Georg Cantor's absolute infinity, the paradoxical Burali-Forti class Ω of all ordinals, is a monstrous non-entity for which being called a "class" is an undeserved dignity. This must be the ultimate vexation for mathematical philosophers who hold on to some residual sense of realism in set theory. By careful use of Ω, we can rescue Georg Cantor's 1899 "proof" sketch of the Well-Ordering Theorem––being generous, considering his declining health. We take the contrapositive of Cantor's suggestion and add Zermelo's choice function. (...) This results in a concise and uncomplicated proof of the Well-Ordering Theorem. (shrink)

In this essay, our goal is to discover science in Martin Heidegger's Introduction to Metaphysics, lecture notes for his 1935 summer semester course, because, after all, his subject is metaphysica generalis, or ontology, and this could be construed as a theory of the human brain. Here, by means of verbatim quotes from his text, we attempt to show that indeed these lectures can be viewed as suggestion for an objective scientific theory of human perception, the human capacity for deciphering phenomena, (...) ie. hermeneutics in its broadest sense. His added notes from the 1953 edition, all of which are comments, not corrections, imply that he never abandoned these thoughts on metaphysics, despite all of his utterances about a need to overcome it, and their popular interpretations to that effect. In his presentation, he further develops the colorful and intuitive style, an hermeneutic language, that he had created in his earlier work Being and Time. Of human existence he speaks in such expressions as being-there -- ``Dasein" -- and being-in-the-world, the latter term no longer explicit in the 1935 lectures. The lectures can be read as a pre-scientific analysis of how man, being-there, perceives his environment, artfully managing to deal with the manifold challenges posed by the phenomenal structures of the universe. Man attentively recognizes and deciphers their pre-linguistic contents and, while trying to make sense of it all, puts into words his awareness. There are numerous passages in Heidegger's work where he in fairly concrete terms provides us with hints for a perceptive science that, as it turns out and is demonstrated below in this essay, can be explained in terms of recent advances in neuroscience. It would be implausible, even unthinkable, unimaginable, for there not to be found essential agreement between on one hand his philosophical insights gained by hermeneutics of Dasein, into how our brain functions to let us know what's happening & on the other hand, scientific discoveries obtained through anatomy, EEG, fMRI, TMS, electrode implants, etc, of brain structures & functions employed in perception of the momentary scene. A nexus between science and philosophy is provided in Heidegger's definitive treatment of the Logos, here interpreted as a structural version of Platonic forms (Burchard, 2014). This allows for neurolinguistic brain functions to serve as meta-context for Heidegger's being-in-the-world. The logical functions of Dasein's anatomical brain are performed by the logos machine, formerly the human soul, using top-down processing based on a global context, the noumenal cosmos which humans maintain internally. Heidegger's 1942/43 winter semester lectures Parmenides extend in unbroken fashion his 1935 work, proving that he never abandoned, as is widely claimed, his metaphysical avenue of thought. (shrink)

The essay brings a summation of human efforts seeking to understand our existence. Plato and Kant & cognitive science complete reduction of philosophy to a neural mechanism, evolved along elementary Darwinian principles. Plato in his famous Cave Allegory explains that between reality and our experience of it there exists a great chasm, a metaphysical gap, fully confirmed through particle-wave duality of quantum physics. Kant found that we have two kinds of perception, two senses: By the spatial outer sense we perceive (...) phenomena, objects in space. Our temporal inner sense lets us perceive our inner state, noumena . Kant's two senses are fully confirmed through bilateral brain duality of cognitive science. The bilateral brain serves inner, temporal sense, logic & noumena in the left hemisphere. The right brain half is for the outer, spatial sense, geometry & phenomena. We form a whole system, a bilateral interior cosmos, a kind of world model, expressing what may lie beyond the metaphysical gap. In the right brain we build a phenomenal cosmos, to resemble the outer environment. In the brain's left hemisphere a noumenal cosmos, a model of our private world including Saint Teresa of Avila's castillo interior. The cosmos is regularly updated with novel sense data integrated into our memory banks. This was recognized early by Helmholtz (1860s). Our lives, health & well-being depend on us keeping our interior cosmos in good order. This used to be seen as saving one's precious soul from perdition. While we endeavour to keep our phenomenal cosmos neat & orderly by protecting the environment from harm, our noumenal cosmos to be livable requires us to engage in ethical conduct. This bilateral cosmos is responsible for our common sense judgment power, that we depend on for being able to lead a good & benign life. The 200 million neurons of BA10 in the prefrontal lobe have global access to the interior cosmos, & apply massive feedback to identify environmental conditions rapidly. The global access also gives conscious presence of the individual to itself, all that is present in the interior cosmos, for total freedom of action. In the left brain private ego, we are guarded by faith in divine mercy, & guided to choose the best course of action, able to survive under the most adverse conditions. For this, we receive directions from the Holy Ghost in Saint Teresa's castillo interior. (shrink)

Conscious existence is the product of a neural brain mechanism, which is largely identical with Immanuel Kant's Oneness Function, a service performed by 200 million neurons in the prefrontal lobe, & makes possible our interior cosmos, the record of our interconnected, or general, experience. Essential for us humans is the well-being of our interior cosmos, or Saint Teresa of Avila's interior castle, in all interactions with each other \& the greater environment. Any disorders of our cosmos are liable to make (...) us fall ill, setting our existence on a path of psychosomatic etiology of a large class of mysterious undiagnosed diseases. (shrink)

From the earliest times, American ethics, the rules for the moral \& intellectual life of the West, used to be founded upon the two principles of self-reliance and good neighborliness. Here we consider the underlying functions of neural brain circuits, organic structures that have evolved adaptively by Darwinian rules subject to selection pressure. In the left brain resides our self-reliant private Ego, making plans, launching initiatives. Your public Ego dwells in the right brain, looking around, meeting with your friendly neighbor. (...) A main component is our bilateral interior cosmos, providing us with all the detailed information about our environment as well as the universe at large. (shrink)

