend the principle. In particular, I outline a picture of how natural kind terms function based on (...) Kripke’s and Putnam’s considerations, and I use it to rebut Schwartz’s arguments, showing that if it works for natural kind terms, it can work for artifactual kind terms too, or at least that Schwartz did not provide good enough reasons to the contrary. (shrink)

In this paper, I try to outline what I take to be Naming and Necessity’s fundamental legacy to my generation and those that follow, and the new perspectives it has opened up for twenty-first century philosophy. The discussion is subdivided into three sections, concerning respectively philosophy of language, metaphysics, and metaphilosophy. The general unifying theme is that Naming and Necessity is helping philosophy to recover a Golden Age, by freeing it from the strictures coming from the empiricist and Kantian traditions (...) and reconnecting it to the world and the objects that populate it. Because of this, in the concluding paragraph I tentatively suggest that Kripke’s philosophy may be seen as a sui generis form of naturalism. (shrink)

John MacFarlane promette di dare una formulazione comprensibile dell’oscura dottrina del relativismo della verità senza far ricorso ad altre nozioni che non siano quelle, chiare e ben comprese, della logica intensionale e a una generalizzazione della nozione classica di proposizione che è nota da tempo. MacFarlane ha proposto due definizioni diverse in successione. Secondo la prima, il relativismo della verità è la dottrina per cui (a) la verità di alcuni enunciati o proposizioni generalizzat...

The Test Your Memory is a brief self-administered, cognitive screening test, currently used in several settings. It requires minimal administrator supervision and the computation of the final test score takes approximately 2 min. We assessed the discrimination ability of the Italian version of the TYM in detecting Mild Cognitive Impairment in clinical setting. TYM-I was administered to 94 MCI patients and 134 healthy controls. The clinical diagnosis of MCI was considered as the gold standard. An extended formal neuropsychological test battery (...) was used to define MCI subtypes. Receiver Operating Characteristic analyses were conducted to find the optimal cut-off and measure discrimination ability of TYM-I in detecting MCI. TYM-I had a similar area under the curve point estimate as Mini Mental State Examination. A TYM-I score lower or equal to 36 was found to be optimal cut off to detect MCI. The TYM-I showed the highest discrimination ability among individuals aged more than 70 and high educational level. The amnestic MCI subtype patients, compared to non-amnestic MCI patients, had worse performance in recall, orientation and visuospatial abilities TYM-I subscores. The TYM-I is a valid screening test in detecting cognitive dysfunction, easily carried out in clinical practice. The TYM-I subscores may allow to identify amnestic and non-amnestic MCI subtypes. (shrink)

A rational subject who believes that a = b, and also believes that j, cannot at the same time disbelieve that j, i.e. believe that not-j. John Searle points out that no such constraint holds for desire and some other propositional attitudes. Which ones, exactly? Where is the divide located and what determines it? These are no minor questions, as they directly bear on the larger issue of how far rationality reaches and the extent to which practical reasoning obeys logical (...) rules. It will be argued that there is no reason for despairing that deductive logic will find a way of dealing with practical reasoning, contrary to Searle’s pessimistic attitude. (shrink)

Around 1970, both Keith Donnellan and Saul Kripke produced powerful arguments against description theories of proper names. They also offered sketches of positive accounts of proper name reference, highlighting the crucial role played by historical facts that might be unknown to the speaker. Building on these sketches, in the following years Michael Devitt elaborated his well-known causal theory of proper names. As I have argued elsewhere, however, contrary to what is commonly assumed, Donnellan’s and Kripke’s sketches point in two rather (...) different directions, by appealing to historical or causal facts of different sorts. In this paper, I shall discuss and criticize Devitt’s causal theory, which confuses things, I shall argue, by mixing, so to speak, Donnellan’s and Kripke’s sketches. (shrink)

Famously, both Saul Kripke and Keith Donnellan opposed description theories and insisted on the role of history in determining the reference of a proper name token. No wonder, then, that their views on proper names have often been assimilated. By focusing on reference borrowing—an alleged phenomenon that Kripke takes to be fundamental—we argue that they should not be. In particular, we claim that according to Donnellan a proper name token never borrows its reference from preceding tokens which it is historically (...) connected to. On the contrary, its reference is always fixed anew on who or what the speaker has in mind when he or she produces it. In fact, what is important to realize is that Donnellan and Kripke took two different histories to be relevant: that of the proper name token produced by the speaker , and that of the cognitive status of the speaker when he or she produces it . We end by suggesting that this difference between Kripke’s and Donnellan’s accounts of proper names rests on a more general difference in their approach to language. (shrink)

Until is a notoriously difficult temporal operator as it is both existential and universal at the same time: A∪B holds at the current time instant w iff either B holds at w or there exists a time instant w' in the future at which B holds and such that A holds in all the time instants between the current one and ẃ. This “ambivalent” nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in (...) contrast, we make explicit this duality of until by introducing a new temporal operator ∇ that allows us to formalize the “history” of until, i.e., the “internal” universal quantification over the time instants between the current one and ẃ. This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system N(LTL∇) for a linear-time logic LTL∇ endowed with the new history operator. We show that LTL∇ is equivalent to the linear temporal logic LTL with until, which follows by formalizing back and forth translations between the two logics. We also define an indirect translation from LTL∇ into LTL via temporal logics with past operators; such a result provides an upper bound to the problem of satisfiability for LTL∇ formulas. (shrink)

