Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) <p><em>Philosophical Problems in Science</em> (Polish: <em>Zagadnienia Filozoficzne w Nauce</em>, abbrev. ZFN) is the oldest Polish journal dedicated to the philosophy in science.</p> <p>ZFN covers a wide range of topics of general interest to those working on philosophical problems involved in and intertwined with modern science (see <a title="Focus and Scope" href="/index.php/zfn/about#focusAndScope" rel="noopener">Focus and Scope</a>).</p> <p>ZFN has originated from a long tradition of Krakow philosophy of nature dating back to the second half of the nineteenth century (see <a title="Journal History" href="/index.php/zfn/about#history" rel="noopener">Journal History</a>). The journal policy is to continue the tradition of mutual discussion between philosophers and scientists.</p> en-US (Secretary of Editorial) (Piotr Urbańczyk) Wed, 30 Dec 2020 00:00:00 +0100 OJS 60 “Is logic a physical variable?” Introduction to the Special Issue <p>“Is logic a physical variable?” This thought-provoking question was put forward by Michael Heller during the public lecture “Category Theory and Mathematical Structures of the Universe” delivered on 30th March 2017 at the National Quantum Information Center in Sopot. It touches upon the intimate relationship between the foundations of physics, mathematics and philosophy. To address this question one needs a conceptual framework, which is on the one hand rigorous and, on the other hand capacious enough to grasp the diversity of modern theoretical physics. Category theory is here a natural choice. It is not only an independent, well-developed and very advanced mathematical theory, but also a holistic, process-oriented way of thinking.</p> Michał Eckstein, Bartłomiej Skowron Copyright (c) 2020 Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) & Michał Eckstein, Bartłomiej Skowron Wed, 30 Dec 2020 16:16:47 +0100 Mathematics as a love of wisdom: Saunders Mac Lane as philosopher <p>This note describes Saunders Mac Lane as a philosopher, and indeed as a paragon naturalist philosopher. He approaches philosophy as a mathematician. But, more than that, he learned philosophy from David Hilbert’s lectures on it, and by discussing it with Hermann Weyl, as much as he did by studying it with the mathematically informed Göttingen Philosophy professor Moritz Geiger.</p> Colin McLarty Copyright (c) 2020 Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) & Colin McLarty Mon, 28 Dec 2020 00:00:00 +0100 Creating new concepts in mathematics: freedom and limitations. The case of Category Theory <p>In the paper we discuss the problem of limitations of freedom in mathematics and search for criteria which would differentiate the new concepts stemming from the historical ones from the new concepts that have opened unexpected ways of thinking and reasoning.</p> <p>We also investigate the emergence of category theory (CT) and its origins. In particular we explore the origins of the term functor and present the strong evidence that Eilenberg and Carnap could have learned the term from Kotarbiński and Tarski.</p> Zbigniew Semadeni Copyright (c) 2020 Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) & Zbigniew Semadeni Mon, 28 Dec 2020 23:47:48 +0100 Abstract logical structuralism <p>Structuralism has recently moved center stage in philosophy of mathematics. One of the issues discussed is the underlying logic of mathematical structuralism. In this paper, I want to look at the dual question, namely the underlying structures of logic. Indeed, from a mathematical structuralist standpoint, it makes perfect sense to try to identify the abstract structures underlying logic. We claim that one answer to this question is provided by categorical logic. In fact, we claim that the latter can be seen—and probably should be seen—as being a structuralist approach to logic and it is from this angle that categorical logic is best understood.</p> Jean-Pierre Marquis Copyright (c) 2020 Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) & Jean-Pierre Marquis Tue, 29 Dec 2020 00:13:09 +0100 On the validity of the definition of a complement-classifier <p>It is well-established that topos theory is inherently connected with intuitionistic logic. In recent times several works appeared concerning so-called complement-toposes (co-toposes), which are allegedly connected to the dual to intuitionistic logic. In this paper I present this new notion, some of the motivations for it, and some of its consequences. Then, I argue that, assuming equivalence of certain two definitions of a topos, the concept of a complement-classifier (and thus of a co-topos as well) is, at least in general and within the conceptual framework of category theory, not appropriately defined. For this purpose, I first analyze the standard notion of a subobject classifier, show its connection with the representability of the functor <em>Sub</em> via the Yoneda lemma, recall some other properties of the internal structure of a topos and, based on these, I critically comment on the notion of a complement-classifier (and thus of a co-topos as well).</p> Mariusz Stopa Copyright (c) 2020 Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) & Mariusz Stopa Tue, 29 Dec 2020 00:28:06 +0100 No-signaling in topos formulation and a common ontological basis for classical and non-classical physical theories <p>Starting from logical structures of classical and quantum mechanics we reconstruct the logic of so-called no-signaling theories, where the correlations among subsystems of a composite system are restricted only by a simplest form of causality forbidding an instantaneous communication. Although such theories are, as it seems, irrelevant for the description of physical reality, they are helpful in understanding the relevance of quantum mechanics. The logical structure of each theory has an epistemological flavor, as it is based on analysis of possible results of experiments. In this note we emphasize that not only logical structures of classical, quantum and no-signaling theory may be treated on the same ground but it is also possible to give to all of them a common ontological basis by constructing a “phase space” in all cases. In non-classical cases the phase space is not a set, as in classical theory, but a more general object obtained by means of category theory, but conceptually it plays the same role as the phase space in classical physics.