Recent advances in neuroscience lead to a wider realm for philosophy to include the science of the Darwinian-evolved computational brain, our inner world producing organ, a non-recursive super- Turing machine combining 100B synapsing-neuron DNA-computers based on the genetic code. The whole system is a logos machine offering a world map for global context, essential for our intentional grasp of opportunities. We start from the observable contrast between the chaotic universe vs. our orderly inner world, the noumenal cosmos. So far, philosophy (...) has been rehearsing our thoughts, our human-internal world, a grand painting of the outer world, how we comprehend subjectively our experience, worked up by the logos machine, but now we seek a wider horizon, how humans understand the world thanks to Darwinian evolution to adapt in response to the metaphysical gap, the chasm between the human animal and its environment, shaping the organism so it can deal with its variable world. This new horizon embraces global context coded in neural structures that support the noumenal cosmos, our inner mental world, for us as denizens of the outer environment. Kant’s inner and outer senses are fundamental ingredients of scientific philosophy. Several sections devoted to Heidegger, his lizard debunked, but his version of the metaphysical gap & his doctrine of the logos praised. Rorty and others of the behaviorist school discussed also. (shrink)

Guided by key insights of the four great philosophers mentioned in the title, here, in review of and expanding on our earlier work (Burchard, 2005, 2011), we present an exposition of the role played by language, & in the broader sense, λογοζ, the Logos, in how the CNS, the brain, is running the human being. Evolution by neural Darwinism has been forcing the linguistic nature of mind, enabling it to overcome & exploit the cognitive gap between an animal and its (...) world by recognizing environmental structures. Our work was greatly influenced by Heidegger’s lecture notes on metaphysics (Heidegger, 1935). We found agreement with recent progress in neuroscience, but also mathematical foundations of language theory, equating Logos with the mathematical concept of structure. The mystery of perception across the gap is analyzed as radiation and molecules impinging on sensory neurons that carry linguistic information about gross environmental structures, and only remotely about the physical reality of elementary particles. The most important logical brain function is Ego or Self, guiding the workings of the brain as a logos machine. Ego or Self operates from neurons in frontopolar cortex with global receptive fields. The logos machine can function only by availing itself of global context, its internally stored noumenal cosmos NK, and the categorical-conceptual apparatus CCA, updated continually through the neural default mode network (Raichle, 2005). In the Transcendental Deduction, Immanuel Kant discovered that Ego or Self is responsible for conscious control in perception relying on concepts & categories for a fitting percept to be incorporated intoNK. The entire CNS runs as a “movie-in-the-brain” (Parvizi & Damasio, 2001), at peak speed processing simultaneously in a series of cortical centers a stack of up to twelve frames in gamma rhythm of 25 ms intervals. We equate global context, or NK, with our human world, Heidegger’s Dasein being-in-the-world, and are able to demonstrate that the great philosopher in EM parallels neuro-science concerning the human mind. (shrink)

In Bertrand Russell's 1903 Principles of Mathematics, he offers an apparently devastating criticism of the neo-Kantian Hermann Cohen's Principle of the Infinitesimal Method and its History (PIM). Russell's criticism is motivated by his concern that Cohen's account of the foundations of calculus saddles mathematics with the paradoxes of the infinitesimal and continuum, and thus threatens the very idea of mathematical truth. This paper defends Cohen against that objection of Russell's, and argues that properly understood, Cohen's views of limits and (...) infinitesimals do not entail the paradoxes of the infinitesimal and continuum. Essential to that defense is an interpretation, developed in the paper, of Cohen's positions in the PIM as deeply rationalist. The interest in developing this interpretation is not just that it reveals how Cohen's views in the PIM avoid the paradoxes of the infinitesimal and continuum. It also reveals some of what is at stake, both historically and philosophically, in Russell's criticism of Cohen. (shrink)

Hermann Cohen’s 1871 classic, Kants Theorie der Erfahrung, had a formative influence, not only on the Marburg school’s reading of Kant, but on their entire conception of philosophy. This influence was further magnified by the substantially revised and expanded second edition of 1885 and the yet further expanded third edition of 1918. Neo-Kantianism was the dominant philosophical movement in Germany in the late nineteenth and twentieth centuries, which means that a work, ostensibly, of Kant scholarship had an influence on (...) the development of German philosophy that few works of secondary literature can claim. (shrink)

Nineteenth-century scientist Hermann von Helmholtz’s peculiar wavering between empiricism and transcendentalism in his philosophy of science in general, and in his theory of perception in particular, is a much debated and well-documented topic in the history and philosophy of science. This contribution aims at providing a fresh angle on this classical issue, by considering Helmholtz’s account of differential consciousness against the background of a centuries-old philosophical debate between the empiricist tradition and the tradition of transcendental idealism. By placing Helmholtz’s (...) psychology against the background of a historical narrative stretching from Hume to Fichte, one can gain insight into the possible merits of his empirico-transcendentalism with regard to the problem of differentiation. More particularly, it is argued that Helmholtz’s psychology tilted towards transcendentalism when met with the classical theoretical problems of strict empiricism in dealing with the foundation of consciousness, most notably circularity and infinite regress. Without claiming that Helmholtz’s theorizing presented a self-conscious attempt to overcome the latter issues, his well-known wavering between perspectives in general, and his appropriation of the a priori in particular, might have served him well in avoiding the deadlocks of empiricism. As noted at the end, however, Helmholtz’s account produced complex philosophical problems of its own. (shrink)

Grete Hermann’s essay “Die naturphilosophischen Grundlagen der Quantenmechanik” has received much deserved scholarly attention in recent years. In this paper, I follow the lead of Elise Crull who sees in Hermann’s work the general outlines of a neo-Kantian interpretation of quantum theory. In full support of this view, I focus on Hermann’s central claim that limited spatio-temporal, and even analogically causal, representations of events exist within an overall relational structure of entangled quantum mechanical states that defy any (...) unified spatio-temporal description. In my view, Hermann also advances an important transcendental argument that perspectival spatio-temporal representations of nature have their foundations in general relational networks that are not spatio-temporal. The key point is that the adoption of a perspectival system within the general network induces the representation but only for that context. These ideas are consistent with a perspectival subject–object principle in Kant and also with Weyl’s work on Lie groups and their representations. (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)

