: Scientific observation is determined by the human sensory system, which generally relies on instruments that serve as mediators between the world and the senses. Instruments came in the shape of Heron's Dioptra, Levi Ben Gerson's Cross-staff, Egnatio Danti's Torqvetto Astronomico, Tycho's Quadrant, Galileo's Geometric Military Compass, or Kepler's Ecliptic Instrument. At the beginning of the seventeenth century, however, it was unclear how an instrument such as the telescope could be employed to acquire new information and expand knowledge about the (...) world. To exploit the telescope as a device for astronomical observations Galileo had to: 1. establish that telescopic images are not optical defects, imperfections in the eye of the observer, or illusions caused by lenses; 2. develop procedures for systematically handling errors that may occur during observation and measurement and methods of processing data. Galileo made it clear that in order to measure and interpret natural phenomena accurately, a suitable method and instrument would need to be developed. It is intriguing, therefore, to regard the Galilean telescope in this light and to discover the linkage established by Galileo among theory, method, and instrument—the telescope. Although the telescope was not invented through science, it is instructive to see how Galileo used optics to employ a theory-laden instrument for bridging the gulf between picture and scientific language, between drawing and reporting physical facts, and between merely sketching the world and actually describing it. (shrink)

After the publication of Sidereus Nuncius, in the controversy with Ch. Scheiner, Galileo developed several arguments on behalf of the hypothesis that sunspots are contiguous to the surface of the Sun, and presented them in his Istoria e dimostrazioni intorno alle macchie solari e loro accidenti. One of them, named by Galileo a Practical Method, advocates very clearly the correctness of the hypothesis. In the paper the method in question is briefly described. It is argued that the Practical Method is (...) not a thought experiment, but rather a mental model proposed precisely in order to solve the problem of sunspots’ location. (shrink)

This paper aims to reassess the philosophical puzzle of the “applicability of mathematics to physical sciences” as a misunderstood disciplinary interplay. If the border isolating mathematics from the empirical world is based on appropriate criteria, how does one explain the fruitfulness of its systematic crossings in recent centuries? An analysis of the evolution of the criteria used to separate mathematics from experimental sciences will shed some light on this question. In this respect, we will highlight the historical influence of three (...) major disciplinary paradigms. According to the Aristotelian classification of the sciences, the separation of mathematics from physics is based on their respective objects of study. The Baconian system distinguishes these sciences by the type of knowledge involved in each field. Finally, the Whewellian disciplinary layout categorises these disciplines by their respective methods. In this paper, we argue that the cascading effect of such disciplinary categorisations—based successively on ontological, epistemological, and heuristic criteria—resulted in a profound redefinition of the border between mathematics and physics, with the consequence of obscuring the foundations of the interplay between these fields. Our approach intends to put forward such a mechanism as a constitutive piece of the puzzle of the applicability of mathematics. (shrink)