The aim of this note is to discuss the general form and role of identity criteria. We have taken two readings into consideration which express two different functions of identity criteria. The first expresses the epistemic function whilst the second deals with the ontological function. We argue that there are several problems related to the specification of both these functions. As a consequence, we conclude that identity criteria are not necessary to provide ontological legitimacy.

Stewart Shapiro and John Myhill tried to reproduce some features of the intuitionistic mathematics within certain formal intensional theories of classical mathematics. Basically they introduced a knowledge operator and restricted the ways of referring to numbers and to finite hereditary sets. The restrictions are very interesting, both because they allow us to keep substitutivity of identicals notwithstanding the presence of an epistemic operator and, especially, because such restrictions allow us to see, by contrast, which ways of reference are not compatible (...) with the simultaneous maintenance of substitutivity of identicals and the classical notions of truth and knowledge. In this paper the difference between the restricted and the unrestricted kind of reference is put in relation with Russell's ideas on naming and it is argued that the latter as well is compatible with a certain Russellian conception of the understanding of sentences. Then it is discussed whether and how numbers could be conceived as objects of acquaintance. Finally a general question about the notion of logical form is raised. (shrink)

First, language and axioms of Church's paper 'Comparison of Russell's Resolution of the Semantical Antinomies with that of Tarski' are slightly modified and a version of the Liar paradox tentatively reconstructed. An obvious natural solution of the paradox leads to a hierarchy of truth predicates which is of a different kind from the one defined by Church: it depends on the enlargement of the semantical vocabulary and its levels do not differ in the ramified-type-theoretical sense. Second, two attempts are made (...) in order to justify the Russellian, and perhaps Churchian, idea that language should not be fragmented beyond what is required by type distinctions. After all, because of reducibility, which seems to allow a semantics without propositions, this comes out to be possible only at the cost of resorting to two disputable theses. (shrink)

In this paper, we claim that the problem of conditionals should be dealt with by carefully distinguishing between thinking conditional propositions and conditional thinking, i.e. thinking on the basis of some supposition. This distinction deserves further investigation, if we are to make sense of some old and new experimental data concerning the understanding and the assertion of conditional sentences. Here we will argue that some of these data seem to refute the mental models theory of conditional reasoning, setting the ground (...) for a different approach to the cognitive study of conditionals. (shrink)

In the unpublished work Theory of Knowledge a complex is assumed to be “anything analyzable, any‐ thing which has constituents” , and analysis is presented as the “discovery of the constituents and the manner of combination of a given complex” . The notion of complex is linked in various ways with the notions of relating relation, logical form and proposition, taken as a linguistic expression provided with meaning. This paper mainly focuses on these notions, on their links and, more widely, (...) on the role of logical form, by offering a new way of understanding what Russell was doing in TK as concerns the logical‐ontological matter of this manuscript. In particular, a new account of Russell's theory of judgment will be given, by taking a stand with respect to the main accounts already given, and it will be argued for the presence in TK of a notion of type different from the one applied to propositional functions in ML and PM. (shrink)

In the unpublished work Theory of Knowledge a complex is assumed to be “anything analyzable, any‐ thing which has constituents”, and analysis is presented as the “discovery of the constituents and the manner of combination of a given complex”. The notion of complex is linked in various ways with the notions of relating relation, logical form and proposition, taken as a linguistic expression provided with meaning. This paper mainly focuses on these notions, on their links and, more widely, on the (...) role of logical form, by offering a new way of understanding what Russell was doing in TK as concerns the logical‐ontological matter of this manuscript. In particular, a new account of Russell's theory of judgment will be given, by taking a stand with respect to the main accounts already given, and it will be argued for the presence in TK of a notion of type different from the one applied to propositional functions in ML and PM. (shrink)

The paradox of knowability and the debate about it are shortly presented. Some assumptions which appear more or less tacitly involved in its discussion are made explicit. They are embedded and integrated in a Russellian framework, where a formal paradox, very similar to the Russell-Myhill paradox, is derived. Its solution is provided within a Russellian formal logic introduced by A. Church. It follows that knowledge should be typed. Some relevant aspects of the typing of knowledge are pointed out.