Two seemingly contradictory tendencies have accompanied the development of the natural sciences in the past 150 years. On the one hand, the natural sciences have been instrumental in effecting a thoroughgoing transformation of social structures and have made a permanent impact on the conceptual world of human beings. This historical period has, on the other hand, also brought to light the merely hypothetical validity of scientific knowledge. As late as the middle of the 19th century the truth-pathos in the natural (...) sciences was still unbroken. Yet in the succeeding years these claims to certain knowledge underwent a fundamental crisis. For scientists today, of course, the fact that their knowledge can possess only relative validity is a matter of self-evidence. The present analysis investigates the early phase of this fundamental change in the concept of science through an examination of Hermann von Helmholtz's conception of science and his mechanistic interpretation of nature. Helmholtz (1821-1894) was one of the most important natural scientists in Germany. The development of this thoughts offers an impressive but, until now, relatively little considered report from the field of the experimental sciences chronicling the erosion of certainty. (shrink)

This article intends to shed new light on the impressive series of “war writings,” in which Hermann Cohen developed the idea of a possible messianic collaboration of German imperial ambitions and a modern Jewish Diaspora regenerated by German Spirit (from Russia to America). My paper pays special attention to two lecture tours planed by Cohen in the year 1914, one to Petersburg, Moscow, Riga, Vilna and Warsaw in May 1914, a few weeks before the outbreak of WWI; the other (...) a propaganda trip to America imagined at the beginning of WWI (Autumn 1914) by Cohen and a group of Jews linked to the Centralverein deutscher Staatsbürger jüdischen Glaubens – a plan which failed and turned only into the publication of an article in several American newspapers in German, English and Yiddish in early 1915. The article brings into consideration new archival material concerning the political background of these two initiatives. The article demonstrates how Cohen’s writings and activities during WWI were deploying a new Jewish and Imperial politics – which sought to pave the way for a messianic integration of Jewish Diaspora in the Imperial project of Germany, understood as the political realization of German Idealism. (shrink)

Lotze’s "Microcosm" was published in three volumes, in 1856, 1858 and 1864, respectively. It was soon one of the most widely read philosophy books of the time. It was translated into French and Russian immediately, into English in 1885/87, and into Italian in 1911/16. The book saw six editions in Germany alone by 1923.

The purpose of this study is to assess Husserl’s debt to Lotze’s philosophy during the Halle period (1886-1901). I shall first track the sources of Husserl’s knowledge of Lotze’s philosophy during his studies with Brentano in Vienna and then with Stumpf in Halle. I shall then briefly comment on Husserl’s references to Lotze in his early work and research manuscripts for the second volume of his Philosophy of Arithmetic. In the third section, I examine Lotze’s influence on Husserl’s antipsychologistic turn (...) in the mid-1890s. The fourth section is a commentary on Husserl’s manuscript entitled “Microcosmus,” to which he explicitly refers in his Prolegomena, and which he planned to publish as an annex of his Logical Investigations. This work contains a detailed analysis of the third book of Lotze’s 1874 Logic. The last section examines Husserl’s arguments against logical psychologism in his Prolegomena, which I discuss through the lens of Stumpf’s critique of psychologism in his paper “Psychology and theory of knowledge”. I argue that Stumpf’s early works on this topic make it possible to establish a connection between Lotze’s interpretation of Plato’s theory of Ideas and Husserl’s antipsychologism. My hypothesis is that Stumpf’s analyses represent the background of Husserl's critique of logical psychologism in his Logical Investigations. I shall conclude this study by showing that Husserl’s position with respect to Lotze’s philosophy remains basically unchanged after the publication of his Logical Investigations, and that Husserl’s main criticism of Lotze pertains, in the final analysis, to the absence of a theory of intentionality in Lotze’s philosophy. (shrink)

The Prussian Protestant Daniel Hermann is an important Neo-Latin poet. He lived from probably 1543 until 1601. Hermann studied at Königsberg, Straßburg, Basel and Wittenberg. Afterwards he served as a secretary at the Imperial Court at Vienna, later as a secretary of the city of Danzig and permanent ambassador of Danzig at the Royal Polish court during the wars against Russia. After the war he married and settled down in Riga and became the secretary of the Polish governor (...) Cardinal Radziwil and later of the general Georg Fahrensbach. Besides lots of poems on academical, political and private occasions he wrote letters in poetic form as well as theological, philosophical and political poems. This paper provides an overview over Hermann ’s life and his poetry, especially the poems written and published in Riga, and a short summary of the research on this poet. (shrink)

Some commentators on Hermann Cohen have remarked on what they take to be a puzzle about the origins of his mature anti-psychologism. When Cohen was young, he studied a kind of psychology, the Völkerpsychologie of Moritz Lazarus and Heymann Steinthal, and wrote apparently psycholgistic accounts of knowledge almost up until the moment he first articulated his anti-psychologistic neo-Kantianism. To be sure, Cohen's mature anti psycholgism does constitute a rejection of certain central commitments of Völkerpsychologie. However, the relation between Völkerpsychologie (...) and Cohen's mature anti-psychologism is not one of straightforward opposition. This paper argues that Cohen had significantly less distance to travel than it appears to get from his early Völkerpsychologie to his mature anti-psychologism. In particular, this paper argues that Cohen always had an anti-psychologistic account of knowledge, even during the period when he was studying Völkerpsychologie, and further, that key features of his Völkerpsychologie partly shaped his mature account of knowledge. Finally, the paper identifies how Cohen’s views did change over the transition from his völkerpsychological period to his later anti-psychologism. It thus identifies what changes in Cohen’s views do need to be explained. (shrink)

