Philosophy of Science

Abstract The study of the certainty and inexorability of mathematical theorems is one of the important topics in the philosophy of mathematics. Various schools such as logicism, intuitionism, Platonism and naturalism have tried to present theories on this subject. These schools usually seek the foundation for mathematics in order to justify the certainty of mathematical theorems and logic. This has always been accompanied by numerous failures. In this article, we try to examine this issue from Wittgenstein's point of view. That is, instead of asking "What is the foundation of logic and mathematics?" we ask "Why does mathematics need the foundation?". Therefore, we first examine foundationalism. Then we show that mathematics is a language-game. In this regard, we examine geometry and logic as two language-games in mathematics. Finally, we show that, according to Wittgenstein's philosophy, the certainty and inexorability of a valid inference or a correct calculation comes from the practical procedure of inference and calculation. Keywords Wittgenstein, practice, philosophy of mathematics, language-game, foundationalism Extended Abstract 1. Introduction The question “Where does the certainty of logical and mathematical propositions come from?” has been the central preoccupation of the philosophy of mathematics. Logicism (Frege, Russell) sought to reduce mathematics to logic, thereby grounding its certainty in the apparent indubitability of logical truths. Intuitionism (Brouwer) located the foundation in basic mental constructions, arguing that mathematical objects are products of intuitive temporal processes. Platonism posits a mind‑independent realm of abstract entities, making mathematical truth a matter of discovery rather than invention. Naturalism treats mathematics as continuous with empirical science, justifying its claims through their overall role in successful theories. Despite their differences, these schools share a foundationalist assumption: that the certainty of mathematics must be justified by appealing to a privileged class of basic, self‑evident beliefs or entities. However, as we show, each programme faces insurmountable difficulties—regress problems, circularity, or the inability to account for the actual practices of mathematicians. This paper, therefore, proposes a radical shift: instead of seeking a foundation, we investigate why mathematics is thought to need one. Drawing on Wittgenstein’s later philosophy, we argue that the search for a foundation is itself a grammatical misunderstanding. Mathematics, like any language‑game, is not a structure built upon a base; it is an activity embedded in our form of life. Its certainty is not derived from something external but is exhibited in the way we use its rules. Our aim is to articulate this practice‑based view and to show how it resolves the puzzle of mathematical necessity without metaphysical commitments. 2. Materials and Methods This study is a philosophical analysis, not an empirical experiment. Our method consists of a critical reinterpretation of Wittgenstein’s later works, primarily Philosophical Investigations, Remarks on the Foundations of Mathematics, and On Certainty, combined with a historical and comparative examination of foundationalist projects. We adopt the following conceptual tools: · Language‑game: we treat mathematics as a multiplicity of language‑games, each with its own vocabulary and rules. A language‑game is a rule‑governed activity that is learned and practiced in a community. · Rule‑following: we analyse the notion that obeying a rule is a practice. A rule cannot be a private mental object; it is publicly taught, learned, and applied in repeated situations. · Grammar: we distinguish between empirical propositions (which can be true or false) and grammatical rules (which determine what counts as a meaningful statement and what counts as a valid inference). Questions about the truth of rules are category mistakes. To illustrate our method, we examine two case studies: 1. Geometry as a language‑game: we reconstruct Hilbert’s axiomatic method as a paradigmatic example. Hilbert’s primitive terms (point, line, plane) receive their meaning solely through the axioms, which function as rules for manipulating symbols. By changing a single axiom (the parallel postulate), we obtain new, consistent language‑games (Euclidean vs. hyperbolic geometry). This shows that geometry is not about a pre‑existing spatial reality but about a formal system whose “truth” is replaced by consistency and usability. 2. Logic as a language‑game: we analyse propositional logic, with its vocabulary (sentence letters, connectives) and rules (modus ponens, double negation, non‑contradiction). We argue that logical rules are not discovered a priori but are constitutive of what we call “reasoning”. They are part of the normative framework of our inferential practices. Additionally, we employ comparative anthropological data (Lévy‑Bruhl on the Ipon tribe; counting practices in the Torres Strait) to demonstrate that alternative inferential and computational practices exist, which suggests that our logical and mathematical rules are contingent upon our social forms of life rather than being universally necessary. 