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.

In the unpublished work Theory of Knowledge a complex is assumed to be “anything analyzable, any‐ thing which has constituents” , and analysis is presented as the “discovery of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)

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)

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)

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)

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)

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 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)

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)

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)