The neo-Kantian Hermann Cohen is famously anti-empiricist in that he denies that sensations can make a definable contribution to knowledge. However, in the second edition of Kant’s Theory of Experience (1885), Cohen considers a proposition that contrasts with both his other work and that of his followers: a Kantian who studies scientific claims to truth—and the grounds on which they are made—cannot limit himself to studying mathematics and logical principles, but needs to also investigate underlying presuppositions about the empirical (...) element of science. Due to his subjectivist approach, Cohen argues, Kant not only failed to explain how scientific observation and experiments are possible, but also misconceived the role of the ideas, particularly the idea of a system of nature. (shrink)

The article includes a short biography of Hermann of Dalmatia and gives an account of his translations and philosophical and scientific work. In order to have a better understanding of Hermann’s philosophy, a reminder of Greek and Arabic philosophy of nature, on which he relies in his interpretation of the world picture, needs to be presented. Cosmological models by Plato, Aristotle, Eudoxus, Heraclides of Pont, Apollonius of Perga, Hipparchus, Ptolemy, and the Arab scientist Abu Ma’shar, are presented. The (...) main focus of interest is on Hermann’s translations. The immense importance of his translations from Greek and Arabic into Latin is due to the fact that some of the seminal Greek and Arabic works became known in Western Europe in the middle of the twelfth century. Hermann is also important as the author of the original work De essentiis, which presented a blend of Platonian and Aristotelian as well as Western European and Arab traditions. (shrink)

The paper focuses on the problem of anthropodicy in the philosophical system of Hermann Cohen and its interpretation by Jacob Gordin (1896—1947). Gordin was one of the last followers of Cohen in Russia. He developes his interpretation in the lecture “Anthropodicy”, which was given in the Philosophical Circle at the Petrograd University in December 1921. For the study of the problem of anthropodicy he was apparently inspired by the discussions at the Free Philosophical Association in 1919—1921. Gordin places Cohen’s (...) concept of man in the wide intellectual context given by the ideas of the Russian religious philosophy, German classical philosophy, Neo-Kantianism, and the West European and Jewish mysticism (cabbala). Gordin compares Cohen’s anthropodicy with Vladimir Soloviev’s one and shows that there is a similarity in their approaches. Both philosophers point out that the justification of man is possible only in form of the justification of humanity and not as for Berdyaiev in form of the justification of personality. But Gordin uses Soloviev’s concept of all-unity and Berdyaiev’s concept of creativity in order to “improve” Cohen’s conception and to reveal the contribution of a person to the justification of humanity. Stronger as Cohen Gordin connects the programm of anthropodicy with individuality and underlines the participation of the individual in creating culture. (shrink)

This paper for an upcoming journal volume examines Grete Hermann's Naturphilosophischen Grundlagen der Quantenmechanik (1935) and the relative context, or perspectival, interpretation of standard quantum mechanics found therein. I find an argument for the emergence of limited spatio-temporal and retrocausal stories, from a chosen experimental perspective, within a larger set of entangled systems not subject to a spatio-temporal interpretation. This argument can be read in reverse as giving some of the necessary preconditions of spatio-temporal representations as based upon perspectival (...) relations, carrying on a Kantian transcendental argument on one hand, and on the other hand, looking forward to Weyl's use of symmetry groups, Lie algebras and their representations in quantum mechanics. (shrink)

German supporters of the Kantian philosophy in the late 19th century took one of two forks in the road: the fork leading to Baden, and the Southwest School of neo-Kantian philosophy, and the fork leading to Marburg, and the Marburg School, founded by Hermann Cohen. Between 1876, when Cohen came to Marburg, and 1918, the year of Cohen's death, Cohen, with his Marburg School, had a profound influence on German academia.

Carl Stumpf (1848–1937) is a key figure in the fin de siècle germanophone philosophy. Unfortunately, after the World War One, the interest towards Stumpf as a philosopher waned. One of the reasons was that already in the 1920s the attention of the mainstream philosophers shifted in direction of the rising rivalry between analytic and continental philosophy. The interest towards Carl Stumpf’s philosophy was revived only in the last twenty years or so. Great service in this provided the Neo-Brentanists. But while (...) the association of Carl Stumpf with Franz Brentano fostered Stumpf studies, it also gave rise of one-sided interpretations of Stumpf as a philosopher. In this way his importance and idiosyncrasy as philosopher remained in shadow. (shrink)

A new form of skepticism is described, which holds that objectivity and understanding are incompossible ideals of modern science. This is attributed to Weyl, hence its name: Weylean skepticism. Two general defeat strategies are then proposed, one of which is rejected.

As a philosopher, psychologist, and physician, the German thinker Hermann Lotze defies classification. Working in the mid-nineteenth-century era of programmatic realism, he critically reviewed and rearranged theories and concepts in books on pathology, physiology, medical psychology, anthropology, history, aesthetics, metaphysics, logic, and religion. Leading anatomists and physiologists reworked his hypotheses about the central and autonomic nervous systems. Dozens of fin-de-siècle philosophical contemporaries emulated him, yet often without acknowledgment, precisely because he had made conjecture and refutation into a method. In (...) spite of Lotze's status as a pivotal figure in nineteenth-century intellectual thought, no complete treatment of his work exists, and certainly no effort to take account of the feminist secondary literature. Hermann Lotze: An Intellectual Biography is the first full-length historical study of Lotze's intellectual origins, scientific community, institutional context, and worldwide reception. (shrink)