3. Discussion and Results Our analysis reveals that foundationalism fails because it mistakes the grammatical status of rules for the propositional status of factual claims. When we ask for the justification of modus ponens or of the principle of non‑contradiction, we are trying to measure our measuring rod. The certainty of these rules is not a property of their correspondence with reality; it is a reflection of their role as standards of correctness within the practice of inference. Wittgenstein explicitly states: “Inference is part of a language‑game. And the person who makes logical inferences follows certain instructions that have been given to him in learning the language‑game” (RFM, p. 378). Thus, the “hardness” of logic is not a metaphysical necessity but a pragmatic one: we call something “valid inference” only if it conforms to these rules. This is analogous to using a metre stick: we cannot question the correctness of the metre stick itself in the same way we question the length of a table, because the metre stick is the standard by which correctness is determined. The two case studies support this conclusion. In geometry, the shift from Euclidean to non‑Euclidean systems shows that no axiom is intrinsically certain; its role is determined by the game we choose to play. The consistency of the system is all that matters for internal validity. In logic, the law of non‑contradiction is not a high‑level empirical generalisation; it is a rule that tells us when to stop playing—it signals that a contradiction has arisen and we cannot continue with the same moves. As Wittgenstein notes, “Contradiction can only occur among the rules of a game” (Notebooks, p. 321). Its force is not ontological but procedural. Our anthropological examples further illustrate that alternative practices are entirely coherent within their own contexts. The Ipon tribe do not infer death from a wound in the way we do; they invoke sorcery. This does not mean they are irrational; they are following a different set of rules for explanation. The Torres Strait counting method is not an inferior version of our arithmetic; it is a different practical technique for enumeration. These examples underscore that what we call “necessary” is only necessary relative to the practices we have adopted. There is no trans‑cultural, trans‑historical foundation for arithmetic or logic; there is only the practical skill and shared training that enable us to count and infer in the ways we do. Consequently, the certainty of a valid inference or a correct calculation derives from our trust in the practice—our confidence, built through repeated successful applications, that following the rules will lead to a determinate outcome. This is not a blind faith but a trained ability. As Wittgenstein puts it: “I examine the proof and then accept its result. That is simply what we do. This is a custom and a practice among us, or a fact of our natural history” (RFM, p. 61). The “inexorability” of mathematics is therefore not a property of the propositions themselves but of our commitment to the practice. 4. Conclusion We conclude that the traditional foundationalist project for mathematics is misconceived. The later Wittgenstein offers a viable alternative: mathematics is a language‑game, and its rules are not in need of external justification because they are constitutive of the activity of reasoning and calculating. The certainty and inexorability that we attribute to mathematical and logical propositions arise from the grammatical role these rules play within the practical procedure (practice) of inference and computation. This certainty is a form of practical trust and skill, not a reflection of metaphysical necessity. Our analysis shows: 1. The demand for a foundation stems from a grammatical error: confusing a rule with a proposition that can be true or false. 2. Hilbert’s axiomatic geometry and classical logic are best understood as language‑games with their own internal standards of correctness; these standards are arbitrary in the sense that they could be different, but they are not arbitrary in the sense that they are freely chosen by individuals—they are embedded in our shared forms of life. 3. The “hardness” of logic and mathematics is the hardness of the practice itself; it is the result of our training and the social consensus that sustains the practice. 4. We do not need a foundation to justify mathematics; we need a clarification of its grammar. The task of philosophy is not to reform or justify mathematics but to describe what mathematicians actually do and how their practices hang together. In sum, the paper provides a robust Wittgensteinian response to the problem of mathematical certainty, showing that the practice‑based approach dissolves the classical foundationalist anxieties without reducing mathematics to mere convention. It invites philosophers and mathematicians to abandon the search for an indubitable ground and instead to appreciate the rich, dynamic, and socially embedded character of mathematical activity.