In order to know what a belief is, we need to know when it is appropriate to say that two subjects (or the same subject at two different times) believe(s) the same or entertain the same thought. This is not entirely straightforward. Consider for instance1. Tom thinks that he himself is the smartest and Tim believes the same2. In 2001, Bill believed that some action had to be taken to save the rain forest and today he believes the same.What does (...) Tim think? That he, Tim, is the smartest, or that Tom is? And what does Bill believe today? That action had to be taken in 2001 or that it has to be taken now? Both answers are intuitively acceptable. This has to be accounted for somehow.Building on Mark Richard's work on tense, Scott Soames 1 claims that the substitutional interpretation of the quantifiers is unable to account for the intended meaning of such statements as (2) and the validity of some inferences involving them. I will show that his argument is not convincing. Not only does the substitutional interpretation fare no worse than the objectual one, but it seems to be able to avoid a problem which could be seriously damaging for any account of the sameness of thoughts based on the notion of structured proposition. In the first section, I state the problem allegedly raised by tensed belief ascriptions to the substitutional interpretation of the quantifiers. In the second, Soames's argument is shown to be flawed. I also show that the content of the that-clause in (2) is not faithfully represented by any kind of structured proposition. Finally, I show how the substitutional interpretation can handle all such statements as (1) and (2) and the inferences involving them. (shrink)

Esseri umani, paesi, paesaggi, sono alcuni dei maggiori oggetti del nostro amore. Lo stesso si può dire di certi ideali, per esempio dell’ideale di giu­stizia. Harry Frankfurt ha dedicato par­te della sua riflessione alla feno­me­no­logia dell’amore, ma dice relativamente poco riguardo al­la possibilità che sorgano conflitti tra i nostri oggetti d’amore – specialmente quando è in gio­­co la giustizia. Questo saggio prende spunto, ancora una volta, dal caso del­l’uomo su una bar­ca troppo piccola per trasportare tre persone, che si tro­va (...) a dover decidere chi salvare tra le due che sono con lui, una delle qua­li è sua moglie. Il problema è più arduo di quanto pensi Frankfurt.Human beings, countries, landscapes, are among the things most of us love. So are some ideals, such as that of justice. Harry Frankfurt has some ar­res­ting thoughts about the phenomenology of love. He says comparatively lit­tle about the possibility that conflicts arise between the objects of our love – especially when justice is involved. In this paper, the case will be taken up once again of the man on a boat too small to take three, who has to de­cide whom to rescue of two persons – one being his wife. The case is har­der than Frankfurt thinks it is. (shrink)

Many philosophers who thought about democracy in the Twentieth century haverejected the notion of absolute truth and even that of truth as such. Hans Kelsendraws a parallel between, on the one hand, philosophical absolutism and autocracy and, on the other, relativism and democracy. For the very same reasons, Hannah Arendt directly infers from her democratic conception of politics that truth is to be rejected. It seems that such views are closely reminiscent of some statements by John Rawls about the notion (...) of truth. I claim that the similarity is only superficial. Joshua Cohen’s interpretation of some passages of Political Liberalism concerning truth will be discussed, in an attempt at showing that Rawls’ view is not the No Concept View, which Cohen ascribes to him. Rawls endorses no particular conception of truth, but he freely uses the notion with its ordinary meaning. The arguments of public reason should start not just from agreed premises, but from true ones, if that is possible. This is quite consistent with the view that the conclusions of those arguments are put forward as being only reasonable – not as being true.Relativism about truth, on the other hand, is definitely inconsistent with Rawls’conception of public reason and, in particular, cannot jibe with his notion of over-lapping consensus. (shrink)

Until is a notoriously difficult temporal operator as it is both existential and universal at the same time: A∪B holds at the current time instant w iff either B holds at w or there exists a time instant w' in the future at which B holds and such that A holds in all the time instants between the current one and ẃ. This “ambivalent” nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in (...) contrast, we make explicit this duality of until by introducing a new temporal operator ∇ that allows us to formalize the “history” of until, i.e., the “internal” universal quantification over the time instants between the current one and ẃ. This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system N(LTL∇) for a linear-time logic LTL∇ endowed with the new history operator. We show that LTL∇ is equivalent to the linear temporal logic LTL with until, which follows by formalizing back and forth translations between the two logics. We also define an indirect translation from LTL∇ into LTL via temporal logics with past operators; such a result provides an upper bound to the problem of satisfiability for LTL∇ formulas. (shrink)

Eye movement desensitization and reprocessing therapy is a well-established therapeutic method to treat post-traumatic stress disorder. However, how EMDR exerts its therapeutic action has been studied in many types of research but still needs to be completely understood. This is in part due to limited knowledge of the neurobiological mechanisms underlying EMDR, and in part to our incomplete understanding of PTSD. In order to model PTSD, we used a biologically inspired computational model based on firing rate units, encompassing the cortex, (...) hippocampus, and amygdala. Through the modulation of its parameters, we fitted real data from patients treated with EMDR or classical exposure therapy. This allowed us to gain insights into PTSD mechanisms and to investigate how EMDR achieves trauma remission. (shrink)