The philosophical foundations of science are situated within the scaffolding of scientific knowledge encompassing the queries of functions in scientific cognition considering the elements of meta-theoretical level of scientific knowledge that also encompasses general scientific knowledge with methodological ideals of science, scientific landscape of the world and paradigm-related scientific theories. When compared with general scientific knowledge, philosophical foundations of science rest on different branches of philosophy such as axiology, praxeology, ontology, gnoseology, social philosophy, and so forth. To extend this aspect, philosophy of science focuses on epistemic, semantic and metaphysical aspects of scientific practice overlapping with logic, epistemology, ontology and metaphysics. Diversity in philosophical concepts and qualitative delineation of scientific knowledge suggest that both the diachrony of scientific development and synchronistic state in historical course exist in relation to each other. As for the functions of science’s philosophical foundations, deductive reasoning of axioms along with laws and principles concerning scientific theories are at stake. Moreover, empirical and inductive reasoning can be included besides the interpretation of scientific knowledge based on philosophical perspective. Another point is the consideration of the relationship between science and philosophy as significant fields of culture as well as creative resourcefulness is another asset that comes with philosophical mindset and knowledge associated with science and scientific cognition. These features indicate that philosophy of science is both a theoretical and empirical discipline which relies on theorizing philosophically and researching meta-studies of scientific practice.
Historical traces of philosophical thought related to science are originated to the time of Aristotle who is the author of both a scientific and philosophical system which was accepted as a means and framework for Christian Scholasticism and medieval Islamic philosophy. Following the intellectual revolutions of the Renaissance, the Reformation as well as the Enlightenment, the concepts of Aristotle remained to be inherent in Western way of thinking. The intellectual range of Aristotle is very rich with an extension of most scientific disciplines as well as arts some of which are biology, botany, physics, chemistry, history, ethics, logic, philosophy of science, political theory, psychology and zoology on scales of theories and observations. As the founder of formal logic, Aristotle’s devise was considered to be the sum of the discipline as a finished system. The contributions of Aristotle to physical sciences are deemed to be less impressive compared to his research in the life sciences. In his work entitled On Generation and Corruption and On the Heavens, he presents a world-picture encompassing many features inherited from his pre-Socratic predecessors [Witt, C. (1991)]. The general philosophy of science emerged as a distinctive discipline in the 20th century at the dawn of the logical positivist movement which has the aim of formulating criteria to ensure the meaningfulness and objective assessment of all the philosophical statements. Karl Popper is a figure who provided criticism of logical positivism, helping to establish modern sets of standards concerning scientific methodology [Popper, K. (2005)]. Thomas Kuhn’s work titled The Structure of Scientific Revolutions (1962) is also significant as a formative effort to challenge the view of scientific progress as steady and cumulative acquisition of knowledge relying on fixed method of scientific experimentation. A paradigm refers to the set of questions, notions as well as practices defining a scientific discipline in a particular historical period. According to Kuhn, a paradigm shift starts when scientists detect an anomaly that cannot be fit into the existing model. This could be a new theory that does not overlap with the current paradigm or an observation that is not aligned with what was previously expected. When this dealignment occurs, scientists need to break apart from traditional knowledge and look for a model that can fit into the new piece of information, which is marked as the scientific revolution [Kuhn, T. S., & Hacking, I. (2012)].
While philosophy-free science cannot be conceived, science carries the load of philosophy and its tenets, addressing the questions in an occupied manner though the investigation of foundational problems in particular sciences with their implications that open up broader philosophical questions. Consequently, the 20th and 21st centuries have witnessed an increase in the number of practitioners engaged in philosophy of particular sciences which are sketched below:
The philosophy of mathematics addresses the philosophical foundations as well as implications of mathematics, with central questions focusing on the nature of mathematical propositions and whether mathematical entities exist independent of the human mind or not. In addition, the philosophy of mathematics, as a branch of epistemology, addresses the special problems arising from the possession of mathematical knowledge of ours, studying how we know things. When compared to other forms of knowledge learnt by experience, mathematical knowledge appears to be purely related to the realm of thought. Furthermore, the way mathematical knowledge fits into the broader scheme of things is also discussed. Russel asserts that “logic is the youth of mathematics and mathematics is the manhood of logic”, which highlights the interconnected nature of these disciplines [Russell, B., & Potter, M. (2022)]. The mathematics is also defined as a science of patterns, based on structuralist philosophy of mathematics, is the definitive exposition of a system of ideas on the nature of mathematics which is a science with factual subject matter with its knowledge on a par with other forms of scientific knowledge. The distinctive philosophy of mathematics as a systematic form is of value to researchers in the field as well as to logicians and philosophers in relation to realism, truth and epistemology [Resnik, M. (1981)]. Given these, philosophers of mathematics aim at refining the relationships between mathematics and logic, including the human capabilities like intuition, as well as the material universe.
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