The anti-metaphysical attitude of the neo-positivist movement is notorious. It is an essential mark of what its members regarded as the scientific world view. The paper focuses on a metaphysical variation of the scientific world view as proposed by Heinrich Scholz and his Münster group, who can be regarded as a peripheral part of the movement. They used formal ontology for legitimizing the use of logical calculi. Scholz's relation to the neo-positivist movement and his contributions to logic and foundations are (...) discussed. His heuristic background can be drawn from a set of six methodological ‘articles of faith’, formulated in 1942 and published here for the first time. I would like to thank Gudrun Mikus (Paderborn) for her assistance in collecting the material, Neil Tennant (Ohio State University, Columbus) for his efforts to improve the paper not only in lingual aspects, and Christian Thiel (Erlangen) and two anonymous referees for their helpful comments. CiteULike Connotea Del.icio.us What's this? (shrink)

The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in Posterior (...) analytics is used to distinguish between conceptions that share the same name but are substantively different: for example the search for a broader genus including all mathematical objects; the search for a common character of different species of mathematical objects; and the effort to treat magnitudes as numbers. (shrink)

Descartes understood the subject matter of physics (or natural philosophy) to encompass the whole of nature, including living things. It therefore comprised not only nonvital phenomena, including those we would now denominate as physical, chemical, minerological, magnetic, and atmospheric; it also extended to the world of plants and animals, including the human animal (with the exception of those aspects of the human mind that Descartes assigned to solely to thinking substance: pure intellect and will). Descartes wrote extensively on physiology and (...) on the physiology and psychology of the senses. This chapter examines the notions of *physiology* and *psychology* in medical and natural philosophical works of Descartes' day; follows his efforts to bring physiology into his mechanistic idiom; considers the relation between physiology of the animal machine and psychological functions that yield functionally appropriate behavior; goes into his physiology and psychology of vision; and elaborates the tension in Descartes' works between his metaphysically supported micro-corpuscularism and his discussion of the animal machine as an organic unity comprising various functionally and teleologically characterized systems. The chapter draws on Descartes' works in both metaphysics and natural philosophy, including his Treatise on Man (originally published as L'Homme, 1664). (shrink)

This paper opens by reviewing Aristotle’s conception of the natural slave and then familiar treatments of the internal conflict between the ruling and subject parts of the soul in Aristotle and Plato; I highlight especially the figurative uses of slavery and servitude when discussing such problems pertaining to incontinence and vice—viz., being a ‘slave’ to the passions. Turning to Campanella, features of the City of the Sun pertaining to slavery are examined: in sketching his ideal city, Campanella both rejects Aristotle’s (...) natural slave and is critical of the European institutions of slavery. The fact that slavery has no place in the City of the Sun takes on added significance when complemented with Campanella’s remarks on dominion and servitude in his Quaestiones de politiciis: I show that Campanella’s conception of slavery is intimately bound to sin, and consider whether his employment of the trope of slavery within the context of vice diverges from familiar usage. (shrink)

Descartes’ Rules for the direction of the mind presents us with a theory of knowledge in which imagination, considered as an “aid” for the intellect, plays a key role. This function of schematization, which strongly resembles key features of Proclus’ philosophy of mathematics, is in full accordance with Descartes’ mathematical practice in later works such as La Géométrie from 1637. Although due to its reliance on a form of geometric intuition, it may sound obsolete, I would like to show that (...) this has strong echoes in contemporary philosophy of mathematics, in particular in the trend of the so called “philosophy of mathematical practice”. Indeed Ken Manders’ study on the Euclidean practice, along with Reviel Netz’s historical studies on ancient Greek Geometry, indicate that mathematical imagination can play a central role in mathematical knowledge as bearing specific forms of inference. Moreover, this role can be formalized into sound logical systems. One question of general epistemology is thus to understand this mysterious role of the imagination in reasoning and to assess its relevance for other mathematical practices. Drawing from Edwin Hutchins’ study of “material anchors” in human reasoning, I would like to show that Descartes’ epistemology of mathematics may prove to be a helpful resource in the analysis of mathematical knowledge. (shrink)

Françios Viète was a geometer in search of better techniques for astronomical calculation. Through his theorem on angular sections he found a use for higher-dimensional geometric magnitudes which allowed him to create an algebra for geometry. We show that unlike traditional numerical algebra, the knowns and unknowns in Viète’s logistice speciosa are the relative sizes of non-arithmetized magnitudes in which the “calculations” must respect dimension. Along with this foundational shift Viète adopted a radically new notation based in Greek geometric equalities. (...) His letters stand for values rather than types, and his given values are undetermined. Where previously algebra was founded in polynomials as aggregations, Viète became the first modern algebraist in working with polynomials built from operations, and the notations reflect these conceptions. Viète’s innovations are situated in the context of sixteenth-century practice, and we examine the interpretation of Jacob Klein, the only historian to have conducted a serious inquiry into the ontology of Viète’s “species”. (shrink)

The ArgumentIn this paper, I argue that the most significant contribution of the Jesuits to early modern science consists in the introduction of a new “image of knowledge.”In contradistinction to traditional Scholasticism, this image of knowledge allows for the possibility of a science of hypothetical entities.This problem became crucial in two specific areas. In astronomy, knowledge of mathematical entities of unclear ontological status was nevertheless proclaimed certain. In theology, God's knowledge of the future acts of man, logically considered as future (...) contingents, was also proclaimed certain. In both cases the concept of certain knowledge of hypothetical entities was problematic and challenged a central premise of the accepted canons of logic, i.e., that the objects of true knowledge must be real objects.The main argument of this paper is that the practical orientation of the Jesuit cultural milieu enabled Jesuit scientists and theologians to ignore accepted logical considerations and to modify traditional Thomist images of knowledge. Nevertheless, this modification was not so radical as to change the contemporary organization of knowledge. This was due to the peculiar status of the Jesuits within the church establishment, which exposed them to harsh criticism and created a deep need for legitimation. Thus, the limitations of Jesuit scientific culture are accounted for in institutional, rather than in logical terms. (shrink)

Ever since its foundation in 1540, the Society of Jesus had had one mission—to restore order where Luther, Calvin and the other instigators of the Reformation had brought chaos. To stop the hemorrhage of believers, the Jesuits needed to form a united front. No signs of internal disagreement could to be shown to the outside world, lest the congregation lose its credibility. But in 1570s two prominent Jesuits, Cristophorus Clavius and Benito Perera, had engaged in a bitter controversy. The issue (...) at stake had apparently nothing to do with the values on which Ignazio of Loyola had built the Society of Jesus. And yet the dispute between Clavius and Perera was matter of concern for the entire Jesuit community. They were... (shrink)