According to some philosophers, the Liar paradox arises because of a mistaken theory of truth. Its lesson is that we must reject some instances of the naive propositional truth-schema \It is true that \ if and only if \\. In this paper, I construct a novel semantic paradox in which no principle even analogous to the truth-schema plays any role. I argue that this undermines the claim that we ought to respond to the Liar by revising our theory of truth.

The paper addresses three main issues drawing on Husserl’s writings on logic. First, what gives the logical objects their objective status, given the fact that these are intimately connected with human mental processes? Second, if logical objects are objective then how is logical knowledge at all possible? The answer to this question leads to a transcendental foundation of formal logic. Third, how do the principles of logic apply to the real world? This question can be addressed by positing a formal (...) ontology. Against Russell and Whitehead, it has been pointed out that even if logical implication does not in any way depend on human mind, inference is definitely mind-dependent. But this thesis does not necessarily lead to psychologism, as has been pointed out by contemporary Indian logicians. Indian theories of inference deal with the question of truth and falsity but lack a formal ontology. Both pure logic and modern physics claim to be independent of human existence. This claim becomes evident in the conversation between Heisenberg and Tagore. Husserl had distinguished between logical grammar and logic of consequences. The notions of truth and falsity are relevant only in the context of logic of consequences. However, none of the well-known theories of truth, correspondence, coherence or pragmatic theory is free from defects. Following in the footprints of the Advaita Vedantins, it has been maintained that falsity is more fundamental than truth. In the process of cognitive history, a proposition is taken to be true, unless its falsity is proven. Hence the conclusion: since Philosophy is search for the truth, all Philosophy—infinitely—is a gradual rejection of all claims to truth and finally, destroys itself. (shrink)

After a brief introduction, “cultures: multi-culture, cross-culture, interculture”, this essay proceeds in two major sections, “China and the West in Contrast” on how China and the West inter-differ, and “China and the West in Interculture” on how China and the West interculture. First, three ac- tual examples are cited to show how the West is digital, analytical, in either-or, while China is concrete, subtle, in both-and. Next, logic, time, music, kids, etc., are cited to tell of how China and the (...) West inter-differ to inter-critique to inter-correct, to compose the hope of the world. The vast, exciting, and crucial theme of world interculture, concrete and general, is thus compressed in less than twenty pages. Global interculture is so vast that any essay on it risks playing with vague generality. This essay concretely details two extremely contrasting cultures, the West and China, even on general time, logic, and grammar, starkly how the centralities of eternity and time are reversed, how logic is all bare in the West but turned invisible as bone-structure in China, and how the West strictly enforces explicit grammar while China subtly slides from one word-category to another. Typically, elusive “no do” unintelligible in the West but constantly concrete is story-ex- plained to highlight the West-China contrast. Concrete elucidation of general “global interculture” makes this short essay significant. (shrink)

This paper is concerned with De Morgan’s explanation of the validity of arguments that involve relational notions. It discusses De Morgan’s expansion of traditional logic aimed at accommodating those inferences, and makes the point that his endeavour is not successful in that the rules that made up his new logic are not sound. Nevertheless, the most important scholarly work on De Morgan’s logic, and contrary to that De Morgan’s mistake is not beyond repair. The rules that determine his new logic (...) are in fact monotonie replacement rules. And provided they are restricted in the correct way, these rules are demonstrably sound. (shrink)

Is the sense-data theory, otherwise known as indirect realism, a form of representationalism? This question has been underexplored in the extant literature, and to the extent that there is discussion, contemporary authors disagree. There are many different variants of representationalism, and differences between these variants that some people have taken to be inconsequential turn out to be key factors in whether the sense-data theory is a form of representationalism. Chief among these are whether a representationalist takes the phenomenal character of (...) an experience to be explicable in virtue of the properties of an experience that represent something or explicable in virtue of that which gets represented. Another is whether representationalists hold a non-reductionist, or naturalistically or non-naturalistically reductionist variant of representationalism. In addition, subtle differences in what one takes phenomenal character to be on the sense-data theory – either awareness of sense-data or the sense-data themselves – together with one's account of representation, are crucial factors in determining whether sense-data theory is compatible with representationalism. This paper explores these relationships and makes manifest the complexities of the metaphysics of two central theories of perception. (shrink)