Abstract In humoral medicine, the symptoms of many diseases were localized, but from the pathological point of view, the disease was not localized. In the 18th and 19th centuries, by using the anatomo-clinical method, the disease was localized both in terms of clinical manifestations - symptoms and signs - and in terms of pathology. In other words, the relationship between a disease and its pathological cause (anatomical or physiological) was the most important work that clinical medicine did in the late 19th century. In this article, we first examine the philosophical foundations of this method - sensualism and the philosophy of observation - in the atmosphere of those centuries. Then we describe the characteristics of its two main components, i.e., clinical examination and pathological analysis. Although dissection of the human body was common during the Renaissance period, it was not done for the purpose of etiology of diseases. From the 18th century onwards, under the influence of the philosophy of observation, this doctrine was formed that the cause of the disease corresponds to a lesion under the external organs of the body. Therefore, the dissection was a fundamental step towards the pathology of diseases. In this way, the data obtained from detailed clinical examination and pathological analysis formed two important parts of case reports, which are one of the pillars of research and new achievements of clinical medicine. In the last part of the article, we examine the structure and characteristics of these types of reports.

Abstract Hysteria is one of the diseases that have been known for more than two thousand years, and the research about it led to the emergence of psychoanalysis in the late 19th century. But in the 80s of the 20th century, this disease was removed from the list of mental diseases. The change of the etiology of hysteria should be examined in two parts: pre-modern medicine and clinical medicine. In this article, we examine the etiology of hysteria in pre-modern medicine. The article has three parts: In the first part, the etiology of hysteria - the wandering uterus - in humoral medicine is examined. In the second part, the controversies related to the influence of magic factors in the late Middle Ages and early Renaissance in the investigation of the etiology of hysteria are examined. In the final part, the impact of the mechanical attitude ruling the 17th century on the etiology of hysteria will be described by the theory of spirits.

Abstract Study the titles of body organs as well as counting them in the anatomical texts of humoural medicine indicates an important issue: in these texts and in comparison with modern anatomical texts, there is no mention of a significant number of body organs. This is while these two different conclusions are the result of the observations of the same action: the dissection of the corpse. In addition, some of these organs are visible to the naked eye, including lymphatic vessels. Therefore, the humoural physician has seen some organs in the process of dissection, but has not. According to the authors of this article, the reason for the invisibility of these organs lies in the connection between observation and theory. In short, the observation of the humoural physician's dissection practice, unlike the observation of the modern anatomist dissection practice, has been based on the humoural theory. Hence, the humoural physician, in the process of dissection, has seen organs which have a humoural function. The rest of the body organs were either not seen or reduced to a fleshy appendages.

Abstract The spread of Covid 19 disease in early 2020, which quickly became a global epidemic, drastically changed human relationships. The use of quarantine technique to prevent the spread of the disease has sparked much controversy in the areas of public health and social control. It is necessary to be aware of these widespread changes and the resulting conflicts, to know the history of the epidemic and its effects in the field of public health and its consequences in changing the political pattern and social control. In this article, we first try to briefly describe the evolution of the concept of pandemics from Greece to the Middle Ages, and show that the dominant method of controlling pandemics was segregation. Then we show how in the fourteenth century the quarantine technique was invented to control epidemics. The invention of this technique was the beginning of the emergence of new knowledge such as statistics and social control. Finally, in the eighteenth and nineteenth centuries, public health became a new object. In fact, urban medicine in the eighteenth century was the continuation and development of the medical-political institution of quarantine in the late Middle Ages, which included the study of places that spread the phenomena of epidemics. In other words, the public health program was introduced as a health regime for the population that required authoritarian medical interventions and controls. .

Abstract Motion is one of the main features of natural philosophy, which together with the formation of Newtonian-Galilean physics, is the most important subject of kinematics and dynamics in the new physics. One of the scientists who played an important role in shaping Galileo's views was Ibn Bajjah (Avempace) (1098-1138). He was a natural philosopher of the 12th century AD. Ibn Bajjah' s mechanics is built upon two general Aristotelian axioms that emphasize natural motion and Algebraic (Qasri) motion. In this article, the bases of movement by Ibn Bajjah are studied based on the motive factors in the movement of the natural body, ie, "form" and "weight". This review is based on the important theory of "matter and form" and the essential principle of "nature does not work in vain " and was done for the first time