Nach einer kurzen Übersicht über das Leben und Werk von Helmholtz, diskutiere ich die drei Themenbereiche, die für die Beurteilung seines Verhältnisses zu Kant vornehmlich ins Gewicht fallen. Der erste Bereich bildet die Begründung des Energieerhaltungssatzes von 1847, den der späte Helmholtz selbst „durch Kant’s erkenntnistheoretische Ansichten […] beeinflusst“ gesehen hat. Während viele Interpreten diese Selbstauskunft für berechtigt halten, sehe ich in der Struktur der Begründung einen Ausdruck der gegensätzlichen Wissenschaftsauffassungen von Helmholtz und Kant. Als zweites gehe ich auf die (...) Rolle der Kausalität in der Wahrnehmungstheorie ein. In diesem Kontext bezieht sich Helmholtz erstmals und durchaus positiv explizit auf Kant. Seine Rede "Über das Sehen des Menschen" von 1855 zur Einweihung eines Kantdenkmals in Königsberg gilt als eines der Gründungsdokumente des Neukantianismus und spiegelt doch zugleich die tiefgreifenden Differenzen zwischen empiristischer und idealistischer Wissenschaftsphilosophie wider. Zeitlich wiederum nachfolgend steht die Begründung der nichteuklidischen Geometrien als dritter Bereich für die deutlichste Kritik an Kants transzendentaler Begründung der Wissenschaft. Sie ist zugleich wohl auch Helmholtz’ bekanntester Beitrag zur Hypothetisierung der Wissenschaftssauffassung. -/- der Gründungsdokumente des Neukantianismus und spiegelt doch zugleich die tiefgreifenden Differenzen zwischen empiristischer und idealistischer Wissenschaftsphilosophie wider. Zeitlich wiederum nachfolgend steht die Begründung der nichteuklidischen Geometrien als dritter Bereich für die deutlichste Kritik an Kants transzendentaler Begründung der Wissenschaft. Sie ist zugleich wohl auch Helmholtz’ bekanntester Beitrag zur Hypothetisierung der Wissenschaftssauffassung. Dem Werk von Hermann von Helmholtz wird gemeinhin ein maßgeblicher Stellenwert bei der Begründung der neukantianischen Bewegung im 19. Jahrhundert beigemessen. Wo diese Zuordnung Helmholtz’ positive Bezüge auf Immanuel Kant ohne hinreichende Kontextualisierung hervorhebt, läuft sie Gefahr, die Distanz zu übersehen, die zwischen den wissenschaftsphilosophischen Positionen von Helmholtz und Kant bestand. In meinem Beitrag gewinnt das Verhältnis von Helmholtz zu Kant erst seine Bedeutung vor dem Hintergrund ihrer konträren ontologischen und erkenntnistheoretischen Grundannahmen. Helmholtz betrachte ich als repräsentativen Vertreter einer szientistischen Wissenschaftsauffassung in der Naturforschung des 19. Jahrhunderts. Demgegenüber bietet Kant ein paradigmatisches Beispiel einer metaphysischen Wissenschaftsbegründung. Im Gegensatz zu Kant beschränkt Helmholtz seinen Ausgangspunkt nicht auf erfahrungsfreie Prinzipien, sondern entwickelt und stützt seine Begründung des Geltungsanspruches der wissenschaftlichen Erkenntnis auf forschungsbewährte Theorien und Experimente. Eine Differenz zwischen den beiden Positionen findet sich ebenfalls in den Strukturen der jeweils vertretenen Naturkonzeptionen. Führt Kants dynamischer Mechanismus alle Eigenschaften der Materie auf Kräfte zurück, so geht Helmholtz von einer Dualität von Kraft und Materie aus. (shrink)

In searching for the origins of current conceptions of science in the history of physics, one encounters a remarkable phenomenon. A typical view today is that theoretical knowledge-claims have only relativized validity. Historically, however, this thesis was supported by proponents of a conception of nature that today is far from typical, a mechanistic conception within which natural phenomena were to be explained by the action of mechanically moved matter. Two of these proponents, Hermann von Helmholtz and his pupil Heinrich (...) Hertz, contributed significantly to the modernization of the conception of science. Paradigmatic for their common contribution to this development is the way in which they employed the concept of image. By considering the origin and the different meanings of this concept we may trace a line of development which begins with Helmholtz's original claim that a universally and forever valid theory provides a unique representation of nature. It continues with the realization that the status of scientific knowledge is capable of revision; and it arrives at Hertz's admission that a variety of theories over a domain of objects is possible, at least at times. (shrink)

Hermann Cohen made a distinction between the logic of science and the ideal of ethics, and noted that the natural world and the world of ethics are perceived very differently. This is because the order of the physical world is unchangeable (e.g, the sun sets in the west, night follows day, etc), while in the ideal world ethical rules can be accepted or rejected. It seems there should be one explanation for science, which is empirically self-evident, and another for (...) ethics, which is something that is open to debate. Cohen reasoned there must be something that allows science and ethics to coexist and interrelate. (shrink)

This paper examines Hermann Cohen's idiosyncratic construction of a medieval Jewish philosophical tradition, focusing primarily, though not exclusively, on his Charakteristik der Ethik Maimunis . This construction, not unlike modern accounts, is filtered through the central place of Maimonides. For Cohen, however, Maimonides' centrality is defined not by his systematization of Aristotelianism, but by his elevation of ethics over metaphysics. The ethical and pantheistic concerns of Maimonides' precursors, according to this reading, anticipate his uniqueness. Whereas Shlomo ibn Gabirol's pantheistic (...) doctrine of emanation, for example, assigned little weight to ethics, Abraham ibn Daud rebelled against such a doctrine. Ibn Daud—much like Bahya ibn Paquda and Abraham ibn Ezra—becomes part of a Jewish philosophical tradition that culminates in Maimonides' rejection of Aristotelian metaphysics. In particular, this paper examines the way in which Cohen envisaged the pre-Maimonidean philosophical tradition, putting his highly critical reading of Shlomo ibn Gabirol and his pantheistic obsession with prime matter in counterpoint with his more favorable readings of Abraham ibn Daud and Bahya ibn Paquda. (shrink)

