Quentin Meillassoux is one of the leading French philosophers of today. His first book, Après la finitude : Essai sur la nécessité de la contingence, (2006, translated into English in 2008), has already become a cult classic. It features a préface by his former mentor, Alain Badiou. One of Meillassoux’s main goals is to rehabilitate the distinction between primary and secondary qualities, typical of pre-Kantian philosophies. Specifically, he claims that mathematics is capable of disclosing the primary qualities of any object (...) : “all those aspects of the object that can be formulated in mathematical terms can be meaningfully conceived as properties of the object in itself”. Here we will use Bunge’s philosophy of mathematics in order to challenge the preceding assumption. (shrink)

Between World War I and World War II, the students of Columbia University's John Dewey and Frederick J. E. Woodbridge built up a school of philosophical naturalism sharply critical of claims to value-neutrality. In the 1930s and 1940s, the second-generation Columbia naturalists and their students who later joined the department reacted with dismay to the arrival on American shores of logical empiricism and other analytic modes of philosophy. These figures undermined their colleague Ernest Nagel's attempt to build an alliance with (...) the logical empiricists, accusing them of ignoring the scholar's primary role as a public critic. After the war, the prestige of analytic approaches and a tendency to label philosophies either???analytic??? or???Continental??? eclipsed the Columbia philosophers??? normatively inflected naturalism. Yet in their efforts to resist logical empiricism, the Columbia naturalists helped to construct a sturdy, canonical portrait of???American philosophy??? that proponents still hold up as a third way between analytic and Continental approaches. (shrink)

Philosophical questions about minds and computation need to focus squarely on the mathematical theory of Turing machines (TM's). Surrogate TM's such as computers or formal systems lack abilities that make Turing machines promising candidates for possessors of minds. Computers are only universal Turing machines (UTM's)—a conspicuous but unrepresentative subclass of TM. Formal systems are only static TM's, which do not receive inputs from external sources. The theory of TM computation clearly exposes the failings of two prominent critiques, Searle's Chinese room (...) (1980) and arguments from Gödel's Incompleteness theorems (e.g., Lucas, 1961; Penrose, 1989), both of which fall short of addressing the complete TM model. Both UTM-computers and formal systems provide an unsound basis for debate. In particular, their special natures easily foster the misconception that computation entails intrinsically meaningless symbol manipulation. This common view is incorrect with respect to full-fledged TM's, which can process inputs non-formally, i.e., in a subjective and dynamically evolving fashion. To avoid a distorted understanding of the theory of computation, philosophical judgments and discussions should be grounded firmly upon the complete Turing machine model, the proper model for real computers. (shrink)

Though my ultimate concern is with issues in epistemology and metaphysics, let me phrase the central question I will pursue in terms evocative of philosophy of religion: What are the implications of our logic-in particular, of Cantor and G6del-for the possibility of omniscience?

This paper proposes a new metaphysical framework for distinguishing between human and machine intelligence by drawing on Kant’s incongruent counterparts as an analogy. Specifically, the paper posits two deterministic worlds that are superficially identical but ultimately different. Using ideas from Wittgenstein, Gödel, and Cantor, the paper defines “deterministic knowledge” and investigates how this knowledge is processed differently in those two worlds. The paper considers computationalism and causal determinism for the new framework. Then, the paper introduces new concepts to illustrate why (...) human and machine agents display different causal characteristics in processing verbal information. Overall, the paper’s framework provides a theoretical basis for the uniqueness of the human mind. (shrink)

[[THIS IS THE COMPLETE FIRST ISSUE OF MΕTASCIENCE]] -/- This inaugural issue of the journal Mεtascience is also a special issue since it pays tribute to Mario Bunge (1919-2020) to high light his contribution to knowledge and our filiation with his thought. Mario Bunge's project is part of the humanist and scientific tradition of the Enlightenment. At the end of his intellectual journey, he wrote more than 150 books and 540 articles or chapters, including translations into several languages. The work (...) covers almost all branches of philosophy, from ontology to ethics, semantics, episte mology, methodology, praxeology and axiology, as well as a large number of scientific disciplines, ranging from physics to sociology, chemistry, biology and psychology. Without a doubt, Bunge's mag num opus is the Treatise on Basic Philosophy in nine volumes (1974- 1989). The six contributions gathered here come from authors from differ ent backgrounds. Like Bunge's project, they are neither part of the an alytic or continental movement in philosophy. The reader will find studies on the Bungean system, applications of Bungean thought, re flections and testimonies, and metascientific contributions. From the point of view of metascience as theorized in these pages, Bunge is the last of the philosophers and the first metascientific. He kept from philosophy the idea of a complete system that would inte grate semantics, ontology, epistemology, ethics, axiology and praxe ology, but he refused to problematize scientific knowledge in a tradi tional way. The result is surprising: even by accepting science as it is, he finds room for questioning. May Mεtascience be a place of questioning and deployment of the approach designed by Mario Bunge. (shrink)

