This paper explores the relationship between informal reasoning, creativity in mathematics, and problem solving. It underscores the importance of environments that promote interaction, hypothesis generation, examination, refutation, derivation of new solutions, drawing conclusions, and reasoning with others, as key factors in enhancing mathematical creativity. Drawing on argumentation logic, the paper proposes a novel approach to uncover specific characteristics in the development of formalized proving using “proof-events.” Argumentation logic can offer reasoning mechanisms that facilitate these environments. This paper proposes how argumentation (...) can be implemented to discover certain characteristics in the development of formalized proving with “proof-events”. The concept of a proof-event was introduced by Goguen who described mathematical proof as a multi-agent social event involving not only “classical” formal proofs, but also other informal proving actions such as deficient or alleged proofs. Argumentation is an integral component of the discovery process for a mathematical proof since a proof necessitates a dialogue between provers and interpreters to clarify and resolve gaps or assumptions. By formalizing proof-events through argumentation, this paper demonstrates how informal reasoning and conflicts arising during the proving process can be effectively simulated. The paper presents an extended version of the proof-events calculus, rooted in argumentation theories, and highlights the intricate relationships among proof, human reasoning, cognitive processes, creativity, and mathematical arguments. (shrink)

In this essay, we will try to provide a formal analysis of practical inference, attentive to the various phases in which it is articulated, and being so capable of explaining both the logical conclusiveness of the inference and the probabilistic nature of its conclusion. An innovative purpose of this article is to show how the final deliberation leading to action—the ultimate practical judgment—takes place according to a logic consistent with the use of Bayes’ theorem. This is why we refer to (...) Bayesian practical inference in the title of this essay. (shrink)

The humanistic disciplines aim to offer explanations of a wide variety of phenomena. Philosophical theories of explanation have focused mostly on explanations in the natural sciences; a much discussed theory of explanation is the causal theory of explanation. Recently it has come to be recognized that the sciences sometimes offer respectable explanations that are non-causal. This paper broadens the discussion by discussing explanations that are offered in the fields of history, linguistics, literary theory, and archaeology that do not seem to (...) fit the causal theory of explanation. We conducted an exploratory survey in acclaimed humanities textbooks to find explicitly so-called explanations and analyze their nature. The survey suggests that non-causal explanations are an integral part of the humanities and that they are of distinct kinds. This paper describes three kinds that are suggested by our survey: teleological, formal, and normative explanations. We suggest that such humanistic explanations strengthen the case for explanatory pluralism. (shrink)

Perhaps the most influential historian of science of the last century, Alexandre Koyré, famously argued that the icon of modern science, Galileo Galilei, was a Platonist who had hardly performed experiments. Koyré has been followed by other historians and philosophers of science. In addition, it is not difficult to find examples of Platonists in contemporary science, in particular in the physical sciences. A famous example is the icon of twenty century physics, Albert Einstein. This paper addresses two questions related to (...) the Platonism of modern physical science. The first is: How is Galileo’s Platonism compatible with the fact that he did perform experiments? The solution to this apparent paradox can be found in Plato’s late dialogue Timaeus. In the dialogue the world has been created by a divine craftsman according to an original plan. The task of the scientist is not primarily to describe the material world, but to reconstruct the original plan. This view has later been known as “God’s Eye View”. The second question is: If a God’s Eye View is unattainable, how is it possible to give a “rational reconstruction” of Galileo’s Platonism? The key-word is idealisation. It is further argued that idealisation is intimately related to technology. Technology is required to realize ideal experimental conditions, and the results are in its turn implemented in technology. The implication is that the quest for unity in science, based on physics as the basic science, should be replaced by the recognition of the diversity of the sciences. (shrink)

It is widely believed that mathematics carries a substantial part of the explanatory burden in science. However, mathematics can also play important heuristic roles of a different kind, being a source of new ideas and approaches, allowing us to build toy models, enhancing expressive power and providing fruitful conceptualizations. In this paper, we focus on the application of dynamical systems theory (DST) within the extended cognition (EC) field of cognitive science, considering this case study to be a good illustration of (...) a general phenomenon. In the paper, we justify both a negative and a positive claim. The negative claim is that dynamical systems theory hardly plays any explanatory role in EC research. We justify our claim by analyzing several accounts of the explanatory role of mathematics and stressing the way mathematical arguments are used in explanations. Our positive claim is that even though, for now, DST has no explanatory power in many of the EC approaches, it still plays an important heuristic role there. In particular, using mathematical notions improves the expressive power of the language and gives a sense of understanding of the phenomena under investigation. The case study of EC allows us to identify and analyze this important role of mathematics, which seems to be neglected in contemporary discussions. (shrink)

To believe that logic has no history might at first seem peculiar today. But since the early 20th century, this position has been repeatedly conflated with logical monism of Kantian provenance. This logical monism asserts that only one logic is authoritative, thereby rendering all other research in the field marginal and negating the possibility of acknowledging a history of logic. In this paper, I will show how this and many related issues have developed, and that they are founded on only (...) one prominent statement by Kant. I will argue, however, that this statement takes on a very different meaning in a broader context of the history and philosophy of science, and that Kant and his supporters never advocated the logical monism that they are still said to hold today. (shrink)