This paper argues that the ‘scientific dispute’ between Hermann Cohen and Rudolf Stammler is symptomatic of a philosophical movement of left-wing Kant interpretations at the turn of the twentieth century. By outlining influential predecessors that shaped Cohen’s and Stammler’s thinking, I show that their Kantian justifications of socialism differ regarding their conception of law, history, and the political implications that follow from their practical philosophies. Against scholars who suggest that the Marburg School’s view on socialism was a coherent school (...) of thought, I introduce the concept of ‘left-Kantianism’ as an open term that includes a wide variety of novel socialist approaches to Kant at the time. (shrink)

With his influence on the development of physiology, physics and geometry, Hermann von Helmholtz – like few scientists of the second half of the 19th century – is representative of the research in natural science in Germany. The development of his understanding of science is not less representative. Until the late sixties, he emphatically claimed the truth of science; later on, he began to see the conditions for the validity of scientific knowledge in relative terms, and this can, in (...) summary, be referred to as hypothesizing. Already in the past century, HeImholtz made first approaches to an understanding of science, which were incompatible with his own former position and which pointed to the modern age to an astonishingly large extent. A comparison with Karl R. Popper's logic of research will illustrate how closely he nevertheless approached modern understanding of science. In Popper's logic of research, hypothesizing of scientific knowledge is definitely much more advanced than in Helmholtz's theory of science. What begins vaguely to emerge with Helmholtz has already become an explicitly formulated programme with Popper. Although HeImholtz and Popper are not on a direct line of epistemological development and Popper refers to HeImholtz only rarely and casually, there are in fact surprising points of contact which have not been taken notice of so far and which appear above all if one looks at Helmholtz's understanding of science against the background of Popper's logic of research. (shrink)

I demonstrate that Bell's theorem is based on circular reasoning and thus a fundamentally flawed argument. It unjustifiably assumes the additivity of expectation values for dispersion-free states of contextual hidden variable theories for non-commuting observables involved in Bell-test experiments, which is tautologous to assuming the bounds of ±2 on the Bell-CHSH sum of expectation values. Its premises thus assume in a different guise the bounds of ±2 it sets out to prove. Once this oversight is ameliorated from Bell's argument by (...) identifying the impediment that leads to it and local realism is implemented correctly, the bounds on the Bell-CHSH sum of expectation values work out to be ±2√2 instead of ±2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by any of the Bell-test experiments is not local realism but the linear additivity of expectation values, which does not hold for non-commuting observables in any hidden variable theories to begin with. I also identify similar oversight in the GHZ variant of Bell's theorem, invalidating its claim of having found an inconsistency in the premisses of the argument by EPR for completing quantum mechanics. Conceptually, the oversight in both Bell's theorem and its GHZ variant traces back to the oversight in von Neumann's theorem against hidden variable theories identified by Grete Hermann in the 1930s. (shrink)

This essay recounts a controversy between a pioneer electrophysiologist, Emil du Bois-Reymond (1818–1896), and his student, Ludimar Hermann (1838–1914). Du Bois-Reymond proposed a molecular explanation for the slight electrical currents that he detected in frog muscles and nerves. Hermann argued that du Bois-Reymond's ‘resting currents’ were an artifact of injury to living tissue. He contested du Bois-Reymond's molecular model, explaining his teacher's observations as electricity produced by chemical decomposition. History has painted Hermann as the wronged party in (...) this dispute. I seek to set the record straight. (shrink)

Hermann Weyl was one of the most important figures involved in the early elaboration of the general theory of relativity and its fundamentally geometrical spacetime picture of the world. Weyl’s development of “pure infinitesimal geometry” out of relativity theory was the basis of his remarkable attempt at unifying gravitation and electromagnetism. Many interpreters have focused primarily on Weyl’s philosophical influences, especially the influence of Husserl’s transcendental phenomenology, as the motivation for these efforts. In this article, I argue both that (...) these efforts are most naturally understood as an outgrowth of the distinctive mathematical-physical tradition in Göttingen and also that phenomenology has little to no constructive role to play in them. (shrink)

Cohen’s “Logic of Pure Knowledge” marks a transformation of transcendental philosophy through its new and radical interpretation of pure thinking. For Cohen, thought is in its essence creative and needs no external elements in order to produce knowledge. This study is an attempt to reconstruct the way in which Cohen understands how thinking can create its pure content from nothing. My thesis is that Kant’s distinction between the determinable and the determining I offers the theoretical context in which the productivity (...) of thinking in Cohen’s system can be understood. Thinking creates its pure content by questioning the nothing that stands before it. (shrink)

Hermann Cohen agreed with Immanuel Kant that ethics must be directed towards the well-being of humanity. The essential feature of this is its universality. As Cohen saw it, progress was (or at least ought to be) moving towards universal suffrage and democratic socialism. Following Kant, Cohen defended the so-called categorical imperative; that we should treat humanity in other persons always as an end and never as a means only. (Kant’s famous definition of the categorical imperative is to “act only (...) according to that maxim whereby you can, at the same time, will that it should become a universal law.”). (shrink)

Helmholtz's public reflection about the nature of the experiment and its role in the sciences is a historically important description, which also helps to analyze his own works. It is a part of his conception of science and nature, which can be seen as an ideal type of science and its goals. But its historical reach seems to be limited in an important respect. Helmholtz's understanding of experiments is based on the idea that their planning, realization and evaluation lies in (...) the hands of a person or group acting according to decisions of free will. In my opinion this idea is characteristic for the foundation of the experimental method in early modern times, not however for several forms of its present structures. Above all, the increasing technization of producing knowledge reduces the roIe of the subject in conducting experiments. My lecture consists of three parts. In its first part I would like to present a summary of Helmholtz's own theory of experiment and the change of his conception of science and nature. In the second part I would like to discuss three examples of his experimental practice, which were taken in chronological order from three different periods of his work; in the third part I would like to compare the examples with the change of his conception of science and nature. (shrink)