Abstract Observation, as an action, is one of the most important and controversial topics of philosophy of science. Analytic philosophers of science have examined this subject from a variety of perspectives. They have shown that what is observed is influenced by the observer’s goals and his/her past experiences, thus observation is influenced by epistemological, semantic, psychological or sociological factors. However observation is not only of interest to analytic philosophers, but it also has been addressed by continental philosophers. One of these philosophers is Michel Foucault, who in his book the birth of the clinic, describes how human body turns into the object of observation in medicine. He points out that in addition to the factors influencing observation as expressed by analytic philosophers, it should be noted that observation basically is a political act. We use Foucault's views in this regard. Although Foucault referred to this issue in his various works, it can be said that observation is the central theme of the birth of the clinic. The purpose of this article is to reveal this political aspect of observation. We discuss what is exactly mean for observation to be a political act, and why the philosophers of science should consider the political aspect of observations in their studies

Abstract Since the publication of Scientific Image, van Fraassen has criticized scientific realism and, instead, introduced constructive empiricism as an appropriate alternative. Adhering to the tenet of empiricism that ‘experience is our only source of information about the world’, he considered acquiring any knowledge of the unobservable level of the world as impossible. According to van Fraassen, the realistic belief in the (approximate) truth of scientific theories has no epistemic basis; and, in this case, he only allowed belief in the empirical adequacy of these theories. The present assay explains and examines the key elements of constructive empiricism and contrasts it with scientific realism. We will indicate that van Fraassen’s argumentation in rejecting realism and defending his position is not able to provide the necessary and sufficient justifications for the replacement of scientific realism with constructive empiricism

Abstract   Bruno Latour, redefining human and their artifacts and defending their multi-threaded nature, considering their intermediaries (not only as devices), defends their status as citizens. Doing this he frees us from the duality of the autonomous technology and therefore from the domination atmosphere (domination of human over non-human and domination of non-human over man).

Abstract  
Allan Franklin is a contemporary physicist and philosopher who take some sort of extremist opinion about the experiments in physics and the position of social constructivism. Proposing a philosophical model, which we call ‘Pragmatist Rationality’, Franklin wants to defend of a kind of logic of scientific discovery and the possibility of crucial experiments occurring and through which He wants to rebut the contingency thesis which is a vital characteristic of social constructivism.
Although he denies that he is proposing a kind of theory of rationality, such theory is evident throughout his works. In this paper we review and evaluate his claims and are going to measure its soundness compared to the contemporary social constructivism theories.

Abstract Logicism is one of the important schools in philosophy of mathematics which reduce the concepts and propositions of mathematics into the concepts and propositions of logic. Bolzano was the pioneer mathematician who based mathematics on logic, and then Ferege continued this project through propounding a new version of logic. Ultimately, in the early decades of 20^th century, this project was finalized by Russel and Withead. In this paper, I, attempt to review the historical development of logicism from Bolzano to Russel, and then through the examination of strengths and weaknesses of the project, I try to answer to this question: has logicism been satisfactory?

Abstract Thinking about the relation between mathematical thinking and modern science is necessary for understanding the modern world. Martin Heidegger analyzes this subject from a unique perspective. In this essay, the concept of "mathematical" and its relation to mathematics and modern science is explained. The dangers of ascendancy of mathematical thinking are discussed; and finally, the differences between Heidegger’s views on mathematics and the prevalent philosophy of mathematics are considered.

Abstract One of the popular theories of rationality of science is rationality as foundationism according to which rationality of a scientific theory is based on sense data upon which the theory has been constructed. The issue of certain data is, however, followed by many debates. In the present article, appealing to Wittgenstein ideas about "certainty", authors present a new understanding of certainties in a scientific theory. According to this new understanding, each and every scientific theory consists of two kinds of propositions: fixed and fluid. Based on this classification of propositions of a scientific theory, a new idea is presented concerning rationality of scientific theories according to which a theory is rational if, firstly it is consistent and, second, it retains fixed propositions of the scientific society and replaces fluid propositions by other proper ones.
Presenting historical evidence, the authors try to show that this idea is efficient and realistic if it is assessed according to standards of rationality which are based on evidency of sense data.

Abstract Descartes was one of the key figures in the scientific revolution. Here placed Aristotle’s explain with the mechanical explain of the world. Descartes created analytic geometry, and discovered an early form of the law of conservation of momentum. He outlined his views on the universe in his Principles of Philosophy. The following essay describes the principles and methods of Descartes.