Species are considered the basic unit of biological classification and evolution. Hence, they are used as a benchmark in several fields, although the ontological status of such a category has always been a matter of debate. This paper aims to discuss the problem of the definition of species within the new mechanistic approach. Nevertheless, the boundary between entities, activities, and mechanisms remains difficult to establish and always requires an analysis of what is meant by explanation. As a case study, the (...) paper describes the debate concerning the species category by considering different kingdoms: Animals, Bacteria, and Fungi. The inherently biological differences between those groups prevent the use of a single, universally applicable concept of species that could fit the mechanisms responsible for the variability present in these kingdoms. The same issue is encountered within each group, as highlighted through a focus on mammals and microbes. This controversy has given rise to opposite approaches, namely: monism, which looks for a single definition that might account for all species, and pluralism, which admits that different groups of organisms require somewhat different definitions. In order to develop an adequate definition of species, we propose to apply a new mechanistic framework, which considers the ontic-epistemic dimensions of scientific explanation in close parallel. The apt correlation between epistemic and the ontic aspects highlights the way in which the concept of species and the reference to data are strictly co-determined. This suggests that the concept of species is better understandable within a dual ontic-epistemic approach. (shrink)

By justification we understand what makes a belief epistemologically viable: generally this is considered knowledge that is true. The problem is defining this with a higher degree of precision because this is where different conflicting conceptions appear. On the one hand, we can understand justification as what makes it reasonable to acquire or maintain a belief; on the other, it is what increases the probability that the belief is true. This work tries to prove that beliefs depend on other beliefs (...) that are epistemically justified and that such beliefs are the result of (i.e., they arise from) our privileged intuition of reality. For this, we examine the concept of epistemic regress. Epistemic reasons authorize a proposition P to be the conclusion of an argument in which such reasons function as premises and are vulnerable to epistemic regress. The three most important approaches to epistemic regress are Infinitism, Coherentism and Foundationalism. (shrink)

Technologies are undeniably having a decisive, transformative impact on Earth, yet the currently prevailing empirically orientated approaches in the philosophy of technology seem unable to get to conceptual grips with this fact. Some thinkers have therefore been trying to develop alternative methods capable of clarifying it. This paper focuses on Vincent Blok’s call for rehabilitating an ontologically oriented approach. It reconstructs the rationale of his method as well as its key elements and structure. Elucidating Blok’s emphasis on the experience of (...) climate change, the paper clarifies his call for a terrestrial turn in the philosophy of technology. This turn is indisputably needed, but Blok’s conceptualisation of Earth is problematic: Apart from its speculative nature, it underestimates the impact of humans on Earth. Blok seeks to clarify how ontic phenomena, especially particular technologies, can have an ontological impact, but there is a friction between his Heideggerian concept of the world as grounding inner-worldly beings and the idea of technologies as founding a new world. Identifying the elements where the undoubtedly required ontological approach needs to be rethought, the paper suggests that we need more mundane conceptualisations of both Earth and the world, accompanied by more attention to ontic processes. (shrink)

In this paper, we examine the issue of the empirical or non-empirical status of philosophical metatheories. In particular, we ask whether a specific type of metatheoretical product, formal reconstructions of scientific theories, can be empirically tested. To answer this, we take Metatheoretical Structuralism as a metatheory and Classical Mechanics as our case studies. We show how classical mechanics can be reconstructed from structuralism. We then present a computer program, called Reconstructor, and show how it can be used to test the (...) adequacy of the reconstruction. Finally, we discuss some philosophical points regarding these tests, namely, the issues of holism, circularity and metatheoretical predictions. (shrink)

I will argue that the ontological doctrine of physicalism inevitably entails the denial that there is anything conceptual in logic and mathematics. The elements of a formal system, even if they are tagged by suggestive names, are merely meaningless parts of a physically existing machinery, which have nothing to do with concepts, because they have nothing to do with the actual things. The only situation in which they can become meaning-carriers is when they are involved in a physical theory. But (...) in this role they refer to elements of the physical reality, i.e. they represent a physical concept. “Mathematical concepts” are just idols, that philosophy can completely deny and physics can completely ignore. (shrink)

In recent years, much research has been devoted to exploring contextuality in systems that are not strictly quantum, like classical light, and many theory-independent frameworks for contextuality analysis have been developed. It has raised the debate on the meaning of contextuality outside the quantum realm, and also on whether—and, if so, when—it can be regarded as a signature of non-classicality. In this paper, we try to contribute to this debate by showing a very simple “thought experiment” or “toy mechanism” where (...) a classical object (i.e., an object obeying the laws of classical physics) is used to generate experimental data violating the KCBS inequality. As with most thought experiments, the idea is to simplify the discussion and to shed light on issues that in real experiments, or from a purely theoretical perspective, may be cumbersome. We give special attention to the distinction between classical realism and classicality, and to the contrast between contextuality within and beyond quantum theory. (shrink)

How to understand new encounters between the living and the technological? Exemplary of such new encounters are the biotechnological creations of synthetic biology, where life and technology are increasingly intertwined in complex and intimate ways. This developing biotechnological field frames its novel entities as ‘artificial life’, ‘living technology’, and ‘biohybrid systems’. While synthetic biology too easily uses machine metaphors and technological frames for living entities, traditional philosophical frameworks also risk ontological reductionism in their efforts to understand life and technology in (...) relation to each other. In contrast, Gilbert Simondon’s theory of individuation helps to understand the similarities between life and technology without reducing life forms to machines and without conflating technological objects with living systems. The aim of this article is twofold: first, to shed light on the relationship between life and technology, and second, to examine the emergence of new borderline cases resulting from synthetic biology, all with the help of the theory of individuation. Our hypothesis is that individuation facilitates our understanding of these new encounters between living beings and technologies, and provides conceptual clarity to prevailing dualisms such as life and technology, artificial and natural. We will develop Simondon’s theory into a framework and apply it to the case of synthetic biology, thus opening up the possibility that individuation can also help us to think about future encounters between life and technology. (shrink)