The late Mario Mignucci was one of the most authoritative, original, and influential scholars in the area of ancient philosophy, especially ancient logic. Collected here for the first time are sixteen of his most important essays on ancient logic, language, and metaphysics. These essays show a perceptive historian and a skillful logician philosophically engaged with issues that are still at the very heart of history and philosophy of logic, such as the nature of predication, identity, and modality. As well as (...) essays found in disparate publications, often not easily available online, the volume includes an article on Plato and the relatives translated into English for the first time and an unpublished paper on De interpretatione7. Mignucci thinks rigorously and writes clearly. He brings the deep knowledge of a scholar and the precision of a logician to bear on some of the trickiest topics in ancient philosophy. This collection deserves the close attention of anyone concerned with logic, language, and metaphysics, whether in ancient or contemporary philosophy. t philosophy. This collection deserves the close attention of anyone concerned with logic, language, and metaphysics, whether in ancient or contemporary philosophy. (shrink)

1. Introduzione Immaginate di guardare in una certa direzione nel cielo. Vedete un oggetto avvicinarsi. A un certo punto, dopo un alcuni istanti di incertezza, pensate di aver capito di cosa si tratta e dite al vostro amico: «È un uccello!». L’oggetto continua ad avvicinarsi e le ali che prima vi sembravano in movimento ora vi appaiono decisamente ferme. Inoltre la velocità non può essere quella di un uccello. Vi correggete ed esclamate: «È un aereo!». Cominciate a essere preoccupati perché (...) l... (shrink)

Michelangelo thought that stone statues pre-exist their sculptors’ performance. Michelangelo’s view gives rise to a puzzle, which we call Michelangelo’s puzzle. Michelangelo’s puzzle looks structurally similar to so-called problems of material constitution ; so it is tempting to suppose that it can be similarly accounted for. This paper argues that the supposition is misguided. Michelangelo’s puzzle raises specific problems, which cannot be adequately dealt with unless one is prepared to give up either the natural view that stone sculptures are human (...) creations, or a very plausible principle concerning the persistence of middle-sized material objects. A tentative solution to the puzzle is provided, in which borders can play an ontological role in the making of material objects. This solution is intuitively more palatable than Michelangelo’s view, but is nonetheless at odds with a commonsensical, realist attitude towards material objects. Thus, Michelangelo’s puzzle poses a serious challenge to common sense, which is unparalleled by other problems of material constitution. (shrink)

This is an excerpt from the contentIn the introduction to part I of the symposium we stated that a rational agent could be thought of as an agent who has good reasons for its actions. In formal analyses of economic, medical, political, military and forensic decisions rationality, that is the “goodness” of those reasons, is inextricably intertwined with probability. Typically, those analyses concern decisions in a particular class of uncertain situations, namely “risky” situations, where all the relevant available alternative actions (...) are known, each or most actions are non-deterministic , and the probability of each outcome is known to some degree of approximation. As yet, formal analyses have only begun to scratch the surface of the subtleties implicated in uncertain, but not risky, situations, where the available courses of actions, and/or their possible outcomes, and/or the probabilities of those outcomes, are not all. (shrink)

An argument can be superficially valid and rhetorically effective even if what is plausibly meant, what is derived from what, and how it is derived is not at all clear. An example of such an argument is provided by Socrates’s famous refutation of Euthyphro’s second definition of holy, which is generally regarded as clearly valid and successful. This paper provides a stricter logical analysis than the ones in the literature. In particular, it is shown that the argument contains a syntactically (...) ambiguous expression, a passage that needs to be read charitably, and a previously unnoticed but crucial shift between two notions of unholy. Different analyses may be provided, depending on how these interpretation problems are solved. The conditions under which the refutation is valid and successful are far from obvious, and are here explicitly specified. (shrink)

This is an excerpt from the contentThis symposium on Cognition and Rationality originated from two conferences held in Padua on March 17–21, 2003. The title of the first conference was Reasoning and understanding: mental models, relevance, and limited rationality approaches. The second one was entitled: Being rational. Models and limits of rationality in scientific research, economic behaviour, common sense reasoning. The papers published in these two issues are a selection of the ones presented.Why Cognition and Rationality? Let a cognitive agent (...) be defined as one whose actions are at least partially driven by internal representations that are not the direct result of external physical states. On the contrary, an organism which is able to mentally represent contingent physical reality through perception, but which cannot mentally represent non-present realities, (e.g. past or future events, events o. (shrink)