</p> Marek Kuś Copyright (c) 2020 Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) & Marek Kuś Tue, 29 Dec 2020 00:25:22 +0100 Quantum contextuality as a topological property, and the ontology of potentiality <p>Quantum contextuality and its ontological meaning are very controversial issues, and they relate to other problems concerning the foundations of quantum theory. I address this controversy and stress the fact that contextuality is a universal topological property of quantum processes, which conflicts with the basic metaphysical assumption of the definiteness of being. I discuss the consequences of this fact and argue that generic quantum potentiality as a real physical indefiniteness has nothing in common with the classical notions of possibility and counterfactuality, and that also it reverses, in a way, the classical mirror-like relation between actuality and definite possibility.</p> Marek Woszczek Copyright (c) 2020 Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) & Marek Woszczek Tue, 29 Dec 2020 00:33:12 +0100 Quantum geometry, logic and probability <p>Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these ‘lattice spacing’ weights do not have to be independent of the direction of the arrow. We use this greater freedom to give a quantum geometric interpretation of discrete Markov processes with transition probabilities as arrow weights, namely taking the diffusion form ∂<sub>+</sub>f = (−Δ<sub>θ</sub> + q − p)f for the graph Laplacian Δ<sub>θ</sub>, potential functions q, p built from the probabilities, and finite difference ∂<sub>+</sub> in the time direction. Motivated by this new point of view, we introduce a ‘discrete Schrödinger process’ as ∂+ψ = ı(−Δ + V )ψ for the Laplacian associated to a bimodule connection such that the discrete evolution is unitary. We solve this explicitly for the 2-state graph, finding a 1-parameter family of such connections and an induced ‘generalised Markov process’ for f = |ψ|<sup>2</sup> in which there is an additional source current built from ψ. We also mention our recent work on the quantum geometry of logic in ‘digital’ form over the field F<sub>2</sub> = {0, 1}, including de Morgan duality and its possible generalisations.</p> Shahn Majid Copyright (c) 2020 Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) & Shahn Majid Tue, 29 Dec 2020 22:41:49 +0100 Information and physics <p>This is an overview article that contains the discussion of the connection between information and physics at the elementary level. We present a derivation of Lindauer’s bound for heat emission during irreversible logical operation. In this computation the Szilard’s version of Maxwell’s demon paradox is used as a model to design thermodynamic implementation of a single bit of computer memory. Lindauer’s principle also motivates the discussion on the practical and emergent nature of the information. Apart from physics, the principle has implications in philosophy.</p> Radosław Kycia, Agnieszka Niemczynowicz Copyright (c) 2020 Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) & Radosław Kycia, Agnieszka Niemczynowicz Tue, 29 Dec 2020 00:38:11 +0100 The homunculus brain and categorical logic <p>The interaction between syntax (formal language) and its semantics (meanings of language) is one which has been well studied in categorical logic. The results of this particular study are employed to understand how the brain is able to create meanings. To emphasize the toy character of the proposed model, we prefer to speak of the homunculus brain rather than the brain per se. The homunculus brain consists of neurons, each of which is modeled by a category, and axons between neurons, which are modeled by functors between the corresponding neuron-categories. Each neuron (category) has its own program enabling its working, i.e. a theory of this neuron. In analogy to what is known from categorical logic, we postulate the existence of a pair of adjoint functors, called Lang and Syn, from a category, now called BRAIN, of categories, to a category, now called MIND, of theories. Our homunculus is a kind of “mathematical robot”, the neuronal architecture of which is not important. Its only aim is to provide us with the opportunity to study how such a simple brain-like structure could “create meanings” and perform abstraction operations out of its purely syntactic program. The pair of adjoint functors Lang and Syn model the mutual dependencies between the syntactical structure of a given theory of MIND and the internal logic of its semantics given by a category of BRAIN. In this way, a formal language (syntax) and its meanings (semantics) are interwoven with each other in a manner corresponding to the adjointness of the functors Lang and Syn. Higher cognitive functions of abstraction and realization of concepts are also modelled by a corresponding pair of adjoint functors. The categories BRAIN and MIND interact with each other with their entire structures and, at the same time, these very structures are shaped by this interaction.</p> Steve Awodey, Michał Heller Copyright (c) 2020 Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) & Steve Awodey, Michał Heller Tue, 29 Dec 2020 00:42:07 +0100 Category Theory in the hands of physicists, mathematicians, and philosophers <div class="csl-bib-body" style="line-height: 1.35;"> <div class="csl-entry"> <p>Book review: <em>Category Theory in Physics, Mathematics, and Philosophy</em>, Kuś M., Skowron B. (eds.), Springer Proc. Phys. 235, 2019, pp.xii+134.</p> </div> </div> Mariusz Stopa Copyright (c) 2020 Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) & Mariusz Stopa Tue, 29 Dec 2020 00:00:00 +0100 Contemporary Polish ontology. Where it is and where it is going <p>Book review: <em>Contemporary Polish Ontology</em>. Skowron, B. (ed.), Philosophical Analysis, 82. Berlin; Boston: De Gruyter, 2020. pp.320.</p> Roman Krzanowski Copyright (c) 2020 Philosophical Problems in Science (Zagadnienia Filozoficzne w Nauce) & Roman Krzanowski Tue, 29 Dec 2020 00:52:58 +0100