The alleged proof of the non-mechanical, or non-computational, character of the human mind based on Gödel’s incompleteness theorem is revisited. Its history is reviewed. The proof, also known as the Lucas argument and the Penrose argument, is refuted. It is claimed, following Gödel himself and other leading logicians, that antimechanism is not implied by Gödel’s theorems alone. The present paper sets out this refutation in its strongest form, demonstrating general theorems implying the inconsistency of Lucas’s arithmetic and the semantic inadequacy (...) of Penrose’s arithmetic. On the other hand, the limitations to our capacity for mechanizing or programming the mind are also indicated, together with two other corollaries of Gödel’s theorems: that we cannot prove that we are consistent, and that we cannot fully describe our notion of a natural number. (shrink)

Ce premier numéro de Mεtascience rend un hommage posthume à Mario Bunge, décédé en février 2020. Ce n’est pas la première fois, et certainement pas la dernière, que des penseurs rendent hommage à Mario Bunge ou que son oeuvre fait l’objet d’une étude, à juste titre d’ailleurs, car l’homme est un humaniste et l’oeuvre digne héritière des Lumières. Bunge a contribué de façon significative à un très grand nombre de disciplines : physique, philosophie, sociologie, psychologie, sciences cognitives. Ce numéro est (...) aussi une façon de faire connaître sa pensée à un lectorat francophone. (shrink)

In the paper some applications of Gödel's incompleteness theorems to discussions of problems of computer science are presented. In particular the problem of relations between the mind and machine (arguments by J.J.C. Smart and J.R. Lucas) is discussed. Next Gödel's opinion on this issue is studied. Finally some interpretations of Gödel's incompleteness theorems from the point of view of the information theory are presented.

This paper presents, from a historical and logical-philosophical perspective, the Gödelian arguments of two Oxford scholars, John Lucas and Roger Penrose. Both have been based on Gödel's Theorem to refute mechanism, computationalism and the possibility of creating an AI capable of simulating or duplicating the human mind. In the conclusions, the growing application of empirical methods in mathematics is mentioned and a possible path that would support Lucas and Penrose's arguments is speculated.

This paper reassesses the criticism of the Lucas-Penrose anti-mechanist argument, based on Gödel’s incompleteness theorems, as formulated by Krajewski : this argument only works with the additional extra-formal assumption that “the human mind is consistent”. Krajewski argues that this assumption cannot be formalized, and therefore that the anti-mechanist argument – which requires the formalization of the whole reasoning process – fails to establish that the human mind is not mechanistic. A similar situation occurs with a corollary to the argument, that (...) the human mind allegedly outperforms machines, because although there is no exhaustive formal definition of natural numbers, mathematicians can successfully work with natural numbers. Again, the corollary requires an extra-formal assumption: “PA is complete” or “the set of all natural numbers exists”. I agree that extra-formal assumptions are necessary in order to validate the anti-mechanist argument and its corollary, and that those assumptions are problematic. However, I argue that formalization is possible and the problem is instead the circularity of reasoning that they cause. The human mind does not prove its own consistency, and outperforms the machine, simply by making the assumption “I am consistent”. Starting from the analysis of circularity, I propose a way of thinking about the interplay between informal and formal in mathematics. (shrink)

. The question of whether or not our universe is deterministic remains of interest to both scientists and theologians. In this essay I argue that this question can be solved only by metaphysical decision and that no scientific evidence for either determinism or indeterminism will ever be conclusive. No finite being, no matter how powerful its cognitive abilities, will ever be able to establish the deterministic nature of the universe. The only being that would be capable of doing so would (...) be one that is at once transcendent and immanent. Such a being is compatible with the God of the Christian tradition, which yields that a deterministic worldview is compatible with a deterministic worldview. A more important point is that because science is never able to establish the determinism of our universe, it can never definitely rule out divine action except on metaphysical grounds. (shrink)