Leon Henkin (1921–2006) was not only an extraordinary logician, but also an excellent teacher, a dedicated professor and an exceptional person. The first two sections of this paper are biographical, discussing both his personal and academic life. In the last section we present three aspects of Henkin’s work. First we comment part of his work fruit of his emphasis on teaching. In a personal communication he affirms that On mathematical induction, published in 1969, was the favourite among his articles with (...) a somewhat panoramic nature and not meant exclusively to specialists. This subject is covered in the first subsection. Needless to say that we also analyse Henkin’s better known contribution: his completeness method. His renowned results on completeness for both type theory and first order logic were part of his thesis, The Completeness of Formal Systems, presented at Princeton in 1947 under the advise of Alonzo Church. It is interesting to note that he obtained the proof of completeness for first order logic readapting the argument for the theory of types. The last subsection is devoted to philosophy. The work most directly related to philosophy is an article entitled: Some Notes on Nominalism which appeared in the Journal of Symbolic Logic in 1953. Unfortunately, we are not covering his contribution to the field of cylindric algebras. As a matter of fact, Henkin spent many years investigating algebraic structures with Alfred Tarski and Donald Monk, among others. (shrink)

Tries to identify some strands in the birth of analytic philosophy and to identify in consequence some of its distinctive features.

The main purpose of this paper is to present a formal systemPin which we enjoy a smooth-running technique and which countenances a universe of classes which is symmetrical as between large and small. More exactly,Pis a system which differs from the inconsistent system of [1] only in the introduction of a rather natural new restrictive condition on the defining formulas of the elements. It will be proved that if the weaker system of [2] is consistent, thenPis also consistent.After the discovery (...) of paradoxes, it may be recalled, Russell and Zermelo in the same year proposed two different ways of safeguarding logic against contradictions. Since then various simplifications and refinements of these systems have been made. However, in the resulting systems of Zermelo set theory, generation of classes still tends to be laborious and uncertain; and in the systems of Russell's theory of types, complications in the matter of reduplication of classes and meaningfulness of formulas remain. In [2], Quine introduced a system which seems to be free from all these complications. But later it was found out that in it there appears to be an unavoidable difficulty connected with mathematical induction. Indeed, we encounter the curious situation that although we can prove in it the existence of a class V of all classes, and we can also prove particular existence theorems for each of infinitely many classes, nobody has so far contrived to prove in it that V is an infinite class or that there exists an infinite class at all. (shrink)

The article rebutts Michael Kremer’s contention that Russell’s contextual definition of set-theoretic language in Principia Mathematica constituted the ontological achievement of eliminating commitment to classes. Although Russell’s higher-order quantifiers, used in the definition, need not range over classes, none of the plausible substitutes provide a solid basis for eliminating them. This point is used to defend the presentation, in The Dawn of Analysis, of Russell’s logicist reduction, using a first-order version of naive set theory.

Philosophers have recently expressed interest in accounting for the usefulness of mathematics to science. However, it is certainly not a new concern. Putnam and Quine have each worked out an argument for the existence of mathematical objects from the indispensability of mathematics to science. Were Quine or Putnam to disregard the applicability of mathematics to science, he would not have had as strong a case for platonism. But I think there must be ways of parsing mathematical sentences which account for (...) applicability of mathematics and also do not require us to believe in entities we have no evidence for, other than through reading these sentences literally. We will explore a particular way to interpret sentences of arithmetic which promises to account for their applicability without bringing in metaphysics not also brought in by science. The investigation will be limited to the arithmetic of cardinal numbers. The general strategy is to argue for the analogy between arithmetic and science, rather than to argue for one case having a particular characteristic independently of the other. (shrink)

According to Garfield and Priest’s interpretation, the positive use of the catuskoti by Nāgārjuna in Mūlamadhyamakakārikā (MMK) shows that he endorses a four-valued semantics similar to that of Belnap’s First-Degree Entailment (FDE), while the negative use of the catuskoti by Nāgārjuna in MMK indicates that what he really has in mind is a plurivalent five-valued semantics. This paper argues that their interpretation suffers from a number of problems: adequate logic, collapse of kotis, lack of literature support, and a suitable explanation (...) of the third koti. The final part of the paper combines insights from Westerhoff, Cotnoir, Garfield and Priest together and describes the right interpretation of Nāgārjuna’s use of the catuskoti in MMK with the right semantics and the right logic of MMK. The authors argue that Nāgārjuna’s ‘rebuttal’ of all four kotis in a catuskoti should be understood as a mere denial or a mere rejection of these kotis. (shrink)

