Friedrich Albert Lange (1828-1875) author of a famous History of Materialism and Critique of Its Present Significance (1866, English transI. 1877-79, repr. 1925 with introduction by Bertrand Russell), was also interested in the epistemological foundations of formal logic. Part I of his intended two-volume Logische Studien was published posthumously in 1877 by Hermann Cohen, head of the Marburg school of neo-Kantianism. Lange, departing from Kant, claims that spatial intuition is the source of the apodeictic character not only of the truths (...) of mathematics, but also of the truths of logic. He aims at showing this by basing validity and invalidity of syllogistic inferences on an interpretation of the standard forms (of proposition in assertoric syllogistic) with the help of the five kinds of possible relations (in fact what is known today as the Gergonne-Euler relations) between extensions of concepts given to us as areas in a plane, i.e.in space. Generality is achieved by considering all possible variations within each type of spatial relation, exhibiting a connection between concept and intuition reminding Lange of the Kantian "schema". Lange is well aware of the contemporary English "algebraic" logic, but he considers its approach as the appropriate one for a logic of content (Inhaltslogik) and not for a logic of extension (Umfangslogik). Lange did not live to enjoy the recognition by some leading logicians (amongst them John Venn, to whose reference in 1881 to Lange's "admirable Logische Studien" the present paper owes it title), nor could he respond to the many critics of his proposed foundation of logic. Its radicality as well as its broad reception (and discussion up to at least 1959) seem to entitle Lange's Logische Studien to an, if modest, place in the history of logic in the 19th century. (shrink)

In the nineteenth century, the separation of naturalist or psychological accounts of validity from normative validity came into question. In his 1877 Logical Studies (Logische Studien), Friedrich Albert Lange argues that the basis for necessary inference is demonstration, which takes place by spatially delimiting the extension of concepts using imagined or physical diagrams. These diagrams are signs or indications of concepts' extension, but do not represent their content. Only the inference as a whole captures the objective content of the proof. (...) Thus, Lange argues, the necessity of an inference is independent of psychological accounts of how we grasp the content of a proposition. (shrink)

In the 1860s and 1870s the logic of Boole and the calculating machines of Babbage were key resources in W. S. Jevons’s attempt to construct a mechanical model of the mind, and both therefore played an important role in Jevons’s attempted revolution in economic theory. In this same period both Boole and Babbage were studied within the Cambridge Moral Sciences Tripos, but the Cambridge reading of Boole and Babbage was much more circumspect. Implicitly following the division of the moral sciences (...) into material and ‘real’ as established by the Rev. Grote, John Venn treated Boole’s logic as a purely formal science, while Alfred Marshall based his psychological model of the mechanical part of the human mind upon Babbage’s two-level machine. From the different perspectives of logic and psychology, Venn and Marshall did not simply incorporate their readings of Boole and Babbage, but also attempted to establish the limits to any mechanical explanation of the mind. This comparison of the attitudes to mental science of Jevons and Marshall provides a foundation from which the differing conceptions of economic theory of the two men can be established.Keywords: Alfred Marshall; Charles Babbage; George Boole; John Venn; Logic; Psychology. (shrink)

In my dissertation, I present Hermann Cohen's foundation for the history and philosophy of science. My investigation begins with Cohen's formulation of a neo-Kantian epistemology. I analyze Cohen's early work, especially his contributions to 19th century debates about the theory of knowledge. I conclude by examining Cohen's mature theory of science in two works, The Principle of the Infinitesimal Method and its History of 1883, and Cohen's extensive 1914 Introduction to Friedrich Lange's History of Materialism. In the former, Cohen gives (...) an historical and philosophical analysis of the foundations of the infinitesimal method in mathematics. In the latter, Cohen presents a detailed account of Heinrich Hertz's Principles of Mechanics of 1894. Hertz considers a series of possible foundations for mechanics, in the interest of finding a secure conceptual basis for mechanical theories. Cohen argues that Hertz's analysis can be completed, and his goal achieved, by means of a philosophical examination of the role of mathematical principles and fundamental concepts in scientific theories. (shrink)