. 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)

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 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)

The German physicist Heinrich Hertz played a decisive role for Wittgenstein's use of a unique philosophical method. Wittgenstein applied this method successfully to critical problems in logic and mathematics throughout his life. Logical paradoxes and foundational problems including those of mathematics were seen as pseudo-problems requiring clarity instead of solution. In effect, Wittgenstein's controversial response to David Hilbert and Kurt Gödel was deeply influenced by Hertz and can only be fully understood when seen in this context. To comprehend the arguments (...) against the metamathematical programme, and to appreciate how profoundly the philosophical method employed actually shaped the content of Wittgenstein's philosophy, it is necessary to make an intellectual biographical reconstruction of their philosophical framework, tracing the Hertzian elements in the early as well as in the later writings. In order to write Wittgenstein's biography, we have to take seriously the coherence of his thought throughout his life, and not let convenient philosophical ideologies be our guidance in drawing up a “Wittgensteinian philosophy”. To do so, we have to take a second look upon what he actually wrote, not only in the already published material, but in the entire Nachlass. Clearly, this is not easily done, but it is a necessary task in the historical reconstruction of Wittgenstein's life and work. (shrink)

We explore the possibility of using quantum mechanical principles for hypercomputation through the consideration of a quantum algorithm for computing the Turing halting problem. The mathematical noncomputability is compensated by the measurability of the values of quantum observables and of the probability distributions for these values. Some previous no-go claims against quantum hypercomputation are then reviewed in the light of this new positive proposal.

Exact sciences are described as sciences whose theories are formalized. These are contrasted to inexact sciences, whose theories are not formalized. Formalization is described as a broader category than mathematization, involving any form/content distinction allowing forms, e.g., as represented in theoretical models, to be studied independently of the empirical content of a subject-matter domain. Exactness is a practice depending on the use of theories to control subject-matter domains and to align theoretical with empirical models and not merely a state of (...) a science. Inexact biological sciences tolerate a degree of “mismatch” between theoretical and empirical models and concepts. Three illustrations from biological sciences are discussed in which formalization is achieved by various means: Mendelism, Weismannism, and Darwinism. Frege’s idea of a “conceptual notation” is used to further characterize the notion of a form/content distinction. (shrink)

It is shown that the method of operationaldefinition of theoretical terms applied inphysics may well support constructivist ideasin cognitive sciences when extended toobservational terms. This leads to unexpectedresults for the notion of reality, inductionand for the problem why mathematics is sosuccessful in physics.A theory of cognitive operators is proposedwhich are implemented somewhere in our brainand which transform certain states of oursensory apparatus into what we call perceptionsin the same sense as measurement devicestransform the interaction with the object intomeasurement results. Then, (...) perceivedregularities, as well as the laws of nature wewould derive from them can be seen asinvariants of the cognitive operators concernedand are by this human specific constructsrather than ontologically independent elements.. So, reality in so far it isrepresented by the laws of nature has no longeran independent ontological status. This isopposed to Campbell's `natural selectionepistemology'. From this it is shown that thereholds an incompleteness theorem for physicallaws similar to Gödels incompletenesstheorem for mathematical axioms, i.e., there isno definitive or object `theory of everything'.This constructivist approaches to cognitionwill allow a coherent and consistent model ofboth cognitive and organic evolution. Whereasthe classical view sees the two evolutionrather dichotomously. (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)

Development has been themain strategy in addressing the problemof sustainability since at least the mid-1980s. The results of this strategy have been mixed, if not disappointing. In their objections to this approach, critics frequently invoke constraints imposed by physical reality of which the most important one is entropy production. They question the belief that technological innovations are capable of solving the problem of sustainability. Is development the right response to this problem and is the current course capable of attaining sustainability? (...) The article examines closely and critiques the principal theoretical objection to sustainable development that emphasizes physical constraints, and more specifically entropy production. It also offers a critique of the current approach to sustainable development. The article advocates a systems approach as a way to anchor a broad consensus in the ongoing sustainability debates. (shrink)

A fundamental problem in science is how to make logical inferences from scientific data. Mere data does not suffice since additional information is necessary to select a domain of models or hypotheses and thus determine the likelihood of each model or hypothesis. Thomas Bayes’ Theorem relates the data and prior information to posterior probabilities associated with differing models or hypotheses and thus is useful in identifying the roles played by the known data and the assumed prior information when making inferences. (...) Scientists, philosophers, and theologians accumulate knowledge when analyzing different aspects of reality and search for particular hypotheses or models to fit their respective subject matters. Of course, a main goal is then to integrate all kinds of knowledge into an all-encompassing worldview that would describe the whole of reality. A generous description of the whole of reality would span, in the order of complexity, from the purely physical to the supernatural. These two extreme aspects of reality are bridged by a nonphysical realm, which would include elements of life, man, consciousness, rationality, mental and mathematical abstractions, etc. An urgent problem in the theory of knowledge is what science is and what it is not. Albert Einstein’s notion of science in terms of sense perception is refined by defining operationally the data that makes up the subject matter of science. It is shown, for instance, that theological considerations included in the prior information assumed by Isaac Newton is irrelevant in relating the data logically to the model or hypothesis. In addition, the concepts of naturalism, intelligent design, and evolutionary theory are critically analyzed. Finally, Eugene P. Wigner’s suggestions concerning the nature of human consciousness, life, and the success of mathematics in the natural sciences is considered in the context of the creative power endowed in humans by God. (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)

I argue that our sensory fields are photon fields. The philosophical foundation here is informed by mind/brain identity theory, such as we find in Russell, Feigl, Lockwood and Chalmers. In brief, given Dyson's observation that all material things consist of quantum fields, and given an identity of mind and brain, our sensory fields are then most plausibly photon fields.