Philosophical issues often turn into logic. That is certainly true of Moore’s Paradox, which tends to appear and reappear in many philosophical contexts. There is no doubt that its study belongs to pragmatics rather than semantics or syntax. But it is also true that issues in pragmatics can often be studied fruitfully by attending to their projection, so to speak, onto the levels of semantics or syntax — just in the way that problems in spherical geometry are often illuminated by (...) the study of projections onto a plane. To begin I will describe a potentially vast landscape of logics of a certain form, with some illustrations of how they appear naturally in response to some problems in philosophical logic. Then I will turn Moore’s Paradox into logic, within that landscape, and show how far it can be illuminated therein. (shrink)

According to his own account, Russell was “led to” the Theory of Descriptions by “the desire to avoid Meinong’s unduly populous realm of being”. This “official view” has been subjected to severe criticism. However stimulating this criticism may be, it is too extreme and therefore not critical enough. It fails to fully acknowledge both the way it is itself opposed to Russell and the way Russell and Meinong were opposed to _their_ opponents. In order to avoid these failures, a more (...) “dialectical” kind of analysis will be applied. It leads to unravelling two confusions shared by the official and the unofficial views: the confusion between _conception_ and _adoption_ of the theory of descriptions and the confusion between _three varieties of Meinongianism_. By means of these distinctions both a significant kernel of truth contained in Russell’s account and the underlying motive for his distortion of the historical facts can be laid bare. (shrink)

The theory of descriptions, presented informally in "On Denoting" and more formally in Principia Mathematica, has been endorsed by many linguists and philosophers of language as a contribution to natural-language semantics. However, the syntax of Principia’s formal language is far from ideal as a tool for the analysis of natural language. Stephen Neale has proposed a reconstruction of the theory of descriptions in a language of restricted quantification that gives a better approximation of the syntax of English (and, arguably, of (...) other natural languages). This has led to resistance from some Russell scholars who object to the identification of descriptions with quantifiers at the level of logical form in this new language on the grounds that the identification fails to respect the Russellian conception of descriptions as incomplete symbols. I defend Neale’s reconstruction of the theory and argue that he has preserved everything essential to the theory, including the notion of an incomplete symbol. However, I then go on to argue, contrary to Neale and his objectors as well as Russell himself, that the doctrine of incomplete symbols is a superfluous and undesirable element of the theory that is best jettisoned from the theory. (shrink)

In this paper, I investigate type theories from several perspectives. First, I present and elaborate the philosophical and technical motivations for these theories. I then offer a formal analysis of various TTs, focusing on the cardinality of the set of types contained in each. I argue that these TTs can be divided into four formal categories, which are derived from the cardinality of the set of their basic elementary types and the finiteness of the lengths of their molecular types. The (...) paper provides proofs of the cardinality of the universe of types for each of the specified theories. (shrink)

This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science. The range of contributions includes material on the extension of natural deduction with higher-order (...) rules, as opposed to higher-order connectives, and a paper discussing the application of natural deduction rules to dealing with equality in predicate calculus. The volume continues with a key chapter summarizing work on the extension of the Curry-Howard isomorphism, via methods of category theory that have been successfully applied to linear logic, as well as many other contributions from highly regarded authorities. With an illustrious group of contributors addressing a wealth of topics and applications, this volume is a valuable addition to the libraries of academics in the multiple disciplines whose development has been given added scope by the methodologies supplied by natural deduction. The volume is representative of the rich and varied directions that Prawitz work has inspired in the area of natural deduction. (shrink)

Both Carnap and Quine made significant contributions to the philosophy of mathematics despite their diversed views. Carnap endorsed the dichotomy between analytic and synthetic knowledge and classified certain mathematical questions as internal questions appealing to logic and convention. On the contrary, Quine was opposed to the analytic-synthetic distinction and promoted a holistic view of scientific inquiry. The purpose of this paper is to argue that in light of the recent advancement of experimental mathematics such as Monte Carlo simulations, limiting mathematical (...) inquiry to the domain of logic is unjustified. Robustness studies implemented in Monte Carlo Studies demonstrate that mathematics is on par with other experimental-based sciences. (shrink)

An interview with Charles McCarty by Piotr Urbańczyk concerning mathematical explanation.