The subjectivism of the Austrian school of economics is a special case of Dewey's transactional philosophy, also known as pragmatism or pragmatic epistemology. The Austrian economists Carl Friedrich Menger (1840-1921) and Ludwig von Mises (1881-1973) adopted an Aristotelian deductive approach to economic issues such as social behavior and exchange. Like Menger and Mises, Friedrich A. Hayek (1899-1992) viewed scientific knowledge, even in the social sciences, as asserting and aiming for objective certainty. Hayek was particularly critical of attempts to apply the (...) empiricism of the natural sciences in the social sciences. Though Hayek was not a positivist in the sense ascribed to Milton Friedman (1912-), because he accepted the possibility of final, objective certainty, Hayek's view of scientific knowledge was closer to that of the logical positivists of the Vienna circle than to Dewey's pragmatism. Mises' a priorism, asserting and aiming for apodictic certainty, represented a more extreme form of objectivism even than Hayek's. Mises was similar in this regard to non-Austrian axiomatists such as Gerard Debreau (1921-2005), though he joined Hayek in eschewing mathematical formalism. In Dewey's contrasting view, the scientist commends new, alternative ways of knowing to the scientific community, offering more profound insight or more efficacious practical applications. Alternative ways of knowing which do not offer practical or intellectual benefits are to be rejected. Both the radical subjectivism of the Austrian school and Dewey's transactional strategy justify rejection of the mirage of social justice. Dewey's knowledge as ways of knowing suggests a broader and more fundamental critique of the socialist position in the calculation debate. The arguments presented by the Austrian school can be reformulated in terms of Dewey's pragmatic philosophy. (shrink)

This is a paper for a special issue of Semiotic Studies devoted to Stanislaw Krajewski’s paper. This paper gives some supplementary notes to Krajewski’s on the Anti-Mechanist Arguments based on Gödel’s incompleteness theorem. In Section 3, we give some additional explanations to Section 4–6 in Krajewski’s and classify some misunderstandings of Gödel’s incompleteness theorem related to AntiMechanist Arguments. In Section 4 and 5, we give a more detailed discussion of Gödel’s Disjunctive Thesis, Gödel’s Undemonstrability of Consistency Thesis and the definability (...) of natural numbers as in Section 7–8 in Krajewski’s, describing how recent advances bear on these issues. (shrink)

An alternative view to the traditionally held view that schizophrenia is characterised by severely disordered cognition is presented. It is possible that apparently self- contradictory expressions of schizophrenics are well-formed communicative expressions of highly ordered cognitive systems. Building on the premise that behavior is in general communicative, and using Godel’s Incompleteness Theorem from logic as a model, it is shown that the most characteristic symptoms of schizophrenia may indicate truths that cannot be derived within highly ordered cognitive systems.

Gödel's Incompleteness Theorems have the same scientific status as Einstein's principle of relativity, Heisenberg's uncertainty principle, and Watson and Crick's double helix model of DNA. Our aim is to discuss some new faces of the incompleteness phenomenon unveiled by an information-theoretic approach to randomness and recent developments in quantum computing.

This article deals with a question of a most general, comprehensive and profound content as it is the nature of mathematical–logical objects insofar as these are considered objects of knowledge and more specifically objects of formal mathematical theories. As objects of formal theories they are dealt with in the sense they have acquired primarily from the beginnings of the systematic study of mathematical foundations in connection with logic dating from the works of G. Cantor and G. Frege in the last (...) decades of the nineteenth century. Largely motivated by a phenomenologically founded view of mathematical objects/states-of-affairs, I try to consistently argue for their character as objects shaped to a certain extent by intentional forms exhibited by consciousness and the modes of constitution of inner temporality and at the same time as constrained in the form of immanent ‘appearances’ by what stands as their non-eliminable reference, that is, the world as primitive soil of experience and the mathematical intuitions developed in relations of reciprocity within-the-world. In this perspective and relative to my intentions I enter, in the last section, into a brief review of certain positions of G. Sher’s foundational holism and R. Tieszen’s constituted platonism, among others, respectively presented in Sher and Tieszen. (shrink)

Both science itself, and the human culture of which it is a part, would benefit from a story of science that encourages wider engagement with and participation in the processes of scientific exploration. Such a story, based on a close analysis of scientific method, is presented here. It is the story of science as story telling and story revising. The story of science as story suggests that science can and should serve three distinctive functions for humanity: providing stories that may (...) increase human well-being, serving as a supportive nexus for human exploration and story telling in general, and exemplifying a commitment to skepticism and a resulting open-ended and continuing exploration of what might yet be. Some practical considerations that would further the development and acceptance of such a story of science as a widely shared nexus of human activity are described. (shrink)

The doctrine of the arbitrary assertion is a key part of Objectivist epistemology as elaborated by Leonard Peikoff. For Peikoff, assertions unsupported by evidence are neither true nor false; they have no context or place in the hierarchy of conceptual knowledge; they are meaningless and paralyze rational cognition; their production is proof of irrationality. A thorough examination of the doctrine reveals worrisomely unclear standards of evidence and a jumble of contradictory claims about which assertions are arbitrary, when they are arbitrary, (...) and what ought to be done about them when they are. A wholesale rejection of the doctrine is recommended. (shrink)