This article focuses on issues related to improving an argument about minds and machines given by Kurt Gödel in 1951, in a prominent lecture. Roughly, Gödel’s argument supported the conjecture that either the human mind is not algorithmic, or there is a particular arithmetical truth impossible for the human mind to master, or both. A well-known weakness in his argument is crucial reliance on the assumption that, if the deductive capability of the human mind is equivalent to that of a (...) formal system, then that system must be consistent. Such a consistency assumption is a strong infallibility assumption about human reasoning, since a formal system having even the slightest inconsistency allows deduction of all statements expressible within the formal system, including all falsehoods expressible within the system. We investigate how that weakness and some of the other problematic aspects of Gödel’s argument can be eliminated or reduced. (shrink)

In contrast to dominant approaches to human reason involving essentially a logical and instrumental conception of rationality easily modeled by artificial intelligence mechanisms, I argue that the specific capacities of the human mind are meta-analytic in nature, understood as irreducible to the analytic or the logical, or else the computational. Firstly, the assumption of a meta-analytical level of rationality is derived from key insights developed in various branches of the social sciences. This meta-analytical level is then inferred from Gödel’s incompleteness (...) theorem. On these bases, and with the help of psychological approaches to consciousness, I argue that human rationality may be characterized as the capacity to make meaningful use of signs. (shrink)

In 1928 Edmund Husserl wrote that “The ideal of the future is essentially that of phenomenologically based (“philosophical”) sciences, in unitary relation to an absolute theory of monads” (“Phenomenology”, Encyclopedia Britannica draft) There are references to phenomenological monadology in various writings of Husserl. Kurt Gödel began to study Husserl’s work in 1959. On the basis of his later discussions with Gödel, Hao Wang tells us that “Gödel’s own main aim in philosophy was to develop metaphysics—specifically, something like the monadology of (...) Leibniz transformed into exact theory—with the help of phenomenology.” (A Logical Journey: From Gödel to Philosophy, p. 166) In the Cartesian Meditations and other works Husserl identifies ‘monads’ (in his sense) with ‘transcendental egos in their full concreteness’. In this paper I explore some prospects for a Gödelian monadology that result from this identification, with reference to texts of Gödel and to aspects of Leibniz’s original monadology. (shrink)

Lucas-Penrose type arguments have been the focus of many papers in the literature. In the present paper we attempt to evaluate the consequences of Gödel’s incompleteness theorems for the philosophy of the mind. We argue that the best answer to this question was given by Gödel already in 1951 when he realized that either our intellectual capability is not representable by a Turing Machine, or we can never know with mathematical certainty what such a machine is. But his considerations became (...) known only in recent times when many scholars were already aware of Benacerraf’s and Chihara’s analyses on the consequences of Gödel’s incompleteness theorems for the philosophy of the mind. Benacerraf and Chihara, in fact, discussing Lucas’ paper, arrived at the same conclusions as Gödel in the sixties, but in a more formal way. After Penrose’s provocative arguments, Shapiro again shed light on the question. In our paper, after a broad and simple presentation of the contributions to the debate made by different authors, we show how to present Gödel’s argument in a rigorous way, highlighting the necessary philosophical premises of Gödel’s argument and more in general of Gödelian arguments. (shrink)