It is argued that the finitist interpretation of wittgenstein fails to take seriously his claim that philosophy is a descriptive activity. Wittgenstein's concentration on relatively simple mathematical examples is not to be explained in terms of finitism, But rather in terms of the fact that with them the central philosophical task of a clear 'ubersicht' of its subject matter is more tractable than with more complex mathematics. Other aspects of wittgenstein's philosophy of mathematics are touched on: his view that mathematical (...) propositions are 'grammatical propositions' (and so, Strictly speaking, Not genuine propositions at all) and his view that in mathematics 'everything is algorithm, Nothing meaning'. His views on consistency and his anti-Foundationalism are linked with this central thesis. (shrink)

Set theory, it has been contended, developed from its beginnings through a progression ofmathematicalmoves, despite being intertwined with pronounced metaphysical attitudes and exaggerated foundational claims that have been held on its behalf. In this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership (...) distinction, a distinction only clarified at the turn of this century, remarkable though this may seem. Russell runs with this distinction, but is quickly caught on the horns of his well-known paradox, an early expression of our motif. The motif becomes fully manifest through the study of functionsof the power set of a set into the set in the fundamental work of Zermelo on set theory. His first proof in 1904 of his Well-Ordering Theoremis a central articulation containing much of what would become familiar in the subsequent development of set theory. Afterwards, the motif is cast by Kuratowski as a fixed point theorem, one subsequently abstracted to partial orders by Bourbaki in connection with Zorn's Lemma. Migrating beyond set theory, that generalization becomes cited as the strongest of fixed point theorems useful in computer science.Section 1 describes the emergence of our guiding motif as a line of development from Cantor's diagonal proof to Russell's Paradox, fueled by the clarification of the inclusion vs. membership distinction. Section 2 engages the motif as fully participating in Zermelo's work on the Well-Ordering Theorem and as newly informing on Cantor's basic result that there is no bijection. Then Section 3 describes in connection with Zorn's Lemma the transformation of the motif into an abstract fixed point theorem, one accorded significance in computer science. (shrink)

Rips, in The Psychology of Proof, argues that, through the processes of evolution, logic (e.g., modus ponens) has become established in the human mind as the basis for thinking, and that production systems rest on this foundation. In this paper we defend the converse argument that, through evolution, a production system architecture has become the basis for human thinking, and that formal logics rest on this production system and the accompanying mechanisms for recognition and search. It is through the “automaticity” (...) of the execution of productions that we experience the compellingness of deductive arguments. (shrink)

This article claims that events, facts and states of affairs need to be differentiated. It takes as a starting point Chisholm’s claim that only his ontology of states of affairs explains effectively thirteen sentences related to propositions and events. He does this by reducing propositions and events to states of affairs. We argue that our ontology also solves those problems. We defend a hierarchized Platonist ontology that has concrete entities and abstract entities. The distinctions we propose allow us to explain (...) the pre-analytic data analyzed by Chisholm without reducing entities. We claim that our ontology provides a different way of explaining that data, and is, thus, promissory. (shrink)

The Analytic Tradition in Philosophy is an excellent successor to an excellent book : It is a fine an example of the necromantic style in the history of philosophy where the object of the exercise is to resurrect the mighty dead in order to get into an argument with them, either because we think them importantly right or instructively wrong. However what was a pardonable a simplification and a reasonable omission in the earlier book has now metamorphosed into a sin (...) of omission and an oversimplification in its successor—the book lacks is an adequate discussion of the Ramified Theory of Types and Russell’s reasons for adopting it. I conclude with a brief meditation on Open Question Arguments and the threats that they pose to some of the analyses proposed by Russell and Moore themselves. (shrink)