The conventional wisdom has it that between 1905 and 1919 Russell was critical to pragmatism. In particular, in two essays written in 1908–9, he sharply attacked the pragmatist theory of truth, emphasizing that truth is not relative to human practice. In fact, however, Russell was much more indebted to the pragmatists, in particular to William James, as usually believed. For example, he borrowed from James two key concepts of his new epistemology: sense-data, and the distinction between knowledge by acquaintance and (...) knowledge by description. Reasonable explanation of this is that, historically, Russell’s logical realism and James’s pragmatism have the same roots—the German philosopher Rudolph Hermann Lotze (1817–1881). In this paper we are going to explore the fact that in 1905, under Lotze’s influence, Russell married propositions with beliefs. A few years later this step also made Russell prone to embrace the theory of truth-making that has its roots in James. In contrast to the concept of sense-data and to the distinction between knowledge by acquaintance and knowledge by description, however, the understanding that we believe propositions—and not, for example, simply grasp them—was in tension with Russell’s Principle of Extensionality, according to which propositions can be logically connected with other propositions only as truth-functions. The point is that when we judge a mind-relation (for example, a relation of belief) to a proposition, the latter cannot be determined as true or false. The two most talented pupils of Russell, Wittgenstein and Ramsey, severely criticized the central place propositional attitudes play in Russell’s logic. Wittgenstein analyzed “A believes that p” to “ ‘p’ says p” (5.542). Ramsey criticized Russell’s beliefs in propositions the other way round: He stressed that belief is an ambiguous term that can be interpreted for the better in the sense of pragmatism. Prima facie surprisingly, he maintained that his “pragmatism is derived from Mr Russell.” (1927: 51). (shrink)

This paper examines the origin, range and meaning of the Principle of Action and Reaction in Kant’s mechanics. On the received view, it is a version of Newton’s Third Law. I argue that Kant meant his principle as foundation for a Leibnizian mechanics. To find a ‘Newtonian’ law of action and reaction, we must look to Kant’s ‘dynamics,’ or theory of matter. I begin, in part I, by noting marked differences between Newton’s and Kant’s laws of action and reaction. I (...) argue that these are explainable by Kant’s allegiance to a Leibnizian mechanics. I show (in part II) that Leibniz too had a model of action and reaction, at odds with Newton’s. Then I reconstruct how Jakob Hermann and Christian Wolff received Leibniz’s model. I present (in Part III) Kant’s early law of action and reaction for mechanics. I show that he devised it so as to solve extant problems in the Hermann-Wolff account. I reconstruct Kant’s views on ‘mechanical’ action and reaction in the 1780s, and highlight strong continuities with his earlier, pre-Critical stance. I use these continuities, and Kant’s earlier engagement with post-Leibnizians, to explain the un-Newtonian features of his law of action and reaction. (shrink)

Hermann von Helmholtz (1821-1894) established results both controversial and enduring: analysis of mixed colors and of combination tones, arguments against nativism, and the analysis of sensation and perception using the techniques of natural science. The paper focuses on Helmholtz’s account of sensation, perception, and representation via “physiological psychology”. Helmholtz emphasized that external stimuli of sensations are causes, and sensations are their effects, and he had a practical and naturalist orientation toward the analysis of phenomenal experience. However, he argued as (...) well that sensation must be interpreted to yield representation, and that representation is geared toward objective representation (the central thesis of contemporary intentionalism). The interpretation of sensation is based on “facts” revealed in experiment, but extends to the analysis of the quantitative, causal relationships between stimuli and responses. A key question for Helmholtz’s theory is the extent to which mental operations are to be ascribed a role in interpreting sensation. (shrink)

The influence of Brentano on the emergence of Husserl's notion of intentionality has been usually perceived as the key of understanding the history of intentionality, since Brentano was credited with the discovery of intentionality, and Husserl was his discipline. This much debated question is to be revisited in the present essay by incorporating recent advances in Brentano scholarship and by focusing on Husserl's very first work, his habilitation essay (Über den Begriff der Zahl), which followed immediately after his study years (...) at Brentano, and also on manuscript notes from the same period. It is to be shown that (i) although Brentano failed to enact a direct influence on Husserl's notion of intentionality (much in line with K. Schuhmann's claim), (ii) yet the core of Brentano's notion remained operative in Husserl's theory of relations, which is seemingly influenced by John Stuart Mill and Hermann Lotze. This investigation is intended as a contribution towards the proper understanding of the complexities of Husserl's early philosophy. (shrink)

Ernst Cassirer has been proclaimed a follower of Hermann Cohen. However, Cassirer modified the basic concepts of Cohen’s theory of knowledge, so that Cassirer’s philosophical positions in many aspects actually stand in opposition to Cohen’s. Although Cassirer did follow Cohen’s methodology coherently, in that path he refuted the main positions of his teacher. Cohen’s philosophical task was forwarding Kant’s critical method to construct a theory of knowledge. He aimed not only to renew Kant’s method in the way he interpreted (...) it, but also to revise, in accordance with Kant’s method, the uncritical positions of Kant's own theory of knowledge. Cohen’s methodology was intended to achieve this goal. In following his teacher’s task, however, Cassirer developed a set of functional concepts which coherently reveal and overturn the uncritical positions in the theory of knowledge, including the one essential for Cohen himself. Consequently, it may be said, Cassirer “revises” Cohen’s system in a same way that Cohen revised Kant. (shrink)

This chapter aims to examine parallels between two ancient Indian philosophical schools, Jaina (Jainism) of Mahāvīra and Ajñāna (Unending Agnosticism) of Sañjaya Belaṭṭhiputta. Jaina and Ajñāna traditions were a part of the Non-Vedic larger Śramaṇa movement of seventh to sixth-century BCE India, where Śramaṇa were monastics, who dwelled in forests and lived a retired life, focussing themselves in the search of discovering the knowledge of truth, reality and existence. Sañjaya and Mahāvīra were contemporaries and were a prominent and well-known Śramaṇa (...) of their time. The chapter is broadly divided into two parts, with two sections each. The first part aims to discuss Sañjaya’s ajñānavāda (epistemological method) and Mahāvīra’s doctrine of anekāntavāda (metaphysical pluralism) and saptabhanginaya (sevenfold predication). The second part aims to explore the logical relationship and similarities between ajñānavāda and anekāntavāda and its metaphysical consequences, and conclusively the major part of the paper will discuss the claim first made by the German Jaina scholar Hermann Jacobi, about the possible influence that Sañjaya’s ajñānavāda had on the establishment of Mahāvīra’s anekāntavāda. In brief, the chapter intends to present and discuss the contemporary scholarship claims on Sañjaya and his possible influence it had on the development of the Jaina thought. (shrink)