The book's aim is to give a working representation of what metaphysics is today. The historical contributions reveal the roots of metaphysical themes and how today's methods are linked to their Aristotelian and Leibnizian past. The volume also touches on the relationships between ontological and linguistic analysis, the questions of realism and ontological commitment, the nature of abstract objects, the existential meaning of particular quantification, the primitiveness of identity, the question of epistemic versus ontological vagueness, the necessity of origin, the (...) nature of natural necessity, the possibility of intermittent existence, the notion of a temporal part and its place in an account of persistence, the question of identity and change across time and possible worlds, and many more. Readership: A toolbox for any researcher in metaphysics and an essential source for any PhD student with ontological interests. (shrink)

This volume provides analyses of the logic-reality relationship from different approaches and perspectives. The point of convergence lies in the exploration of the connections between reality – social, natural or ideal – and logical structures employed in describing or discovering it. Moreover, the book connects logical theory with more concrete issues of rationality, normativity and understanding, thus pointing to a wide range of potential applications. -/- -/- The papers collected in this volume address cutting-edge topics in contemporary discussions amongst specialists. (...) Some essays focus on the role of indispensability considerations in the justification of logical competence, and the wide range of challenges within the philosophy of mathematics. Others present advances in dynamic logical analysis such as extension of game semantics to non-logical part of vocabulary and development of models of contractive speech act. -/- Table of Contents: Introduction: Majda Trobok, Nenad Miščević and Berislav Žarnić.- I. Logical and Mathematical Structures.- Life on the Ship of Neurath: Mathematics in the Philosophy of Mathematics: Stewart Shapiro.- Applied Mathemathics in the Sciences: Dale Jacquette.- The Philosophical Impact of the Löwenheim-Skolem Theorem: Miloš Arsenijević.- Debating (Neo)logicism: Frege and the neo-Fregeans: Majda Trobok.- II. Epistemology and Logic.- Informal Logic and Informal Consequence: Danilo Šuster.- Logical Consequence and Rationality: Nenad Smokrović.- Logic, Indispensability and Aposteriority: Nenad Miščević.- III . Dynamic Logical Models of Meaning.- Extended Game-Theoretical Semantics: Manuel Rebuschi.- Dynamic Logic of Propositional Commitments: Tomoyuki Yamada.- Is Unsaying Polite?: Berislav Žarnić.- IV Logical Methods in Ontological and Linguistic Analyses.- Towards a Formal Account of Identity Criteria: Massimiliano Carrara and Silvia Gaio.- A Mereology for the Change of Parts: Pierdaniele Giaretta and Giuseppe Spolaore.- Russell versus Frege: Imre Rusza.- Goodman’s OnlyWorld: Vladan Djordjević.-. (shrink)

L.E.J. Brouwer made a mistake in the formulation of his famous bar theorem, as was pointed out by S.C. Kleene. By repeating this mistake several times, Brouwer has caused confusion. We consider the assumption underlying his bar theorem, calling it Brouwer’s Thesis. This assumption is not refuted by Kleene’s example and we use it to obtain a conclusion different from Brouwer’s. Thus we come to support a view first expressed and defended by E. Martino and P. Giaretta in [Martino (...) 1981]. We also indicate that Brouwer’s Thesis has many more applications than Brouwer dreamt of. (shrink)

L.E.J. Brouwer made a mistake in the formulation of his famous bar theorem, as was pointed out by S.C. Kleene. By repeating this mistake several times, Brouwer has caused confusion. We consider the assumption underlying his bar theorem, calling it Brouwer’s Thesis. This assumption is not refuted by Kleene’s example and we use it to obtain a conclusion different from Brouwer’s. Thus we come to support a view first expressed and defended by E. Martino and P. Giaretta in [Martino (...) 1981]. We also indicate that Brouwer’s Thesis has many more applications than Brouwer dreamt of. (shrink)