Some interpreters have ascribed to Wittgenstein the view that mathematical statements must have an application to extra-mathematical reality in order to have use and so any statements lacking extra-mathematical applicability are not meaningful (and hence not bona fide mathematical statements). Pure mathematics is then a mere signgame of questionable objectivity, undeserving of the name mathematics. These readings bring to light that, on Wittgenstein’s offered picture of mathematical statements as rules of description, it can be difficult to see the role of (...) mathematical statements which relate to concepts that are not employed in empirical propositions e.g. set-theoretic concepts. I will argue that Wittgenstein’s picture is more flexible than might at first be thought and that Wittgenstein sees such statements as serving purposes not directly related to empirical description. Whilst this might make such systems fringe cases of mathematics, it does not bring their legitimacy as mathematical systems into question. (shrink)

Bernard Linsky, The Evolution of Principia Mathematica; Bertrand Russell's Manuscripts and Notes for the Second Edition. Cambridge: Cambridge University Press. 2011. 407 pp. + two plates. $150.00/£...

We classify two of Bertrand Russell's theories of events within the point-free ontology. The first of such approaches was presented informally by Russell in ‘The World of Physics and the World of Sense’ (Lecture IV in Our Knowledge of the External World of 1914). Based on this theory, Russell sketched ways to construct instants as collections of events. This paper formalizes Russell's approach from 1914. We will also show that in such a reconstructed theory, we obtain all axioms of Russell's (...) second theory from 1936 and all axioms of Thomason's theory of events from 1989. Russell's work certainly influenced the works of Stanisław Leśniewski, his student Alfred Tarski, and Czesław Lejewski – prominent members of the Lvov-Warsaw School (LWS). We see our work in the tradition of the research of Leśniewski and Tarski. Building on the technical tools developed in this environment and in the spirit of the traditional research of the LWS, we engage here, in particular, with two classic works by Russell on fundamental ontology. (shrink)

The authors believe that the questions raised at the beginning of Frege’s On Sense and Reference – ‘Is [identity] a relation? A relation between objects, or between names or signs of objects?’ – set the course for a long-lasting but not at all satisfying discussion. For the disputants tend to advocate, either a ‘name-view’ of identity in a straightforward but rudimentary and logically untenable form, or else a version of an ‘object-view’ that makes all too light of the analysandum–analysans distinction (...) and hence is damned to analytical barrenness. In contrast, by unfolding the underlying idea of the original ‘name-view’, the authors offer three alternative and mutually compatible interpretations of identity that may best be characterized as the ‘name-based’, the ‘hybrid’ and the ‘sense-based’ variant of a ‘concept-view of identity’. At the same time, however, these interpretations may well be considered variants of a non-barren ‘object-view’. (shrink)

Using a base of philosophical athropology, this article suggests that an ethical analysis of persuasion must include not just the logic human response, but culture and experience as well. The authors propose potential maxims for ethical behavior in advertising and public relations and applies them to two case studies, political advertising and the Bridgestone/Firestone controversy.

What seem to be Kurt Gödel’s first notes on logic, an exercise notebook of 84 pages, contains formal proofs in higher-order arithmetic and set theory. The choice of these topics is clearly suggested by their inclusion in Hilbert and Ackermann’s logic book of 1928, the Grundzüge der theoretischen Logik. Such proofs are notoriously hard to construct within axiomatic logic. Gödel takes without further ado into use a linear system of natural deduction for the full language of higher-order logic, with formal (...) derivations closer to one hundred steps in length and up to four nested temporary assumptions with their scope indicated by vertical intermittent lines. (shrink)

Salmon and Soames argue against nominalism about numbers and sentence types. They employ (respectively) higher-order and first-order logic to model certain natural language inferences and claim that the natural language conclusions carry commitment to abstract objects, partially because their renderings in those formal systems seem to do that. I argue that this strategy fails because the nominalist can accept those natural language consequences, provide them with plausible and non-committing truth conditions and account for the inferences made without committing themselves to (...) abstract objects. I sketch a modal account of higher-order quantification, on which instead of ranging over sets, higher order quantifiers are used to make (logical) possibility claims about which predicate tokens can be introduced. This approach provides an alternative account of truth conditions for natural language sentences which seem to employ higher-order quantification, thus allowing the nominalist to evade Salmon’s argument. I also show how the nominalist can account for the occurrence of apparently singular abstract terms in certain true statements. I argue that the nominalist can achieve this by, first, dividing singular terms into real singular terms (referring to concrete objects) and only apparent singular terms (called onomatoids), introduced for the sake of brevity and simplicity, and then providing an account of nominalistically acceptable truth conditions of sentences containing onomatoids. I develop such an account in terms of modally interpreted abstraction principles and argue that applying this strategy to Soames’s argument allows the nominalists to defend themselves. (shrink)