In spite of Ernst Cassirer’s criticisms of psychologism throughout Substance and Function, in the final chapter he issues a demand for a “psychology of relations” that can do justice to the subjective dimensions of mathematics and natural science. Although these remarks remain somewhat promissory, the fact that this is how Cassirer chooses to conclude Substance and Function recommends it as a topic worthy of serious consideration. In this paper, I argue that in order to work out the details of Cassirer’s (...) psychology of relations in Substance and Function, we need to situate it within two broader frameworks. First, I position Cassirer’s view in relation to the view of psychology and logic endorsed by his Marburg Neo-Kantian predecessors, Hermann Cohen and Paul Natorp. Second, I augment Cassirer’s early account of the psychology of relations in Substance and Function with the more mature view of psychology that he presents in The Philosophy of Symbolic Forms. By placing Cassirer’s account within these contexts, I claim that we gain insight into his psychology of relations, not just as it pertains to mathematics and natural science, but to culture as a whole. Moreover, I maintain that pursuing this strategy helps shed light on one of the most controversial features of his philosophy of mathematics and natural science, viz., his theory of the a priori. (shrink)

One of the key episodes of history of modern physics – Paul Dirac’s startling contrivance of the relativistic theory of the electron – is elicited in the context of lucid epistemological model of mature theory change. The peculiar character of Dirac’s synthesis of special relativity and quantum mechanics is revealed by comparison with Einstein’s sophisticated methodology of the General Relativity contrivance. The subtle structure of Dirac’s scientific research program and first and foremost the odd principles that put up its powerful (...) heuristics is scrutinized with special emphasis on the highly controversial tenet of “mathematical beauty.” It is contended that despite the relentless Dirac’s remarks denigrating the controversial role of philosophy one can trace its indirect influence through Arthur Eddington’s and Hermann Weyl’s whimsical mathematical models. Accordingly, the milestones of Dirac’s research programme realization in the distinctive context of the applied epistemological doctrine are indicated. (shrink)

The paper aims to establish if Grassmann’s notion of an extensive form involved an epistemological change in the understanding of geometry and of mathematical knowledge. Firstly, it will examine if an ontological shift in geometry is determined by the vectorial representation of extended magnitudes. Giving up homogeneity, and considering geometry as an application of extension theory, Grassmann developed a different notion of a geometrical object, based on abstract constraints concerning the construction of forms rather than on the homogeneity conditions required (...) by the modern version of the theory of proportions. Secondly, Grassmann’s conception of mathematical knowledge will be investigated. Parting from the traditional definition of mathematics as a science of magnitudes, Grassmann considered mathematical forms as particulars rather than universals: the classification of the branches of mathematics was thus based on different operational rules, rather than on empirical criteria of abstraction or on the distinction of different species belonging to a common genus. It will be argued that a different notion of generalization is thus involved, and that the knowledge of mathematical forms relies on the understanding of the rules of generation of the forms themselves. Finally, the paper will analyse if Grassmann’s approach in the first edition of the Ausdehnungslehre should be explained in terms of the notion of purity of method, and if it clashes with Grassmann’s later conventionalism. Although in the second edition the features of the operations are chosen by convention, as it is the case for the anti-commutative property of the multiplication, the choice is oriented by our understanding of the resulting forms: a simplification in the algebraic calculus need not correspond to a simplification in the ‘dimensional’ interpretation of the result of the multiplicative operation. (shrink)

I. Introduction Siris, Berkeley's last major work, is undeniably a rather odd book. It could hardly be otherwise, given Berkeley's aims in writing it, which are three-fold: 'to communicate to the public the salutary virtues of tar-water,'1 to provide scientific background supporting the efficacy of tar-water as a medicine, and to lead the mind of the reader, via gradual steps, toward contemplation of God.2 The latter two aims shape Berkeley's extensive use of contemporary natural science in Siris. In particular, Berkeley's (...) focus on what he calls fire (or aether or light) as a quasiuniversal 'cause' of natural change3 serves these purposes, for the 'activity' of the aether, in his view, can both explain the miraculous virtues of a certain medicine, i.e. tar-water, and reveal God's action and his divine order.4 Berkeley's corpuscular speculations, including his use of fire-theory, are not especially idiosyncratic as natural philosophy. In his theorizing, as Jessop and other have noted, he is heavily indebted to the work of Hermann Boerhaave, the Dutch chemist, botanist, and physician whose teachings were highly influential in mid-eighteenth century Britain.5 Boerhaave, along with other Dutch natural philosophers cited by Berkeley, assigned a central role in accounting for physio-chemical activity to fire, a subtle, insensible particulate substance, sometimes identified with light. (shrink)

This paper looks at the ways in which Mikhail Bakhtin had appropriated the ideas of Kant and of the Marburg neo-Kantian school. While Bakhtin was greatly indebted to Kantian philosophy, and is known to have referred to himself as a neo-Kantian, he rejects the main tenets of neo-Kantianism. Instead, Bakhtin offers a substantial re-interpretation of Kantian thought. His frequent borrowings from neo-Kantian philosophers (Hermann Cohen, Paul Natorp, and others) also follow a distinctive pattern of appropriation, whereby blocks of interconnected (...) ideas are removed from their original context, and made to serve Bakhtin’s own—substantially different—philosophical purposes in the context of his own thought. Bakhtin’s thought thus remains original even as he is borrowing ideas from others. (shrink)