The laws of physics, because they are cast in terms of homogeneous variables, fall short of determining outcomes in heterogeneous biological systems that are capable of an immense number of combinatoric changes. The universal laws are not violated and they continue to constrain, but specification of results is accomplished instead by stable configurations of processes that develop in a nonrandom, but indeterminate manner. The indeterminacy of physical laws puts an end to Deist speculations and necessitates an alternative to the mechanical-reductionistic (...) metaphor for nature. An antithetical Heraclitan metaphysics, called ‘Process Ecology,’ entails a dialectic between centripetal creation and centrifugal decay in which nature, humanity and the Divine can all potentially participate. The dialectic can be quantified and tracked using information measures applied to networks of processes to allow for the statement and testing of falsifiable hypotheses. Creation no longer appears as an emergent enigma, but rather as a core phenomenon of Process Ecology that allows for free will, Divine intervention, intercessory prayer and a necessary tolerance for petty evil. No longer is ‘heat death’ the inevitable and only endpoint of the cosmos. Rather, the course of the universe may include as well the production of ‘perpetual harmonies’ akin to Teilhard’s ‘Omega Point.’. (shrink)

Andrew Bacon, John Hawthorne, and Gabriel Uzquiano have recently argued that free logics—logics that reject or restrict Universal Instantiation—are ultimately not promising approaches to resolving a family of intensional paradoxes due to Arthur Prior. These logics encompass ramified and contextualist approaches to paradoxes, and broadly speaking, there are two kinds of criticism they face. First, they fail to address every version of the Priorean paradoxes. Second, the theoretical considerations behind the logics make absolutely general statements about all propositions, properties of (...) propositions, etc., but because this sort of intensional quantification is always restricted in the logics, they cannot even express those considerations. I present a novel sort of free logic, which rejects the standard Universal Instantiation but validates a restricted form of the rule, and which addresses both kinds of criticism by allowing some propositions to be unrestricted in their quantification. (shrink)

In his “The Foundations of Mathematics”, Ramsey attempted to marry the Tractarian idea that all logical truths are tautologies and vice versa, and the logicism of the Principia. In order to complete his project, Ramsey was forced to introduce propositional functions in extension (PFEs): given Ramsey's definitions of 1 and 2, without PFEs even the quantifier-free arithmetical truth that 1 ≠ 2 is not a tautology. However, a number of commentators have argued that the notion of PFEs is incoherent. This (...) response was first given by Wittgenstein but has been best developed by Sullivan. While I agree with Wittgenstein and Sullivan's common conclusion, I believe that even the most compelling of Sullivan's arguments is importantly mistaken and that Wittgenstein's remarks are too opaque to be left as the end of the matter. In this article I uncover the fault in Sullivan's argument and present an alternative criticism of PFEs which is Wittgensteinian in spirit without being too mystifying. (shrink)

C. I. Lewis’ systems were the first axiomatisations of modal logics. However some of those systems are non-normal modal logics, since they do not admit a full rule of necessitation, but only a restricted version thereof. We provide G3-style labelled sequent calculi for Lewis’ non-normal propositional systems. The calculi enjoy good structural properties, namely admissibility of structural rules and admissibility of cut. Furthermore they allow for straightforward proofs of admissibility of the restricted versions of the necessitation rule. We establish completeness (...) of the calculi and we discuss also related systems. (shrink)

In this article, I suggest an original solution to the Liar Paradox, based on the pragmatic theory of speech acts. This solution implies making a distinction between two concepts of truth: the intentional truth of a speaker’s utterances directed toward an addressee with the objective of obtaining a consensual agreement; the effective truth objectively recognized by the addressee in the speaker’s utterances. In view of reaching this new solution to the classic paradox, I conduct a critical review of solutions put (...) forward by Tarski, Kripke and Strawson. (shrink)

para o domínio da Ciência Cognitiva funcionalista neurocomputacional. A descrição de tal transição é feita por meio de uma breve análise das idéias de Post, Church, Gödel e Turing sobre a possibilidade de formalização do pensamento criador na matemática, enfatizando as contribuições deste último.